#help-26 | Mathematics | Page 229

timber hill Nov 17, 2021, 7:20 PM

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.close

topaz sinewBOT Nov 17, 2021, 7:20 PM

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worldly pelican Nov 17, 2021, 7:50 PM

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could someone explain with a? i'm completely lost

topaz sinewBOT Nov 17, 2021, 7:50 PM

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worldly pelican could someone explain with a? i'm completely lost

south ivy Nov 17, 2021, 7:51 PM

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So what have you tried??

worldly pelican Nov 17, 2021, 7:53 PM

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so ive gotten 0<2t <= pi

south ivy Nov 17, 2021, 7:55 PM

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Okay

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And??

worldly pelican Nov 17, 2021, 7:55 PM

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nothing else

south ivy Nov 17, 2021, 7:55 PM

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What can be the maximum value of sin(x)

worldly pelican Nov 17, 2021, 7:56 PM

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1?

south ivy Nov 17, 2021, 7:56 PM

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Yes

worldly pelican Nov 17, 2021, 7:56 PM

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but why does sin(x) matter here?

south ivy Nov 17, 2021, 7:56 PM

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And when is that??

south ivy Nov 17, 2021, 7:56 PM

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worldly pelican but why does sin(x) matter here?

You need to maximize y=20sin(2t)

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y is representing the height

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And you need max height

worldly pelican Nov 17, 2021, 7:57 PM

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oh i see

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so it would be sin2t = 1?

south ivy Nov 17, 2021, 7:58 PM

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Yeah but is it in your interval

worldly pelican Nov 17, 2021, 7:59 PM

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so rearrange for t?

south ivy Nov 17, 2021, 7:59 PM

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No

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For what t when is sin(2t)=1

worldly pelican Nov 17, 2021, 8:01 PM

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t = pi/2?

south ivy Nov 17, 2021, 8:01 PM

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NO

worldly pelican Nov 17, 2021, 8:03 PM

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t = (arcsin(1))/2 ?

south ivy Nov 17, 2021, 8:08 PM

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And what is arcsin(1)

worldly pelican Nov 17, 2021, 8:08 PM

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pi/2

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so just pi/4?

south ivy Nov 17, 2021, 8:10 PM

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Yes and is that in your given interval??

worldly pelican Nov 17, 2021, 8:10 PM

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yup

south ivy Nov 17, 2021, 8:10 PM

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So there you have it

worldly pelican Nov 17, 2021, 8:11 PM

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thanks for that

south ivy Nov 17, 2021, 8:11 PM

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Yw

worldly pelican Nov 17, 2021, 8:11 PM

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should i just close it?

south ivy Nov 17, 2021, 8:11 PM

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Yes

worldly pelican Nov 17, 2021, 8:11 PM

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thanks again dude

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.close

topaz sinewBOT Nov 17, 2021, 8:11 PM

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wispy kiln Nov 17, 2021, 8:15 PM

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I need to find for which x'es this is true, but I can't find any real number for which the condition is false.

topaz sinewBOT Nov 17, 2021, 8:15 PM

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wispy kiln I need to find for which x'es this is true, but I can't find any real number for...

merry mason Nov 17, 2021, 8:24 PM

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What is this bracket

gentle owl Nov 17, 2021, 8:24 PM

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ceiling function

merry mason Nov 17, 2021, 8:24 PM

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Oh

gentle owl Nov 17, 2021, 8:25 PM

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round up basically

merry mason Nov 17, 2021, 8:27 PM

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How bout x=2

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It seems to be true for that x

gentle owl Nov 17, 2021, 8:29 PM

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-1.5 it is false for

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wait no

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it seems to be true for like everything

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huh

merry mason Nov 17, 2021, 8:29 PM

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There should be a method to prove that

wispy kiln Nov 17, 2021, 8:32 PM

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gentle owl it seems to be true for like everything

that's what I'm finding too, but that would make the question really silly

merry mason Nov 17, 2021, 8:33 PM

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Just to make sure, ceiling 2.1 gives 3 right?

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Ceiling of a integer gives integer right?

wispy kiln Nov 17, 2021, 8:35 PM

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merry mason Just to make sure, ceiling 2.1 gives 3 right?

yes

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here are all my testcases

merry mason Nov 17, 2021, 8:37 PM

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You wrote uneven instead of odd 🤔

wispy kiln Nov 17, 2021, 8:38 PM

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lmao that's what happens when you translate directly from another language

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but yes uneven is supposed to say odd

merry mason Nov 17, 2021, 8:39 PM

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Also in case of even positive 2 cases will form

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One where x is 4n and one where x is just 2n

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Coz x being 4n will make it a integer and x being 2n will make LHS and RHS a fraction whose ceiling nonetheless matches the condition

wispy kiln Nov 17, 2021, 8:43 PM

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in conclusion; works for all real numbers?

merry mason Nov 17, 2021, 8:43 PM

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Can't be sure, I'm doing comprehensive reading atm

wispy kiln Nov 17, 2021, 8:47 PM

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that's enough tests, I'm gonna have to prove that it's true for all real numbers

merry mason Nov 17, 2021, 8:47 PM

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Yeah it works for all real nos

wispy kiln Nov 17, 2021, 8:53 PM

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any idea how to prove it?

merry mason Nov 17, 2021, 8:54 PM

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Yeah

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You may try converting the ceiling function to fractional function

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Like

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Ceiling of x =x+ (1- {x})

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Here you know the range of {x} is [0,1)

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So that should make it easier I guess

wispy kiln Nov 17, 2021, 8:56 PM

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what is {x}?

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what do the curly brackets mean?

merry mason Nov 17, 2021, 8:56 PM

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Fractional part of x

wispy kiln Nov 17, 2021, 8:56 PM

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hmm

merry mason Nov 17, 2021, 8:56 PM

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I dunno how you symbolise that there

topaz sinewBOT Nov 17, 2021, 9:11 PM

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@wispy kiln Has your question been resolved?

wispy kiln Nov 17, 2021, 9:12 PM

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kind of

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lets go with yes

topaz sinewBOT Nov 17, 2021, 9:13 PM

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topaz sinewBOT Nov 17, 2021, 9:47 PM

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waxen spruce Nov 17, 2021, 10:47 PM

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could someone walk me through this?

topaz sinewBOT Nov 17, 2021, 10:47 PM

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waxen spruce could someone walk me through this?

tough nest Nov 17, 2021, 10:49 PM

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do you know what the rules for exponents are

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and the rules for logarithms?

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@waxen spruce

waxen spruce Nov 17, 2021, 10:51 PM

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yes

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well theres one rule im a little confused about

leaden tusk Nov 17, 2021, 10:51 PM

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this seems like a see or no see question, wouldn't you say katharine

tough nest Nov 17, 2021, 10:51 PM

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fuck off

leaden tusk Nov 17, 2021, 10:52 PM

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rude

tough nest Nov 17, 2021, 10:52 PM

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ha

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says you

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comes in here

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while i'm trying to help chao

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being a rude

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@waxen spruce what rule are you confused about?

waxen spruce Nov 17, 2021, 10:52 PM

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this one

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ive tried to use it in the past but its never worked out

tough nest Nov 17, 2021, 10:53 PM

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what you should think when you see that

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take both sides to the power a

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so

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if you have

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$\log_a(x) = \log_a(y)$

thorny flameBOT Nov 17, 2021, 10:54 PM

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Katharine

tough nest Nov 17, 2021, 10:54 PM

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$a^{\log_a(x)} = a^{\log_a(y)}$

thorny flameBOT Nov 17, 2021, 10:54 PM

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Katharine

tough nest Nov 17, 2021, 10:54 PM

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the exponent and the logarithm are inverse functions

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this means they cancel

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like add and subtract

waxen spruce Nov 17, 2021, 10:55 PM

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ahh

tough nest Nov 17, 2021, 10:55 PM

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and multiply and divide

chrome glen Nov 17, 2021, 10:55 PM

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I mean thats not really a log rule

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Its just a function rule

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$f(x)=f(y) \to x=y$

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Assuming f(x) is just any function

thorny flameBOT Nov 17, 2021, 10:55 PM

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PapaBread

tough nest Nov 17, 2021, 10:55 PM

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waxen spruce could someone walk me through this?

lets go back to your question

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what is the rule of multiplying numbers that have exponents?

waxen spruce Nov 17, 2021, 10:56 PM

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so i got as far as getting ln(xy) = ln(5)

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from the first equation

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could i then just say xy = 5?

tough nest Nov 17, 2021, 10:56 PM

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$e^{x}e^{y} = e^{5}$

thorny flameBOT Nov 17, 2021, 10:56 PM

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Katharine

tough nest Nov 17, 2021, 10:57 PM

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what we know is that when you multiply the e

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it adds the exponents

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do you remember that rule?

waxen spruce Nov 17, 2021, 10:57 PM

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yeah

tough nest Nov 17, 2021, 10:57 PM

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so that means

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$e^{x + y} = e^{5}$

thorny flameBOT Nov 17, 2021, 10:57 PM

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Katharine

waxen spruce Nov 17, 2021, 10:57 PM

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ah so youd have ln(x + y) = ln(5)

tough nest Nov 17, 2021, 10:58 PM

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you just have x + y = 5

waxen spruce Nov 17, 2021, 10:58 PM

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true

tough nest Nov 17, 2021, 10:58 PM

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because ln(e^x) = x

leaden tusk Nov 17, 2021, 10:58 PM

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thorny flame **PapaBread**

.

tough nest Nov 17, 2021, 10:59 PM

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you can now express x in terms of y and the other way around

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you see that?

waxen spruce Nov 17, 2021, 10:59 PM

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yeah

tough nest Nov 17, 2021, 10:59 PM

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can you try simplifying the second equation?

chrome glen Nov 17, 2021, 11:00 PM

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Wait whyd you e^x it twice?

waxen spruce Nov 17, 2021, 11:00 PM

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ln(2x + y) = ln(12)

chrome glen Nov 17, 2021, 11:00 PM

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thorny flame **Katharine**

Up here

tough nest Nov 17, 2021, 11:00 PM

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x and then y

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that's correct btw

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and now

waxen spruce Nov 17, 2021, 11:01 PM

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waxen spruce ln(2x + y) = ln(12)

so can i then just say 2x + y = 12?

tough nest Nov 17, 2021, 11:01 PM

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exactly

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and now you have 2 simple equations with 2 variables

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that means you can find both x and y

waxen spruce Nov 17, 2021, 11:01 PM

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ye ty

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<3

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.close

topaz sinewBOT Nov 17, 2021, 11:02 PM

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sinful roost Nov 17, 2021, 11:17 PM

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How would I evaluate this on my calculator for cot^-1 (5.4) I plugged in 1/tan^-1 (5.4) into my calculator and got something else

topaz sinewBOT Nov 17, 2021, 11:17 PM

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sinful roost How would I evaluate this on my calculator for cot^-1 (5.4) I plugged in 1/tan^-...

thorny flameBOT Nov 17, 2021, 11:17 PM

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Theophania

leaden tusk Nov 17, 2021, 11:18 PM

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sinful roost How would I evaluate this on my calculator for cot^-1 (5.4) I plugged in 1/tan^-...

your calculator is probably in radian mode, you're dealing with degrees here

sinful roost Nov 17, 2021, 11:19 PM

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ye its in degree mode im getting something else

topaz sinewBOT Nov 17, 2021, 11:34 PM

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@sinful roost Has your question been resolved?

topaz sinewBOT Nov 18, 2021, 12:06 AM

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@sinful roost Has your question been resolved?

topaz sinewBOT Nov 18, 2021, 1:08 AM

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@sinful roost Has your question been resolved?

sinful roost Nov 18, 2021, 1:58 AM

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!close

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.close

topaz sinewBOT Nov 18, 2021, 1:58 AM

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topaz sinewBOT Nov 18, 2021, 2:31 AM

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topaz sinewBOT Nov 18, 2021, 2:46 AM

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@neon iron Has your question been resolved?

topaz sinewBOT Nov 18, 2021, 3:01 AM

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topaz sinewBOT Nov 18, 2021, 5:05 PM

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cunning wind Nov 18, 2021, 5:48 PM

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How do i do this? Like, i don't even know where to start with this one. I tried rationalizing the denominator but its not like that does anything useful for me.

topaz sinewBOT Nov 18, 2021, 5:48 PM

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cunning wind How do i do this? Like, i don't even know where to start with this one. I tried ...

spark plover Nov 18, 2021, 5:54 PM

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cunning wind How do i do this? Like, i don't even know where to start with this one. I tried ...

is the ans 1 ??
just a guess if its crt I can explain the method

wooden matrix Nov 18, 2021, 5:54 PM

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cunning wind How do i do this? Like, i don't even know where to start with this one. I tried ...

What's the -inf limit of (2-x)/(1-x)?

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Nvm mine fails

spark plover Nov 18, 2021, 5:55 PM

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wooden matrix What's the -inf limit of (2-x)/(1-x)?

there we can multiply num and den by -1 as root is not there

topaz sinewBOT Nov 18, 2021, 6:03 PM

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@cunning wind Has your question been resolved?

topaz sinewBOT Nov 18, 2021, 6:18 PM

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west granite Nov 18, 2021, 7:46 PM

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topaz sinewBOT Nov 18, 2021, 7:46 PM

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west granite

west granite Nov 18, 2021, 7:46 PM

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Just confirm, this is false

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Just to confirm a

delicate goblet Nov 18, 2021, 7:47 PM

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west granite

yes, this is false

west granite Nov 18, 2021, 7:47 PM

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thank you

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.close

topaz sinewBOT Nov 18, 2021, 7:48 PM

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topaz sinewBOT Nov 22, 2021, 4:31 PM

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coral flame Nov 22, 2021, 4:34 PM

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What is the value of w + x + y + z?
180 - 30
30 + (180 - z + y) + (180 - w + x) = 180
30 + 180 - z + y + 180 - w + x = 180
30 + 180 + 180 - z + y - w + x = 180
390 - z + y - w + x = 180

z + y - w + x = 180 - 390
z + y - w + x = -210
z + y - w + x = 210
w + x + y + z? z + y - w + x = 210

topaz sinewBOT Nov 22, 2021, 4:34 PM

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coral flame What is the value of w + x + y + z? 180 - 30 30 + (180 - z + y) + (180 - w + x) ...

coral flame Nov 22, 2021, 4:34 PM

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What did I do wrong???

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or what can i do next?

restive inlet Nov 22, 2021, 4:44 PM

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you messed up your signs near the start

30 + (180 - z + y) + (180 - w + x) = 180

topaz sinewBOT Nov 22, 2021, 4:58 PM

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@coral flame Has your question been resolved?

coral flame Nov 22, 2021, 5:03 PM

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restive inlet you messed up your signs near the start > 30 + (180 - z + y) + (180 - w + x) = 1...

which ones?

restive inlet Nov 22, 2021, 5:03 PM

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redo that step

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where's

(180 - z + y)
coming from

coral flame Nov 22, 2021, 5:05 PM

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this part

restive inlet Nov 22, 2021, 5:05 PM

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but why did you write

(180 - z + y)
specifically

coral flame Nov 22, 2021, 5:06 PM

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because the line is 180 degrees, if we do z + y, and then minus the total from 180, we can get that 1 angle degree from the triangle

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if that makes sense lol

restive inlet Nov 22, 2021, 5:07 PM

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(180 - z + y)
does NOT represent z + y being subtracted from 180

coral flame Nov 22, 2021, 5:07 PM

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will I have to do (180 - (z + x))??

restive inlet Nov 22, 2021, 5:07 PM

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you mean (180 - (z + y))

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that would be more appropriate

coral flame Nov 22, 2021, 5:08 PM

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ye

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Oh so thats what I did wrong

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and btw, when I remove the brackets, do I have to remove the brackets from (z + y) after that?

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right?

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well ig it will make sense...

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.close

topaz sinewBOT Nov 22, 2021, 5:11 PM

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young vale Nov 22, 2021, 5:13 PM

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I have to demonstrate this

topaz sinewBOT Nov 22, 2021, 5:13 PM

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young vale I have to demonstrate this

young vale Nov 22, 2021, 5:13 PM

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How?

spark plover Nov 22, 2021, 5:14 PM

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uk sum of ap formula ?

young vale Nov 22, 2021, 5:14 PM

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no

restive inlet Nov 22, 2021, 5:14 PM

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that's what they're trying to show, so they can't apply that directly

spark plover Nov 22, 2021, 5:15 PM

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restive inlet that's what they're trying to show, so they can't apply that directly

induction will work ?

young vale Nov 22, 2021, 5:15 PM

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Ye

restive inlet Nov 22, 2021, 5:15 PM

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depends on the course

young vale Nov 22, 2021, 5:15 PM

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or reduction to absurd

restive inlet Nov 22, 2021, 5:15 PM

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if you're required to do induction

young vale Nov 22, 2021, 5:15 PM

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I got direct form, induction or absurd

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Any of them will work

restive inlet Nov 22, 2021, 5:15 PM

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alternatively you could derive it how it was originally derived

young vale Nov 22, 2021, 5:15 PM

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I just have to state if this is true or not and why

restive inlet Nov 22, 2021, 5:16 PM

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by considering pairs of values that will have the same sum

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i.e. 1 with n
2 with n-1
etc

spark plover Nov 22, 2021, 5:16 PM

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@young vale u need to say true or false or derive it ?

restive inlet Nov 22, 2021, 5:16 PM

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and the numbers of pairs there are

young vale Nov 22, 2021, 5:16 PM

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Wdym by derive it

spark plover Nov 22, 2021, 5:17 PM

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what romonov is saying

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ya both will endup the same though

young vale Nov 22, 2021, 5:17 PM

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Investigate and prove the following statements

spark plover Nov 22, 2021, 5:17 PM

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here u derive it

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there u assume it is crt and prove it

young vale Nov 22, 2021, 5:17 PM

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restive inlet i.e. 1 with n 2 with n-1 etc

I dont get u

restive inlet Nov 22, 2021, 5:18 PM

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1 + n = ?

young vale Nov 22, 2021, 5:18 PM

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Aha

restive inlet Nov 22, 2021, 5:18 PM

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2 + (n-1) = ?

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3 + (n-2) = ?

spark plover Nov 22, 2021, 5:18 PM

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n+1

young vale Nov 22, 2021, 5:19 PM

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n+1 yeah

spark plover Nov 22, 2021, 5:19 PM

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so there are n terms
when u pair up number of terms = n/2

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so u are adding n+1 n/2 terms

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so we get n/2 x n+1
which is n(n+1)/2

young vale Nov 22, 2021, 5:20 PM

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spark plover so there are n terms when u pair up number of terms = n/2

Why hen pairing up number of terms = n/2

spark plover Nov 22, 2021, 5:20 PM

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young vale Why hen pairing up number of terms = n/2

1+n = 2+(n-1) =.....

young vale Nov 22, 2021, 5:21 PM

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but where the /2 comes from

spark plover Nov 22, 2021, 5:21 PM

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young vale but where the /2 comes from

total terms are n right ?

young vale Nov 22, 2021, 5:21 PM

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Yeah

spark plover Nov 22, 2021, 5:21 PM

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when u pair them up how much terms will be there ?

young vale Nov 22, 2021, 5:21 PM

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1

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wait

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n/2

spark plover Nov 22, 2021, 5:21 PM

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ya

young vale Nov 22, 2021, 5:21 PM

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Okay

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And why we pairing number of terms?

spark plover Nov 22, 2021, 5:22 PM

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young vale And why we pairing number of terms?

to get same sum

spark plover Nov 22, 2021, 5:22 PM

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spark plover 1+n = 2+(n-1) =.....

^^

young vale Nov 22, 2021, 5:22 PM

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Oh ok

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Yes

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i got it

spark plover Nov 22, 2021, 5:23 PM

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cool

young vale Nov 22, 2021, 5:25 PM

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So, 1+2+3+...+n = n(n+1)/2 is true because, knowing there are n terms, pairing them we will have n/2 terms, and knowing that 1+n = 2+(n-1) and so on, we get n/2*n+1

spark plover Nov 22, 2021, 5:34 PM

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young vale So, 1+2+3+...+n = n(n+1)/2 is true because, knowing there are n terms, pairing t...

you can say it is true and
write the proof below it

young vale Nov 22, 2021, 5:34 PM

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Okay

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thanks

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.close

topaz sinewBOT Nov 22, 2021, 5:34 PM

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neon iron Nov 22, 2021, 5:38 PM

#

topaz sinewBOT Nov 22, 2021, 5:38 PM

#

neon iron

neon iron Nov 22, 2021, 5:38 PM

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5c pls

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What would be the suitable percentile

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maybe try to find the E(X)

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What's that?

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@neon iron

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actually it dm, you should make a frequency diagram according to your results

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then that will help you get your percentile

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Ight I'll try that thanks

topaz sinewBOT Nov 22, 2021, 6:06 PM

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neon iron Nov 22, 2021, 6:16 PM

#

<@&286206848099549185>

topaz sinewBOT Nov 22, 2021, 6:16 PM

#

neon iron <@&286206848099549185>

neon iron Nov 22, 2021, 6:16 PM

#

#

could you please explain to me how i can solve the second part of this question

topaz sinewBOT Nov 22, 2021, 6:32 PM

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@neon iron Has your question been resolved?

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topaz sinewBOT Nov 23, 2021, 12:36 AM

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thin plover Nov 23, 2021, 1:03 AM

#

topaz sinewBOT Nov 23, 2021, 1:03 AM

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thin plover

thin plover Nov 23, 2021, 1:04 AM

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hey all, part A is 21,090$, but for part B im having trouble figuring out where id go from

#

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this being the formula used to solve for A

dense elbow Nov 23, 2021, 1:13 AM

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2(cos(45))⁴ =1/2x3/5+1-2/2 cos=

topaz sinewBOT Nov 23, 2021, 1:19 AM

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@thin plover Has your question been resolved?

thin plover Nov 23, 2021, 1:30 AM

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how did we use cos in the formula?

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or why*

vestal hinge Nov 23, 2021, 1:36 AM

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Use arithmetic sum to find out the value that's ≥ 27000

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Don't use cos

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I think he's asking a question

thin plover Nov 23, 2021, 1:36 AM

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xd

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would I use the same formula from above? the one i sent

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27000 ≥ (1+.045/12)

vestal hinge Nov 23, 2021, 1:38 AM

#

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27000 ≤

thin plover Nov 23, 2021, 1:44 AM

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what does r stand for in the formula ? @vestal hinge

vestal hinge Nov 23, 2021, 1:45 AM

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Rate of change

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In your case it would be 1.045

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Find n first and then divide by 12

thin plover Nov 23, 2021, 1:45 AM

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n is .045/12

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?

vestal hinge Nov 23, 2021, 1:45 AM

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It's quite messy putting 12 into the formula I think

vestal hinge Nov 23, 2021, 1:46 AM

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thin plover n is .045/12

No

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n is what you have to solve for

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You know Sn, a, and r

thin plover Nov 23, 2021, 1:48 AM

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so R would be (27,000 - 7350)?

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the difference between values

vestal hinge Nov 23, 2021, 1:48 AM

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No

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R is 1.045

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i.e. 104.5%

thin plover Nov 23, 2021, 1:50 AM

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so

vestal hinge Nov 23, 2021, 1:50 AM

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Interest is 4.5% but that doesn't mean that you have 4.5% what you initially put in a monthl later. You have the initial money PLUS 4.5% of it so it's 100%+4.5%

Ergo r = 1.045

thin plover Nov 23, 2021, 1:50 AM

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27,000 = 7350(1+(0.045))^12(t)

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or

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27000 = (7350)(1 + (0.045/12))^((12)(t))

vestal hinge Nov 23, 2021, 1:50 AM

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Don't use 12

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Can you use the formula I sent you

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Without using 12

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Once you get n, just divide by 12 later

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It's dumb to put in 12 into the equation

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Also it's 27000 ≤ and not =, because you could end up with more (but you should never have less)

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i.e. at least n/12 amount of years

thin plover Nov 23, 2021, 1:53 AM

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what is S in the formula you sent ?

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27,000

vestal hinge Nov 23, 2021, 1:54 AM

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Yes

thin plover Nov 23, 2021, 1:54 AM

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27,000 ≤ (1 - 1.045^n) / 1- 1.045

vestal hinge Nov 23, 2021, 1:54 AM

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You forgot n

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And a

thin plover Nov 23, 2021, 1:55 AM

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what is A in the equation ?

vestal hinge Nov 23, 2021, 1:55 AM

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7350

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Initial deposit

thin plover Nov 23, 2021, 1:56 AM

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so

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27,000 ≤ (7350(1-1.045)^n) / 1 - 1.045

vestal hinge Nov 23, 2021, 1:57 AM

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No

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Why did you add extra brackets

thin plover Nov 23, 2021, 1:57 AM

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to make it easier to read but maybe not

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27,000 ≤ 7350(1-1.045)^n / (1 - 1.045)

vestal hinge Nov 23, 2021, 1:57 AM

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Still no

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You added brackets in wrong place

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No

thin plover Nov 23, 2021, 1:58 AM

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LOL

vestal hinge Nov 23, 2021, 1:59 AM

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Bro

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It's

thin plover Nov 23, 2021, 1:59 AM

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bare with me

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so sorry

vestal hinge Nov 23, 2021, 1:59 AM

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The n is supposed to be attributable to 1.045 only

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You n powered the whole bracket

thin plover Nov 23, 2021, 1:59 AM

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27,000 ≤ 7350(1-1.045^n) / (1 - 1.045)

vestal hinge Nov 23, 2021, 1:59 AM

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No?

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What happened to 1

thin plover Nov 23, 2021, 2:00 AM

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let me get a paper

vestal hinge Nov 23, 2021, 2:00 AM

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...

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27,000 ≤ 7350(1-1.045^n) / (1 - 1.045)

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Ok now solve for n

thin plover Nov 23, 2021, 2:04 AM

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so n ≥ 3.47

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non rounded

vestal hinge Nov 23, 2021, 2:05 AM

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Actually wtf

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I'm ill

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I've made you use wrong formula this whole time

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thin plover Nov 23, 2021, 2:06 AM

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ok good cause ive never seen it before

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in my life

vestal hinge Nov 23, 2021, 2:07 AM

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Same values

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Same ≤

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Solve for n

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Ceil n,

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Divide n by 12

thin plover Nov 23, 2021, 2:11 AM

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id get 7350n ≤ 7350(1.045)^n/12

vestal hinge Nov 23, 2021, 2:12 AM

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What

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No

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No

thin plover Nov 23, 2021, 2:13 AM

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I ended up trying to use a log of base (1+ (.045/12)) on both sides and got 28.96832582... or ~29 years

vestal hinge Nov 23, 2021, 2:13 AM

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Stop putting 12 into the equation please

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That's wrong

thin plover Nov 23, 2021, 2:14 AM

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what would the new equation be with An = A1(r)^n-1

vestal hinge Nov 23, 2021, 2:14 AM

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27000 ≤ 7350(1.045)^(n-1)

thin plover Nov 23, 2021, 2:17 AM

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i was close

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i got n ≥ 31

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rounded

vestal hinge Nov 23, 2021, 2:18 AM

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No rounding

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You ceil it

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N is 30.5.... but the required months is ceiling of N

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Which is 31

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Not sure if you're supposed to divide N by 12 or ceiling of N by 12

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Probably N by 12

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Idk

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Maybe ceil of n

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Actually don't know

thin plover Nov 23, 2021, 2:20 AM

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in conclusion fuck this class for not teaching me

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id assume 12

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i say 31 since

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but im sure i wouldnt get points docked off for it

topaz sinewBOT Nov 23, 2021, 2:50 AM

#

@thin plover Has your question been resolved?

topaz sinewBOT Nov 23, 2021, 3:20 AM

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patent kestrel Nov 23, 2021, 5:51 AM

#

how to factor

$\frac{9^{\left(2n-1\right)}+9^{\left(2n+6\right)}}{9^{\left(2n-1\right)}+9^{\left(n+5\right)}}$

topaz sinewBOT Nov 23, 2021, 5:51 AM

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patent kestrel how to factor $\frac{9^{\left(2n-1\right)}+9^{\left(2n+6\right)}}{9^{\left(2n-1...

thorny flameBOT Nov 23, 2021, 5:51 AM

#

Tom Joney

wide juniper Nov 23, 2021, 5:53 AM

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TOM

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Oh what's n again

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Imaginary number right

patent kestrel Nov 23, 2021, 5:53 AM

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No

wide juniper Nov 23, 2021, 5:53 AM

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Oh what's that

patent kestrel Nov 23, 2021, 5:53 AM

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'i' is imaginary number

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'n' is just a variable

wide juniper Nov 23, 2021, 5:53 AM

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Ohhh

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So whats m

topaz sinewBOT Nov 23, 2021, 6:08 AM

#

@patent kestrel Has your question been resolved?

crimson rampart Nov 23, 2021, 6:12 AM

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The best I could do for the bottom is $9^{n-1}(9^n + 9^6)$

thorny flameBOT Nov 23, 2021, 6:12 AM

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RESIDGE

next tree Nov 23, 2021, 6:16 AM

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crimson rampart The best I could do for the bottom is $9^{n-1}(9^n + 9^6)$

Nice!

crimson rampart Nov 23, 2021, 6:18 AM

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I got $\frac{9^{n-1}(9^n)(1+9^7)}{9^{n-1}(9^n + 9^6)}$

thorny flameBOT Nov 23, 2021, 6:18 AM

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RESIDGE

crimson rampart Nov 23, 2021, 6:19 AM

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Hopefully it's right. Then I see that I can cancel 9^(n-1)

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I think you can also factor out 9^n from the bottom and cancel again.

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$\frac{1+9^7}{1+9^{6-n}}$

thorny flameBOT Nov 23, 2021, 6:21 AM

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RESIDGE

topaz sinewBOT Nov 23, 2021, 6:23 AM

#

Channel closed

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next tree Nov 23, 2021, 6:23 AM

#

topaz sinew

lol

topaz sinewBOT Nov 23, 2021, 6:24 AM

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pliant leaf Nov 23, 2021, 7:46 AM

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Could use some help here

topaz sinewBOT Nov 23, 2021, 7:46 AM

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pliant leaf Could use some help here

pliant leaf Nov 23, 2021, 7:46 AM

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I'm not sure how to proceed with this question.

#

Could I maybe find the first derivative of the function and insert 0 as x?

plain mica Nov 23, 2021, 7:47 AM

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try minimizing the square of the distance

pliant leaf Nov 23, 2021, 7:48 AM

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Alright

plain mica Nov 23, 2021, 7:48 AM

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do you know calculus?

pliant leaf Nov 23, 2021, 7:48 AM

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I do. (roughly 😅 )

pliant leaf Nov 23, 2021, 7:49 AM

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plain mica try minimizing the square of the distance

Any chance you could explain how I should minimize the square of the distance?

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Could I set the original equation =0?

plain mica Nov 23, 2021, 7:49 AM

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pliant leaf Any chance you could explain how I should minimize the square of the distance?

.... calculus?

pliant leaf Nov 23, 2021, 7:49 AM

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and then solve for x?

plain mica Nov 23, 2021, 7:50 AM

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https://www.mathsisfun.com/calculus/maxima-minima.html

Finding Maxima and Minima using Derivatives

Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

pliant leaf Nov 23, 2021, 7:50 AM

#

plain mica .... calculus?

I am in a calculus 1 course but this is the first time i've heard that.

plain mica Nov 23, 2021, 7:51 AM

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pliant leaf I am in a calculus 1 course but this is the first time i've heard that.

this is the best way i can think of

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or.. do you know normals?

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find the normal to this curve passing through the given point

pliant leaf Nov 23, 2021, 7:52 AM

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I do not sadly.

plain mica Nov 23, 2021, 7:52 AM

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the point of intersection of the normal with the curve is the point, the distance between it and the gievn point will be minimum

pliant leaf Nov 23, 2021, 7:52 AM

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Do you mean finding where the slope is 0?

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Maybe the terminology is different.

#

So would I accomplish that by taking the first derivative of the function and setting it =0 maybe?

#

@plain mica I'm still not sure what to do even after reading through the link you sent. Should I just ask someone else?

plain mica Nov 23, 2021, 7:56 AM

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pliant leaf <@!811582650342440970> I'm still not sure what to do even after reading through ...

yes, if i havent been able to help

pliant leaf Nov 23, 2021, 7:56 AM

#

.close

topaz sinewBOT Nov 23, 2021, 7:56 AM

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Channel closed

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topaz sinewBOT Nov 23, 2021, 8:55 AM

#

plain mica Nov 23, 2021, 8:57 AM

#

google

#

https://sciencing.com/10-can-used-everyday-life-8710568.html

Sciencing

10 Ways Simultaneous Equations Can Be Used in Everyday Life

Simultaneous equations can be used to solve everyday problems, especially those that are more difficult to think through without writing anything down.

#

you're welcome

#

.close

topaz sinewBOT Nov 23, 2021, 9:13 AM

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@brave tulip Has your question been resolved?

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lucid fog Nov 23, 2021, 9:32 AM

#

bh

topaz sinewBOT Nov 23, 2021, 9:32 AM

#

lucid fog bh

lucid fog Nov 23, 2021, 9:32 AM

#

hi

#

help?

topaz sinewBOT Nov 23, 2021, 9:48 AM

#

@lucid fog Has your question been resolved?

topaz sinewBOT Nov 23, 2021, 10:21 AM

#

@lucid fog Has your question been resolved?

lucid fog Nov 23, 2021, 11:11 AM

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.close

topaz sinewBOT Nov 23, 2021, 11:11 AM

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regal folio Nov 23, 2021, 12:38 PM

#

How do I find v

topaz sinewBOT Nov 23, 2021, 12:38 PM

#

regal folio How do I find v

regal folio Nov 23, 2021, 12:51 PM

#

.close

topaz sinewBOT Nov 23, 2021, 12:51 PM

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clever temple Nov 23, 2021, 2:16 PM

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Hi I have to differentiate this

topaz sinewBOT Nov 23, 2021, 2:16 PM

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clever temple Hi I have to differentiate this

clever temple Nov 23, 2021, 2:16 PM

#

#

But the textbook answer is 2/3x^4/3

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How can I get 2?

wooden matrix Nov 23, 2021, 2:17 PM

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there's a 2 already there...

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it's the coefficient

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your 3rd line, you just simply ignored the 2

clever temple Nov 23, 2021, 2:19 PM

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Oh

#

#

I got it thanks!

#

.close

topaz sinewBOT Nov 23, 2021, 2:19 PM

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Channel closed

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rich finch Nov 23, 2021, 2:30 PM

#

can anybody explain to me how ones brain can come up with this way of splitting this fraction? I realise I'm in advanced maths but im doing university late and am a bit rusty on basics like this and they sometimes trip me up ;p

topaz sinewBOT Nov 23, 2021, 2:30 PM

#

rich finch can anybody explain to me how ones brain can come up with this way of splitting ...

rich finch Nov 23, 2021, 2:31 PM

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i get that he is adding an s and subtracting an s but idk how that splits the fracction like that 😮

#

is it just partial fractions but written weirdly?

keen venture Nov 23, 2021, 2:32 PM

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Skipping this step:
[(s + 1) - s] / s(s + 1)
= (s + 1)/s(s + 1) - s/s(s + 1)

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As always, the denominator can distribute over the numerator.

rich finch Nov 23, 2021, 2:34 PM

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ooo ok

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so very simples 😂

#

ty

keen venture Nov 23, 2021, 2:34 PM

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Np, feel free to ask if you have anything else

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Btw this is partial fractions, but without the algebra.

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That is, they figured out the coefficients by messing with the fraction

rich finch Nov 23, 2021, 2:36 PM

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id probably do it via actual method

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gonna do that now ;p

#

thanks!

#

.close

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merry pier Nov 23, 2021, 3:00 PM

#

Hello, can anyone tell me if the problem is correct. It is an arithmetic progression

topaz sinewBOT Nov 23, 2021, 3:00 PM

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merry pier Hello, can anyone tell me if the problem is correct. It is an arithmetic progres...

merry pier Nov 23, 2021, 3:00 PM

#

topaz sinewBOT Nov 23, 2021, 3:15 PM

#

@merry pier Has your question been resolved?

merry pier Nov 23, 2021, 3:16 PM

#

<@&286206848099549185>

restive inlet Nov 23, 2021, 3:22 PM

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you haven't solved it properly

#

$a_m + a_n \neq a_{m+n}$

thorny flameBOT Nov 23, 2021, 3:23 PM

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ℝamonov

merry pier Nov 23, 2021, 3:25 PM

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Yeah, I get it, but now how to solve?

restive inlet Nov 23, 2021, 3:26 PM

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it feels like you have an idea of what to do, you just need to notate it properly

#

i.e. show that
a_1 + a_12 = a_5 + a_8
using the definition of (the nth term of) an arithmetic sequence

merry pier Nov 23, 2021, 3:31 PM

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Clear. Now I will try again. I was confused precisely because of this property.

#

I think I've already fixed the mistake

#

neon iron Nov 23, 2021, 3:41 PM

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merry pier

,rotate

thorny flameBOT Nov 23, 2021, 3:41 PM

#

wispy kiln Nov 23, 2021, 3:41 PM

#

neon iron ,rotate

this is by far the best bot cmd

topaz sinewBOT Nov 23, 2021, 4:10 PM

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@merry pier Has your question been resolved?

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spare lodge Nov 23, 2021, 6:44 PM

#

topaz sinewBOT Nov 23, 2021, 6:44 PM

#

spare lodge

spare lodge Nov 23, 2021, 6:44 PM

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I dont know what the 2 rules could be

#

A and D cant fit any of the rules, B has to fit both and I think C can either fit both or just fit 1 rule

#

.close

topaz sinewBOT Nov 23, 2021, 7:00 PM

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naive grove Nov 23, 2021, 8:37 PM

#

and isosceles triangle's inner circle's radius = 10
what's the smallest perimeter of the triangle

topaz sinewBOT Nov 23, 2021, 8:37 PM

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naive grove and isosceles triangle's inner circle's radius = 10 what's the smallest perimete...

naive grove Nov 23, 2021, 8:37 PM

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Hello, I'm having issues with the problem above

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i've trieg going at it with trigonometry and algebra

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where I would end up with an equation with 2 unknown variables, and said equations seemed like a pain in the ass to express one variable from

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naive grove Nov 23, 2021, 8:46 PM

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naive grove where I would end up with an equation with 2 unknown variables, and said equatio...

this being

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trigonometric approach lead here

#

topaz sinewBOT Nov 23, 2021, 9:13 PM

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@naive grove Has your question been resolved?

naive grove Nov 23, 2021, 9:24 PM

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D:

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.close

topaz sinewBOT Nov 23, 2021, 9:24 PM

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topaz sinewBOT Nov 28, 2021, 4:52 PM

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tribal zephyr Nov 28, 2021, 4:55 PM

#

How do I show that 1/(x+1) is not a probability measure

topaz sinewBOT Nov 28, 2021, 4:55 PM

#

tribal zephyr How do I show that 1/(x+1) is not a probability measure

topaz sinewBOT Nov 28, 2021, 5:11 PM

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odd frigate Nov 28, 2021, 5:57 PM

#

$f(x) = 1 + \frac{4}{(x-7)(x-3)}$

topaz sinewBOT Nov 28, 2021, 5:57 PM

#

odd frigate $f(x) = 1 + \frac{4}{(x-7)(x-3)}$

thorny flameBOT Nov 28, 2021, 5:57 PM

#

Guilhotina

odd frigate Nov 28, 2021, 5:58 PM

#

when i have this, and has to integrate it, but the range of my domain is [7;10] how should i proceed?

toxic swift Nov 28, 2021, 6:01 PM

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I would use a substitution to make it simpler, u = x - 7, so x-3 = u+4, and du = dx.

modern bloom Nov 28, 2021, 6:05 PM

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odd frigate when i have this, and has to integrate it, but the range of my domain is [7;10] ...

Hello, you can use a limit: integral of f(x) from t to 10 where t approaches 7, so you can show that the integral approaches infinity

odd frigate Nov 28, 2021, 6:07 PM

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modern bloom Hello, you can use a limit: integral of f(x) from t to 10 where t approaches 7, ...

because i need to see what the function looks at the points of the domain, rght ?

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i would resolve that by partial integration and then get a ln(x-7) where x approaches 7+

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how do i found this limit? L'Hopital ?

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i know it is $-\infty$

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i know it is $-\infty$

#

a

thorny flameBOT Nov 28, 2021, 6:17 PM

#

Guilhotina

odd frigate Nov 28, 2021, 6:17 PM

#

but how to prove it

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is this right?
$lim_{x \to 0+}(lnx) = lim_{y \to - \infty}(ln(e^{y})) = -\infty$ where $e^{y} = x$ and $ln(x) = y$

#

?

thorny flameBOT Nov 28, 2021, 6:21 PM

#

Guilhotina

modern bloom Nov 28, 2021, 6:29 PM

#

Mmm I think that should be enough if a proof is required. I mean, I think you can just assume that ln(0) approaches -infty from the right in this problem, but what you've done is correct :thumbsup_tone3:

topaz sinewBOT Nov 28, 2021, 6:35 PM

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heady pendant Nov 28, 2021, 7:00 PM

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topaz sinewBOT Nov 28, 2021, 7:00 PM

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heady pendant Nov 28, 2021, 7:14 PM

#

topaz sinewBOT Nov 28, 2021, 7:14 PM

#

heady pendant

heady pendant Nov 28, 2021, 7:15 PM

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ocean hare Nov 28, 2021, 7:27 PM

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@heady pendant are you aware of first and second differences?

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you need to determine what type of function this is before you can do anything

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btw (it's a quadratic i think)

topaz sinewBOT Nov 28, 2021, 7:35 PM

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forest rune Nov 28, 2021, 8:22 PM

#

topaz sinewBOT Nov 28, 2021, 8:22 PM

#

forest rune

forest rune Nov 28, 2021, 8:23 PM

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how can I solve this?

topaz sinewBOT Nov 28, 2021, 8:38 PM

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@forest rune Has your question been resolved?

topaz sinewBOT Nov 28, 2021, 9:08 PM

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@forest rune Has your question been resolved?

topaz sinewBOT Nov 28, 2021, 10:08 PM

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@forest rune Has your question been resolved?

still void Nov 28, 2021, 10:22 PM

#

forest rune

I would do (A+B).(A+B) = (6j).(6j)

#

Then solve for A.B and find angle between them from that

topaz sinewBOT Nov 29, 2021, 12:08 AM

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neon iron Nov 29, 2021, 12:14 AM

#

Got some issue with this task need to find lim x-> 0 (1-root(x))/x
But that schoudlnt be possible as we cant divide by 0... and its not 0/0 so i cant use l‘hospital or am i mistaken?

topaz sinewBOT Nov 29, 2021, 12:14 AM

#

neon iron Got some issue with this task need to find lim x-> 0 (1-root(x))/x But that...

neon iron Nov 29, 2021, 12:16 AM

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So can i just say there is no limit ( if my conclusion is right ) or would i need to prove this somehow?

#

Thanks in advance

leaden tusk Nov 29, 2021, 12:18 AM

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limit doesn't exist, correct

topaz sinewBOT Nov 29, 2021, 12:31 AM

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lusty ravine Nov 29, 2021, 1:10 AM

#

What's the difference between these two notations?
$x^{(i)}$ and $x_{i}$

topaz sinewBOT Nov 29, 2021, 1:10 AM

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lusty ravine What's the difference between these two notations? $x^{(i)}$ and $x_{i}$

thorny flameBOT Nov 29, 2021, 1:11 AM

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THEBIGTHREE

empty sail Nov 29, 2021, 1:14 AM

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lusty ravine What's the difference between these two notations? $x^{(i)}$ and $x_{i}$

Depends on the context, but in my experience $x^{(i)}$ is the iteration, like $x_{1}^{(1)}$ is first iteration of $x_{1}$, $x_{1}^{(2)}$ is second iteration, etc. And $x_{i}$ is the term you're at like $x_{1}$ is first term, $x_{2}$ is second term, etc

thorny flameBOT Nov 29, 2021, 1:14 AM

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dldh06

lusty ravine Nov 29, 2021, 1:14 AM

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ah alright, thank you!

empty sail Nov 29, 2021, 1:15 AM

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lusty ravine ah alright, thank you!

That's just from my experience though, so I could be incorrect

topaz sinewBOT Nov 29, 2021, 1:29 AM

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shy grotto Nov 29, 2021, 2:19 AM

#

topaz sinewBOT Nov 29, 2021, 2:19 AM

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shy grotto

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@shy grotto Has your question been resolved?

shy grotto Nov 29, 2021, 2:35 AM

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<@&286206848099549185>

wheat laurel Nov 29, 2021, 2:39 AM

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wait

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what's the standard deviation?

topaz sinewBOT Nov 29, 2021, 3:05 AM

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@shy grotto Has your question been resolved?

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meager glacier Nov 29, 2021, 4:54 AM

#

Can you guys give me a tip in dividing fractions. I am good at it but I would like to know about it more.

topaz sinewBOT Nov 29, 2021, 4:54 AM

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meager glacier Can you guys give me a tip in dividing fractions. I am good at it but I would li...

meager glacier Nov 29, 2021, 4:55 AM

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answer

burnt badger Nov 29, 2021, 4:56 AM

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Dividing with a fraction is really multiplying with the reciprocal

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This is the ultimate tip

cunning urchin Nov 29, 2021, 4:56 AM

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Yeah that’s all I do ^

meager glacier Nov 29, 2021, 4:56 AM

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ok thanks

burnt badger Nov 29, 2021, 4:56 AM

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In fact all division is really multiplying with the reciprocal

cunning urchin Nov 29, 2021, 4:57 AM

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(1/3) / (4/5) just do (1/3) x (5/4)

meager glacier Nov 29, 2021, 4:57 AM

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yeah I know

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ok thanks

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this really helps me

burnt badger Nov 29, 2021, 4:57 AM

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This gets you from here to calculus and beyond

At least for dealing with fractions xD

meager glacier Nov 29, 2021, 4:57 AM

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hehe

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anyways thx

burnt badger Nov 29, 2021, 4:58 AM

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There are some other things you learn along the way

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Yw

topaz sinewBOT Nov 29, 2021, 5:13 AM

#

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topaz sinewBOT Nov 29, 2021, 5:28 AM

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loud coyote Nov 29, 2021, 5:31 AM

#

I dont get why k*x^2 is removed for this induction problem? can someone teach me why

topaz sinewBOT Nov 29, 2021, 5:31 AM

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loud coyote I dont get why k*x^2 is removed for this induction problem? can someone teach me...

snow basalt Nov 29, 2021, 5:40 AM

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As in why you can remove kx^2 or why removing kx^2 is neeeded for the proof?

loud coyote Nov 29, 2021, 5:41 AM

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why you can remove kx^2

snow basalt Nov 29, 2021, 5:44 AM

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so first, k>=0 and x^2>=0 so kx^2>=0. Adding 1-(k+1)x to both sides of that, 1-(k+1)x+kx^2>=1-(k+1)x

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So, we can rewrite the earlier inequality adding that in, $\(1-x)^{k+1}\geq 1-(k+1)x+kx^2\geq 1-(k+1)x$

thorny flameBOT Nov 29, 2021, 5:45 AM

#

Sneaky

snow basalt Nov 29, 2021, 5:47 AM

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which leads to whats written

topaz sinewBOT Nov 29, 2021, 5:56 AM

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@loud coyote Has your question been resolved?

loud coyote Nov 29, 2021, 5:56 AM

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ok so basically since kx^2 is positive

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and because 1-(k+1)x+kx^2>=1-(k+1)x, the kx^2 can be removed because the statement still holds true yes

topaz sinewBOT Nov 29, 2021, 6:11 AM

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grand bough Nov 29, 2021, 6:34 AM

#

topaz sinewBOT Nov 29, 2021, 6:34 AM

#

grand bough

grand bough Nov 29, 2021, 6:34 AM

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How do I find the vertical stretch of c and d?

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Like for c) my answer is 4 VS but according to the textbook it is 8

topaz sinewBOT Nov 29, 2021, 6:55 AM

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sudden leaf Nov 29, 2021, 7:27 AM

#

is this asking me what the net force is? if so is the net force <-4,0>?

topaz sinewBOT Nov 29, 2021, 7:27 AM

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sudden leaf is this asking me what the net force is? if so is the net force <-4,0>?

snow basalt Nov 29, 2021, 7:27 AM

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yes and no

sudden leaf Nov 29, 2021, 7:28 AM

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oh hm

snow basalt Nov 29, 2021, 7:28 AM

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The net force is just gonna be the sum of those vectors

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you might have done some wrong arithmetic in the y coordinate? I only suggest that because you have the x coordinate of the net force correct so your method might be correct

sudden leaf Nov 29, 2021, 7:28 AM

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ohh i see

cunning urchin Nov 29, 2021, 7:28 AM

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-11 for y

sudden leaf Nov 29, 2021, 7:29 AM

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yeah i did -5+1+4

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instead of -5+1-7

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thank you!

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.close

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neon iron Nov 29, 2021, 9:09 AM

#

How do you write a transformation of f(x) —> af(bx) with matrices or vectors?

topaz sinewBOT Nov 29, 2021, 9:09 AM

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neon iron How do you write a transformation of f(x) —> a*f(b*x) with matrices or vectors?

neon iron Nov 29, 2021, 9:15 AM

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As in f(x) goes to a * f(b * x)

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Just generally

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@proven anvil

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R for both

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Continuous

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Yes

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Of f(x)

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So for translations you can write it T_v(f(x)) = f(x-a) + b for v= vector (a; b)

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So the translation of f(x) by vector ab is f(x-a)+b

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I guess that's what I'm looking for then

neon iron Nov 29, 2021, 9:23 AM

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neon iron So the translation of f(x) by vector ab is f(x-a)+b

This is what my textbook says so I dunno

#

#

I know how matrices work yes

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So something like [a 0]
0 b

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You forgot the second $

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It could be a vector I'm not even sure

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Scaled by vector (a,b)?

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That's confusing

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I don't see how f(x) would really be a matrix

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Although f(x) is technically an infinite set of vectors

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Basically, the textbook says that you can translate f(x) by a vector, so I'm guessing scaling should work in a similar way

thorny flameBOT Nov 29, 2021, 9:34 AM

#

KurtDee

neon iron Nov 29, 2021, 9:35 AM

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Not really...

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So I don't really know if it would work as v(a, b)*f(x) or maybe instead of v a matrix

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I should have formulated that better but I don't know how

thorny flameBOT Nov 29, 2021, 9:37 AM

#

KurtDee

#

KurtDee

neon iron Nov 29, 2021, 9:39 AM

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Yep

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Not an equation, a function

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But yeah

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So like every point of the function is moved by a vector ab

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That's what they mean

thorny flameBOT Nov 29, 2021, 9:42 AM

#

KurtDee

neon iron Nov 29, 2021, 9:44 AM

#

Should we try first having vector ab * f(x) see if that works?

#

Lemme try plug that into wolfram alpha

thorny flameBOT Nov 29, 2021, 9:46 AM

#

KurtDee

#

KurtDee

neon iron Nov 29, 2021, 9:49 AM

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neon iron Lemme try plug that into wolfram alpha

Wolfram alpha dies

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So f(x) becomes [f(x) x] (as a matrix)

#

?

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Oh okay tnhat makes sense

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-b or +b?

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Cause it's f(x-a)+b

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Normally

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Me too lol

thorny flameBOT Nov 29, 2021, 9:53 AM

#

KurtDee

#

KurtDee

neon iron Nov 29, 2021, 9:55 AM

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So a and b are the opposite from what I have? As in f(x-b)+a?

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Fair

#

So I can write:

#

$$ for m = \begin{bmatrix}a \ b\end{bmatrix}: \T_m(f(x)) = \begin{bmatrix}f(x) + a \ x +b\end{bmatrix}$$

thorny flameBOT Nov 29, 2021, 9:58 AM

#

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

neon iron Nov 29, 2021, 9:59 AM

#

Shit

#

For $$ m = \begin{bmatrix}a \ b\end{bmatrix}: \T_m(f(x)) = \begin{bmatrix}f(x) + a \ x +b\end{bmatrix}$$

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Whatever, you get it

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Perfect

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Now, what about scaling?

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Would $\begin{bmatrix}f(x) \ x\end{bmatrix} * \begin{bmatrix}a \ b\end{bmatrix} = 0 \Rightarrow \begin{bmatrix}f(x) * a \ x *b\end{bmatrix}$

thorny flameBOT Nov 29, 2021, 10:01 AM

#

KurtDee

#

Etienne

#

KurtDee

neon iron Nov 29, 2021, 10:01 AM

#

2s

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Fair yeah

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So what would it look like?

thorny flameBOT Nov 29, 2021, 10:04 AM

#

KurtDee

neon iron Nov 29, 2021, 10:05 AM

#

A is alpha beta right?

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Yes, matrix [alpha]
beta

#

My bad

#

Identity but with alpha and beta isntead of 1s

#

From $\begin{bmatrix}\alpha f(x) \ \beta x\end{bmatrix}$ how do we get to af(bx) though?

thorny flameBOT Nov 29, 2021, 10:08 AM

#

Etienne

neon iron Nov 29, 2021, 10:10 AM

#

with $\chib = x, \begin{bmatrix}f(\chib)*a \ \chi\end{bmatrix}$ ?

thorny flameBOT Nov 29, 2021, 10:10 AM

#

Etienne

neon iron Nov 29, 2021, 10:14 AM

#

So can I write for example, $A \begin{bmatrix}f(x)\x\end{bmatrix} = f(bx)a$ ?

thorny flameBOT Nov 29, 2021, 10:14 AM

#

Etienne

neon iron Nov 29, 2021, 10:15 AM

#

If I write A before

#

@proven anvil

#

Hello

#

So how do I kinda convert it back to a function?

#

f(bx)a

thorny flameBOT Nov 29, 2021, 10:18 AM

#

KurtDee

#

KurtDee

#

KurtDee

#

KurtDee

#

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

neon iron Nov 29, 2021, 10:21 AM

#

Wait why 11, 12, 21, 22?

#

Wdym?

#

So alpha_1 or 2 or 3 or 4 also works

#

Okay

#

However, still don't get how we go back to af(bx) at the end

#

So we do this the other way, have A and then got to af(bx)?

#

Okay

#

👍

#

So, let A = [3 0]
0 2
We can just say that because of what we did above, g(x) = 3*f(2x) ?

#

But if I write what we did earlier is that insufficient?

#

Shit

#

Oh

#

But didn't we start off with A = alpha, 0; beta, 0 ?

#

Oh okay

#

So how do we do it without assuming a = alpha, 0; beta, 0

#

?

thorny flameBOT Nov 29, 2021, 10:37 AM

#

KurtDee

neon iron Nov 29, 2021, 10:43 AM

#

I'm not really familiar with matrice equations

#

I can solve a system of linear equations with matrices, which is pretty easy, but solving to get a matrix like this that I don't know how to do

#

@proven anvil

#

Hello again, sorry

#

I should, but I may have cheated my way through high school

#

Yeah

#

Me too

#

Oh

#

I won't bother you anymore then

#

.close

topaz sinewBOT Nov 29, 2021, 10:48 AM

#

Channel closed

Closed by @tacit wind

Use .reopen if this was a mistake.

neon iron Nov 29, 2021, 10:49 AM

#

Cheers

#

Thanks alot dude

topaz sinewBOT Nov 29, 2021, 11:01 AM

#

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visual sorrel Nov 29, 2021, 11:10 AM

#

need help with this please

A 40cm length of wire is cut into three lengths and these lengths are used to form an isosceles triangle of maximum area. Use calculus to determine the lengths of the sides of this triangle.

topaz sinewBOT Nov 29, 2021, 11:10 AM

#

visual sorrel need help with this please A 40cm length of wire is cut into three lengths and...

inner oracle Nov 29, 2021, 11:17 AM

#

What's the formula for area of isoceles triangle

visual sorrel Nov 29, 2021, 11:19 AM

#

1/2.b.h?

topaz sinewBOT Nov 29, 2021, 11:34 AM

#

@visual sorrel Has your question been resolved?

topaz sinewBOT Nov 29, 2021, 12:09 PM

#

@visual sorrel Has your question been resolved?

topaz sinewBOT Nov 29, 2021, 1:09 PM

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@visual sorrel Has your question been resolved?

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topaz sinewBOT Nov 29, 2021, 1:37 PM

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Channel closed

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winged marsh Nov 29, 2021, 1:37 PM

#

.close

topaz sinewBOT Nov 29, 2021, 1:47 PM

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urban timber Nov 29, 2021, 2:08 PM

#

So I'm a bit lost with some calculus again
In the following, we start with the gradient of some integral
$$\nabla \int P(\tau | \theta) R(\tau)$$
Then (I think?) because of the cyclic relationship between the derivative and integral, we're allowed to just move the gradient under the integral expression to it becomes
$$\int \nabla P(\tau | \theta) R(\tau)$$

But... isn't there an implicit parenthesis there? I mean, isn't it the gradient of the entire expression, not just the first factor?
It looks like they substitute $\nabla P(\tau|\theta)$ for its expansion and just leave $R(\tau)$ as is.

How does this work?

topaz sinewBOT Nov 29, 2021, 2:08 PM

#

urban timber So I'm a bit lost with some calculus again In the following, we start with the g...

urban timber Nov 29, 2021, 2:08 PM

#

thorny flameBOT Nov 29, 2021, 2:10 PM

#

Amnesia

urban timber Nov 29, 2021, 2:19 PM

#

It might be worth mentioning btw that R(T) does not depend on the parameters, so its gradient is 0
I still feel like, if that's the reason, then it should cancel out completely, and not just be left as is

topaz sinewBOT Nov 29, 2021, 2:34 PM

#

@urban timber Has your question been resolved?

wheat laurel Nov 29, 2021, 2:34 PM

#

i think you should post this in one of the advanced maths channels @urban timber

urban timber Nov 29, 2021, 2:43 PM

#

wheat laurel i think you should post this in one of the advanced maths channels <@!3116041828...

Thank you, I'll try that. Although I don't really feel like an "advanced maths"-kind of person...
Perhaps I'm just biting over more than I can chew, with just the absolute bare minimum of knowledge about calculus?
Like, I feel like my problem is rather simple. It just happens to appear in the context of some advanced maths

topaz sinewBOT Nov 29, 2021, 2:44 PM

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opal lance Nov 29, 2021, 3:03 PM

#

Find T if:
\
$a=\sqrt{8} + 2$
\
$b=\sqrt{8} - 2$
\
$T = a^2 - b^2$

topaz sinewBOT Nov 29, 2021, 3:03 PM

#

opal lance Find T if: \\ $a=\sqrt{8} + 2$ \\ $b=\sqrt{8} - 2$ \\ $T = a^2 - b^2$

thorny flameBOT Nov 29, 2021, 3:03 PM

#

slayer

opal lance Nov 29, 2021, 3:04 PM

#

In this question i tried to put each a and b in brackets and power them up to 2 to get this which i think is probably wrong:

restive inlet Nov 29, 2021, 3:04 PM

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that's one way to do it

opal lance Nov 29, 2021, 3:05 PM

#

$a^2= \sqrt{8}^2 + 2^2$
\

$b^2= \sqrt{8}^2 - 2^2$

thorny flameBOT Nov 29, 2021, 3:05 PM

#

slayer

opal lance Nov 29, 2021, 3:05 PM

#

@restive inlet is this right?

restive inlet Nov 29, 2021, 3:05 PM

#

that however is wrong

opal lance Nov 29, 2021, 3:05 PM

#

Yeah i was quite sure something was wrong

restive inlet Nov 29, 2021, 3:05 PM

#

classic freshman's dream

opal lance Nov 29, 2021, 3:06 PM

#

Oh and it tells me to give your final answer in c sqrt 2

restive inlet Nov 29, 2021, 3:06 PM

#

recall the definition of exponentiation/distributive property and/or binomial theorem

opal lance Nov 29, 2021, 3:06 PM

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where c is an jnteger

opal lance Nov 29, 2021, 3:06 PM

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restive inlet recall the definition of exponentiation/distributive property and/or binomial th...

the what

restive inlet Nov 29, 2021, 3:07 PM

#

what does it mean to square something

opal lance Nov 29, 2021, 3:07 PM

#

Multiply each other

restive inlet Nov 29, 2021, 3:07 PM

#

poor wording

opal lance Nov 29, 2021, 3:07 PM

#

a x a = a^2

restive inlet Nov 29, 2021, 3:08 PM

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opal lance a x a = a^2

yes

opal lance Nov 29, 2021, 3:08 PM

#

well i never get asked to define it 😅

restive inlet Nov 29, 2021, 3:08 PM

#

apply that here and expand (properly)

opal lance Nov 29, 2021, 3:08 PM

#

Oh expand

restive inlet Nov 29, 2021, 3:09 PM

#

(applying something like the distributive property)

topaz sinewBOT Nov 29, 2021, 3:23 PM

#

@opal lance Has your question been resolved?

topaz sinewBOT Nov 29, 2021, 3:38 PM

#

Channel closed

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topaz sinewBOT Nov 29, 2021, 10:39 PM

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strong talon Nov 29, 2021, 11:28 PM

#

I keep mixing up my stuff and I'm not sure where I'm going wrong

topaz sinewBOT Nov 29, 2021, 11:28 PM

#

strong talon I keep mixing up my stuff and I'm not sure where I'm going wrong

#

@strong talon Has your question been resolved?

grim jacinth Nov 30, 2021, 12:23 AM

#

strong talon I keep mixing up my stuff and I'm not sure where I'm going wrong

In order to simplify this complex fraction, you'll want to multiply by the common denominator of each of the 4 fractions (these 4 fractions are the 2 in the numerator of the big fraction, and 2 in the denominator of said big fraction)

topaz sinewBOT Nov 30, 2021, 12:33 AM

#

@strong talon Has your question been resolved?

grim jacinth Nov 30, 2021, 1:24 AM

#

Bro man didn't take my advice one bit lmao

topaz sinewBOT Nov 30, 2021, 1:44 AM

#

@strong talon Has your question been resolved?

slow zenith Nov 30, 2021, 1:58 AM

#

strong talon I keep mixing up my stuff and I'm not sure where I'm going wrong

What have you tried?

topaz sinewBOT Nov 30, 2021, 2:44 AM

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quartz shale Nov 30, 2021, 4:11 AM

#

how do you find sine of any angle/radian?

topaz sinewBOT Nov 30, 2021, 4:11 AM

#

quartz shale how do you find sine of any angle/radian?

chrome glen Nov 30, 2021, 4:17 AM

#

Wdym

quartz shale Nov 30, 2021, 4:19 AM

#

chrome glen Wdym

the values that are given are for 0,30,45,60,90 right, now how would you find the sine of 42 for example

#

without a calculator

restive inlet Nov 30, 2021, 4:19 AM

#

convert to radians,
use power series to get a decent approximation

chrome glen Nov 30, 2021, 4:19 AM

#

Taylor series bleak

quartz shale Nov 30, 2021, 4:20 AM

#

restive inlet convert to radians, use power series to get a decent approximation

idk what that means

#

ik how to convert to radians

#

but what is this power series

restive inlet Nov 30, 2021, 4:20 AM

#

then

find the sine of 42 for example
without a calculator
is not something you should worry about atm

quartz shale Nov 30, 2021, 4:22 AM

#

restive inlet then > find the sine of 42 for example > without a calculator is not something y...

in my book they are talking something about angle to minutes and seconds but there is question with theta equal to 42 degrees

restive inlet Nov 30, 2021, 4:23 AM

#

why are you trying to do this without a calculator

quartz shale Nov 30, 2021, 4:23 AM

#

restive inlet why are you trying to do this without a calculator

idk if they would allow calculator in tests/exams

restive inlet Nov 30, 2021, 4:23 AM

#

ask them?

quartz shale Nov 30, 2021, 4:24 AM

#

restive inlet ask them?

im a homeschooler...

restive inlet Nov 30, 2021, 4:24 AM

#

ask through email

quartz shale Nov 30, 2021, 4:24 AM

#

ok

restive inlet Nov 30, 2021, 4:24 AM

#

or phone

quartz shale Nov 30, 2021, 4:24 AM

#

but there is no way to calculate sine of any angle/radian without calculator?

restive inlet Nov 30, 2021, 4:24 AM

#

most places allow approved calculators unless its jee

#

i mentioned what you could use earlier but its too advanced for you to apply atm

quartz shale Nov 30, 2021, 4:26 AM

#

restive inlet i mentioned what you could use earlier but its too advanced for you to apply atm

oh ok

#

so i use a calculator to find the sine in my question?

#

alr thank you very much

#

.close

topaz sinewBOT Nov 30, 2021, 4:29 AM

#

Channel closed

Closed by @quartz shale

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drifting jasper Nov 30, 2021, 4:33 AM

#

-3 (4-3x) =9 - 12

topaz sinewBOT Nov 30, 2021, 4:33 AM

#

drifting jasper -3 (4-3x) =9 - 12

drifting jasper Nov 30, 2021, 4:34 AM

#

I think that has no solutions, But somebody said it has infinite solutions

#

Can someone double check?

restive inlet Nov 30, 2021, 4:35 AM

#

you're both wrong

quartz shale Nov 30, 2021, 4:35 AM

#

drifting jasper I think that has no solutions, But somebody said it has infinite solutions

i think the answer is 1?

empty sail Nov 30, 2021, 4:35 AM

#

drifting jasper -3 (4-3x) =9 - 12

Are you sure this is typed correctly, because it has a solution

drifting jasper Nov 30, 2021, 4:35 AM

#

quartz shale i think the answer is 1?

no

#

i got 6 = -13

empty sail Nov 30, 2021, 4:36 AM

#

You mathed wrong

restive inlet Nov 30, 2021, 4:36 AM

#

where'd the x disappear off to

drifting jasper Nov 30, 2021, 4:36 AM

#

Shoot

#

Can you walk me threw it?

empty sail Nov 30, 2021, 4:36 AM

#

Distribute, combine like terms, get x on one side and everything else on the other

quartz shale Nov 30, 2021, 4:37 AM

#

drifting jasper -3 (4-3x) =9 - 12

-3(4-3(1)) = 9 - 12
-3(4-3) = 9 - 12
-3(1) = -3
-3 = -3

#

so ya x is 1?

drifting jasper Nov 30, 2021, 4:38 AM

#

So, Does it have infinite solutions or 1 solution or none?

empty sail Nov 30, 2021, 4:38 AM

#

It has a solution

quartz shale Nov 30, 2021, 4:38 AM

#

drifting jasper So, Does it have infinite solutions or 1 solution or none?

1 solution

drifting jasper Nov 30, 2021, 4:40 AM

#

Its on paper, But i basically butchered it, i got 6=-13

empty sail Nov 30, 2021, 4:40 AM

#

drifting jasper Its on paper, But i basically butchered it, i got 6=-13

Post a picture of it and we can tell you what went wrong

drifting jasper Nov 30, 2021, 4:41 AM

#

Ill draw it on note rq, I only have discord on a desktop

#

omg, before i post this, i see the mistakes lol, I messed this up in the worst way possible

#

I messed that up really hard lol

restive inlet Nov 30, 2021, 4:45 AM

#

also this is different from the equation you initially gave

quartz shale Nov 30, 2021, 4:45 AM

#

restive inlet also this is different from the equation you initially gave

ya...

drifting jasper Nov 30, 2021, 4:45 AM

#

it is?

empty sail Nov 30, 2021, 4:45 AM

#

This is a different problem than what you gave before, which is why I asked if you typed it properly

drifting jasper Nov 30, 2021, 4:45 AM

#

That is a ss of it

restive inlet Nov 30, 2021, 4:45 AM

#

#

that is nonsense

drifting jasper Nov 30, 2021, 4:46 AM

#

ik, Im relearning this material, I got it all mixed up

empty sail Nov 30, 2021, 4:46 AM

#

-3 (4-3x) =9 - 12 is what you had originally sent

drifting jasper Nov 30, 2021, 4:46 AM

#

i forgot the X

quartz shale Nov 30, 2021, 4:46 AM

#

infinite solutions?

restive inlet Nov 30, 2021, 4:47 AM

#

anyway what were you trying to do with
-3(4-3x)

empty sail Nov 30, 2021, 4:47 AM

#

quartz shale infinite solutions?

Doesn't help if you just give the person the answers

drifting jasper Nov 30, 2021, 4:47 AM

#

restive inlet anyway what were you trying to do with -3(4-3x)

Was i suppose to multiply?

empty sail Nov 30, 2021, 4:47 AM

#

Actually check their work and see what went wrong @quartz shale

restive inlet Nov 30, 2021, 4:47 AM

#

multiply / distribute properly yes

#

alternatively dividing both sides of the equation by -3 would also be acceptable

drifting jasper Nov 30, 2021, 4:48 AM

#

Let me redo this rq

#

Got 9x and -12 Which cancels the other 9x and -12

#

So it has infinite solutions

#

Ok

#

It is that

#

Yes

#

.close

topaz sinewBOT Nov 30, 2021, 4:59 AM

#

Channel closed

Closed by @drifting jasper

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topaz sinewBOT Nov 30, 2021, 3:17 PM

#

Available help channel!

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Remember:
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• After 15 minutes, feel free to ping <@&286206848099549185>.
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green arch Nov 30, 2021, 4:47 PM

#

Screen_Shot_2021-11-30_at_8.47.29_AM.png

topaz sinewBOT Nov 30, 2021, 4:47 PM

#

green arch

leaden tusk Nov 30, 2021, 4:48 PM

#

what do you think the answer is?

green arch Nov 30, 2021, 4:48 PM

#

no solution

leaden tusk Nov 30, 2021, 4:48 PM

#

right

green arch Nov 30, 2021, 4:49 PM

#

i also had a few more

#

im either just dumb or its just because its the morning

#

Screen_Shot_2021-11-30_at_8.49.24_AM.png

#

no solution right?

leaden tusk Nov 30, 2021, 4:49 PM

#

not quite

#

look at the example on the left side of your screen

green arch Nov 30, 2021, 4:50 PM

#

oh

#

its infinte solution

#

lol

leaden tusk Nov 30, 2021, 4:50 PM

#

yep, it's the same line

green arch Nov 30, 2021, 4:50 PM

#

Screen_Shot_2021-11-30_at_8.50.32_AM.png

#

than this is one solution

leaden tusk Nov 30, 2021, 4:50 PM

#

yes

green arch Nov 30, 2021, 4:51 PM

#

perfect

#

thanks

#

.close

topaz sinewBOT Nov 30, 2021, 4:51 PM

#

Channel closed

Closed by @green arch

Use .reopen if this was a mistake.

leaden tusk Nov 30, 2021, 4:51 PM

#

👍

topaz sinewBOT Nov 30, 2021, 4:57 PM

#

Available help channel!

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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

topaz sinewBOT Nov 30, 2021, 5:38 PM

#

@neon iron Has your question been resolved?

#

Channel closed

Closed due to the original message being deleted

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stark solstice Nov 30, 2021, 6:20 PM

#

Hi

topaz sinewBOT Nov 30, 2021, 6:20 PM

#

stark solstice Hi

stark solstice Nov 30, 2021, 6:20 PM

#

I did a chi squared test

#

And got a value of 1

#

What does that mean

topaz sinewBOT Nov 30, 2021, 6:35 PM

#

@stark solstice Has your question been resolved?

stark solstice Nov 30, 2021, 6:48 PM

#

Hello?

topaz sinewBOT Nov 30, 2021, 7:18 PM

#

@stark solstice Has your question been resolved?

topaz sinewBOT Nov 30, 2021, 7:48 PM

#

Channel closed

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covert oriole Nov 30, 2021, 8:12 PM

#

I have answered this question already I just want to see if i did it correctly

if "cathetus 1" = 7 1.e, and the "hypotenuse" = 9 1.e. Then what does "cathetus 2" equal?

topaz sinewBOT Nov 30, 2021, 8:12 PM

#

covert oriole I have answered this question already I just want to see if i did it correctly ...

subtle mountain Nov 30, 2021, 8:13 PM

#

what

#

is a

#

catetus

covert oriole Nov 30, 2021, 8:14 PM

#

my bad

#

speling error

subtle mountain Nov 30, 2021, 8:15 PM

#

what