#help-23

1 messages · Page 446 of 1

broken yew
#

(-2)(-3) = 6
1 - 12 + 12 = 1

tawdry salmon
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$x^2+x-6$

flat frigateBOT
#

geoxcaliber

tawdry salmon
#

nvm you don't plug it into this one

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$(x-2)(x+3)$

flat frigateBOT
#

geoxcaliber

broken yew
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Im just saying for a quick mistake check.

tawdry salmon
#

sorry I'm lost

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$-2x^3(x+3)^2$

flat frigateBOT
#

geoxcaliber

tawdry salmon
#

so I did x^2 and 3^2 = 9 in the top then -2x^3 in the left

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ohh am so stupid

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$-2x^5 - 18x^3$

flat frigateBOT
#

geoxcaliber

tawdry salmon
#

Ok I get it better now, thanks a lot. My main confusing point was the fact that x = (x - 0)

tawdry salmon
#

put 1 into each x?

broken yew
#

.

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I mean thats not guaranteed to check if its correct

#

its just checking if its wrong.

broken yew
broken yew
safe radishBOT
#

@tawdry salmon Has your question been resolved?

tawdry salmon
broken yew
#

bruh

tawdry salmon
#

so does that mean doing x^2 and + 9 is wrong?

broken yew
#

your (x+3) squared

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is big wrong

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$$(1+3)^2 \neq 1^2 + 3^2$$

flat frigateBOT
#

Shuri2060

tawdry salmon
#

What would it equal?

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ohh lol

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wait no

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but (x)^2 = x^2

broken yew
#

$$(a+b)^2 \neq a^2 + b^2$$

flat frigateBOT
#

Shuri2060

broken yew
#

You realise this right?

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Where have all the middle terms gone

tawdry salmon
#

does it equal

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$$(a+b)^2 = a + b^2$$

flat frigateBOT
#

geoxcaliber

broken yew
#

???????

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bruh 🤦

tawdry salmon
#

lmao

broken yew
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Really - practice these expansions

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expansion of factors

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And get a better method

tawdry salmon
#

so what would it be?

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ohh lmao

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do you add the two things in parenthesis first

broken yew
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idk, look up videos

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how to multiply out brackets

tawdry salmon
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this shit is so confusing

broken yew
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just look up a video how to multiply out brackets

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cus this aint working for you clearly

broken yew
tawdry salmon
tawdry salmon
#

but it's supposed to be 9 right

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(x+3) = 3x

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(3x)^2 = 9x^2

broken yew
#

??????????????????

tawdry salmon
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im gonna get an algebra book and just start algebra from over lmao

broken yew
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(x+3) = 3x

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what is this?????/

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Yes, you need to start basic algebra again

tawdry salmon
#

is it wrong

broken yew
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yes

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wrong

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bruh

tawdry salmon
#

you can't add x and 3?

barren rose
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3x is 3 times x

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x+3 is x plus 3

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what is the question again? the discussion is super long lol

tawdry salmon
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$-2x^3(x+3)^2$

flat frigateBOT
#

geoxcaliber

tawdry salmon
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trying to factor this

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I did

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$$(a+b)^2 \neq a^2 + b^2$$

flat frigateBOT
#

geoxcaliber

tawdry salmon
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so if that doesn't work I turned to PEMDAS, which has parenthesis first so I attempted adding the two

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so if neither that or this doesn't work

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$$(a+b)^2 = a + b^2$$

flat frigateBOT
#

geoxcaliber

tawdry salmon
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I have no clue

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oh

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so it's just

barren rose
tawdry salmon
#

$$(x+3) (x+3)$$

flat frigateBOT
#

geoxcaliber

barren rose
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first of all the equation(first one) is wrong

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$$(a+b)^2 = a^2 + 2ab + b^2$$

flat frigateBOT
#

blackmamba[they/them]

barren rose
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I don't remember factoring too much but I think the best thing to do right here is to open the brackets

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either through calculating (x+3)^2 via the equation I posted

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or calculating it via $-2x^3(x+3)(x+3)$

flat frigateBOT
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blackmamba[they/them]

tawdry salmon
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I see

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well all imma say is I hate algebra :/

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that one has nothing to do with this right

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Oh I see, nevermind. I had notes on this "square of a binomial" which calculates like you said

barren rose
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no

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you don't need cube ones here

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calculate $(x+3)^2$ via the equation I gave you

flat frigateBOT
#

blackmamba[they/them]

barren rose
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then open the brackets by multiuplying each element with $-2x^3$

flat frigateBOT
#

blackmamba[they/them]

tawdry salmon
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Okay, thanks

#

by the way, when you do this, does (a+b) count as the factor?

barren rose
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probably yes but don't think you're gonna get to that

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you'll get a cube but the factor won't look like that

tawdry salmon
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oh ok

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is it because a factor is supposed to look like x - 5 and that looks like 3 -/+ 5? (a + b)

barren rose
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not sure what you're talking about

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try doing what I suggested and come w/ an answer

tawdry salmon
#

for this, to get the root of x - 2 do you do
x - 2 = 0
x = 2
or
x + 2 = 0
x = -2

barren rose
#

the root?

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you mean the limit

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or like

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not limit

tawdry salmon
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it's called zero, x-intercept, solution (of a function)

barren rose
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an intercept is when the lines reach the x or y axis

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that;'s when the entire equation equals 0

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(for x-intercept)

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not the root, that's where the function is undefined

tawdry salmon
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teacher's notes

barren rose
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notice

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f(r)=0

barren rose
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in other words

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to find r... you need to find an x such that f(x) = 0

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or (x^3 + 5x^2 -3x + 6) / (x-2) = 0

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2 is NOT a root here

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2 is undefined

safe radishBOT
#

@tawdry salmon Has your question been resolved?

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lean otter
safe radishBOT
lean otter
#

im solving for tan2x

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where sinx is 4/radical 19

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is the answer positive or negative

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when i plug that expression in the calculator, it says negative

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but this is in quadrant 1

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so is the answer positive?

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this is the formula i used

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this is what it says in the calculator

safe radishBOT
#

@lean otter Has your question been resolved?

safe radishBOT
#

@lean otter Has your question been resolved?

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slim urchin
safe radishBOT
slim urchin
#

can someone explain why i am getting the critical point wrong?

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it is meant to be -3/2 but i got 0 and -5/3

broken yew
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cant read the q

slim urchin
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i can send it in enlarged peices

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1 sec

broken yew
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can u just write it

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Find the point

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on

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the

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line

slim urchin
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yep

broken yew
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that is closest to

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to what?

slim urchin
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find the point on the line y=3x+5 that is closest to the origin

broken yew
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ok

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by the way

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critical point

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has a different meaning

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so avoid using that

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i was confused

slim urchin
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should i say critical values in stead?

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sorry

broken yew
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no, avoid critical

slim urchin
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or just zeroes of the first derivative?

broken yew
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wait what

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ok ignore me

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i just assumed from your picture we were doing a linear function lmao

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didnt actually read

slim urchin
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thats okay 🙂

broken yew
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wait but

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no im still confused lmao

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we are just doing it for

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y=3x+5

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right

slim urchin
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yes i think so

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its an optimisation problem

broken yew
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i dont get where all that math comes from

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i think it can be done a lot simpler than that?

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oh i see,

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ur finding the circle which is tangent to it

slim urchin
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ahh im not sure, this is from organic chemistry tutor. i am practicing optimisation problems

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he used this as an example

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it is a common optimisation problem it hink

broken yew
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well alright

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i feel like basic trig should get u answer

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but i can check your way as well

slim urchin
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i mean i am watching him do it

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it all seemed fine until the critical point'

broken yew
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just gonna try it this way first to check

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hyp = 5sqrt10/3

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sqrt10 is ratio

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1/6-5/3

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yh so i get x = -3/2

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Then calculus way 🤔

slim urchin
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im so confused haha

broken yew
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I think i found it

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its

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2x + ....

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not multiply?

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or wait

slim urchin
#

i am thinking he has made a mistake

broken yew
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yh thats it

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the answer is x = -3/2 for sure

slim urchin
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thats so weird no one pointed it out

broken yew
slim urchin
#

in the comment section

broken yew
#

?

slim urchin
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wait nvm its me who made a mistake

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give me a second

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oh yeah

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that makes sense

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thank you :3

broken yew
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way quicker with geometry lol

slim urchin
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ahh yeah...

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i am trying to practice optimisation problems though

broken yew
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oh ic

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so the video just chose this example

slim urchin
#

thanks for the help

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yeah i think so

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yeah il close channel

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.close

safe radishBOT
#
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slim urchin
#

you can just use the channel

#

i just closed it so it doesnt have my name on it anymore

safe radishBOT
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ancient escarp
#

<@&268886789983436800> (posting in all channels)

hot thistle
#

.close

safe radishBOT
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peak jetty
#

What does it mean by a>1?

safe radishBOT
latent flume
#

That a is greater than 1

peak jetty
#

Yeah but why does it mention it in the question

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It has no use or am I wrong?

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<@&286206848099549185>

latent flume
#

It’s so that the denominator will never be negative

peak jetty
#

But why does that matter?

hot thistle
#

because if it was you'd need to change the direction of the inequality

peak jetty
#

So let’s say a<-1

peak jetty
hot thistle
#

probably the same way

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but when dividing by 3a-2

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you flip the inequality

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side it would be negative

peak jetty
#

So can we write this equation -ax<=2x+1/3 if it was a<-1

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Then solve for x

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?

hot thistle
#

I believe so

peak jetty
#

Ahh ok

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Makes more sense to me now

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Cheers Danny devito

#

.close

safe radishBOT
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lean otter
safe radishBOT
ancient escarp
#

what exactly is your goal here

bronze rivet
#

I think they wanna factor it

lean otter
#

yep

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im confused how to

ancient escarp
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p/q

lean otter
#

oh?

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is it not grouping factoring

ancient escarp
#

uhm

lean otter
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why r u saying uhm

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use ur words

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yes or no question

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how do u know when to use p/q

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cuz theres also a grouping fcoting method

ancient escarp
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lmfao calm down chief i'm trying to see if i can factor this by grouping

lean otter
#

where u group it by 2 and 2

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or 3 and 1

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or 1 and 3

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ok

ancient escarp
#

yes i'm aware of what factoring is lmao

lean otter
#

k

ancient escarp
#

i'm not sure you can

lean otter
#

yea

#

well how do u know when to use p/q

ancient escarp
#

when other methods fail

lean otter
#

k.

#

thanks.

#

.close

safe radishBOT
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meager chasm
#

hi

safe radishBOT
meager chasm
#

suppose t ∈ (0, 1)

#

for any x, y ∈ R, if x < y, why is x < tx + (1 - t)y < y true?

inner tapir
#

this is kind of like a one-dimensional bezier curve

#

you can think of it like having some percent of x added to some percent ofy
that percent will always be between 0 and 100

meager chasm
#

bezier curve??

meager chasm
#

i’ve been told it is

inner tapir
#

sorry didn't mean to scare you; some people are familiar, you use them a lot in like paint applications

#

you can ignore it tho

meager chasm
#

what ways do i have to prove this

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currently in calc 1

inner tapir
#

are you asked to prove this, or are you looking for intuition?

meager chasm
#

prove

#

it’s intuitively true but why

inner tapir
#

i was always bad at analysis and inequalities lol
hmm maybe rearrange center t (x - y) + y
just thinking out loud

meager chasm
#

how does that help

meager chasm
#

i suppose that’s not analysis

inner tapir
#

idk you gotta play with it, again i'm just thinking out loud

meager chasm
#

<@&286206848099549185> ?

broken yew
#

suppose t ∈ (0, 1)
for any x, y ∈ R, if x < y, why is x < tx + (1 - t)y < y true?

#

Can you see what that middle expression represents?

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@meager chasm

meager chasm
#

yes

broken yew
#

visually?

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as you vary t from 0 to 1

meager chasm
#

congrats on your role

inner tapir
meager chasm
broken yew
#

ty

#

you are kinda like varying from x to y

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as t goes from 1 to 0

meager chasm
#

yea

broken yew
#

anyways, I don't think its too hard to show if you tackle one inequality at a time

broken yew
#

x < tx + (1 - t)y
x - tx < (1 - t)y
(1 - t)x < (1 - t)y

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then same for other side

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this is me showing it backwards

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you show forwards ofc

meager chasm
#

oh shit yea

#

never thought of going backwards

#

.close

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lean otter
safe radishBOT
lean otter
#

I just don't get q 27 ;-;

inner tapir
#

,rotate

lean otter
#

How do I do it

flat frigateBOT
lean otter
inner tapir
#

i'd prob just factorize it; don't really see another way

#

like 216 = 6^3 = 2^3 * 3^3

#

then use exponent rules

lean otter
#

ok

#

. close

#

.close

safe radishBOT
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safe radishBOT
inner tapir
#

the taylor series one?

#

do you know the definition for the terms of a taylor series?

safe radishBOT
#

@copper wraith Has your question been resolved?

safe radishBOT
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shy dune
#

Let T be the smallest positive integer which, when divided by 11, 13, 15 leaves remainders in the sets {7, 8, 9}, {1, 2, 3}, {4, 5, 6} respectively.

shy dune
#

how a number gives 3 remainder when divided by one number

broken yew
#

16 divided by 13

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gives 1 remainder 3

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cus 16 = 1(13) + 3

split ether
#

I think they meant that the remainders are somewhere in sets

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And not that all of the elements in each set is a remainder

broken yew
#

oh 3 different ones

shy dune
broken yew
#

I see

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Think of it as an OR

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I think

shy dune
#

hm

broken yew
#

x = 7 mod 11
x = 3 mod 13
x = 6 mod 15

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Is possible

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You choose 1 from each set

shy dune
#

maybe

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i ll check the solution later

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i was trying it on my own first

#

this is what they meant

#

whoever is wondering

#

thanks Shuri2060

#

.close

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safe radishBOT
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kind beacon
#

for sinsiduoal functions, when i find the k value and x value on a graph and write the equation, do i still need to factor

lean otter
#

Can u be a bit more specific

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Like show the exact question

#

What do u mean by K value

kind beacon
#

Ok

#

oh nvm

#

.close

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lean otter
#

Ok

safe radishBOT
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zinc bronze
#

Stuck again on a similar problem as last time 😩

zinc bronze
#

Again I can do the zero vector axiom, but when it comes to showing X + Y is closed on addition or scalar multiplication, I'm stuck

broken yew
#

.

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alright lets try

broken yew
zinc bronze
#

$Let a,b \in X and c,d \in Y$

flat frigateBOT
#

hello2248

broken yew
#

ehh u can do that

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yes that is fine

#

Let $\boldsymbol{v_1},\boldsymbol{v_2}\in X+Y$.

Then let $\boldsymbol{x_1}, \boldsymbol{x_2}\in X, \boldsymbol{y_1}, \boldsymbol{y_2}\in Y$ such that $\boldsymbol{v_1} = \boldsymbol{x_1} +\boldsymbol{ y_1}$, $\boldsymbol{v_2} = \boldsymbol{x_2} + \boldsymbol{y_2}$.

flat frigateBOT
#

Shuri2060

broken yew
#

Perhaps I would prefer this lettering

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Then it is clearer than a, b, c, d?

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it doesnt matter in the end, though

zinc bronze
#

Yah makes sense

broken yew
#

So if we know X and Y are subspaces

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What can we say about those 4 vectors

broken yew
#

First we are doing addition

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Usually to prove a property, you just use the same property (if you have something combined from vector spaces)

zinc bronze
#

$x_1 + x_2 + y_1 + y_2 \in X + Y$ because $x_1 + x_2 \in X$ and $y_1 + y_2 \in Y$

flat frigateBOT
#

hello2248

zinc bronze
#

So $v_1 + v_2 \in X+Y$

broken yew
#

yes, thats the way

flat frigateBOT
#

hello2248

broken yew
#

yes good

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Ok, scalar multiplication

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Do you know how to start the proof?

#

By the way, it's been a long time for me. We just need to prove closure for both and 0 is in it? I forgot haha

zinc bronze
#

Yep, just those 3

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Let $v \in X + Y$ such that $v = x + y$ where $x \in X$ and $y \in Y$ and $λ \in (howToDoInLatex?)$
$λx \in X$ and $λy \in Y$
thus $λx + λy \in X + Y$ hence $λv \in X + Y$
X + Y is closed on scalar multiplication

flat frigateBOT
#

hello2248

zinc bronze
#

idk how to use latex apparently

broken yew
#

aha I just use it because looks nice and practice

#

$$\bR$$

flat frigateBOT
#

Shuri2060

broken yew
#

Sure, your proof is fine

zinc bronze
#

Aha alrighty thanks again!

broken yew
#

Usually, since the concepts are so simple

#

I write out every step

#

v = x + y

#

kx, ky in V

#

you had those

#

but then i write

#

kx + ky = k(x + y) = kv in V

zinc bronze
#

Ok sure yeah, makes sense to be detailed

broken yew
#

wait what am i doing

#

@zinc bronze wait lol

#

oh right nvm

#

all is good 💤 haha

broken yew
zinc bronze
#

Mhm thanks for the help and advice!

broken yew
#

👌

zinc bronze
#

.close

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fathom parcel
#

$e^(iy)*sin(x)/(cos(x)-1)=O$

safe radishBOT
fathom parcel
#

does this stay true if i swap around the fraction?

worthy hemlock
flat frigateBOT
#

Sparky

rigid oracle
#

$e^{iy}\cdot\frac{\sin(x)}{\cos(x)-1}=O$

flat frigateBOT
fathom parcel
#

thx 😄

worthy hemlock
#

Cause latex says it's the letter

fathom parcel
#

supposed to be zero

#

but can i turn around my fraction and it still stays true?

river granite
#

$e^9×9=

pulsar condor
#

Oh they left bsully

rigid oracle
#

You mean $\frac{\cos(x)-1}{\sin(x)}$?

flat frigateBOT
fathom parcel
#

$e^{-iy}\cdot\frac{\cos(x)-1}{\sin(x)}=O$

flat frigateBOT
#

Sparky

fathom parcel
#

is this also true?

rigid oracle
#

what you wanna say is $e^{iy}\cdot\frac{\sin(x)}{\cos(x)-1}=0=e^{-iy}\cdot\frac{\cos(x)-1}{\sin(x)}$

flat frigateBOT
fathom parcel
#

yeah exactly

rigid oracle
#

you mean if the same x'es satisfy this equation?

broken yew
rigid oracle
#

i am confused by the question

#

$e^{iy}\cdot\frac{\sin(x)}{\cos(x)-1}=0\not =e^{-iy}\cdot\frac{\cos(x)-1}{\sin(x)}$

flat frigateBOT
fathom parcel
#

i have a linear system of equations and one equation is what i posted first. And i want to transform it so that i just turn around my fraction. Am i allowed to do this?

rigid oracle
#

because to turn the equation around $\frac{\cos(x)-1}{\sin(x)} = \frac{\sin(x)}{\cos(x)-1}$ would have to hold

flat frigateBOT
rigid oracle
#

so no, you can't turn around the fraction

#

or do you mean this

#

$e^{iy}\cdot\frac{\sin(x)}{\cos(x)-1}=0\qquad\bigg|()^{-1}\\ \frac{1}{e^{iy}}\cdot\frac{\cos(x)-1}{\sin(x)}=0$

flat frigateBOT
fathom parcel
#

yes thats what i want to do

rigid oracle
#

that you can do

fathom parcel
#

thank you very much.

#

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lean otter
#

Hi! I don’t get q 11

safe radishBOT
scarlet sage
#

What have you tried so far

#

nvm i cant do this

#

mb

quasi bison
#

@lean otter how familiar are you with exponent laws?

lean otter
#

Idk mb 50%?

quasi bison
#

kind of weird that you'd give a percentage like that.

#

but ok

#

can you say which exponent laws you are familiar with enough to remember them off the top of your head?

lean otter
#

.close

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frozen sluice
#

I want to find the zeros of $f(x)=x^4+4$. Wolfram Alpha tells me its $\pm(1+i)$ and $\pm(1-i)$. But when i use the quadratic formula i get $\pm\sqrt{2i}$ and $\pm i \sqrt{2i}$

flat frigateBOT
#

Kurama

frozen sluice
#

what am i doing wrongPU_peeporeWide

marsh walrus
#

can i ask a dumb question

#

how are you using the quadratic formula

#

just substitution?

frozen sluice
#

yes, just substituting x^2

marsh walrus
#

hmm i dont get the root

#

,w x^2+4=0

flat frigateBOT
marsh walrus
#

without the root both answers make sense

frozen sluice
#

you have to substitute it back. now you have the solution for x^2, and to get it for x^4 you have to take the root again

#

but i might be doing something worng

marsh walrus
#

idk if you start from like 2i and then just solve x^2=2i

#

youll get out the two sensible solutions

#

same with -2i

#

these correspond well with the original solution set you got

#

like 2i=(i+i+1-1)=(1+i+i-1)=(1+i)(1+i)=(1+i)^2

frozen sluice
#

ah, so what i did was correct then

#

thanks

#

.close

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fleet saddle
#

I know I'm supposed to explain what I've tried and how far I've gotten, but I have basically no clue how to even approach these. A push in the right direction at minimum or a good explanation would be great.

half cove
#

f-1(x) = -2 ==> x = f(-2)

#

Then find x

safe radishBOT
#

@fleet saddle Has your question been resolved?

fleet saddle
#

Is that a known rule or just intuitively finding the inverse?

#

Also for the middle one do I just assume f(x)=x-5?

#

Never mind, that doesn't work.

safe radishBOT
#

@fleet saddle Has your question been resolved?

safe radishBOT
#

@fleet saddle Has your question been resolved?

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bitter geode
#

hi

safe radishBOT
bitter geode
#

look at this question

#

it is an right riemann sum approximation for a definite integral from 1 to 4

#

the function we are integrating is rf(r)

#

let's say we know r is increasing

#

and f(r) is also increasing

#

is that enough reason to say that their product (rf(r)) is also increasing?

sonic shoal
#

not necessarily

#

say f(r) = r

#

r f(r) = r^2

#

r, f(r) both increasing

#

r^2 not increasing in (-inf, 0)

#

is (rf(r))' > 0 ?

bitter geode
#

oh yeah I guess

#

wait but

#

well

#

yeah

#

ok what about this

#

(rf(r))' = f(r) + f(r)'r

#

since f(r) is increasing, f(r)' is positive

#

hence, f(r)'r is also increasing

sonic shoal
#

do you know exactly what f(r) is or do you only know that f(r) is increasing

bitter geode
#

it's a table

#

we know it's increasing from a table

sonic shoal
#

ah okay

bitter geode
#

so its derivative is positive

sonic shoal
#

can you limit the range of r?

bitter geode
#

the integral is from 1 to r

#

1 to 4*

#

so r is in [1, 4]

sonic shoal
#

is f(r) > 0 hopefully when r in [1, 4]

bitter geode
#

hence it's also positive and increasing

bitter geode
sonic shoal
#

yeah then (rf(r))' = f(r) + r f'(r)

#

and we know that f(r) > 0, r >0, f'(r) > 0

bitter geode
#

wait butt

sonic shoal
#

so (r f(r))' > 0

#

that's fine then

bitter geode
#

since they're both positive

#

over the interval

#

r*f(r) is always positive

#

and

#

r*f(r) is increasing

#

ah nvm

#

yeah the other way is much better

#

yeah trhanks

#

brother

sonic shoal
#

np

safe radishBOT
#

@bitter geode Has your question been resolved?

safe radishBOT
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stray granite
#

I want to find a cubic function with a y-intercept at 12,000, a minimum at (5, 6000), and a maximum at (10, 10000). I've tried ax^3 + bx^2 + cx + d and its derivative, but I can't get all of the equations into one system.

stray granite
#

.close

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lean otter
#

Ok, this is might be a very silly question but this isn't working for me. This is how the question goes, "If the unit price for almonds is $0.13 per oz, how much does a 3 pound tub cost?". Isn't the answer suppose to be $0.39? Because that what I got and the answer to the problem is $6.24. Is there a step that I am missing because I'm just using cross multiplication. Thanks.

frigid geyser
#

check units

#

a pound is 16 ounces iirc

lean otter
#

wow, ok

#

I didn't think that they would use that in way

#

thanks

#

.close

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spark lagoon
safe radishBOT
spark lagoon
#

How do you get the domain?

plucky elk
sonic shoal
#

you can start from the fact that a fraction is not defined if the denominator is zero

spark lagoon
#

.close

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next gulch
safe radishBOT
next gulch
#

i am trying to calculate this from x=0 to x= 10 with 5 rectangles only

#

the solution is above im trying to figure this out

#

what i do know so far

#

but im a little stumped as to where to go from here

#

do i have to plug x into this?

sonic shoal
#

you just find the area of each rectangle

inner tapir
#

essentially yes
but it looks scarier than it is

sonic shoal
#

and add them up

inner tapir
#

those function values are the heights of each rectangle

next gulch
#

right this makes sense let me try

ember bough
next gulch
sonic shoal
#

screen capture lol

ember bough
inner tapir
#

drag a region for the screenshot

next gulch
#

ohh yeah im not too familiar with this stuff

#

noted

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#

@next gulch Has your question been resolved?

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lean otter
#

$\int x^3e^x^2dx$

safe radishBOT
marsh walrus
#

almost did it again lol

#

$\int x^3 e^{x^2} \dd x$

lean otter
#

look man im new to this

flat frigateBOT
#

jan Niku

marsh walrus
#

ur good

lean otter
#

yeah but why the dd?

marsh walrus
#

it shouldnt be coded that way

marsh walrus
sonic shoal
#

wow \dd, fancy

marsh walrus
#

you can juste use dx

lean otter
#

okey thaks

#

thats what i did? .... kinda

marsh walrus
#

yea

#

you did

#

oo

lean otter
#

do i need to type the \ before the dx?

marsh walrus
#

nonelementary?

#

no

#

\dd x just makes it so the d is straight

#

$\dd x$ vs $dx$

flat frigateBOT
#

jan Niku

marsh walrus
#

anyways

#

wheres this integral from?

lean otter
#

from my book? or what do u mean?

sonic shoal
#

try substituting $t = x^2$

flat frigateBOT
#

xdk1235

lean otter
#

i did

sonic shoal
#

reading the integral as $\int x^3 e^{x^2} dx = \int \left(x^2 e^{x^2} \cdot x \right) dx$ might help

flat frigateBOT
#

xdk1235

marsh walrus
#

$\frac 1 2 \int u e^u \dd u$?

flat frigateBOT
#

jan Niku

lean otter
#

thats where im stuck, do i go ibp now?

sonic shoal
#

yes

#

but honestly i think ibp for that is kinda silly (this is how textbooks tell you to do)

#

$(x e^x)' = x e^x + e^x$ so you can kinda guess the answer from this

flat frigateBOT
#

xdk1235

marsh walrus
#

why does symbo and IC think this needs erfi thonk

#

oh, symbo gets it correct

#

weird

lean otter
#

solved it now, thanks guys

#

i had the answer but didnt know how to solve it

lean otter
safe radishBOT
#

@lean otter Has your question been resolved?

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lean otter
safe radishBOT
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stoic pilot
#

$NN(x) = \sigma ( w^{(3)} \sigma (w^{(2)} \sigma ( w^{(1)} x + b^{(1)} ) + b^{(2)}) + b^{(3)} )$

$\pdv{NN}{x} = ?$

is this WA thing right or did I screw that up

flat frigateBOT
#

THEBIGTHREE

stoic pilot
#

shit thats right isnt it

#

fml

#

.close

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gleaming yacht
#

Hello.
How can I find the number of perfect squares between two number?

ember bough
gleaming yacht
ember bough
lean otter
#

The squares r huge

ember bough
lean otter
#

The values I am getting are 2559999 and 6250001

ember bough
lean otter
#

Then how to solve?

ember bough
#
  1. find the highest possible a^2 in the interval
  2. find the lowest possible b^2 in the interval
  3. find the number of numbers between a and b inclusive
lean otter
#

Getting 3690002

ember bough
#

it's literally the easiest thing in the world

lean otter
#

OH

#

I get it

gleaming yacht
sleek sparrow
#

Hello can I ask for help please?

gleaming yacht
#

.close

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zinc hearth
#

Alright so about these I just don't know how to start and go from there so if we can go through them at least somewhat completely so I can grab the fundamentals that would be great!

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#

@zinc hearth Has your question been resolved?

zinc hearth
#

<@&286206848099549185>

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@zinc hearth Has your question been resolved?

zinc hearth
#

.close

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safe radishBOT
knotty sigil
#

what have u tried

#

do u know the radius of the circle

knotty sigil
#

i dont care

#

tell me what u have tried

knotty sigil
#

arc length = central angle x radius

#

apply this u get ur answer

#

dude i already told u

#

arc length = central angle x radius
apply this u get ur answer

#

arc length = central angle x radius

#

that they must give

#

or assume it as r

#

55

#

take it as r

thin bridge
#

apply the definition / relation between the central angle and the measure of the respective arc

#

(note that you aren't being asked for arc length)

safe radishBOT
#

@lean otter Has your question been resolved?

crisp latch
#

@lean otter arc length formula is (a/360) ( 2 pi r )

thin bridge
#

apply the definition / relation between the central angle and the measure of the respective arc
(note that you aren't being asked for arc length)

#

where does it say that

safe radishBOT
#
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fervent igloo
#

A recursion equation is determined by:
[pic]
a) Show that the equation can be written in the form y_n + 1 = a · y_n
b) write down all the solutions to the equation
c) determine the solution to the equation that satisfies that y0 = 6

fervent igloo
#

So I'm kind of new to this, so I need guidance for this

safe radishBOT
#

@fervent igloo Has your question been resolved?

quasi bison
#

are you able to isolate $y_{n+1}$ from the equatoin $9y_{n+1} - 3y_n = 0$?

flat frigateBOT
fervent igloo
quasi bison
#

"able" and "allowed" are two different things

fervent igloo
#

well I can yes

quasi bison
#

so do it

fervent igloo
#

so 9 - 3y_n = y_n+1

quasi bison
#

???

#

how did you get that?

fervent igloo
#

or should 9 follow with y_n+1

#

im lost ig

#

idk how to isolate

stoic dune
#

Isolate y in:
9y - 3x = 0

fervent igloo
#

then divide with 9 on both sides?

stoic dune
#

Now that you have that, you can see a clearer pattern. What function gets multiplied by 1/3 every increase in n?

fervent igloo
#

y_n

#

or y

stoic dune
#

True lol. I mean, polynomial? Trig? Exponential? Logarithmic?

fervent igloo
#

oh uhm

#

exponential?

#

or linear

stoic dune
#

Linear would be adding something every n

#

Exponential was good, where something gets multiplied every n

#

Namely, (1/3)ⁿ works

fervent igloo
#

aa makes sense

#

I can also use 3^-1 instead of 1/3

#

right?

safe radishBOT
#

@fervent igloo Has your question been resolved?

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lean otter
#

How would we find the range

safe radishBOT
lean otter
#

Can anyone help pls

safe radishBOT
#

@lean otter Has your question been resolved?

opaque sentinel
#

f(x) is decreasing for all x

#

so maximum value will be at x = 5

#

and minimum will be the asymptote at x = infinity

#

range will be b/w them

safe radishBOT
#

@lean otter Has your question been resolved?

safe radishBOT
#
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slate holly
#

I need help for an equation : (-10)-(11,3*x)+(2,67*x^2)=y and i need X in function of Y

slate holly
#

Could anyone help with this please ?

zinc crown
#

use the quadratic formula

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move y to the x side and then use the quadratic formula

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assuming that (-10 - y) = c

sonic shoal
#

huh are these all vectors or

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ahh you use , for the decimal point ig

slate holly
#

yeah these are decimal points lol

slate holly
#

yes

#

.close

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slate holly
#

.reopen

safe radishBOT
#

slate holly
#

except how am i supposed to find the delta

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how am i supposed to know it's positive

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@zinc crown :/

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also Y never goes under 0

zinc crown
#

wait what

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you have to use the + or - notation

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if you want x as a function of y

slate holly
#

i mean for the quadratic formula

zinc crown
#

,w graph 2.67x^2 - 11.3x -10 = y

flat frigateBOT
zinc crown
#

wait wdym a delta?

#

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

slate holly
#

this

flat frigateBOT
#

Yottachad

slate holly
#

yeah ik that

zinc crown
#

well y isn't defined for x values < ~ -23

#

so you don't have to worry about the square root because it would simply be not in the domain of x(y)

slate holly
#

but what guarantees me that b²-4ac will always be positive

#

okok

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nice

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thanks

zinc crown
#

yeah

slate holly
#

gonna try that

zinc crown
# flat frigate

see how the function isn't defined for some y values (that is, it doesn't drop below a certain point)?

#

so we could simply say that our x of y function doesn't have those y values in its domain

safe radishBOT
#

@slate holly Has your question been resolved?

#
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west bison
#

How do I find the resultant force on the right hand side

west bison
#

<@&286206848099549185>

worthy hemlock
west bison
#

Well both but if you explain one of them I’ll know how to di the other

worthy hemlock
#

What's the question asking for?

west bison
#

Magnitude and direction of the resultant force

worthy hemlock
#

That force that is straight down, find the x and y components of that force

#

With respect to the box

#

Then sum up the x forces and the y forces, find the magnitude, then angle

west bison
#

Thanks mate

#

.close

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rancid solstice
#

I’m trying to find the equation used to solve for this sequence but it’s been years since I solved for something like this and even something as simple as this eludes me.
Here’s what I know: the sequence decreases by a set value (at first this value seems to be 10%) then +40 is added and the number decreases by a set value again.

rancid solstice
#

What I’ve tried: I solved for the percent each set goes down by then when I got to the end of the set I calculated the amount it decreased by 707 and divided it by the original number thinking it’s supposed to tell me something I’m not sure what but that did not work. It’s possible that +40 being added to the number chain is being ignored when it decreases by a set value but wouldn’t that have a bigger impact on the larger number and the effect would decrease as the numbers got smaller idk even this simple stuff makes the gears in my head screech to a grinding halt

safe radishBOT
#

@rancid solstice Has your question been resolved?

rancid solstice
#

<@&286206848099549185>

safe radishBOT
#

@rancid solstice Has your question been resolved?

safe radishBOT
#

@rancid solstice Has your question been resolved?

plucky elk
#

@rancid solstice I don't know what you're asking. Can you rephrase your question with only the minimal details

rancid solstice
#

@plucky elk point A is 2583 and point B is 0 how did I get from A to B

#

The sequence is written on that paper but it goes

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2583
2325
+40 2365
2106
+40 2146
1860
+40 1900
1502
+40 1542
835
+40 875
0

safe radishBOT
#

@rancid solstice Has your question been resolved?

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rancid solstice
#

2583
2325
+40 2365
2106
+40 2146
1860
+40 1900
1502
+40 1542
835
+40 875
0
Of this sequence how do I find what it is decreasing by

steel stag
#

idk what those numbers mean, you're just adding 40

rancid solstice
#

So the start is 2583 then it decreases to 2325

#

Then 40 is added and it decreases to 2106

steel stag
#

ok it seems to be decreasing by different amounts, so you'd need more context to know what's happening

rancid solstice
#

What context do I need?

plucky elk
lean otter
#

@rancid solstice give us the exact question

rancid solstice
#

It’s not an exact question nor is it any sort of homework. I could post a video that might give more context but I’m not sure it will help with the math

plucky elk
#

No one's gonna watch a video lol

rancid solstice
#

It’s 15 seconds long

#

Alright let me put it like this you have 2583 health after one second it drops to 2325 then you gain 40 back leaving you with 2365 then another second passes and your health decreases to 2106 and gain 40 back

#

That is all the context I can give in words because that is all the information I have

lean otter
#

Bruh

#

Is this a question from a video game

rancid solstice
#

Yes

#

I remember there is pre calc math or algebra II math that’s supposed to allow you to work out equations by graphing them and running the numbers thru a specific method but I can’t remember how

#

@lean otter is this not what the channels are supposed to be used for

lean otter
#

I’m sorry I’m not interested in this

rancid solstice
#

Lol

#

@lean otter can you tell me the name of math that would be used to solve for this so I can look it up

rancid solstice
lean otter
#

Oh

#

It is basically this

#

Nvm it’s not an AP either

#

It’s some weird shit

#

I thought it was a sequence with an AP and +40 stitched together

#

But nope

rancid solstice
#

No I’m not sure it would be an arithmetic process I want to say the equation y=abX is useful for modeling the relationship and somehow you can do some number wizardry to magic the numbers for the equation up

safe radishBOT
#

@rancid solstice Has your question been resolved?

#
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little mountain
#

(10^(10^76)*((10^(10^100))^(10^185))
How can I express this as a single power tower?

ancient escarp
#

for what possible reason may i ask

#

you might as well write infinity

safe radishBOT
#

@little mountain Has your question been resolved?

quasi bison
#

@little mountain can you write your thing out on paper? the parentheses look a little cluttered

#

actually your parentheses are unbalanced opencry

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undone fiber
#

Can someone solve this puzzle. I am doing this from past 2 days. Anyone knows the answer?
U can only move top cube it means u are not allowed to move two cubes simultaneously or cubes below the top cube. Just top one on the stack you can move. find number of moves

undone fiber
meager chasm
#

wdym by moving?

safe radishBOT
#

@undone fiber Has your question been resolved?

undone fiber
#

Moving= taking the top cube and placing it on any of the stacks

#

<@&286206848099549185>

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#

@undone fiber Has your question been resolved?

safe radishBOT
#
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ruby cloak
#

<@&286206848099549185> I need help doing this problem

lean otter
#

Use the Quadratic formula

ruby cloak
#

What’s my friend

#

Can you tech me foil formula

safe radishBOT
#

@ruby cloak Has your question been resolved?

ruby cloak
#

No

#

@vocal rampart I need help

#

<@&286206848099549185> I need help

quiet vector
#

@ruby cloak u still need help?

ruby cloak
#

Yes I do

#

Please help me factor this

#

@quiet vector

#

You there

#

I need help

quiet vector
#

so do u know what the quadratic formula is?

ruby cloak
#

No

#

Nobody wants to teach me 😔

quiet vector
#

i can teach you but i haven't used it in like... 2+ years so i might be a bit rusty

ruby cloak
#

It’s fine

quiet vector
#

k so this is it

ruby cloak
#

Is there easier method

#

Foil method how about ?

quiet vector
#

and in ur quadratic a is the number before x^2, b is the number before x, and c is the number on it's own

#

this is the easiest method

#

it isn't possible to do another method with ur quadratic i don't think

ruby cloak
#

Can you write my equation into that formula

quiet vector
#

at least not with ease

#

well u need a calculator to do it

#

but first tell me what a b and c are

#

like i said, a is before x^2, b is before x and c is the number on it's own

ruby cloak
#

But I did like this

quiet vector
#

just a sec, i need 2 check something

ruby cloak
#

K

quiet vector
#

ok i'm back

#

there is another method mb

#

like i said i'm rusty

#

ok so this is gonna be a bit hard to explain but i'll try my best

summer ice