#help-13 | Mathematics | Page 448

tropic oxide Dec 29, 2021, 2:23 PM

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what part of "split that fraction" do you not understand?

crimson sedge Dec 29, 2021, 2:23 PM

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i could write it as

tropic oxide Dec 29, 2021, 2:24 PM

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there is no need to bring that up here.

crimson sedge Dec 29, 2021, 2:24 PM

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$\frac{3x}{2}+1$

wraith daggerBOT Dec 29, 2021, 2:24 PM

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crabbo

livid hound Dec 29, 2021, 2:24 PM

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yes

waxen prawn Dec 29, 2021, 2:24 PM

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tropic oxide there is no need to bring that up here.

it is what its doing right tho?

crimson sedge Dec 29, 2021, 2:24 PM

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that is what you meant?

livid hound Dec 29, 2021, 2:24 PM

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yes

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similarly "split the fraction" for the right side too

crimson sedge Dec 29, 2021, 2:24 PM

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why is that called splitting the fraction

crimson sedge Dec 29, 2021, 2:24 PM

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ok

livid hound Dec 29, 2021, 2:25 PM

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because you're literally splitting the fraction (into more fractions)

dense wing Dec 29, 2021, 2:25 PM

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waxen prawn it is what its doing right tho?

No, they're not doing partial fractions

livid hound Dec 29, 2021, 2:25 PM

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(in this case 2)

waxen prawn Dec 29, 2021, 2:25 PM

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dense wing No, they're not doing partial fractions

oh fairs

crimson sedge Dec 29, 2021, 2:25 PM

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$\frac{x}{a}-\frac{b}{a}$

wraith daggerBOT Dec 29, 2021, 2:25 PM

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crabbo

livid hound Dec 29, 2021, 2:25 PM

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identify the coefficient of x on the left side
identify the coefficient of x on the right side
identify the constant term on the left side
identify the constant term on the right side

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equate the respective terms and solve

crimson sedge Dec 29, 2021, 2:28 PM

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$\frac{3x}{2}=\frac{x}{a}$

wraith daggerBOT Dec 29, 2021, 2:28 PM

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crabbo

crimson sedge Dec 29, 2021, 2:28 PM

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$1=-\frac{b}{a}$

livid hound Dec 29, 2021, 2:28 PM

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b/a isn't 1

wraith daggerBOT Dec 29, 2021, 2:29 PM

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crabbo

crimson sedge Dec 29, 2021, 2:30 PM

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wraith dagger

why did you choose 3?

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what happened to what i was doing before

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ah

dense wing Dec 29, 2021, 2:31 PM

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I don't think switching to a completely different method right before they're done is productive

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@wraith blaze

crimson sedge Dec 29, 2021, 2:31 PM

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how do i continue from my previous method

dense wing Dec 29, 2021, 2:31 PM

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crimson sedge how do i continue from my previous method

equation the coefficients as Ram said.

crimson sedge Dec 29, 2021, 2:32 PM

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i did

dense wing Dec 29, 2021, 2:32 PM

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yeah, so you have 3/2 = 1/a and b/a = -1

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Not interested because they were almost done with a more general process.

south juniper Dec 29, 2021, 2:34 PM

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It does seem a bit rude to barge in when ramanov has been helping them for quite some time

dense wing Dec 29, 2021, 2:34 PM

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this this too

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You were but ok

crimson sedge Dec 29, 2021, 2:35 PM

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i will try afterward

livid hound Dec 29, 2021, 2:35 PM

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the calculations are more or less the same anyway

crimson sedge Dec 29, 2021, 2:36 PM

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dense wing yeah, so you have 3/2 = 1/a and b/a = -1

yes

livid hound Dec 29, 2021, 2:36 PM

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since the constant is in terms of both a and b, you'd still need to set up an equation in some way

crimson sedge Dec 29, 2021, 2:36 PM

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system of equations?

livid hound Dec 29, 2021, 2:38 PM

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yeh

crimson sedge Dec 29, 2021, 2:42 PM

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😦

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3/2=1/a
-1=b/a

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elimination, or substitution?

livid hound Dec 29, 2021, 2:43 PM

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don't overthink it

crimson sedge Dec 29, 2021, 2:46 PM

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a = 2/3

livid hound Dec 29, 2021, 2:46 PM

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especially since the solution to one of your variables is (almost) trivial
and from the other you can pretty much get the value of (a+b)/2 by itself without having to do anything else

crimson sedge Dec 29, 2021, 2:49 PM

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livid hound especially since the solution to one of your variables is (almost) trivial and f...

i gotta tink

crimson sedge Dec 29, 2021, 2:59 PM

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livid hound especially since the solution to one of your variables is (almost) trivial and f...

is it that -1=b/a

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a=-1/b

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b=-a

dense wing Dec 29, 2021, 2:59 PM

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crimson sedge b=-a

yes, which is?

crimson sedge Dec 29, 2021, 3:00 PM

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dense wing yes, which is?

a=-b?

dense wing Dec 29, 2021, 3:00 PM

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crimson sedge a = 2/3

..

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what's b?

livid hound Dec 29, 2021, 3:01 PM

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a=-b → a+b = ?

crimson sedge Dec 29, 2021, 3:03 PM

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dense wing ..

-2/3

crimson sedge Dec 29, 2021, 3:03 PM

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livid hound a=-b → a+b = ?

0

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so the answer is 0

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how do i do this If $f(3)=1$ and $f(2x)=2f(x)$ for all $x$, find $f^{-1}(64)$.

wraith daggerBOT Dec 29, 2021, 3:07 PM

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crabbo

crimson sedge Dec 29, 2021, 3:12 PM

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there is no g

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oh well

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im stuck

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i dont really understand

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f(2x)=2f(x)

cedar kilnBOT Dec 29, 2021, 3:29 PM

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@crimson sedge Has your question been resolved?

crimson sedge Dec 29, 2021, 3:29 PM

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<@&286206848099549185>

dense wing Dec 29, 2021, 3:30 PM

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What have you tried?

crimson sedge Dec 29, 2021, 3:36 PM

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dense wing *What have you tried?*

i dont know where to start

livid hound Dec 29, 2021, 3:37 PM

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consider a definition of the inverse
and start with seeing what happens when x=3 etc

cedar kilnBOT Dec 29, 2021, 4:06 PM

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@crimson sedge Has your question been resolved?

crimson sedge Dec 29, 2021, 4:08 PM

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livid hound consider a definition of the inverse and start with seeing what happens when x=3...

when x = 3

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f(x)=1

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f(6)=2

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64 is not a multiple of 3

livid hound Dec 29, 2021, 4:12 PM

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64 is not a multiple of 3
doesn't matter

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you're NOT being asked for f(64)

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consider a definition of the inverse
and what f^-1(64) represents

crimson sedge Dec 29, 2021, 4:52 PM

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livid hound > consider a definition of the inverse and what f^-1(64) represents

I’m confused on how to find the inverse

livid hound Dec 29, 2021, 4:53 PM

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try to describe what f^-1(64) represents without using the word "inverse"

crimson sedge Dec 29, 2021, 5:48 PM

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The function that undoes f

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@livid hound

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U there?

leaden otter Dec 29, 2021, 6:42 PM

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wraith dagger **crabbo**

I don't think there is a way to show inverse exists given only this info. There may be multiple preimages of 64 (best you could do is determine one of them). Maybe they are implicitly assuming that inverse exists

dense wing Dec 29, 2021, 6:58 PM

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Inverse should exist

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~~Given that im aware, you can explicitly find f~~

leaden otter Dec 29, 2021, 7:01 PM

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Can you disprove f(1)=64 only given those facts? (I don't think it is possible to show contradiction if you assume this to be true)

halcyon hound Dec 29, 2021, 7:05 PM

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What's the multiplicative inverse of 0? Also 0

dense wing Dec 29, 2021, 7:06 PM

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halcyon hound What's the multiplicative inverse of 0? Also 0

#❓how-to-get-help

halcyon hound Dec 29, 2021, 7:11 PM

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That wasn't a question

cedar kilnBOT Dec 29, 2021, 7:31 PM

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@crimson sedge Has your question been resolved?

dense wing Dec 29, 2021, 7:34 PM

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halcyon hound That wasn't a question

Ok.. well the multiplicative inverse of 0 doesn't exist

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since 0*0 != 1

halcyon hound Dec 29, 2021, 8:28 PM

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Right

cedar kilnBOT Dec 29, 2021, 8:31 PM

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cedar kilnBOT Dec 30, 2021, 12:03 PM

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glass canopy Dec 30, 2021, 12:06 PM

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cedar kilnBOT Dec 30, 2021, 12:06 PM

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glass canopy

glass canopy Dec 30, 2021, 12:06 PM

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Need help

south tundra Dec 30, 2021, 12:06 PM

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With all of them?

glass canopy Dec 30, 2021, 12:07 PM

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Without 14

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Khinkali?

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Ummm delicious

south tundra Dec 30, 2021, 12:08 PM

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Diax

glass canopy Dec 30, 2021, 12:08 PM

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Diax

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:Ddd

south tundra Dec 30, 2021, 12:09 PM

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Pirvelshi (c^1/6)^5 igivea rac c^5/6

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Da 7c^5/6 - 2c^5/6 radgan gaq

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Pasuxi iqneba 5c^5/6

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Mexuteshi gaaertmnishvneliano unda

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Imedia shedzleb shenit

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Romel klasshi xar ise?

glass canopy Dec 30, 2021, 12:11 PM

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Aha gasagebia

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10

south tundra Dec 30, 2021, 12:13 PM

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Meeqvseshi $(\sqrt2 - 3)^2 - (\sqrt2 + 3)^2 = (\sqrt2 - 3 + \sqrt2 + 3)(\sqrt2 - 3 - \sqrt2 - 3) = -12\sqrt2$

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Kvadratebis sxvaoba gamoviyene ro rame

wraith daggerBOT Dec 30, 2021, 12:14 PM

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Touch My Khinkali

south tundra Dec 30, 2021, 12:16 PM

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Ise zamtris ardadegebia ukve rato swavlob?

cedar kilnBOT Dec 30, 2021, 12:26 PM

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@glass canopy Has your question been resolved?

cedar kilnBOT Dec 30, 2021, 12:41 PM

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hexed abyss Dec 30, 2021, 12:50 PM

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Is my proof true? If so, does this affect other fields of mathematics, e.g., Euler's identity?

cedar kilnBOT Dec 30, 2021, 12:50 PM

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hexed abyss Is my proof true? If so, does this affect other fields of mathematics, e.g., Eul...

hexed abyss Dec 30, 2021, 12:50 PM

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.close

cedar kilnBOT Dec 30, 2021, 12:54 PM

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Channel closed

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south tundra Dec 30, 2021, 12:54 PM

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Why'd you close right away

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He started with (-1)*(-1) = 1 and then used the fact that -1 = e^ipi

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You could start with e^2ipi = 1 right away tho

cedar kilnBOT Dec 30, 2021, 1:00 PM

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Available help channel!

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hard ginkgo Dec 30, 2021, 1:09 PM

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Show that for any positive numbers a, b, c, d the following inequality is true:

ac + bd <= sqrt(a^2 + ^2) * sqrt(c^2 * d^2)

cedar kilnBOT Dec 30, 2021, 1:09 PM

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hard ginkgo > Show that for any positive numbers a, b, c, d the following inequality is true...

hard ginkgo Dec 30, 2021, 1:10 PM

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I squared both

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set ac = x, bd = y

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got
x^2 +2xy + y^2 <= x^2 +a^2 * d^2 + y^2 + b^2 * d^2

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eliminated common factors

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got

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2abc <= d(a^2+b^2)

south tundra Dec 30, 2021, 1:10 PM

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If the inequality supposed to be $ac + bd \le \sqrt{a^2 + b^2}\sqrt{c^2 + d^2}$?

hard ginkgo Dec 30, 2021, 1:10 PM

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dunno what to do now

wraith daggerBOT Dec 30, 2021, 1:10 PM

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Touch Our Beans

hard ginkgo Dec 30, 2021, 1:10 PM

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yes

south tundra Dec 30, 2021, 1:11 PM

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Oof that's a tough one, I still remember going through this inequality

hard ginkgo Dec 30, 2021, 1:11 PM

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hard ginkgo 2abc <= d(a^2+b^2)

?

south tundra Dec 30, 2021, 1:11 PM

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The book asked me to show that in 3 different ways lol

hard ginkgo Dec 30, 2021, 1:11 PM

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what book

south tundra Dec 30, 2021, 1:11 PM

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Wait let me look at my notes

south tundra Dec 30, 2021, 1:11 PM

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hard ginkgo what book

Calculus by Michael Spivak

hard ginkgo Dec 30, 2021, 1:11 PM

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it has this inequality?

south tundra Dec 30, 2021, 1:12 PM

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Yes the first chapters are about numbers in general

hard ginkgo Dec 30, 2021, 1:12 PM

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lol

south tundra Dec 30, 2021, 1:12 PM

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And one of the exercises was that inequality

hard ginkgo Dec 30, 2021, 1:12 PM

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cause this inequality apparently appeared on my country's highschool graduation exam in 2010

south tundra Dec 30, 2021, 1:12 PM

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south tundra Yes the first chapters are about numbers in general

Then it slowly builds up to limits, then derivatives and so on

hard ginkgo Dec 30, 2021, 1:12 PM

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i'm doing a book that prepares for this exam

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and it has this inequality

south tundra Dec 30, 2021, 1:17 PM

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Use the fact that $(ad - bc)^2 \ge 0$

wraith daggerBOT Dec 30, 2021, 1:17 PM

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Touch Our Beans

south tundra Dec 30, 2021, 1:17 PM

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As I remember the inequality follows from that immediately

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Btw the inequality has a name, it's called Schwarz inequality

hard ginkgo Dec 30, 2021, 1:18 PM

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ah

hard ginkgo Dec 30, 2021, 1:19 PM

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south tundra Use the fact that $(ad - bc)^2 \ge 0$

do i have to backtrack then

south tundra Dec 30, 2021, 1:19 PM

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Yeah

hard ginkgo Dec 30, 2021, 1:19 PM

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hard ginkgo 2abc <= d(a^2+b^2)

you can't do anything with ?

south tundra Dec 30, 2021, 1:20 PM

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Let me check

hard ginkgo Dec 30, 2021, 1:20 PM

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i mean

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it's the same thing actually

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i just removed th ed

south tundra Dec 30, 2021, 1:21 PM

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Weird, are you sure you cancelled out everything properly?

hard ginkgo Dec 30, 2021, 1:21 PM

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or is it

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i have

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2abcd <= a^2 *d^2 + b^2 * d^2

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0 <= a^2 *d^2 + b^2 * d^2 - 2abcd

south tundra Dec 30, 2021, 1:22 PM

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Oh

hard ginkgo Dec 30, 2021, 1:23 PM

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this is obv the same as
0 <= a^2 *d^2 + b^2 * d^2 - 2abcd

south tundra Dec 30, 2021, 1:24 PM

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Maybe there's some kind of factorisation needed

south tundra Dec 30, 2021, 1:24 PM

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wraith dagger **Touch Our Beans**

Try this btw, should help

hard ginkgo Dec 30, 2021, 1:24 PM

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yeah but i think if yours is ocrrect

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then mine is incorrrec

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i'm pretty sure i haven't amde a mistake anywhere

south tundra Dec 30, 2021, 1:25 PM

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I mean yeah that might be right, but there's probably factorisation needed at that point

hard ginkgo Dec 30, 2021, 1:25 PM

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are you sure yours is correct

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well

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idk what to do with mine

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0 <= a^2 *d^2 + b^2 * d^2 - 2abcd

south tundra Dec 30, 2021, 1:30 PM

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But here x1 = a, y1 = c, x2 = b, y2 = d

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Different notation but pretty much the same

hard ginkgo Dec 30, 2021, 1:35 PM

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a^2 * d^2 - 2abcd + b^2 * c^2 >= 0
vs
a^2 * c^2 + b^2 * d^2 <= (a^2+b^2)(c^2+d^2)
a^2 * d^2 + b^2 * c^2 >=0

tropic oxide Dec 30, 2021, 1:36 PM

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there is an inequality that in my opinion is much easier to prove and has this as a special case

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but it requires some familiarity with geometry, and more specifically with vectors

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should i present it or should i not bother

hard ginkgo Dec 30, 2021, 1:36 PM

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hard ginkgo a^2 * d^2 - 2abcd + b^2 * c^2 >= 0 vs a^2 * c^2 + b^2 * d^2 <= (a^2+b^2)(c^2+d^2...

@south tundra they are different by

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unless i have made a mistakes somewhere

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mine is smaller by 2abcd

hard ginkgo Dec 30, 2021, 1:37 PM

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tropic oxide but it requires some familiarity with geometry, and more specifically with vecto...

last time i saw vectors was a year ago so better not

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and it was basic stuff

tropic oxide Dec 30, 2021, 1:37 PM

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k

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suit yourself

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have fun getting lost in your sea of algebra

hard ginkgo Dec 30, 2021, 1:38 PM

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well

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i'm practising

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so the question is how do i show
0 <= a^2 *d^2 + b^2 * d^2 - 2abcd

hard ginkgo Dec 30, 2021, 1:38 PM

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hard ginkgo > Show that for any positive numbers a, b, c, d the following inequality is true...

which is equivalent to

tropic oxide Dec 30, 2021, 1:38 PM

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are you sure you meant that and not a^2 c^2 + b^2 d^2 - 2abcd for the right-hand side?

south tundra Dec 30, 2021, 1:39 PM

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Yeah that's what I was confused with as well

hard ginkgo Dec 30, 2021, 1:39 PM

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south tundra Dec 30, 2021, 1:39 PM

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tropic oxide there is an inequality that in my opinion is much easier to prove and has this a...

Yeah there's a proof for this in n dimensions as I know, right?

hard ginkgo Dec 30, 2021, 1:40 PM

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wait a second

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i think i've found my mistake lol

south tundra Dec 30, 2021, 1:41 PM

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It should definitely be a^2 c^2 there

tropic oxide Dec 30, 2021, 1:43 PM

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south tundra Yeah there's a proof for this in n dimensions as I know, right?

yes

hard ginkgo Dec 30, 2021, 1:43 PM

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a^2 * c^2 + 2abcd + b^2 * d^2 <= a^2 * c^2 + a^2 * d^2 + b^2 * c^2 + b^2 * d^2
=> ac = x, bd = y
x^2 + 2xy+ y^2 <= x^2 + a^2 * d^2 + b^2 * c^2 + y^2
eliminate common factors
2abcd <=a^2 * d^2 + b^2 * c^2

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a^2 * d^2 + b^2 * c^2 - 2abcd >= 0

tropic oxide Dec 30, 2021, 1:44 PM

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anyway now you have reduced your inequality to $(ad)^2 + (bc)^2 - 2abcd \overset?\geq 0$

wraith daggerBOT Dec 30, 2021, 1:44 PM

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Ann

tropic oxide Dec 30, 2021, 1:44 PM

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as it appears

hard ginkgo Dec 30, 2021, 1:44 PM

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hard ginkgo a^2 * c^2 + 2abcd + b^2 * d^2 <= a^2 * c^2 + a^2 * d^2 + b^2 * c^2 + b^2 * d^2 =...

.

south tundra Dec 30, 2021, 1:44 PM

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south tundra

Which is true, as shown here

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In the first like 4lines

hard ginkgo Dec 30, 2021, 1:45 PM

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yeah

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thanks

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my dysgraphia struck again lol

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a.k.a. dyslexia

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.close

cedar kilnBOT Dec 30, 2021, 1:46 PM

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Channel closed

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hard ginkgo Dec 30, 2021, 2:05 PM

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sec\

cedar kilnBOT Dec 30, 2021, 2:06 PM

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Channel closed

Closed due to the original message being deleted

hard ginkgo Dec 30, 2021, 2:08 PM

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.close

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.reopen

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@wraith blaze

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see

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yeah so if this one isn't available

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then i've asked in a diff one?

cedar kilnBOT Dec 30, 2021, 2:12 PM

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humble parrot Dec 30, 2021, 2:14 PM

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Is $\lim_{x\to{-1}}\sqrt{x}=i$ true?

cedar kilnBOT Dec 30, 2021, 2:14 PM

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humble parrot Is $\lim_{x\to{-1}}\sqrt{x}=i$ true?

wraith daggerBOT Dec 30, 2021, 2:15 PM

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Rhetorical

calm sierra Dec 30, 2021, 2:17 PM

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whats ur branch cut

humble parrot Dec 30, 2021, 2:22 PM

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What does it mean?

calm sierra Dec 30, 2021, 2:24 PM

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sqrt isnt well defined on negatives w/o branch cut

south tundra Dec 30, 2021, 2:33 PM

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Also on 2d plane there are infinitely many ways to approach -1

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Depends on the path

humble parrot Dec 30, 2021, 2:33 PM

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Would approaching from other ways change the answer?

south tundra Dec 30, 2021, 2:34 PM

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Well not really sure, haven't studied complex analysis

calm sierra Dec 30, 2021, 2:39 PM

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south tundra Depends on the path

the lim doesnt involve a specific path

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picking branch cut is quite important (see principal sqrt), then u can ask what the lim at -1 is

cedar kilnBOT Dec 30, 2021, 2:48 PM

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@humble parrot Has your question been resolved?

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Channel closed

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crimson sedge Dec 30, 2021, 2:56 PM

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If $f(3)=1$ and $f(2x)=2f(x)$ for all $x$, find $f^{-1}(64)$.

cedar kilnBOT Dec 30, 2021, 2:56 PM

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crimson sedge If $f(3)=1$ and $f(2x)=2f(x)$ for all $x$, find $f^{-1}(64)$.

wraith daggerBOT Dec 30, 2021, 2:56 PM

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crabbo

crimson sedge Dec 30, 2021, 2:56 PM

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i asked this question yesterday

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but i had to leave home, so i was away from my computer

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and it we didnt get much in

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all i remember was the sequence:
f(3)=1
f(6)=2
f(12)=4
f(24)=8
etc etc

livid hound Dec 30, 2021, 2:59 PM

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consider what f^-1(64) represents

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they have a habit of disappearing for an hour+

cedar kilnBOT Dec 30, 2021, 3:13 PM

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@crimson sedge Has your question been resolved?

crimson sedge Dec 30, 2021, 3:14 PM

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livid hound > consider what f^-1(64) represents

it undoes f

livid hound Dec 30, 2021, 3:14 PM

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i'm not asking about f^-1 or f^-1(x)

crimson sedge Dec 30, 2021, 3:14 PM

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no

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the inverse is the output

livid hound Dec 30, 2021, 3:14 PM

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i'm asking about f^-1(64) specifically

crimson sedge Dec 30, 2021, 3:14 PM

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so f^-1(64) =
f(x)=64

livid hound Dec 30, 2021, 3:15 PM

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poorly worded

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f^-1(64) is the value of x such that f(x) = 64
or
f(f^-1(64)) = 64

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so if you can reach
f(something) = 64
using the given information, you'll have your answer you seek

crimson sedge Dec 30, 2021, 3:22 PM

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i think i know what the something is

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is it 192?

livid hound Dec 30, 2021, 3:23 PM

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yes

crimson sedge Dec 30, 2021, 3:27 PM

#

ok

#

thank you @livid hound

#

.close

cedar kilnBOT Dec 30, 2021, 3:28 PM

#

Channel closed

Closed by @little wave

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rugged basalt Dec 30, 2021, 3:32 PM

#

Can someone verify this proof? It seems too good to be true and I don't have the intuition to understand why it would be the case.

cedar kilnBOT Dec 30, 2021, 3:32 PM

#

rugged basalt Can someone verify this proof? It seems too good to be true and I don't have the...

rugged basalt Dec 30, 2021, 3:34 PM

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For some context, I'm supposed to write this equation in terms of the mean \bar{x}. I came up with this, which appears correct, but maybe I've missed a step.

violet flume Dec 30, 2021, 3:36 PM

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idk looks okay?

wraith daggerBOT Dec 30, 2021, 3:37 PM

#

#

rugged basalt Dec 30, 2021, 3:39 PM

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The values of x_1, ..., x_30 are fixed, so \bar{x} would be a constant. Though i think my mistake is assuming that \sum_0^n (x_i - \bar{x})^2 = 0

wraith daggerBOT Dec 30, 2021, 3:40 PM

#

rugged basalt Dec 30, 2021, 3:42 PM

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Yeah that's true, but just because it's a summation, i don't see why it can't be a constant, given that n is fixed and x_1, ..., x_n are fixed.

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if i do expand it out, then it would be $ \sum_{i=1}^n \bar{x} - \mu = \sum_{i=1}^n \left( \sum_{i=1}^n x_i \right) - \mu$

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(no idea how to get tex to work)

rugged basalt Dec 30, 2021, 3:47 PM

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rugged basalt if i do expand it out, then it would be $ \sum_{i=1}^n \bar{x} - \mu = \sum_{i=1...

Note that that the i of the inner summation is bound to a different sum operater

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wdym?

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yeah

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a constant

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no, it's not the mean

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it is some random variable which acts as a parameter for the pdf i have to derive

rugged basalt Dec 30, 2021, 3:50 PM

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rugged basalt Note that that the `i` of the inner summation is bound to a different sum operat...

(just want to demonstrate that the summation shouldn't be a problem given that the binding of the i is made explicit)

#

yeah i think that's the issue

#

thanks, i think i can take it from here

#

👍

#

.close

cedar kilnBOT Dec 30, 2021, 3:55 PM

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flat sable Dec 30, 2021, 4:45 PM

#

Number 2

cedar kilnBOT Dec 30, 2021, 4:45 PM

#

flat sable Number 2

flat sable Dec 30, 2021, 4:45 PM

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My exam is comming soon so im revising as my teacher said to

brave aspen Dec 30, 2021, 4:46 PM

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You have the complement of a set right?

fickle trellis Dec 30, 2021, 4:47 PM

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Have you attempted them?

brave aspen Dec 30, 2021, 4:47 PM

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Like A complement is all things that are not in A

flat sable Dec 30, 2021, 4:47 PM

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fickle trellis Have you attempted them?

Nah

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I came late to school after 30 days so i missed the whole chapter

fickle trellis Dec 30, 2021, 4:49 PM

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Oh

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So do you have basic knowledge of set operations

flat sable Dec 30, 2021, 4:50 PM

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fickle trellis So do you have basic knowledge of set operations

No im dumb

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I just need on solving them @fickle trellis

fickle trellis Dec 30, 2021, 4:52 PM

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Ohh

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I need you to know

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Intersection

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Union

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Complement

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And maybe set minus

flat sable Dec 30, 2021, 4:54 PM

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Hmm @fickle trellis

fickle trellis Dec 30, 2021, 4:55 PM

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Yeah

flat sable Dec 30, 2021, 4:55 PM

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Can you do me one of the questions so i can learn a bit faster

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I just need one examplr

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Example*

fickle trellis Dec 30, 2021, 4:55 PM

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Sure

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Okayy lemme show u some general stuff about it

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Do you know what a set is?

flat sable Dec 30, 2021, 4:58 PM

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fickle trellis Okayy lemme show u some general stuff about it

Dont

flat sable Dec 30, 2021, 4:58 PM

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fickle trellis Do you know what a set is?

Dont worry ill figure the other stuff out

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I just dont know abt the diagrams and stuff

fickle trellis Dec 30, 2021, 4:59 PM

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Oh.

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Okay

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This diagram is a venn diagram

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Its just sets (collections of elements) represented as circles.

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So you got two circles

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P and Q

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In the first question

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So that means

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There are two steps

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Now tell me

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What is so special about the shaded region

flat sable Dec 30, 2021, 5:01 PM

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Its intersected

fickle trellis Dec 30, 2021, 5:01 PM

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Yeah

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Actually

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Its common to both circles P and Q

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Or to both sets

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This common thing is called intersection

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So the first one would be.

wraith daggerBOT Dec 30, 2021, 5:02 PM

#

Muhammad Hussaini

fickle trellis Dec 30, 2021, 5:04 PM

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This cap shape

#

Means intersection

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So P intersection Q refers to the common things between P and Q

flat sable Dec 30, 2021, 5:05 PM

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Oh so "a" answer is P ^ Q

fickle trellis Dec 30, 2021, 5:06 PM

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Yeah

flat sable Dec 30, 2021, 5:06 PM

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Alr thx i only needed that

#

👍👍

fickle trellis Dec 30, 2021, 5:06 PM

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Oh so can you figure em out?

flat sable Dec 30, 2021, 5:06 PM

#

fickle trellis Oh so can you figure em out?

Sure yup

fickle trellis Dec 30, 2021, 5:06 PM

#

If youre stuck ping me

cedar kilnBOT Dec 30, 2021, 5:21 PM

#

@flat sable Has your question been resolved?

cedar kilnBOT Dec 30, 2021, 5:36 PM

#

Channel closed

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cedar kilnBOT Dec 30, 2021, 9:31 PM

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inner needle Dec 30, 2021, 10:22 PM

#

Trying to understand the ant on a rubber rope problem, every second that the rope stretches how can I calculate the ants position? https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope
Thanks

Ant on a rubber rope

The ant on a rubber rope is a mathematical puzzle with a solution that appears counterintuitive or paradoxical. It is sometimes given as a worm, or inchworm, on a rubber or elastic band, but the principles of the puzzle remain the same.
The details of the puzzle can vary, but a typical form is as follows:

An ant starts to crawl along a taut rub...

cedar kilnBOT Dec 30, 2021, 10:22 PM

#

inner needle Trying to understand the ant on a rubber rope problem, every second that the rop...

#

@inner needle Has your question been resolved?

inner needle Dec 30, 2021, 10:53 PM

#

<@&286206848099549185>

ionic peak Dec 30, 2021, 10:58 PM

#

https://youtu.be/OM9KepKsg6U

YouTube

Vsauce2

Ant On A Rubber Rope Paradox

An ant is placed on one end of a rubber rope and he begins walking at about 5cm per second. As he’s walking, the rope gets stretched… and stretched… at a rate of 10cm per second. The rope is getting stretched faster and longer relative to the ant’s consistent walking pace.

Can the ant ever get to the end of the rope? Is he caught in an endless,...

▶ Play video

inner needle Dec 30, 2021, 10:58 PM

#

I did see this 3 times 😄

ionic peak Dec 30, 2021, 10:58 PM

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Ah okay, so what exactly are you having trouble understanding?

inner needle Dec 30, 2021, 10:58 PM

#

at 8:38

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when he has the two formula

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thats a - (minus) in between them?

ionic peak Dec 30, 2021, 11:03 PM

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No

inner needle Dec 30, 2021, 11:03 PM

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alright thought so

#

so lets say 1 second has passed, the ant moved 1cm (its own speed) , how can I get the distance it moved due to the rope stretching, then all I have to do is add the 1cm it moved + that distance, correct?

ionic peak Dec 30, 2021, 11:08 PM

#

1 cm it moved, plus how much the length behind the ant has stretched

inner needle Dec 30, 2021, 11:09 PM

#

how can I calc that tho

#

the length behind the ant

ionic peak Dec 30, 2021, 11:10 PM

#

Also, are we assuming both the ant and the rope are moving/stretching continuously or discretely?

inner needle Dec 30, 2021, 11:10 PM

#

so the rope stretches 2cm every second for e.g

ionic peak Dec 30, 2021, 11:11 PM

#

I.e is the rope stretching while the ant is moving, or is it like, “ant moves 1cm” then “rope stretches 2cm” in a loop

inner needle Dec 30, 2021, 11:12 PM

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the ant moves before the rope is stretched

#

so ant moves the 1cm, then the rope stretches

ionic peak Dec 30, 2021, 11:15 PM

#

Okay, so you would take the total distance from the beginning of the rope, and multiply that by how much the rope has increased.

#

For instance, ant moves at 1cm/sec rope grows at 2cm/sec, and the rope is 2cm long

inner needle Dec 30, 2021, 11:16 PM

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how much the rope increased refers to , its current length

#

for the first one then, the ant moved its original 1cm + 0 ( 2 rope length * 0 how much it increased) right?

#

second one , ant is now 2cm + (2 * 2) = 4cm ?

#

nah ive got it wrong

ionic peak Dec 30, 2021, 11:19 PM

#

After the first second:

The ant has moved 1cm
Then, the rope stretches 2cm, the length of the rope is now 4cm, so the rope has doubled.
the 1cm that the ant traveled is now 2cm, because the whole rope doubled

ashen dune Dec 30, 2021, 11:19 PM

#

1 sec = 1cm
2sec = 2cm

inner needle Dec 30, 2021, 11:20 PM

#

hmm alright ty

ashen dune Dec 30, 2021, 11:20 PM

#

1 sec = 1cm
2sec = x
Then
2×1/1

inner needle Dec 30, 2021, 11:20 PM

#

so the second second is
the ant is now 3cm
the rope is now 6cm
ant* is now

ashen dune Dec 30, 2021, 11:20 PM

#

X = 2×1/1

ionic peak Dec 30, 2021, 11:21 PM

#

inner needle for the first one then, the ant moved its original 1cm + 0 ( 2 rope length * 0 h...

(Distance behind the ant) • (new rope length)/(previous rope length)

inner needle Dec 30, 2021, 11:21 PM

#

ionic peak (Distance behind the ant) • (new rope length)/(previous rope length)

ty and that • is multiplication right?

ionic peak Dec 30, 2021, 11:21 PM

#

Yup

inner needle Dec 30, 2021, 11:21 PM

#

tyvm

ionic peak Dec 30, 2021, 11:22 PM

#

Any other questions?

inner needle Dec 30, 2021, 11:22 PM

#

no, ty

#

.close

cedar kilnBOT Dec 30, 2021, 11:22 PM

#

Channel closed

Closed by @inner needle

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cedar kilnBOT Dec 31, 2021, 8:09 AM

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Channel closed

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cedar kilnBOT Jan 1, 2022, 5:01 PM

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crimson sedge Jan 1, 2022, 7:39 PM

#

Hello

cedar kilnBOT Jan 1, 2022, 7:39 PM

#

crimson sedge Hello

crimson sedge Jan 1, 2022, 7:39 PM

#

I have a reiddle

#

I NEED HELP ASAP

#

A farmer’s wife made some chapatis…the farmer had 4 sons…. The fist son came, gave one chapati to the dog,and made four equal parts of remaining chapatis, ate one part of it and left the other three parts for his brothers….other three sons came one after the other and did the same thinking that they came first…then at night all three came to the house, one of them gave one chapati to dog and made four equal parts and the four brothers ate one-one part of it… If no chapati was broken in pieces then how many minimum number chapatis did the mom made?

crimson sedge Jan 1, 2022, 7:40 PM

#

crimson sedge A farmer’s wife made some chapatis…the farmer had 4 sons…. The fist son came, ga...

THERE GOES THE QUESTION.

cedar kilnBOT Jan 1, 2022, 7:55 PM

#

@crimson sedge Has your question been resolved?

cedar kilnBOT Jan 1, 2022, 8:25 PM

#

@crimson sedge Has your question been resolved?

crimson sedge Jan 1, 2022, 8:26 PM

#

I don't need your help now

#

I will do it myself.

#

:((

cedar kilnBOT Jan 1, 2022, 9:26 PM

#

@crimson sedge Has your question been resolved?

cedar kilnBOT Jan 1, 2022, 10:26 PM

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untold rampart Jan 1, 2022, 10:37 PM

#

Shouldn't K(x) be a constant? Why was it written as a linear equation?

cedar kilnBOT Jan 1, 2022, 10:37 PM

#

untold rampart Shouldn't K(x) be a constant? Why was it written as a linear equation?

dense wing Jan 1, 2022, 10:42 PM

#

untold rampart Shouldn't K(x) be a constant? Why was it written as a linear equation?

you divided by a quadratic

#

so your remainder function is linear.

untold rampart Jan 1, 2022, 10:43 PM

#

why?

dense wing Jan 1, 2022, 10:43 PM

#

cause remainder is 1 degree less than divisor.

untold rampart Jan 1, 2022, 10:51 PM

#

Why is the reminder always one degree less than the divisor? Why not 2 or 3 degrees less or whatever?

#

Or does deg[K(x)]=deg[P(x)/Q(x)] ?

cedar kilnBOT Jan 1, 2022, 11:10 PM

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@untold rampart Has your question been resolved?

cedar kilnBOT Jan 1, 2022, 11:25 PM

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novel moth Jan 2, 2022, 12:42 AM

#

hi

cedar kilnBOT Jan 2, 2022, 12:42 AM

#

novel moth hi

novel moth Jan 2, 2022, 12:42 AM

#

this is a short question but

#

for a circle in 3d coorinates, say our circle is on the x-z plane, i know x=rcos(theta) and z=rsin(theta), and for a x-y plane, x=rcos(theta) and y=rsin(theta)

#

what if we have

#

y and z?

dense wing Jan 2, 2022, 12:43 AM

#

same thing.

novel moth Jan 2, 2022, 12:44 AM

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which one is cos

#

which one would be sin?

dense wing Jan 2, 2022, 12:44 AM

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doesn't matter

#

it just affects the direction the parameterization would go

novel moth Jan 2, 2022, 12:44 AM

#

ahhhhh alright, thank you, thats all

#

.close

cedar kilnBOT Jan 2, 2022, 12:44 AM

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stuck snow Jan 2, 2022, 3:06 AM

#

Can anyone help with 16)d

cedar kilnBOT Jan 2, 2022, 3:06 AM

#

stuck snow Can anyone help with 16)d

stuck snow Jan 2, 2022, 3:10 AM

#

Anyone able to help pls

cedar kilnBOT Jan 2, 2022, 3:25 AM

#

@stuck snow Has your question been resolved?

bright surge Jan 2, 2022, 3:27 AM

#

write the vectors the question asks for as the sum of the sides you're given (PW, PX, RP, QZ, QY, RQ)

#

and then use the midpoint thing

#

(sorry for being late i just got out of bed)

#

@stuck snow

stuck snow Jan 2, 2022, 3:28 AM

#

I have I’m just stuck on d)

#

@bright surge

bright surge Jan 2, 2022, 3:29 AM

#

stuck snow I have I’m just stuck on d)

yeah, that's my tip for d)

#

have you rewritten the vectors yet?

stuck snow Jan 2, 2022, 3:31 AM

#

Yep

bright surge Jan 2, 2022, 3:31 AM

#

right

#

R is the midpoint of PQ, so RP=QR

#

which is equal to RQ times something

stuck snow Jan 2, 2022, 3:31 AM

#

Yupp

bright surge Jan 2, 2022, 3:32 AM

#

bright surge which is equal to RQ times something

what is that something?

stuck snow Jan 2, 2022, 3:32 AM

#

#

I got that for RP

bright surge Jan 2, 2022, 3:33 AM

#

stuck snow

you're overthinking this

stuck snow Jan 2, 2022, 3:33 AM

#

Umm sorry

bright surge Jan 2, 2022, 3:33 AM

#

PR = RQ = -QR

#

right?

stuck snow Jan 2, 2022, 3:34 AM

#

Yes

#

Um

#

@bright surge

bright surge Jan 2, 2022, 3:37 AM

#

you can do the same with PW and PX

#

QZ and QY as well

cedar kilnBOT Jan 2, 2022, 4:07 AM

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scenic locust Jan 2, 2022, 4:17 AM

#

WILDEST DREAMS

cedar kilnBOT Jan 2, 2022, 4:17 AM

#

scenic locust WILDEST DREAMS

floral thistle Jan 2, 2022, 4:19 AM

#

@scenic locust send a question or close the channel, don’t troll

scenic locust Jan 2, 2022, 4:21 AM

#

Sorry i didnt see the channel name my apologies

floral thistle Jan 2, 2022, 4:21 AM

#

to close it’s .close

scenic locust Jan 2, 2022, 4:21 AM

#

how can i close the channel?

#

.close

cedar kilnBOT Jan 2, 2022, 4:21 AM

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Channel closed

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pure snow Jan 2, 2022, 4:36 AM

#

hey! i needed help on this math problem

cedar kilnBOT Jan 2, 2022, 4:36 AM

#

pure snow hey! i needed help on this math problem

pure snow Jan 2, 2022, 4:36 AM

#

im doing it for a puzzle and have legit no idea

cedar kilnBOT Jan 2, 2022, 4:51 AM

#

@pure snow Has your question been resolved?

floral thistle Jan 2, 2022, 5:01 AM

#

@pure snow

#

for the limit use lhopitals rule

#

$\sum_{j=0}^{\infty}\left(\frac{3}{4}\right)^j = \sum_{j=0}^{\infty}\left(\frac{4}{3}\right)^{-j}$ \ $\sum_{j=0}^{\infty}a^{-j} = 1+\frac{1}{a-1}$ for $\abs{a}>1$

wraith daggerBOT Jan 2, 2022, 5:06 AM

#

quantum

cedar kilnBOT Jan 2, 2022, 5:22 AM

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@pure snow Has your question been resolved?

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austere plume Jan 2, 2022, 8:37 AM

#

Hii guys

cedar kilnBOT Jan 2, 2022, 8:37 AM

#

austere plume Hii guys

austere plume Jan 2, 2022, 8:38 AM

#

Is AB=I is enough to show that B is the inverse of A? Or we also need BA=I too?

#

A and B are matrix

south tundra Jan 2, 2022, 8:46 AM

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By definition, a square nxn matrix A is invertible iff there exists nxn matrix B such that

#

So yeah

tropic oxide Jan 2, 2022, 8:48 AM

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no

#

who said A and B were square matrices?

cedar kilnBOT Jan 2, 2022, 8:53 AM

#

@austere plume Has your question been resolved?

austere plume Jan 2, 2022, 8:53 AM

#

I see

#

So if both A and B are square matrix then it is true?

#

If not then false right?

tropic oxide Jan 2, 2022, 8:55 AM

#

yes

austere plume Jan 2, 2022, 8:56 AM

#

Thank you! I got it

#

.close

cedar kilnBOT Jan 2, 2022, 8:56 AM

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Channel closed

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crimson sedge Jan 2, 2022, 9:52 AM

#

This is a stupid question but I’m not the greatest at math.

So I would say 25% because it’s a 1/4 but there are 2 25% and it can’t be 50% so is it 60%?

cedar kilnBOT Jan 2, 2022, 9:52 AM

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crimson sedge This is a stupid question but I’m not the greatest at math. So I would say 25% ...

cedar kilnBOT Jan 2, 2022, 10:07 AM

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@crimson sedge Has your question been resolved?

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wild lagoon Jan 2, 2022, 2:43 PM

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find sum of infinite terms of 1/5 +1/7 +1/5^2 + 1/7^2 .. and so on

cedar kilnBOT Jan 2, 2022, 2:43 PM

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wild lagoon find sum of infinite terms of 1/5 +1/7 +1/5^2 + 1/7^2 .. and so on

wild lagoon Jan 2, 2022, 2:43 PM

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<@&286206848099549185> help meh

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D:

bright surge Jan 2, 2022, 2:43 PM

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wild lagoon find sum of infinite terms of 1/5 +1/7 +1/5^2 + 1/7^2 .. and so on

separate this into 2 series

wild lagoon Jan 2, 2022, 2:43 PM

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hokie

bright surge Jan 2, 2022, 2:44 PM

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wild lagoon <@&286206848099549185> help meh

15 minute rule
even if you follow 1, you're probably still not going to get any help by pinging helpers. they're rarely ever active.

wild lagoon Jan 2, 2022, 2:45 PM

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i see-

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D:

cedar kilnBOT Jan 2, 2022, 3:00 PM

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@wild lagoon Has your question been resolved?

cedar kilnBOT Jan 2, 2022, 3:15 PM

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abstract pollen Jan 2, 2022, 9:48 PM

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cedar kilnBOT Jan 2, 2022, 9:48 PM

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abstract pollen

abstract pollen Jan 2, 2022, 9:48 PM

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Can someone talk me through 17 please?

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.close

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final matrix Jan 2, 2022, 10:01 PM

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can someone help me with with this

cedar kilnBOT Jan 2, 2022, 10:01 PM

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final matrix can someone help me with with this

final matrix Jan 2, 2022, 10:01 PM

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#

someonnne

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ps=ls

cedar kilnBOT Jan 2, 2022, 10:23 PM

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@final matrix Has your question been resolved?

proper kernel Jan 2, 2022, 10:26 PM

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final matrix

AD and BC are parallel lines

final matrix Jan 2, 2022, 10:26 PM

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is that all?

proper kernel Jan 2, 2022, 10:27 PM

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i guess that would explain it

final matrix Jan 2, 2022, 10:27 PM

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oh ok

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I have one more

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can you pls help with that one

proper kernel Jan 2, 2022, 10:28 PM

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yea

final matrix Jan 2, 2022, 10:29 PM

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floral thistle Jan 2, 2022, 10:38 PM

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@final matrix you have two channels open, close one

cedar kilnBOT Jan 2, 2022, 10:59 PM

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@final matrix Has your question been resolved?

brazen root Jan 2, 2022, 11:42 PM

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final matrix

how would you do the transformation? notice how they are different right now, and what you would do to "undo" the differences

final matrix Jan 2, 2022, 11:43 PM

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alright thanks

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I got it!

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.close

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lethal wadi Jan 2, 2022, 11:53 PM

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Hi! I'm looking to devise an equation for the width of a building pathway with respect to the number of people forecasted to use that pathway. It's in Minecraft, so the units are blocks/meters. The minimum y-value (width) should be 1 block, and I know how to set the horizontal limit. My problem is getting the graph to start at [0,1], while being able to adjust the curve freely

cedar kilnBOT Jan 2, 2022, 11:53 PM

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lethal wadi Hi! I'm looking to devise an equation for the width of a building pathway with r...

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@lethal wadi Has your question been resolved?

main needle Jan 3, 2022, 12:15 AM

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on hacky way is to adjust it horizontally*

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here you can replace (x-1) with (x-log(7)/log(2)) to get (0,1)

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or just (x-2.8) if you want it close

lethal wadi Jan 3, 2022, 12:36 AM

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sweet thanks!

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.close

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gentle light Jan 3, 2022, 1:20 AM

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How do I use the factor theorem? it says to use (x-a) but how do I find a/

cedar kilnBOT Jan 3, 2022, 1:20 AM

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gentle light How do I use the factor theorem? it says to use (x-a) but how do I find a/

crimson sedge Jan 3, 2022, 1:23 AM

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show me the question please

dense wing Jan 3, 2022, 1:30 AM

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gentle light How do I use the factor theorem? it says to use (x-a) but how do I find a/

do you have a specific question?

cedar kilnBOT Jan 3, 2022, 1:35 AM

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@gentle light Has your question been resolved?

bold vine Jan 3, 2022, 1:41 AM

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@gentle light Always just send the original problem if appropriate

cedar kilnBOT Jan 3, 2022, 1:50 AM

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cedar kilnBOT Jan 3, 2022, 9:51 AM

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mint sentinel Jan 3, 2022, 10:26 AM

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Hi I'm having exam tomorrow and I need this doubt to be resolved

The worksheet says
Simplify
(x-3y+4) (x-3y-4)
This question is from expansions

cedar kilnBOT Jan 3, 2022, 10:26 AM

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mint sentinel Hi I'm having exam tomorrow and I need this doubt to be resolved The worksheet...

bright surge Jan 3, 2022, 10:27 AM

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mint sentinel Hi I'm having exam tomorrow and I need this doubt to be resolved The worksheet...

probably express it as something squared)

mint sentinel Jan 3, 2022, 10:28 AM

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Okay

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Ty

mint sentinel Jan 3, 2022, 10:28 AM

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bright surge probably express it as something squared)

How do I do that?

bright surge Jan 3, 2022, 10:28 AM

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mint sentinel How do I do that?

something^2 = something * something

mint sentinel Jan 3, 2022, 10:29 AM

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Ty

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Thanks

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.close

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neat fossil Jan 3, 2022, 10:37 AM

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so here my lecturer doesnt really show the range of this function
but is there a way i could write it out in set builder notation without solving it

so far i understand the function definition given by the example
is this the correct range of the function? Range = {(e^x + x^2| x in \doubleR

cedar kilnBOT Jan 3, 2022, 10:37 AM

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neat fossil so here my lecturer doesnt really show the range of this function but is there ...

neat fossil Jan 3, 2022, 10:37 AM

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https://cdn.discordapp.com/attachments/903430333888884736/927510857452236850/unknown.png

south tundra Jan 3, 2022, 10:40 AM

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So you want to find the range of the function as I understood?

neat fossil Jan 3, 2022, 10:41 AM

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yes

south tundra Jan 3, 2022, 10:42 AM

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You could find the minimum value of y by setting the derivative of the function to 0 and solving for x

neat fossil Jan 3, 2022, 10:42 AM

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i just want to write it in set builder notation

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i dont really have to solvei t i think

south tundra Jan 3, 2022, 10:43 AM

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Oh, then yeah I guess the range is the same as {$e^x + x^2, x\in{R}$}

wraith daggerBOT Jan 3, 2022, 10:43 AM

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Touch Our Beans

south tundra Jan 3, 2022, 10:43 AM

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You get the point

neat fossil Jan 3, 2022, 10:43 AM

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okay i guess it works out

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ye

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thankss

south tundra Jan 3, 2022, 10:44 AM

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In case if you're curious, the minimum of y is at x = -W(1/2), where w denotes the lambert w function (by definition the inverse function of y = xe^x)

neat fossil Jan 3, 2022, 10:44 AM

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thats a little too complicated

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im only doing a basic discrete math course haha

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but for t his

south tundra Jan 3, 2022, 10:45 AM

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We include the 0 there because R^+ doesn't include 0

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Because x^2 is always either 0 or positive (> 0)

neat fossil Jan 3, 2022, 10:45 AM

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im having trouble understanding the notation

south tundra Jan 3, 2022, 10:45 AM

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So it's either 0 or in the set of positive reals

neat fossil Jan 3, 2022, 10:46 AM

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i understand the rnage

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is just the notation is

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hard 😦

south tundra Jan 3, 2022, 10:46 AM

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You know what $\cup$ denotes, right?

wraith daggerBOT Jan 3, 2022, 10:46 AM

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Touch Our Beans

neat fossil Jan 3, 2022, 10:46 AM

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yes

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thts union

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just the set of the elements in either

south tundra Jan 3, 2022, 10:46 AM

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Yes

neat fossil Jan 3, 2022, 10:46 AM

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uhhh

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like here

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dont i have to specify that the pair is in f for some x

south tundra Jan 3, 2022, 10:47 AM

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Wdym, that's stated above

neat fossil Jan 3, 2022, 10:48 AM

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but for this

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x ^2 range

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shouldnt it be something similar to that

south tundra Jan 3, 2022, 10:49 AM

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Yes it is, it's just that $X = R^{+}\cup${$0$}

wraith daggerBOT Jan 3, 2022, 10:49 AM

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Touch Our Beans

neat fossil Jan 3, 2022, 10:49 AM

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like y in R | (x,y) in f and y = x^2

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shouldnt my range be like that

south tundra Jan 3, 2022, 10:49 AM

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Those are the same

neat fossil Jan 3, 2022, 10:50 AM

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im just confused because in the example given it doesnt say what y is in

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like the {y|y>=0} doesnt have anything about R

south tundra Jan 3, 2022, 10:51 AM

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In which example?

neat fossil Jan 3, 2022, 10:52 AM

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so in the definition it specifies that each pair has to be an element of the func

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but when they just say the answwer is {y|y>=0} wheres the bit about it being an ordered pair in f

south tundra Jan 3, 2022, 10:54 AM

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Generally $x^2 \ge 0$ for all real x, therefore $y \ge 0$

wraith daggerBOT Jan 3, 2022, 10:54 AM

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Touch Our Beans

neat fossil Jan 3, 2022, 10:54 AM

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but do i not have to specify that its an ordered pair inside the function

south tundra Jan 3, 2022, 10:55 AM

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No, because x has no restrictions

neat fossil Jan 3, 2022, 10:55 AM

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but y does right

south tundra Jan 3, 2022, 10:55 AM

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Yes, because it's square of some number

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And in real numbers squaring some number automatically makes it nonnegative

neat fossil Jan 3, 2022, 10:56 AM

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okay i think i get it

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thanks a bunch :>

south tundra Jan 3, 2022, 10:56 AM

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Np

neat fossil Jan 3, 2022, 10:56 AM

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.close

cedar kilnBOT Jan 3, 2022, 10:56 AM

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Channel closed

Closed by @neat fossil

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cedar kilnBOT Jan 3, 2022, 4:30 PM

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solid valve Jan 3, 2022, 4:32 PM

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i need help with this

cedar kilnBOT Jan 3, 2022, 4:32 PM

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solid valve i need help with this

livid hound Jan 3, 2022, 4:41 PM

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consider
a_v = (a_1 * ... * a_v)/(a_1 * ... a_(v-1))

solid valve Jan 3, 2022, 4:43 PM

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that worked thank you very much

cedar kilnBOT Jan 3, 2022, 4:58 PM

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@solid valve Has your question been resolved?

cedar kilnBOT Jan 3, 2022, 5:13 PM

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atomic chasm Jan 3, 2022, 5:30 PM

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cedar kilnBOT Jan 3, 2022, 5:30 PM

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atomic chasm

atomic chasm Jan 3, 2022, 5:30 PM

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here's what i have so far, could anyone help?

south tundra Jan 3, 2022, 5:37 PM

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So there are two possibilities, B is either to the left of A or to the right of A on the graph, let's first consider the case of B being on the left

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Here we're already given the length of AB, that's 6sqrt(5)

atomic chasm Jan 3, 2022, 5:38 PM

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hm yes

south tundra Jan 3, 2022, 5:38 PM

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We're also given the slope as -2, which, by definition, means that difference in Y/difference in X between two point on the graph is -2

atomic chasm Jan 3, 2022, 5:38 PM

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i formed this equation btw sorry is it right

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south tundra Jan 3, 2022, 5:38 PM

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Equation of the line? Yeah that's the general form but that step can be avoided

atomic chasm Jan 3, 2022, 5:39 PM

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atomic chasm

cos of pythagoras

south tundra Jan 3, 2022, 5:39 PM

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Yup

atomic chasm Jan 3, 2022, 5:39 PM

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south tundra We're also given the slope as -2, which, by definition, means that difference in...

could we put this algebraically maybe?

south tundra Jan 3, 2022, 5:39 PM

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So you want to solve this with algebra rather than visually?

atomic chasm Jan 3, 2022, 5:40 PM

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could we do it visually first

south tundra Jan 3, 2022, 5:40 PM

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Yes, surely

south tundra Jan 3, 2022, 5:40 PM

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south tundra

And here, since the slope is -2

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We can deduce that BC/AC = 2

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The reason we pick 2 instead of -2 is that

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BC and AC are lengths, they're supposed to be positive

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That's why we need absolute value of the slope here

atomic chasm Jan 3, 2022, 5:41 PM

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okay im with you

south tundra Jan 3, 2022, 5:41 PM

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Let's denote AC with some number x, and BC with 2x

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Now, since the hypotenuse is 6sqrt(5), and the other sides are x and 2x, we can use Pythagorean theorem

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That will yield x^2 + 4x^2 = 36*5

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5x^2 = 36*5

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x^2 = 36

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And thus x = 6

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And therefore, since x is 6, the x-coordinate of B is 6 less than x-coordinate of A

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So the x-coordinate of B is -3

atomic chasm Jan 3, 2022, 5:44 PM

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why did we subtract 6

south tundra Jan 3, 2022, 5:44 PM

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Because B is on the left of A, not on the right

atomic chasm Jan 3, 2022, 5:44 PM

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imwwith u until x=6 but i would've added it to 3

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OH

south tundra Jan 3, 2022, 5:45 PM

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You see now?

atomic chasm Jan 3, 2022, 5:45 PM

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negative gradient

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yep

south tundra Jan 3, 2022, 5:45 PM

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So we subtract 6 from 3 and get that x-coord of B is -3

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And we can use a similar argument to argue that y-coord of B is therefore 5 - 2x

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5 - 2x = 5 - 6 = -1

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Hm, wait

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Oh nvm we need to add it here

atomic chasm Jan 3, 2022, 5:46 PM

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17

south tundra Jan 3, 2022, 5:46 PM

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Because B is higher than A

atomic chasm Jan 3, 2022, 5:46 PM

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yeah

south tundra Jan 3, 2022, 5:47 PM

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Now the other case, when B is on the right of A, is almost identical

atomic chasm Jan 3, 2022, 5:47 PM

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is there any way to do it algebraically as well

south tundra Jan 3, 2022, 5:47 PM

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south tundra Now the other case, when B is on the right of A, is almost identical

The only different is that you're adding x-coord of A with 3 and 2x from y-coord of A

south tundra Jan 3, 2022, 5:48 PM

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atomic chasm is there any way to do it algebraically as well

Yes, first what we can do is define a,b such that y = ax + b represents the equation of the line

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And since the slope is given, a = -2

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So we have y = -2x + b

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We also need this line to cross (3, 5)

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Meaning that if we plug in x = 3 and y = 5, then the equation must be true

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So what we get is 5 = -2*3 + b => b = 11

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So far so good

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Now, let's say that coordinates of B are x0 and y0

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Since B lies on the line, it means that $y_0 = -2x_0 + b$

wraith daggerBOT Jan 3, 2022, 5:50 PM

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Touch Our Beans

atomic chasm Jan 3, 2022, 5:50 PM

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hm ok yeah

south tundra Jan 3, 2022, 5:51 PM

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Also the distance between A and B is 6sqrt(5), which means that $(x_0 - 3)^2 + (y_0 - 5)^2 = (6\sqrt{5})^2$

wraith daggerBOT Jan 3, 2022, 5:51 PM

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Touch Our Beans

south tundra Jan 3, 2022, 5:51 PM

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Using the distance formula between two points

atomic chasm Jan 3, 2022, 5:52 PM

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we can solve simultaneously

south tundra Jan 3, 2022, 5:52 PM

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wraith dagger **Touch Our Beans**

Here we can also plug in $y_0 = -2x_0 + 11$ to get that $(x_0 - 3)^2 + (-2x_0 + 11 - 5)^2 = 36\cdot{5}$

wraith daggerBOT Jan 3, 2022, 5:52 PM

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Touch Our Beans

south tundra Jan 3, 2022, 5:52 PM

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atomic chasm we can solve simultaneously

Sort of

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So all we need to do it solve for $x_0$ in $(x_0 - 3)^2 + (-2x_0 + 6)^2 = 36\cdot{5}$

wraith daggerBOT Jan 3, 2022, 5:53 PM

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Touch Our Beans

south tundra Jan 3, 2022, 5:53 PM

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We can factor out 2 there

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$(x_0 - 3)^2 + (2)^2(-x_0 + 3)^2 = 36\cdot{5}$

wraith daggerBOT Jan 3, 2022, 5:54 PM

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Touch Our Beans

south tundra Jan 3, 2022, 5:54 PM

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Also, when we're dealing with numbers being squared, we can use the fact that generally $(-z)^2 = z^2$ to get that $(x_0 - 3)^2 + 4(x_0 - 3)^2 = 36\cdot{5}$

wraith daggerBOT Jan 3, 2022, 5:55 PM

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Touch Our Beans

south tundra Jan 3, 2022, 5:55 PM

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Adding similar terms yields $5(x_0 - 3)^2 = 36\cdot{5}$

wraith daggerBOT Jan 3, 2022, 5:55 PM

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Touch Our Beans

south tundra Jan 3, 2022, 5:56 PM

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$\implies (x_0 - 3)^2 = 36 \ \implies x_0 - 3 = \pm{6} \ \implies x_0 = -3$ or $x_0 = 9$

wraith daggerBOT Jan 3, 2022, 5:57 PM

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Touch Our Beans

south tundra Jan 3, 2022, 5:57 PM

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Everything is clear, right?

atomic chasm Jan 3, 2022, 5:57 PM

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yes! im working it out with you

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your explanation was enough, I fully understand it now

south tundra Jan 3, 2022, 5:58 PM

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From here you can find out the both possible values of y0 easily

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And that should do it

atomic chasm Jan 3, 2022, 5:58 PM

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yep just substitute

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17 and -7

south tundra Jan 3, 2022, 5:59 PM

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Yes

atomic chasm Jan 3, 2022, 5:59 PM

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great!

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how do i close

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.close

cedar kilnBOT Jan 3, 2022, 5:59 PM

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Channel closed

Closed by @atomic chasm

Use .reopen if this was a mistake.

atomic chasm Jan 3, 2022, 5:59 PM

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. reopen

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thank you!!

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.close

south tundra Jan 3, 2022, 6:00 PM

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You're welcome

cedar kilnBOT Jan 3, 2022, 6:00 PM

#

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hushed ferry Jan 3, 2022, 6:15 PM

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how to do part c and d ms says answer is 8 for part c and 20 for part d this is a permutation question

cedar kilnBOT Jan 3, 2022, 6:15 PM

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hushed ferry how to do part c and d ms says answer is 8 for part c and 20 for part d this is ...

main needle Jan 3, 2022, 6:18 PM

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mostly, but you have to figure out "the number of ways to place 3 parcels in 3 boxes where none are for the correct person" by hand

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like for c), think about the case where A and B have the right parcel, and all that's left is putting C,D,E in the last 3 boxes incorrectly

hushed ferry Jan 3, 2022, 6:25 PM

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main needle mostly, but you have to figure out "the number of ways to place 3 parcels in 3 b...

yuh i did it that we so if we find for 2 when 2 are correctly placed we also get the ones when 3 are correctly places and 5 are correctly places and as 4 cannt be correct places with one wrong its not possible as if one is wrong another should be wrong so if we find for 2 and deduct it by 3 and 5 i get 12 not 8

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for part c

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if u can try out the question with the working would be greatly apreciated

main needle Jan 3, 2022, 6:28 PM

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I'd try it a different way

hushed ferry Jan 3, 2022, 6:28 PM

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sure

main needle Jan 3, 2022, 6:28 PM

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first find the number of ways to order 1,2,3,4,5, if 1 and 2 are correct and 3,4,5 are incorrectly placed

hushed ferry Jan 3, 2022, 6:30 PM

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main needle first find the number of ways to order 1,2,3,4,5, if 1 and 2 are correct and 3,4...

yuh so thats part a and that will be all correctly placed in each one so it will be 1 ryt to order 1 2 3 4 5

main needle Jan 3, 2022, 6:30 PM

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part a is when 5 are placed correctly

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I'm talking about when 2 are placed correctly in A and B, and the rest are incorrect

hushed ferry Jan 3, 2022, 6:30 PM

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yuh

main needle Jan 3, 2022, 6:31 PM

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like I just want you to try to write out orderings that work

hushed ferry Jan 3, 2022, 6:31 PM

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yuh for then when we find for 2 we also get 3 and 4 correctly places ryt in that sum we find for 1 and 2 when places correctly

hushed ferry Jan 3, 2022, 6:31 PM

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main needle like I just want you to try to write out orderings that work

yuh i did it

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like that

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their are 4 ways

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in where a ia always the same place

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will not change but

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2 can go anywhere from b to e

main needle Jan 3, 2022, 6:32 PM

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I'm not sure we're doing the same thing

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like one thing that works for my question is 1,2,4,5,3

hushed ferry Jan 3, 2022, 6:33 PM

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this question is quite complicated by the matter of facts cannt really tell by just really reading the question i have been working out this for the past 2 hours lol

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but still confused

main needle Jan 3, 2022, 6:33 PM

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oh well

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there are only 2 ways to do what I'm asking
1,2,4,5,3 and
1,2,5,3,4

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so if you have only 2 specific boxes filled correctly, there are two ways to fill the rest incorrectly

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c) is asking for A correct and another correct

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you could have AB correct, or AC, AD, and AE

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so 4*2

hushed ferry Jan 3, 2022, 6:34 PM

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oh

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oh ic i have found all the ways others also can be arrange i think

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ty for the help

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.close

cedar kilnBOT Jan 3, 2022, 6:38 PM

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lofty moat Jan 3, 2022, 6:55 PM

#

im terrible at maths and trying to improve, but if im trying to multiply out off the brackets and the question is 5(x+y) what would the answer be? just making sure i got the answer right

cedar kilnBOT Jan 3, 2022, 6:55 PM

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lofty moat im terrible at maths and trying to improve, but if im trying to multiply out off...

lofty moat Jan 3, 2022, 6:55 PM

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dont judge i suck at maths

south tundra Jan 3, 2022, 6:55 PM

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5x + 5y?

lofty moat Jan 3, 2022, 6:56 PM

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i got 5x + y

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is yours correct?

dense wing Jan 3, 2022, 6:56 PM

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TOB's is correct.

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cause they distributed correctly

south tundra Jan 3, 2022, 6:56 PM

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According to distributive law

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$a(b + c) = ab + ac$

wraith daggerBOT Jan 3, 2022, 6:56 PM

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Touch Our Beans

lofty moat Jan 3, 2022, 6:57 PM

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aaaaaah right, so what would -2(s + 3t) be?

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just trying to get my head round it, ive always been terrible at maths

south tundra Jan 3, 2022, 6:57 PM

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That would be -2s + (-2)*3t

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Same as -2s - 6t

lofty moat Jan 3, 2022, 6:58 PM

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so both would be correct answers?

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how do you get that answer?

south tundra Jan 3, 2022, 6:58 PM

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wraith dagger **Touch Our Beans**

All you need is this

south tundra Jan 3, 2022, 6:59 PM

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lofty moat so both would be correct answers?

Yes because they're the same things

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Since (-2)*3 is -6

lofty moat Jan 3, 2022, 7:00 PM

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aah okay i see, thats helped me understand it a bit more, i'll see if i can get through the rest myself, much appreciated :)

#

.close

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woeful tiger Jan 3, 2022, 7:41 PM

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cedar kilnBOT Jan 3, 2022, 7:41 PM

#

woeful tiger

woeful tiger Jan 3, 2022, 7:42 PM

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does this sentence imply f(x+m) = f(-x +m) or f(x +m) = f(-(x+m)) so f(-x-m) ?

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nvm

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.close

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cedar kilnBOT Jan 3, 2022, 8:22 PM

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graceful karma Jan 3, 2022, 8:25 PM

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Does it have a mass?

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Weird

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Hmm

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Yeah Im not sure how youd solve that without a mass

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Np

faint dirge Jan 3, 2022, 8:32 PM

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mass doesn't matter?

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the only forces you're dealing with are gravity (and friction, which is based off gravity), which scales based on mass

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friction is $$f_k=μ_kmg\cos{\theta}=0.3(9.81)\frac{\sqrt{2}}{2}m$$, accel down the slope due to gravity is just $$F_g=mg\sin{\theta}=9.81\frac{\sqrt{2}}{2}}m$$, and you have an initial speed.

wraith daggerBOT Jan 3, 2022, 8:35 PM

#

Scythe
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

faint dirge Jan 3, 2022, 8:36 PM

#

both acceleration due to gravity and force of friction are down the slope, opposite of the initial speed

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so you just need to find how long it takes to decelerate to 0, then distance covered

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or if you've done energy, you can solve it more easily that way

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with (fg+fk)d+m(8)**2/2=0

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or potential energy or whatever

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but the point is

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in many physics problems where there are NO*** specified forces (like X newtons), gravity and such scale with mass

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so mass ends up canceling

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intuitively what matters is the coefficient of friction, which increases as surface area increases, and usually as objects grow heavier their surface area grows - which is why we expect heavier, bigger objects to have more friction when left alone on a slope, even though it's only the bigger part that matters and not the heavier/more massful part.

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@graceful karma so you can keep this in mind for the future

graceful karma Jan 3, 2022, 8:45 PM

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Still sounds confusing but I suppose that makes sense

cedar kilnBOT Jan 3, 2022, 8:51 PM

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@crimson sedge Has your question been resolved?

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✅

vernal shell Jan 3, 2022, 9:12 PM

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Hello, both forces must have the same direction (negative) because they are going downwards

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You are welcome :thumbsup_tone3:

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Anyway, I'd suggest to use the Work-Energy theorem if you have already learned about that

cedar kilnBOT Jan 3, 2022, 9:28 PM

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brazen valley Jan 3, 2022, 9:54 PM

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Can someone help me with this proof?

cedar kilnBOT Jan 3, 2022, 9:54 PM

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brazen valley Can someone help me with this proof?

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@brazen valley Has your question been resolved?

slim valley Jan 3, 2022, 10:18 PM

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,rotate

wraith daggerBOT Jan 3, 2022, 10:18 PM

#

slim valley Jan 3, 2022, 10:18 PM

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@brazen valley if you are still wondering about the question vote x on the bot or the channel will shortly close

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Channel closed

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brazen valley Jan 3, 2022, 10:29 PM

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.reopen

cedar kilnBOT Jan 3, 2022, 10:29 PM

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✅

brazen valley Jan 3, 2022, 10:37 PM

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This server doesn't do proofs?

cedar kilnBOT Jan 3, 2022, 10:52 PM

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@brazen valley Has your question been resolved?

brave aspen Jan 3, 2022, 11:09 PM

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brazen valley This server doesn't do proofs?

I can help a little but i dont know how to write it for these intro geometry classes

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I can explain some of the logic at least

brazen valley Jan 3, 2022, 11:09 PM

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ok

brave aspen Jan 3, 2022, 11:09 PM

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The given statement

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Tells you AD is parallel to BC

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Because for those angles to be congruent they had to be alternate interior angles

brazen valley Jan 3, 2022, 11:10 PM

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Ok

brave aspen Jan 3, 2022, 11:11 PM

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Similar statement for DC parallel to AB

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It seems like more than one line to jump from 1 to 2

brazen valley Jan 3, 2022, 11:12 PM

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Ok

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Thank you

brave aspen Jan 3, 2022, 11:12 PM

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For 2 to 3

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Once you have the 2 sets of sides parallel that's from the definition at that point

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ABCD is quadrilateral with 2 sets of parallel sides

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Therefore it's a parallelogram

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south delta Jan 4, 2022, 3:43 AM

#

Find the set of values of k for which the curve y = kx² - 3x and the line y = x - k do not meet.

cedar kilnBOT Jan 4, 2022, 3:43 AM

#

south delta Find the set of values of k for which the curve y = kx² - 3x and the line y = x ...

bright surge Jan 4, 2022, 3:51 AM

#

subtract the equations, then use the discriminant to find out if the quadratic has real roots

cedar kilnBOT Jan 4, 2022, 3:58 AM

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solid raptor Jan 4, 2022, 4:41 AM

#

I'm learning group theory and I'm trying to learn what the Alternating group is. I do not understand what an "even permutation" is.

cedar kilnBOT Jan 4, 2022, 4:41 AM

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solid raptor I'm learning group theory and I'm trying to learn what the Alternating group is....

bright surge Jan 4, 2022, 4:42 AM

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solid raptor I'm learning group theory and I'm trying to learn what the Alternating group is....

so basically, you can write the permutation in cycles

solid raptor Jan 4, 2022, 4:42 AM

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I understand that part

bright surge Jan 4, 2022, 4:43 AM

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i'll use one line notation for now

solid raptor Jan 4, 2022, 4:43 AM

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The one like this? "(3 4 5)"

bright surge Jan 4, 2022, 4:47 AM

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the permutation (2 1 4 3) can be written as (2 1 3 4) (1 2 4 3) (both only switch 2 elements, so it's an inversion)
so there are 2 of them
so (2 1 4 3) is an even permutation

solid raptor Jan 4, 2022, 4:52 AM

#

Ok. I think I understand. Side question. Am I allowed to ask about book recommendations in these questions channels?

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vital matrix Jan 4, 2022, 5:43 AM

#

When they say find the area of the triangle in this question, it does mean find that area of this part right (highlighted green)?

cedar kilnBOT Jan 4, 2022, 5:43 AM

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vital matrix When they say find the area of the triangle in this question, it does mean find ...

vital matrix Jan 4, 2022, 5:44 AM

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or is it this part

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or just this as a whole

bright surge Jan 4, 2022, 5:45 AM

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vital matrix When they say find the area of the triangle in this question, it does mean find ...

do they have "and the x-axis" or "and the y-axis"?

vital matrix Jan 4, 2022, 5:45 AM

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yeah

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wait

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right

#

#

?

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someone help?

vital matrix Jan 4, 2022, 5:52 AM

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bright surge do they have "and the x-axis" or "and the y-axis"?

can help?

bright surge Jan 4, 2022, 5:52 AM

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vital matrix When they say find the area of the triangle in this question, it does mean find ...

this is for "and the y-axis"

magic bough Jan 4, 2022, 5:52 AM

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There are 2 questions here

bright surge Jan 4, 2022, 5:52 AM

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vital matrix or is it this part

for "and the x-axis"

vital matrix Jan 4, 2022, 5:52 AM

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bright surge this is for "and the y-axis"

ohh so just take the one that makes a triangle with each axis

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thanks

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that is correct right?

magic bough Jan 4, 2022, 5:53 AM

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Yeah

vital matrix Jan 4, 2022, 5:53 AM

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k

vital matrix Jan 4, 2022, 5:53 AM

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bright surge for "and the x-axis"

so the answer there would be 6.25 right

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imma guess thats correct

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thanks

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.close

cedar kilnBOT Jan 4, 2022, 5:55 AM

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Channel closed

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magic bough Jan 4, 2022, 5:55 AM

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yes hecker @vital matrix

vital matrix Jan 4, 2022, 5:55 AM

#

thanke

magic bough Jan 4, 2022, 5:55 AM

#

You are correct

cedar kilnBOT Jan 4, 2022, 7:17 AM

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cedar kilnBOT Jan 4, 2022, 7:54 AM

#

bright surge Jan 4, 2022, 7:56 AM

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~~excuse me what is this notation~~

neat matrix Jan 4, 2022, 8:02 AM

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bright surge ~~excuse me what is this notation~~

An+1-an=2n+3 n>=0 a0=1
A1=a0+0+3
A2=a1+2+3=a0+2+2(3)
A3=a2+2(2)+3=a0+2+2(2)+3(3)
..
.
.
An=a0+2[1+2+3+…+(n-1)]+n(3)=1+2[n(n-1)/2]+3n=
1+n(n-1)+3n=n^2+2n+1=(n+1)^2 n>0

cedar kilnBOT Jan 4, 2022, 8:02 AM

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neat matrix Jan 4, 2022, 8:05 AM

#

i want write for an+1-an=3n^2-n a0=3

cedar kilnBOT Jan 4, 2022, 8:05 AM

#

neat matrix i want write for an+1-an=3n^2-n a0=3

neat matrix Jan 4, 2022, 8:05 AM

#

An+1-an=2n+3 n>=0 a0=1
A1=a0+0+3
A2=a1+2+3=a0+2+2(3)
A3=a2+2(2)+3=a0+2+2(2)+3(3)
..
.
.
An=a0+2[1+2+3+…+(n-1)]+n(3)=1+2[n(n-1)/2]+3n=
1+n(n-1)+3n=n^2+2n+1=(n+1)^2 n>0

neat matrix Jan 4, 2022, 8:05 AM

#

neat matrix An+1-an=2n+3 n>=0 a0=1 A1=a0+0+3 A2=a1+2+3=a0+2+2(3) A3=a2+2(2)+3=a0+2+2(2)+3(3)...

example like this

cedar kilnBOT Jan 4, 2022, 8:20 AM

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@neat matrix Has your question been resolved?

cedar kilnBOT Jan 4, 2022, 8:51 AM

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@neat matrix Has your question been resolved?

neat matrix Jan 4, 2022, 9:21 AM

#

neat matrix i want write for an+1-an=3n^2-n a0=3

1.Solve each of the following recurrence relations.

cedar kilnBOT Jan 4, 2022, 10:21 AM

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@neat matrix Has your question been resolved?

meager pollen Jan 4, 2022, 10:29 AM

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if you want the general term, Im not sure if this comes out simply

neat matrix Jan 4, 2022, 12:05 PM

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meager pollen if you want the general term, Im not sure if this comes out simply

i think qustion want an

cedar kilnBOT Jan 4, 2022, 2:05 PM

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true cliff Jan 4, 2022, 6:46 PM

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sturdy grove Jan 4, 2022, 7:00 PM

#

guys I'm confused about something

cedar kilnBOT Jan 4, 2022, 7:00 PM

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sturdy grove guys I'm confused about something

sturdy grove Jan 4, 2022, 7:00 PM

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the derivation of newton's law of cooling

#

#

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the rest is history

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but

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what I don't get is how can we say that $dT = d(T-T_s)$

wraith daggerBOT Jan 4, 2022, 7:02 PM

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BigNose99

sturdy grove Jan 4, 2022, 7:02 PM

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why would this be justified?

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this is how my book derived the equation

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please help

cunning quail Jan 4, 2022, 7:03 PM

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T-T_s is just T but shifted by a constant right?

sturdy grove Jan 4, 2022, 7:03 PM

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T_s is a constant?

cunning quail Jan 4, 2022, 7:03 PM

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yup

sturdy grove Jan 4, 2022, 7:03 PM

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shouldn't T_s be a function of time as well?

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that makes no sense

cunning quail Jan 4, 2022, 7:03 PM

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assumed constant surrounding temperature right? unless I forgot my newton's law of cooling

dense wing Jan 4, 2022, 7:03 PM

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T_s is measured sufficiently far enough away st the change in T doesn't affect it

sturdy grove Jan 4, 2022, 7:04 PM

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hmmm

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so it technically only looks at heat loss/gain from one source and assumes a constant temp on the other

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that makes sense

dense wing Jan 4, 2022, 7:04 PM

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yes.

sturdy grove Jan 4, 2022, 7:04 PM

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but I feel like that's a bit innacurate though

dense wing Jan 4, 2022, 7:05 PM

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well yeah

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It's from ~1600

sturdy grove Jan 4, 2022, 7:05 PM

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oh

dense wing Jan 4, 2022, 7:05 PM

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Newton modelled the heat loss in that manner, hence why the formula looks like that

sturdy grove Jan 4, 2022, 7:05 PM

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my book should have mentioned that T_s is assumed to be constant

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'cause that's quite a big assumption in my opinion

dense wing Jan 4, 2022, 7:06 PM

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welcome to physics.

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We model stuff as best as we can given the information we have.

sturdy grove Jan 4, 2022, 7:06 PM

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dense wing We model stuff as best as we can given the information we have.

isn't there a way to model it without assuming T_s is constant

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and isntead a function of time as well?

dense wing Jan 4, 2022, 7:06 PM

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yes

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then you get a system of DEs

sturdy grove Jan 4, 2022, 7:07 PM

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why not teach us that instead

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we're doing DE anyway