#help-39 | Mathematics | Page 38

midnight haven Sep 17, 2023, 6:24 PM

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Alright ill just use the formulas instead

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thanks

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.close

pearl pondBOT Sep 17, 2023, 6:24 PM

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Channel closed

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cedar coyote Sep 17, 2023, 6:27 PM

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pearl pondBOT Sep 17, 2023, 6:27 PM

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cedar coyote

cedar coyote Sep 17, 2023, 6:28 PM

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I am trying to save this linear diff eq

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I put it in the correct form i think

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But i am not sure this is correct because if i differentiate the right side I get an insanely long integral

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Which typically means i did something wrong lol

pearl pondBOT Sep 17, 2023, 6:43 PM

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@cedar coyote Has your question been resolved?

cedar coyote Sep 17, 2023, 6:44 PM

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<@&286206848099549185>

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i have asked for help on diff eq multiple time for past week and no one ever answers

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is this server not for diff eq?

sudden charm Sep 17, 2023, 6:45 PM

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cedar coyote I am trying to save this linear diff eq

u mean solve?

cedar coyote Sep 17, 2023, 6:46 PM

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yes

sudden charm Sep 17, 2023, 6:47 PM

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line 3

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$x^{12} / x = x^{11}$

jolly parrotBOT Sep 17, 2023, 6:47 PM

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Secret

sudden charm Sep 17, 2023, 6:47 PM

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u wrote x^2

cedar coyote Sep 17, 2023, 6:47 PM

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oh yea my bad

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ok but i would still be left with a crazy integral though

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because if we multiply everything by p(x)

sudden charm Sep 17, 2023, 6:48 PM

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cedar coyote ok but i would still be left with a crazy integral though

yeah

cedar coyote Sep 17, 2023, 6:48 PM

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then we would have 3 functions

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and i basically fell into and endless loop of doing integration by parts

sudden charm Sep 17, 2023, 6:49 PM

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cedar coyote and i basically fell into and endless loop of doing integration by parts

actually
there's a niche trick to do series of integration by parts

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i think it's called DI method

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https://www.youtube.com/watch?v=2I-_SV8cwsw

YouTube

blackpenredpen

integration by parts, DI method, VERY EASY

Integration by parts by using the DI method! This is the easiest set up to do integration by parts for your calculus 2 integrals. We will also do 3 integrals to illustrate the 3 stops of the DI method.

Dear calculus teachers, please let students use the DI Method (& why it is really the same as integration by parts) 👉 https://youtu.be/8xPfNuXLS...

▶ Play video

cedar coyote Sep 17, 2023, 6:49 PM

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ive heard of it but the reason i didnt do it

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is because it doesnt work with e

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so i didnt learn it

sudden charm Sep 17, 2023, 6:50 PM

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hmm

cedar coyote Sep 17, 2023, 6:50 PM

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there were some eweird restrictions

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with this trick

sudden charm Sep 17, 2023, 6:50 PM

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riggt it doesn't work

cedar coyote Sep 17, 2023, 6:50 PM

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i remember

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u see the dillema

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and if i do integration by parts normally

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i just am stuck integrating by parts over and over again

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and it doesnt help that online calculators or atleast the ones i use cant solve it

sudden charm Sep 17, 2023, 6:51 PM

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yes lmao

cedar coyote Sep 17, 2023, 6:51 PM

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but did i set up the problem correctly?

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because that was my concern

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i feel like there might be an issue with the way i set it up

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is it even a linear diff eq to begin with

sudden charm Sep 17, 2023, 6:52 PM

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maybe u can write it as
$$( \frac{x}{3} )^11 \cos x

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$$\left( \frac{x}{3} \right)^11 \cos x$$

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$$\left( \frac{x}{3} \right)^{11} \cos x$$

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ok im just terrible lmao

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that should be e^x

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in the denominator

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$$\left( \frac{x}{e^x} \right)^{11} \cos x$$

jolly parrotBOT Sep 17, 2023, 6:53 PM

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Secret

cedar coyote Sep 17, 2023, 6:54 PM

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oh like

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ok so you are saying

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wait

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i dont understand the e^x

sudden charm Sep 17, 2023, 6:56 PM

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lmao i dint notice
but the P(x) is wrong

cedar coyote Sep 17, 2023, 6:56 PM

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would it not be whatever is in front of the y

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yea see i thought there was something incorrect with my setup

sudden charm Sep 17, 2023, 6:57 PM

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differentiate the final equation with respect to x and u will notice

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$$ \frac{d}{dx} e^{-11x} y = \frac{dy}{dx} e^{-11x} - 11 y e^{-11x} $$

jolly parrotBOT Sep 17, 2023, 6:58 PM

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Secret

sudden charm Sep 17, 2023, 6:59 PM

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but u need a
$$ \frac{dy}{dx} - 11 \frac{y}{x}$$

jolly parrotBOT Sep 17, 2023, 6:59 PM

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Secret

cedar coyote Sep 17, 2023, 6:59 PM

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hm

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this is what im going based off of

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here they derived p(x) using whatever was in front of the y

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in this case it is -11

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and if u integrate that

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that would be e^-11x

sudden charm Sep 17, 2023, 7:01 PM

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no

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in this case it's -11/x

cedar coyote Sep 17, 2023, 7:01 PM

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ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

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ok ok

sudden charm Sep 17, 2023, 7:02 PM

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lol there there

cedar coyote Sep 17, 2023, 7:04 PM

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ok so

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x^-11?

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making sure i did that right

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im kind of rust on the natural log stuff

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when i did p(x)

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i got e^(integral of -11/x)

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and then got e^-11lnx

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e and ln would cancel out and i think it becomes x^-11 iirc

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yea?

cedar coyote Sep 17, 2023, 7:42 PM

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<@&286206848099549185>

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This is a similar problem i am doing

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Question is

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My answer is almost correct

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Correct answer is what I got but without a denominator

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please help me someone

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.close

pearl pondBOT Sep 17, 2023, 7:50 PM

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sudden charm Sep 17, 2023, 7:54 PM

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cedar coyote

yes this looks right

pearl pondBOT Sep 17, 2023, 7:54 PM

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sudden charm yes this looks right

sudden charm Sep 17, 2023, 7:56 PM

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.reopen

sudden charm Sep 17, 2023, 7:56 PM

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cedar coyote

here when ur simplifying the LHS
u don't have -13

sudden charm Sep 17, 2023, 7:56 PM

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cedar coyote

same here
u won't have a -11

cedar coyote Sep 17, 2023, 7:57 PM

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Why?

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Because of product rule

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Is it not -13y

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Or -11 y

sudden charm Sep 17, 2023, 8:00 PM

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no

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$$ x^-13 \frac{dy}{dx} - \frac{13y}{x} x^{-13} = \frac{d}{dx} y x^{-13} $$

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$$ x^-{13} \frac{dy}{dx} - \frac{13y}{x} x^{-13} = \frac{d}{dx} y x^{-13} $$

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$$ x^{-13} \frac{dy}{dx} - 13 x^{-12} \frac{y} = \frac{d}{dx} y x^{-13} $$

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$$ x^{-13} \frac{dy}{dx} - 13 x^{-12} y = \frac{d}{dx} y x^{-13} $$

jolly parrotBOT Sep 17, 2023, 8:02 PM

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Secret

cedar coyote Sep 17, 2023, 8:03 PM

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so basically

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it is just integrating factor*y

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because if we differentiate -11yx^-13

cedar coyote Sep 17, 2023, 8:03 PM

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jolly parrot **Secret**

we dont get this if we differentiate that

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however

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if we differentiate yx^-13

cedar coyote Sep 17, 2023, 8:03 PM

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jolly parrot **Secret**

then we obtain this

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which must mean

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the shortcut for this prodcut rule

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is just integrating factor*y(no matter what y has in front of it)?

sudden charm Sep 17, 2023, 8:04 PM

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yeah

cedar coyote Sep 17, 2023, 8:04 PM

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ok ok

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i think i understand now

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i need to be careful on what what is my integrating factor which is what i messed up on earlier

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and for product rule it is always just p(x)*y

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i think those 2 things

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was what i need to fix

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thanks

sudden charm Sep 17, 2023, 8:05 PM

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yeah

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no probs

cedar coyote Sep 17, 2023, 8:05 PM

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i was struggling with this for a while so u saved my ass

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hopefully exam goes well on wed

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have a good day

sudden charm Sep 17, 2023, 8:06 PM

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cedar coyote i was struggling with this for a while so u saved my ass

no probs mate
happens

sudden charm Sep 17, 2023, 8:06 PM

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cedar coyote hopefully exam goes well on wed

good luck

sudden charm Sep 17, 2023, 8:06 PM

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cedar coyote have a good day

u too

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night tho

cedar coyote Sep 17, 2023, 8:07 PM

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oh ok

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good night then

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its 1pm here for me

sudden charm Sep 17, 2023, 8:07 PM

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its around 1am lmao

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.close

pearl pondBOT Sep 17, 2023, 8:08 PM

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pearl pondBOT Sep 17, 2023, 9:41 PM

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glossy hedge Sep 17, 2023, 9:43 PM

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I understand that k< 3/4, but how do u get 0 <or= k

Screenshot_2023-09-17-22-40-38-882_com.sharpened.androidfileviewer.jpg

pearl pondBOT Sep 17, 2023, 9:43 PM

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glossy hedge I understand that k< 3/4, but how do u get 0 <or= k

plush bramble Sep 17, 2023, 9:48 PM

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glossy hedge I understand that k< 3/4, but how do u get 0 <or= k

!show

pearl pondBOT Sep 17, 2023, 9:48 PM

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glossy hedge I understand that k< 3/4, but how do u get 0 <or= k

Show your work, and if possible, explain where you are stuck.

glossy hedge Sep 17, 2023, 9:55 PM

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plush bramble !show

plush bramble Sep 17, 2023, 9:55 PM

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I see

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When you divided by k, you assumed k>0

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Otherwise you'd be dividing by zero or would need to flip the inequality sign

glossy hedge Sep 17, 2023, 9:57 PM

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Ohhhh that makes sensee

glossy hedge Sep 17, 2023, 9:57 PM

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plush bramble Otherwise you'd be dividing by zero or would need to flip the inequality sign

So what should I do instead?

remote roost Sep 17, 2023, 9:58 PM

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Think

plush bramble Sep 17, 2023, 10:00 PM

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glossy hedge So what should I do instead?

You already proved k>0

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And assumed k is nonzero

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I'd go with factoring

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4k^2-3k = k * (...)

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Since that must be negative, the two numbers being multiplied must have opposite signs

pearl pondBOT Sep 17, 2023, 10:12 PM

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@glossy hedge Has your question been resolved?

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glossy hedge Sep 17, 2023, 10:15 PM

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Thanks

pearl pondBOT Sep 17, 2023, 10:15 PM

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shy ginkgo Sep 17, 2023, 10:15 PM

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pearl pondBOT Sep 17, 2023, 10:15 PM

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shy ginkgo

shy ginkgo Sep 17, 2023, 10:15 PM

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can someone help me find lim x->-infinity f(x)

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sin(x) osilicates between -1 and 1 i believe, and since the denominator is infinitely small, sin(x)/x becomes infinitely large?

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so if 1 is infinitely large is it infinity?

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but it also osilates to -1

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so -infinity?

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idk

autumn narwhal Sep 17, 2023, 10:18 PM

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The denominator gets larger, not smaller

shy ginkgo Sep 17, 2023, 10:18 PM

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oh

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wait but its -infinity on the denominator

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-infinity is infitely small

autumn narwhal Sep 17, 2023, 10:20 PM

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Well I meant in absolute value.

shy ginkgo Sep 17, 2023, 10:20 PM

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wah

autumn narwhal Sep 17, 2023, 10:20 PM

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When you divide by something that's approaching -infinity or infinity, you get a number close to 0.

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For example, 1/(-1000000000) is very close to 0

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And so is 1/10000000000

shy ginkgo Sep 17, 2023, 10:22 PM

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so if the denominator is infinity it becomes infinitely small (0) and if the denominator is -infinity it becomes infinitely large...?

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the -infinity is messing me up

west sapphire Sep 17, 2023, 10:22 PM

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it might be helpful to consider |f(x)| instead of f(x)

shy ginkgo Sep 17, 2023, 10:24 PM

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so the - doesn't matter?

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or does it just make the infinitely small value (0) negative? but 0 can't be negative obv

west sapphire Sep 17, 2023, 10:25 PM

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the - doesn't matter in the special case where the result is 0

shy ginkgo Sep 17, 2023, 10:25 PM

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alr now that makes sense

west sapphire Sep 17, 2023, 10:25 PM

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basically f(x) -> 0 if and only if |f(x)| -> 0

shy ginkgo Sep 17, 2023, 10:26 PM

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oop oke ty

west sapphire Sep 17, 2023, 10:26 PM

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more generally:
f(x) -> L if and only if |f(x) - L| -> 0

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here L=0

shy ginkgo Sep 17, 2023, 10:26 PM

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yeh thats how it says it in the textbook

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oke ty

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.close

pearl pondBOT Sep 17, 2023, 10:27 PM

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pearl pondBOT Sep 18, 2023, 1:15 AM

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analog topaz Sep 18, 2023, 1:16 AM

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Whats a trick to graphing 1/3x^2 +8x +36. I want to find a way to get rid of the fraction in front?

pearl pondBOT Sep 18, 2023, 1:16 AM

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analog topaz Whats a trick to graphing 1/3x^2 +8x +36. I want to find a way to get rid of the...

analog topaz Sep 18, 2023, 1:16 AM

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analog topaz Whats a trick to graphing 1/3x^2 +8x +36. I want to find a way to get rid of the...

Could I just multiply by 3 to the entire thing to get rid of 1/3

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But if I did that then the graph wouldn't be similar to the orginial graph

analog topaz Sep 18, 2023, 1:17 AM

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analog topaz Whats a trick to graphing 1/3x^2 +8x +36. I want to find a way to get rid of the...

Or should I just convert this into vertex form?

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.close

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blissful briar Sep 18, 2023, 1:44 AM

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calculus help

pearl pondBOT Sep 18, 2023, 1:44 AM

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blissful briar calculus help

blissful briar Sep 18, 2023, 1:44 AM

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#

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i already have the instant rc formula written but im not sure where to go from hjere

pearl pondBOT Sep 18, 2023, 1:59 AM

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@blissful briar Has your question been resolved?

blissful briar Sep 18, 2023, 2:00 AM

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<@&286206848099549185>

dusty patio Sep 18, 2023, 2:03 AM

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(g(1.001)-g(0.999))/(5.004-4.996)

blissful briar Sep 18, 2023, 2:07 AM

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how does that work?

pearl pondBOT Sep 18, 2023, 2:37 AM

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@blissful briar Has your question been resolved?

blissful briar Sep 18, 2023, 3:12 AM

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<@&286206848099549185>

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dusty patio Sep 18, 2023, 3:14 AM

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I mean (g(1.001)-g(0.999))/(1.001-0.999)

blissful briar Sep 18, 2023, 3:15 AM

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i see

pearl pondBOT Sep 18, 2023, 4:15 AM

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rustic hawk Sep 18, 2023, 3:21 PM

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I’m not sure how to do this do I do it by integration of parts and how do I start

pearl pondBOT Sep 18, 2023, 3:21 PM

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rustic hawk I’m not sure how to do this do I do it by integration of parts and how do I star...

worldly glacier Sep 18, 2023, 3:28 PM

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rustic hawk I’m not sure how to do this do I do it by integration of parts and how do I star...

Start with a u substitution

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Oh wait

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Integration by parts

pearl pondBOT Sep 18, 2023, 3:36 PM

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@rustic hawk Has your question been resolved?

pearl pondBOT Sep 18, 2023, 4:13 PM

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@rustic hawk Has your question been resolved?

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rancid laurel Sep 18, 2023, 5:01 PM

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I'm not doing a maths question, but I just wanted to have some help in understanding: Why do the integration and differentiation formulae work? I've watched the 3b1b videos and I understand the theory of differntiation and integration, I understand the rate of change and the accumulated change, and adding up infinitesimals, I just don't understand the formulae that are used

pearl pondBOT Sep 18, 2023, 5:01 PM

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rancid laurel I'm not doing a maths question, but I just wanted to have some help in understan...

rancid laurel Sep 18, 2023, 5:01 PM

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the formulae:

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$$ Differentiation: x*n^{x-1}, Integration: \frac{n^{x+1}}{x+1}$$

jolly parrotBOT Sep 18, 2023, 5:02 PM

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panica5193

plush bramble Sep 18, 2023, 5:08 PM

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rancid laurel the formulae:

https://tutorial.math.lamar.edu/classes/calci/DerivativeProofs.aspx
For derivatives

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And use fundamental theorem of calculus for integration

rancid laurel Sep 18, 2023, 5:09 PM

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plush bramble https://tutorial.math.lamar.edu/classes/calci/DerivativeProofs.aspx For derivati...

wait im not actually too sure about the limits part

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how does that work?

plush bramble Sep 18, 2023, 5:16 PM

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...

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You should learn limits first

plush bramble Sep 18, 2023, 5:16 PM

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rancid laurel how does that work?

https://www.khanacademy.org/math/calculus-1/cs1-limits-and-continuity

Khan Academy

Limits and continuity | Calculus 1 | Math | Khan Academy

rancid laurel Sep 18, 2023, 5:17 PM

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thanks

pearl pondBOT Sep 18, 2023, 5:32 PM

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@rancid laurel Has your question been resolved?

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gusty prism Sep 18, 2023, 5:49 PM

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pearl pondBOT Sep 18, 2023, 5:49 PM

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gusty prism

gusty prism Sep 18, 2023, 5:49 PM

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shouldnt the set up be 7.5+s=.25(75+s)

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daring abyss Sep 18, 2023, 6:59 PM

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Could anybody online help me with finding the limit of the function (2x)/(16-x^2) as x approaches -4 from the left. Also, the limit of (x-1)/(x^2-4) ax x approaches -2 from the right?

pearl pondBOT Sep 18, 2023, 6:59 PM

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daring abyss Could anybody online help me with finding the limit of the function (2x)/(16-x^2...

buoyant panther Sep 18, 2023, 7:01 PM

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Do you know concept of one-sided limits in general? Or methods of solving them?

daring abyss Sep 18, 2023, 7:04 PM

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I tried substituting x with the number that it's trying to approach.

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Like for this one.

buoyant panther Sep 18, 2023, 7:05 PM

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In this case it won't work because it gives 0 in the bottom, right

daring abyss Sep 18, 2023, 7:06 PM

#

I substituted x with -4, and got -8/0 as the answer.

#

But I know that we can't divide with 0.

buoyant panther Sep 18, 2023, 7:06 PM

#

but you can try numbers near to the -4 (from the left, so close to the -4 but less than it)

daring abyss Sep 18, 2023, 7:06 PM

#

Okay, I'll try it with my calculator.

buoyant panther Sep 18, 2023, 7:07 PM

#

e.g. -4.1, -4.05 etc. and try to determine what does it approach to

#

or alternative method is to look at denom function behaviour

daring abyss Sep 18, 2023, 7:08 PM

#

I inputed -4.1 and got 10.123 as the result.

#

What does 10.123 mean for my case?

daring abyss Sep 18, 2023, 7:08 PM

#

daring abyss But I know that we can't divide with 0.

I got stumped at this step and didn't know how to proceed.

buoyant panther Sep 18, 2023, 7:09 PM

#

generally when dealing with one sided limits we often get -inf or inf as a result (especially for rational functions)

#

10.123 means nothing so far

#

so you should try with numbers closer to the -4

daring abyss Sep 18, 2023, 7:09 PM

#

Oh, okay.

buoyant panther Sep 18, 2023, 7:10 PM

#

it's fine if you can use the calculator

daring abyss Sep 18, 2023, 7:10 PM

#

-4.01 resulted with 100.125

buoyant panther Sep 18, 2023, 7:10 PM

#

okay

daring abyss Sep 18, 2023, 7:10 PM

#

The numbers are increasing the closer I get to -4?

#

Why is that?

buoyant panther Sep 18, 2023, 7:11 PM

#

daring abyss The numbers are increasing the closer I get to -4?

yes that's what I was about to say

#

the closer we are to -4, the output is bigger and bigger

buoyant panther Sep 18, 2023, 7:12 PM

#

daring abyss Why is that?

this is because notice that for numbers close to -4 the denominator becomes less and less

#

dividing by really small number ---> huge result

daring abyss Sep 18, 2023, 7:12 PM

#

Yes, I think I can see that.

buoyant panther Sep 18, 2023, 7:13 PM

#

and now

#

thing is

#

we can deduce the result is +inf

daring abyss Sep 18, 2023, 7:13 PM

#

Ohhh

buoyant panther Sep 18, 2023, 7:13 PM

#

Yeah, exactly

daring abyss Sep 18, 2023, 7:14 PM

#

Nice, thank you.

buoyant panther Sep 18, 2023, 7:14 PM

#

I'll paste the graph

#

to visualize

daring abyss Sep 18, 2023, 7:14 PM

#

How would I write my answer on paper though?

buoyant panther Sep 18, 2023, 7:14 PM

#

daring abyss Sep 18, 2023, 7:14 PM

#

Do I substitute x with -4.01 or something?

buoyant panther Sep 18, 2023, 7:15 PM

#

mhm, you can it below, I'd rewrite only the result or

daring abyss Sep 18, 2023, 7:16 PM

#

This was my answer earlier.

rn_image_picker_lib_temp_41fd3a32-5b54-46ca-b912-82fdf9e78702.jpg

buoyant panther Sep 18, 2023, 7:16 PM

#

$$\lim_{x \to -4^-}\frac{2x}{16-x^2}=\Big[\frac{-8}{0^{-}}\Big]=+\infty$$

#

This is notation I used to use

daring abyss Sep 18, 2023, 7:18 PM

#

How did you get 0+ as the denominator?

buoyant panther Sep 18, 2023, 7:18 PM

#

sorry, mb

jolly parrotBOT Sep 18, 2023, 7:18 PM

#

Modus

daring abyss Sep 18, 2023, 7:19 PM

#

0-?

buoyant panther Sep 18, 2023, 7:19 PM

#

0^- means denom is negative

#

when plugging numbers closer to -4

daring abyss Sep 18, 2023, 7:19 PM

#

Is it different from -0?

#

Wait, is it like the direction where x came from?

#

Since its 0^-, the 0 is approached from the left?

#

Did I get it right?

buoyant panther Sep 18, 2023, 7:21 PM

#

no, it's about sign, direction doesn't matter

daring abyss Sep 18, 2023, 7:22 PM

#

Ah, okay.

daring abyss Sep 18, 2023, 7:23 PM

#

jolly parrot **Modus**

If I were to write this on paper, do I write it directly straight?

buoyant panther Sep 18, 2023, 7:23 PM

#

I'd do that

#

and that's it basically

daring abyss Sep 18, 2023, 7:24 PM

#

I don't need to write it the middle of the solution?

daring abyss Sep 18, 2023, 7:24 PM

#

daring abyss I don't need to write it the middle of the solution?

This is just for example.

daring abyss Sep 18, 2023, 7:25 PM

#

buoyant panther and that's it basically

Ahh, I see.

#

So its that simple, I don't know why I'm trying to overcomplicate things.

buoyant panther Sep 18, 2023, 7:25 PM

#

in fact

#

if you know how graph of the denom looks like

#

(here if you can imagine the parabola 16 - x^2)

#

you can solve in a few seconds

#

without plugging anything

#

in fact

#

16 - x^2 = (4-x)(4+x)

#

zeros: x = -4, x = 4

daring abyss Sep 18, 2023, 7:27 PM

#

Does the limit of a function depend on the denominator?

buoyant panther Sep 18, 2023, 7:28 PM

#

daring abyss Does the limit of a function depend on the denominator?

if we don't have zero in the numerator then yes

#

it's only about the bottom part

#

in fact

daring abyss Sep 18, 2023, 7:28 PM

#

Thank you.

#

#

Then this one should be the same process then?

buoyant panther Sep 18, 2023, 7:29 PM

#

yeah

#

exactly same process

#

but from the right

daring abyss Sep 18, 2023, 7:29 PM

#

Are the zeroes 2, -2?

buoyant panther Sep 18, 2023, 7:30 PM

#

yeah, and a = 1 (leading coeff)

#

so you can easily decide if it's 0^+ or 0^-

#

in the denom

daring abyss Sep 18, 2023, 7:31 PM

#

buoyant panther yeah, and a = 1 (leading coeff)

by leading coefficient, you mean the invisible 1 beside x^2? 1x^2?

buoyant panther Sep 18, 2023, 7:31 PM

#

ye

#

#

look at -2

#

from the right

#

values are negative, right?

#

you see that?

daring abyss Sep 18, 2023, 7:33 PM

#

Uh, wait.

buoyant panther Sep 18, 2023, 7:33 PM

#

if not, then try plugging -1.9, -1.95 etc.

daring abyss Sep 18, 2023, 7:34 PM

#

from the right of -2, are positive number though?

#

Oh wait, they are still negative up to 0

daring abyss Sep 18, 2023, 7:35 PM

#

buoyant panther if not, then try plugging -1.9, -1.95 etc.

okay, I'll try that.

daring abyss Sep 18, 2023, 7:37 PM

#

buoyant panther if not, then try plugging -1.9, -1.95 etc.

-1.9 gave me 7.436, -1.95 gave me 14.937

buoyant panther Sep 18, 2023, 7:37 PM

#

so it's increasing right

daring abyss Sep 18, 2023, 7:38 PM

#

yes

#

Then, the limit is -infinity right?

buoyant panther Sep 18, 2023, 7:39 PM

#

why?

#

whole fraction increases

#

so if we are closer and closer to -2

#

the result is bigger and bigger

#

up to +inf

#

for infinitely close numbers

daring abyss Sep 18, 2023, 7:40 PM

#

Ohhhh

#

if the numbers get bigger and bigger, the limit is positive infinity. And if the numbers become smaller and smaller, the limit is negative infinity.

buoyant panther Sep 18, 2023, 7:41 PM

#

yes

#

to see that you can try same example with x approaches to -2 from the left

#

you should get negative infinity

daring abyss Sep 18, 2023, 7:42 PM

#

Okay, I'll try.

#

-2.1 gave me -7.561, -2.01 gave me -75.062.

#

I can see that the numbers are decreasing the closer I get to -2.

#

Then, the limit should be -infinity right?

buoyant panther Sep 18, 2023, 7:45 PM

#

well

daring abyss Sep 18, 2023, 7:56 PM

#

rn_image_picker_lib_temp_70645a7b-e28e-44b5-a10c-c86bc322a39f.jpg

#

rn_image_picker_lib_temp_e20af8cd-c3be-43fc-b9ca-ae01b1f596ce.jpg

buoyant panther Sep 18, 2023, 7:57 PM

#

-3/0^+ -> -inf

#

it should be -3/0^-

#

because minus divded by minus gives +

daring abyss Sep 18, 2023, 7:59 PM

#

Uh, sorry I don't understand.

buoyant panther Sep 18, 2023, 8:00 PM

#

look at this

daring abyss Sep 18, 2023, 8:00 PM

#

0^+ should be 0^- because dividing what by minus gives +?

buoyant panther Sep 18, 2023, 8:01 PM

#

nope, because for -1.9, -1.95 etc. x^2 - 4 is negative

#

,calc (-1.9)^2 - 4

jolly parrotBOT Sep 18, 2023, 8:01 PM

#

Result:

-0.39

buoyant panther Sep 18, 2023, 8:01 PM

#

,calc (-1.95)^2 - 4

jolly parrotBOT Sep 18, 2023, 8:01 PM

#

Result:

-0.1975

buoyant panther Sep 18, 2023, 8:01 PM

#

,calc (-1.99)^2 - 4

jolly parrotBOT Sep 18, 2023, 8:01 PM

#

Result:

-0.0399

buoyant panther Sep 18, 2023, 8:01 PM

#

etc.

#

this is why it's 0^-

daring abyss Sep 18, 2023, 8:04 PM

#

Ah, I think I see it.

#

rn_image_picker_lib_temp_0fa5cd38-9676-410e-a62a-c734df7ec2a9.jpg

rn_image_picker_lib_temp_6a4aba7b-b623-4114-87f1-5f59173da907.jpg

#

Why does this give increasing numbers as it approaches -2?

#

I'm confused because of my calculator.

buoyant panther Sep 18, 2023, 8:07 PM

#

That's fine, don't confuse the whole fraction with only the denominator

daring abyss Sep 18, 2023, 8:07 PM

#

OHHH

#

I forgot that I was only solving for the denominator!

#

rn_image_picker_lib_temp_4877bce6-50f6-4ddf-9065-bdd74baf7eb3.jpg

rn_image_picker_lib_temp_6a208156-e0cc-42dd-97fd-d5bb5ba2bb1f.jpg

#

The denominator is increasing as it approaches-2.

buoyant panther Sep 18, 2023, 8:10 PM

#

here what matters is sign

#

not monotonicity

#

thing is values are negative, period

#

all in all, values of the whole fraction increases when x goes to -2
values of the denominator are negative when x goes to -2

#

it gives

jolly parrotBOT Sep 18, 2023, 8:12 PM

#

Modus

buoyant panther Sep 18, 2023, 8:14 PM

#

In fact the first information is sufficient to get the result, so you can just rewrite +infty and that's it

daring abyss Sep 18, 2023, 8:14 PM

#

Okay, I think I got it.

#

Thank you for all the help Modus, could I bother you with one more problem?

buoyant panther Sep 18, 2023, 8:18 PM

#

I don't mind

daring abyss Sep 18, 2023, 8:18 PM

#

Alright, thank you.

#

#

This is the problem

buoyant panther Sep 18, 2023, 8:18 PM

#

Let me guess, checking continuity?

daring abyss Sep 18, 2023, 8:19 PM

#

yes

#

This is a piecewise function right?

buoyant panther Sep 18, 2023, 8:19 PM

#

Yes

#

Okay, so can you sketch its graph?

#

It's about drawing three independent graphs for given intervals

daring abyss Sep 18, 2023, 8:20 PM

#

I probably can, it will take me sometime though because I'm learning it as I go.

#

Could you show me the graph for the first one?

buoyant panther Sep 18, 2023, 8:20 PM

#

Do you mean first part (interval)?

daring abyss Sep 18, 2023, 8:21 PM

#

the x-4 if x<-4

buoyant panther Sep 18, 2023, 8:22 PM

#

How to draw it:
It's a line. What do you need to draw a line? Only two points. Because there is exactly one line which passes through two different points.

daring abyss Sep 18, 2023, 8:22 PM

#

Its a linear function! I forgot lol

buoyant panther Sep 18, 2023, 8:22 PM

#

Let's take x = 0 and x = 4 for instance.
So the points are:
(0, -4) and (4, 0)

#

Plot them, connect, period.

daring abyss Sep 18, 2023, 8:23 PM

#

Okay.

buoyant panther Sep 18, 2023, 8:23 PM

#

daring abyss Sep 18, 2023, 8:24 PM

#

Ah I see.

buoyant panther Sep 18, 2023, 8:24 PM

#

Now for the restricted domain it would be

#

daring abyss Sep 18, 2023, 8:26 PM

#

buoyant panther

How did that happen?

buoyant panther Sep 18, 2023, 8:26 PM

#

Line is infinite. We cut it at x = - 4 (we take the part for x's less than -4)

daring abyss Sep 18, 2023, 8:27 PM

#

Ahh

#

Okay, I got it.

#

because x<-4 right?

buoyant panther Sep 18, 2023, 8:27 PM

#

exactly

daring abyss Sep 18, 2023, 8:30 PM

#

Okay, I'll try drawing it.

#

#

at x=-4, I got -8, and at x=4, I got 0

buoyant panther Sep 18, 2023, 8:41 PM

#

should be 0

#

at both

daring abyss Sep 18, 2023, 8:41 PM

#

Hmm?

buoyant panther Sep 18, 2023, 8:41 PM

#

(-4)^2 = 4^2 = 16

#

16 - 16 = 0

#

sqrt(0) = 0

daring abyss Sep 18, 2023, 8:42 PM

#

buoyant panther (-4)^2 = 4^2 = 16

wait, where did these come from?

#

Ohhh

#

Did it come from here?

buoyant panther Sep 18, 2023, 8:43 PM

#

yes

daring abyss Sep 18, 2023, 8:44 PM

#

This was meant for this

daring abyss Sep 18, 2023, 8:44 PM

#

daring abyss at x=-4, I got -8, and at x=4, I got 0

.

buoyant panther Sep 18, 2023, 8:44 PM

#

but you cannot plug x = -4 of x = 4 into that

#

is -4 < -4 or 4 < -4?

#

that's false

daring abyss Sep 18, 2023, 8:45 PM

#

buoyant panther is -4 < -4 or 4 < -4?

They're not, I see what you mean.

#

Modus, thanks for all the help. I need to go to sleep right now because I have a class at 8 am and the current time is 5 am 💀

pearl pondBOT Sep 18, 2023, 9:15 PM

#

@daring abyss Has your question been resolved?

pearl pondBOT Sep 18, 2023, 9:30 PM

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lapis flower Sep 18, 2023, 9:34 PM

#

pearl pondBOT Sep 18, 2023, 9:34 PM

#

lapis flower

#

Please don't occupy multiple help channels.

lapis flower Sep 18, 2023, 9:34 PM

#

help me

#

.

#

last summit Sep 18, 2023, 9:36 PM

#

lapis flower

!status

pearl pondBOT Sep 18, 2023, 9:36 PM

#

lapis flower

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

lapis flower Sep 18, 2023, 9:36 PM

#

1

last summit Sep 18, 2023, 9:36 PM

#

The question you posted isn't even a question

#

it is a statement

#

is there any more context you can provide?

lapis flower Sep 18, 2023, 9:37 PM

#

it asked the value of a

#

?

#

tell me please

midnight haven Sep 18, 2023, 9:40 PM

#

no it doesnt ask for the value of a

#

reread

lapis flower Sep 18, 2023, 9:41 PM

#

it does

midnight haven Sep 18, 2023, 9:41 PM

#

it does not

lapis flower Sep 18, 2023, 9:41 PM

#

it got the options too

last summit Sep 18, 2023, 9:41 PM

#

Show us what you are looking at

midnight haven Sep 18, 2023, 9:41 PM

#

send the options

lapis flower Sep 18, 2023, 9:41 PM

#

#

see

#

now ?

midnight haven Sep 18, 2023, 9:42 PM

#

you could try moving ax-2 to the right

#

and compare the coefficients

lapis flower Sep 18, 2023, 9:43 PM

#

can you show me a answer pic

midnight haven Sep 18, 2023, 9:43 PM

#

no?

lapis flower Sep 18, 2023, 9:43 PM

#

i want answer pic

last summit Sep 18, 2023, 9:44 PM

#

no one is going to give you the answer

#

we are here to help guide you, not to give answers

lapis flower Sep 18, 2023, 9:44 PM

#

ok

#

thanks

pearl pondBOT Sep 18, 2023, 9:59 PM

#

@lapis flower Has your question been resolved?

pearl pondBOT Sep 18, 2023, 10:14 PM

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pearl pondBOT Sep 18, 2023, 11:30 PM

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river aurora Sep 18, 2023, 11:34 PM

#

Could someone double check my work? This was kind of a mess of a question, so I'm not sure if I got all the parts right.

pearl pondBOT Sep 18, 2023, 11:35 PM

#

river aurora Could someone double check my work? This was kind of a mess of a question, so I'...

#

@river aurora Has your question been resolved?

pearl pondBOT Sep 19, 2023, 12:27 AM

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@river aurora Has your question been resolved?

pearl pondBOT Sep 19, 2023, 12:57 AM

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pearl pondBOT Sep 19, 2023, 1:21 AM

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west venture Sep 19, 2023, 1:22 AM

#

missed a day in class cause i got sick. help me with this please

pearl pondBOT Sep 19, 2023, 1:22 AM

#

west venture missed a day in class cause i got sick. help me with this please

shy thistle Sep 19, 2023, 1:25 AM

#

Drawing a picture helps a lot on these.

west venture Sep 19, 2023, 1:25 AM

#

way ahead of ya

#

still dont get it

shy thistle Sep 19, 2023, 1:26 AM

#

If you label the picture you've got 2x+10 combined with x-4, the total of which is 21. Can you write an equation for that?

west venture Sep 19, 2023, 1:27 AM

#

ohhhh

#

okay

#

i see

#

thank you sir

shy thistle Sep 19, 2023, 1:27 AM

#

cheers

west venture Sep 19, 2023, 1:27 AM

#

.close

pearl pondBOT Sep 19, 2023, 1:27 AM

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frozen estuary Sep 19, 2023, 1:47 AM

#

first blank would be 1 as pure nickel is 100%

#

2nd blank would be total weight which would be (6+x) mg

#

no that is incorrect. think about the filled and unfilled spaces in your equation

#

0.45 is purity multiplied by x which is weight

#

yes

pearl pondBOT Sep 19, 2023, 1:52 AM

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obtuse dagger Sep 19, 2023, 1:56 AM

#

Hey! Um just wondering if anyone could help me finding the height of the cliff? Here’s the question and the information it gave me

pearl pondBOT Sep 19, 2023, 1:56 AM

#

obtuse dagger Hey! Um just wondering if anyone could help me finding the height of the cliff? ...

shy thistle Sep 19, 2023, 1:57 AM

#

For what it's worth, the horizontal speed doesn't matter for finding the height.

#

Since you can break the problem up into the vertical bit and the horizontal bit.

obtuse dagger Sep 19, 2023, 1:59 AM

#

ohh

#

K thanks, I think I got it from here!

shy thistle Sep 19, 2023, 2:00 AM

#

cheers

obtuse dagger Sep 19, 2023, 2:00 AM

#

.close

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somber magnet Sep 19, 2023, 2:15 AM

#

Hello! I have 2 integrals that im having a bit of trouble with!

pearl pondBOT Sep 19, 2023, 2:15 AM

#

somber magnet Hello! I have 2 integrals that im having a bit of trouble with!

somber magnet Sep 19, 2023, 2:16 AM

#

Integral of x(1+x)^(1/2)

#

Integral of 1/(1+4x^2)

#

i cant use partial integration for these

#

just u sub

shy thistle Sep 19, 2023, 2:17 AM

#

I like u=1+x for 1.

somber magnet Sep 19, 2023, 2:17 AM

#

i tried that let me post the result

shy thistle Sep 19, 2023, 2:17 AM

#

(You'll need to use the fact that x=u-1 to change the x on the outside.)

somber magnet Sep 19, 2023, 2:18 AM

#

#

How does this look

shy thistle Sep 19, 2023, 2:19 AM

#

Basically what I was thinking. The teacher in me is getting grumpy about a missing du and some missing +c's but you know.

somber magnet Sep 19, 2023, 2:19 AM

#

yeah

#

i was rushing ill put them in

#

for the second integral i dont really know where to start

#

in my mind i feel like ln has to be there but given there would be nothing to solve the chain rule bit

shy thistle Sep 19, 2023, 2:21 AM

#

Like, it looks a lot like arctan doesn't it?

somber magnet Sep 19, 2023, 2:21 AM

#

yeah 1+u^2 maybe

#

how do i get tehre tho?

#

ooh

#

u

#

but in that case wouldnt dx =du/8w?

shy thistle Sep 19, 2023, 2:22 AM

#

$\int \frac{1}{1+4x^2} , dx = \int \frac{1}{1+(2x)^2} , dx$

#

Oh I forgot I wrote code in my LaTeX to do \dx. Anyway.

jolly parrotBOT Sep 19, 2023, 2:23 AM

#

Alti

somber magnet Sep 19, 2023, 2:23 AM

#

ah and then i sub 2x for u?

shy thistle Sep 19, 2023, 2:23 AM

#

That's what I'd do.

somber magnet Sep 19, 2023, 2:23 AM

#

i always forget i can do these algabraic tricks

#

hahaha

#

tyvm

shy thistle Sep 19, 2023, 2:24 AM

#

cheers

somber magnet Sep 19, 2023, 2:24 AM

#

just because ive never done this

#

is u=2x

#

yes

#

nvm i got it

#

so ulitmately i get to

#

1/2 *arctan(2x) +C

shy thistle Sep 19, 2023, 2:33 AM

#

Yeah that looks right.

#

,w integral of 1/(1+4x^2) dx

jolly parrotBOT Sep 19, 2023, 2:34 AM

#

Results provided by WolframAlpha

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shy thistle Sep 19, 2023, 2:34 AM

#

Hax.

somber magnet Sep 19, 2023, 2:35 AM

#

yay!

#

ty for the help!

#

.close

pearl pondBOT Sep 19, 2023, 2:35 AM

#

Channel closed

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midnight haven Sep 19, 2023, 8:45 PM

#

pearl pondBOT Sep 19, 2023, 8:45 PM

#

midnight haven

midnight haven Sep 19, 2023, 8:46 PM

#

if i want to define a set

#

do i use r^4 og r^3

#

i use r^4 because there r 4 equations or?

foggy mason Sep 19, 2023, 8:47 PM

#

x1 + x2 + 3x3 = x1 + x2 + 3x3 + 0 x4

midnight haven Sep 19, 2023, 8:47 PM

#

im asking

#

is is r^4

foggy mason Sep 19, 2023, 8:47 PM

#

midnight haven i use r^4 because there r 4 equations or?

R^4, because thats a vector with four variables you are searching

midnight haven Sep 19, 2023, 8:47 PM

#

since there r 4 equations

#

yes thank you

foggy mason Sep 19, 2023, 8:48 PM

#

not because there are 4 équations

last summit Sep 19, 2023, 8:48 PM

#

It is because there are 4 variables

midnight haven Sep 19, 2023, 8:48 PM

#

ok

#

but then can i not just add another

#

+0 5_x

#

0 6_x

last summit Sep 19, 2023, 8:48 PM

#

Yes but none of them have a non 0 of those

foggy mason Sep 19, 2023, 8:48 PM

#

^

midnight haven Sep 19, 2023, 8:48 PM

#

explain further

#

quite new to this ))

last summit Sep 19, 2023, 8:49 PM

#

There are clearly no x5, or higher terms in any of the equations

midnight haven Sep 19, 2023, 8:49 PM

#

i see

last summit Sep 19, 2023, 8:49 PM

#

Yet there is a nonzero value of x4

midnight haven Sep 19, 2023, 8:49 PM

#

yes okay

#

so you can add 0 values of the highest term presented

#

if that makes sense

#

in the terms missing

last summit Sep 19, 2023, 8:49 PM

#

Yes

#

But it would be useless to add 0 values of other variables that aren’t presented

midnight haven Sep 19, 2023, 8:50 PM

#

yes okay

#

would it be possible to do so

last summit Sep 19, 2023, 8:50 PM

#

Sure

midnight haven Sep 19, 2023, 8:50 PM

#

even if it'll only make it more difficult to solve

#

i'd suppose

last summit Sep 19, 2023, 8:50 PM

#

Right

#

So don’t do that

midnight haven Sep 19, 2023, 8:50 PM

#

i wont

#

ty

#

also

#

in the second term is goes x1 - x3 - x4

#

can i then add a x2

foggy mason Sep 19, 2023, 8:51 PM

#

0 x2

midnight haven Sep 19, 2023, 8:51 PM

#

a 0x_2 term

#

nice

pearl pondBOT Sep 19, 2023, 9:06 PM

#

@midnight haven Has your question been resolved?

pearl pondBOT Sep 19, 2023, 9:21 PM

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devout plinth Sep 19, 2023, 9:23 PM

#

can some1 help me with 5

pearl pondBOT Sep 19, 2023, 9:23 PM

#

devout plinth can some1 help me with 5

sick adder Sep 19, 2023, 9:26 PM

#

What do we know about angle <ABE already?

devout plinth Sep 19, 2023, 9:26 PM

#

OH

devout plinth Sep 19, 2023, 9:26 PM

#

sick adder What do we know about angle <ABE already?

ITS RIGHT ANGLE

sick adder Sep 19, 2023, 9:26 PM

#

See if you can use that to set up an equation in terms of X

devout plinth Sep 19, 2023, 9:28 PM

#

sick adder See if you can use that to set up an equation in terms of X

would i have to add them all

#

because i don’t understand how to find the angles from that

sick adder Sep 19, 2023, 9:29 PM

#

What does <ABE being right angle tell you about <ABD?

devout plinth Sep 19, 2023, 9:31 PM

#

sick adder What does <ABE being right angle tell you about <ABD?

it also equals to 90?

sick adder Sep 19, 2023, 9:33 PM

#

Yup

devout plinth Sep 19, 2023, 9:33 PM

#

okay i think i figured it out

pearl pondBOT Sep 19, 2023, 9:48 PM

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prime bramble Sep 20, 2023, 12:03 AM

#

pearl pondBOT Sep 20, 2023, 12:03 AM

#

prime bramble

prime bramble Sep 20, 2023, 12:03 AM

#

!status

pearl pondBOT Sep 20, 2023, 12:03 AM

#

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

prime bramble Sep 20, 2023, 12:03 AM

#

for b), 2 and for c), 1

#

I know that if h(x) is going to be injective then we assume that h(x1) = h(x2)

#

so that (x1)^2 = (x2)^2

#

but I've tried for a bit to get this to x1 = x2 which is what I want

#

and I cannot do it

pearl pondBOT Sep 20, 2023, 12:20 AM

#

@prime bramble Has your question been resolved?

prime bramble Sep 20, 2023, 12:21 AM

#

<@&286206848099549185>

acoustic spear Sep 20, 2023, 12:26 AM

#

prime bramble so that (x1)^2 = (x2)^2

From here and using 1) you have:
0 = (x1)^2-(x2)^2=(x1-x2)^2

#

since F is a field, you cannot have 0 divisors... ^^

prime bramble Sep 20, 2023, 12:29 AM

#

acoustic spear since F is a field, you cannot have 0 divisors... ^^

I understand this, but how does this help me with the proof?

acoustic spear Sep 20, 2023, 12:30 AM

#

because if (x1-x2) != 0 then is a zero divisor, since (x1-x2)^2 is 0

#

so the only possible answer is that x1-x2 = 0 UwU

prime bramble Sep 20, 2023, 12:36 AM

#

I see

#

thank you

#

.close

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kindred venture Sep 20, 2023, 1:28 AM

#

pearl pondBOT Sep 20, 2023, 1:28 AM

#

kindred venture

kindred venture Sep 20, 2023, 1:29 AM

#

Are the statements and proofs I gave here correct?

pearl pondBOT Sep 20, 2023, 1:44 AM

#

@kindred venture Has your question been resolved?

pearl pondBOT Sep 20, 2023, 2:16 AM

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@kindred venture Has your question been resolved?

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lime salmon Sep 20, 2023, 3:17 AM

#

pearl pondBOT Sep 20, 2023, 3:17 AM

#

lime salmon

lime salmon Sep 20, 2023, 3:19 AM

#

here is my work so far

#

how would i evaluate the top part of the piecewise?

west sapphire Sep 20, 2023, 3:19 AM

#

if x is near -3, then |x| is always -x, right?

lime salmon Sep 20, 2023, 3:21 AM

#

could you please elaborate

plush bramble Sep 20, 2023, 3:25 AM

#

lime salmon could you please elaborate

,tex .abs def

jolly parrotBOT Sep 20, 2023, 3:25 AM

#

riemann

lime salmon Sep 20, 2023, 3:27 AM

#

oh shoot i got it now

#

.close

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jolly basin Sep 20, 2023, 3:27 PM

#

pearl pondBOT Sep 20, 2023, 3:27 PM

#

jolly basin

#

@jolly basin Has your question been resolved?

pearl pondBOT Sep 20, 2023, 4:12 PM

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@jolly basin Has your question been resolved?

pearl pondBOT Sep 20, 2023, 4:42 PM

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spring crystal Sep 20, 2023, 4:53 PM

#

pearl pondBOT Sep 20, 2023, 4:53 PM

#

spring crystal

spring crystal Sep 20, 2023, 4:53 PM

#

Help

plush bramble Sep 20, 2023, 4:54 PM

#

You have -7 and 7

#

Which one is it

spring crystal Sep 20, 2023, 4:54 PM

#

-7

plush bramble Sep 20, 2023, 4:57 PM

#

Show how you got -8 and -7

spring crystal Sep 20, 2023, 5:02 PM

#

plush bramble Show how you got -8 and -7

Bottom factor

#

X=7 and -8

plush bramble Sep 20, 2023, 5:06 PM

#

spring crystal Bottom factor

you factored wrong

spring crystal Sep 20, 2023, 5:07 PM

#

How

plush bramble Sep 20, 2023, 5:07 PM

#

spring crystal How

plug in and see

spring crystal Sep 20, 2023, 5:07 PM

#

(X-7)(x+8)

plush bramble Sep 20, 2023, 5:07 PM

#

spring crystal -7

right so how do you get -7 here

spring crystal Sep 20, 2023, 5:08 PM

#

Idk

#

So which part is wrong

plush bramble Sep 20, 2023, 5:09 PM

#

spring crystal

-7

spring crystal Sep 20, 2023, 5:09 PM

#

Oh so I remove -7 to 7 and the answer is right?

#

@plush bramble

pearl pondBOT Sep 20, 2023, 5:25 PM

#

@spring crystal Has your question been resolved?

pearl pondBOT Sep 20, 2023, 5:40 PM

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midnight haven Sep 20, 2023, 5:56 PM

#

pearl pondBOT Sep 20, 2023, 5:56 PM

#

midnight haven

midnight haven Sep 20, 2023, 5:56 PM

#

How do i do part 3

#

Heres th first 2 parts:

#

pearl pondBOT Sep 20, 2023, 6:11 PM

#

@midnight haven Has your question been resolved?

pearl pondBOT Sep 20, 2023, 6:41 PM

#

@midnight haven Has your question been resolved?

midnight haven Sep 20, 2023, 6:41 PM

#

Can someone help?

#

<@&286206848099549185>

frosty creek Sep 20, 2023, 6:47 PM

#

If you have it in the form R*cos(x-a), then can't you just solve for when that is zero?

midnight haven Sep 20, 2023, 7:07 PM

#

im not sure what you mean. How would i go about doing that?

#

.close

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finite rover Sep 20, 2023, 8:26 PM

#

why is this true? Could someone show me the steps

pearl pondBOT Sep 20, 2023, 8:26 PM

#

finite rover why is this true? Could someone show me the steps

remote roost Sep 20, 2023, 8:28 PM

#

3l = -1 so l = -3^(-1) mod 5

finite rover Sep 20, 2023, 8:29 PM

#

I don't get how u can transition from 3l = -1 into -3^(-1) mod 5

remote roost Sep 20, 2023, 8:30 PM

#

Multiply both sides by 3^(-1)

#

Basically "dividing" both sides by 3

finite rover Sep 20, 2023, 8:31 PM

#

oh ok, I remembered that you couldn't just straight up divide on both sides

#

so multiplying by the inverse is fine

#

.close

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nimble coral Sep 20, 2023, 9:41 PM

#

pearl pondBOT Sep 20, 2023, 9:41 PM

#

nimble coral

nimble coral Sep 20, 2023, 9:41 PM

#

How should i approach this question?

#

I don’t have a clue

#

Can someone guide me please?

normal sigil Sep 20, 2023, 9:43 PM

#

So what does (x+1) giving remainder 0 tell you?

nimble coral Sep 20, 2023, 9:44 PM

#

It is a factor

dusty patio Sep 20, 2023, 9:44 PM

#

,rccw

jolly parrotBOT Sep 20, 2023, 9:44 PM

#

normal sigil Sep 20, 2023, 9:44 PM

#

Good (or you could say x = -1 satisfies the equation)

#

Now, do you know the Remainder Theorem?

#

If not, that’s fine

nimble coral Sep 20, 2023, 9:46 PM

#

I am reviewing lol

#

I should have known

#

normal sigil Sep 20, 2023, 9:49 PM

#

Yes, true.

nimble coral Sep 20, 2023, 9:49 PM

#

so f(-1)=0

normal sigil Sep 20, 2023, 9:50 PM

#

Good, yes. What can you say about f(2)?

nimble coral Sep 20, 2023, 9:50 PM

#

it equals to 45?

#

45 is what you get when you divide the function by (x-2)

normal sigil Sep 20, 2023, 9:51 PM

#

nimble coral it equals to 45?

Yep

#

So, with f(-1) = 0 and f(2) = 45, what can you do?

nimble coral Sep 20, 2023, 9:53 PM

#

I don't know. I am slow on this

#

I could have a table?

#

of the function

normal sigil Sep 20, 2023, 9:53 PM

#

Hint- f(-1) = 0 and f(2) = 45 lead to two equations

#

and you have 2 unknowns

nimble coral Sep 20, 2023, 9:54 PM

#

I don't know man. Sorrrry

normal sigil Sep 20, 2023, 9:54 PM

#

Simultaneous equations is the way to go.

nimble coral Sep 20, 2023, 9:55 PM

#

I dont know what that is

normal sigil Sep 20, 2023, 9:55 PM

#

Oh!

#

Unexpected

nimble coral Sep 20, 2023, 9:56 PM

#

yeah sorry, it is the first time i have heard about it

normal sigil Sep 20, 2023, 9:56 PM

#

Would you know how to solve, for instance,

x + 2y = 5
3x - 2y = -2
?

#

Maybe you use a different term

nimble coral Sep 20, 2023, 9:57 PM

#

no, i didnt learn about it

#

could you please teach me?

normal sigil Sep 20, 2023, 9:57 PM

#

Hmm… that’s interesting.

#

Sure

nimble coral Sep 20, 2023, 9:57 PM

#

it is probably in the last year's lesson

#

it looks like simple algebra

normal sigil Sep 20, 2023, 9:58 PM

#

normal sigil Would you know how to solve, for instance, x + 2y = 5 3x - 2y = -2 ?

The principle is that we can add and subtract equations to get new equations also satisfying the original ones.

#

For example, these two added would give us

nimble coral Sep 20, 2023, 9:58 PM

#

I see

normal sigil Sep 20, 2023, 9:59 PM

#

x + 2y + 3x - 2y = 5 - 2

#

Do you see what has happened?

nimble coral Sep 20, 2023, 9:59 PM

#

Yup

#

I should have known it, but i skipped a lot of lessons

normal sigil Sep 20, 2023, 9:59 PM

#

Good. This gives us
4x = 3 so x = 3/4

normal sigil Sep 20, 2023, 9:59 PM

#

nimble coral I should have known it, but i skipped a lot of lessons

That’s all right

nimble coral Sep 20, 2023, 10:00 PM

#

normal sigil Good. This gives us 4x = 3 so x = 3/4

yes

normal sigil Sep 20, 2023, 10:00 PM

#

normal sigil Good. This gives us 4x = 3 so x = 3/4

Then, we can use one of the original equations to find out y.

#

x + 2y = 5 so 3/4 + 2y = 5

#

2y = 17/4

#

y = 17/8

nimble coral Sep 20, 2023, 10:00 PM

#

that's right

normal sigil Sep 20, 2023, 10:01 PM

#

Good. Now, try substituting -1 into your polynomial and setting equal to 0

#

and do the same with 2, setting equal to 45

nimble coral Sep 20, 2023, 10:04 PM

#

#

This?

normal sigil Sep 20, 2023, 10:06 PM

#

Are you sure about m - 1 and m + 2 ?

nimble coral Sep 20, 2023, 10:06 PM

#

Oh i added the brackets now

#

But where do i put the remainder of 45 in the second equation

normal sigil Sep 20, 2023, 10:06 PM

#

equals 45

#

and the first one equals zero

nimble coral Sep 20, 2023, 10:07 PM

#

Ok

normal sigil Sep 20, 2023, 10:07 PM

#

Now, please expand and simplify. What equations do you have?

nimble coral Sep 20, 2023, 10:12 PM

#

#

@normal sigil

#

Is this right?

normal sigil Sep 20, 2023, 10:17 PM

#

No need to keep the (1)

#

let me just check

#

Oh, you’ve added them already

#

Now, something about the adding

#

You need to add them in such a way that you get rid of a variable by adding them.

normal sigil Sep 20, 2023, 10:20 PM

#

normal sigil Would you know how to solve, for instance, x + 2y = 5 3x - 2y = -2 ?

For instance, adding these guys allowed us to get rid of y.

nimble coral Sep 20, 2023, 10:20 PM

#

How do i do that

normal sigil Sep 20, 2023, 10:20 PM

#

Could you share your two separate equations that you added?

nimble coral Sep 20, 2023, 10:20 PM

#

normal sigil Sep 20, 2023, 10:21 PM

#

I would suggest you explicitly simplify each equation before adding

#

so the top one becomes - m - n = 15, right?

nimble coral Sep 20, 2023, 10:22 PM

#

Can you explain please?🙏

normal sigil Sep 20, 2023, 10:23 PM

#

Sure

#

Go term by term

#

What does m(-1) simplify to?

#

simply -m

#

What about 20(-1)^2 ?

nimble coral Sep 20, 2023, 10:24 PM

#

#

Is this what you mean?

normal sigil Sep 20, 2023, 10:24 PM

#

Oh good

#

Yes

nimble coral Sep 20, 2023, 10:24 PM

#

I see

normal sigil Sep 20, 2023, 10:24 PM

#

Move m and n over and we get m + n = -15

#

Please do the same thing for the second equation and see what you get

nimble coral Sep 20, 2023, 10:26 PM

#

normal sigil Sep 20, 2023, 10:27 PM

#

Not quite

#

Remember it is mx^3

nimble coral Sep 20, 2023, 10:28 PM

#

Oh right

#

So it is 8m?

normal sigil Sep 20, 2023, 10:32 PM

#

Yep

#

But check that number on the RHS

#

We should have

#

8m + 80 + 2n - 35 = 45

#

so 8m + 2n = 0

#

Well, that’s convenient.

nimble coral Sep 20, 2023, 10:35 PM

#

Oh thanks

normal sigil Sep 20, 2023, 10:35 PM

#

normal sigil 8m + 80 + 2n - 35 = 45

Do you see your errors?

nimble coral Sep 20, 2023, 10:36 PM

#

I don’t

#

Could you please tell me?

normal sigil Sep 20, 2023, 10:38 PM

#

You forgot to cube the 2 in front of m

#

You also forgot the -35 entirely

nimble coral Sep 20, 2023, 10:39 PM

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in front of m?

normal sigil Sep 20, 2023, 10:40 PM

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Yes, it was mx^3

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so you forgot to cube the 2

nimble coral Sep 20, 2023, 10:41 PM

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Yeah isn’t it 8?

normal sigil Sep 20, 2023, 10:41 PM

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Yep

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Just saying beforehand

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you forgot

nimble coral Sep 20, 2023, 10:42 PM

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Oh ok

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What is next

normal sigil Sep 20, 2023, 10:42 PM

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Now we have two Wes

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eqs

nimble coral Sep 20, 2023, 10:43 PM

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8m+2n=0

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-m+20-n-35=0

normal sigil Sep 20, 2023, 10:43 PM

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Good, and the other one is m + n = -15

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(rearranged a bit)

nimble coral Sep 20, 2023, 10:44 PM

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Oh it isnt -m+n=-15?

normal sigil Sep 20, 2023, 10:45 PM

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No!

nimble coral Sep 20, 2023, 10:46 PM

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M(-1)3 is not -m?

normal sigil Sep 20, 2023, 10:46 PM

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It is

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But that gets you - m - n = 15

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now if you multiply both sides by -1

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m + n = -15

nimble coral Sep 20, 2023, 10:47 PM

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Oh i see

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-m-n=-15

normal sigil Sep 20, 2023, 10:48 PM

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No

nimble coral Sep 20, 2023, 10:48 PM

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Oh sorry

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I mean m-n=-15

normal sigil Sep 20, 2023, 10:49 PM

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Still no

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Why do you think n has a different sign to m?

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Remember that m(-1)^3 = -m and n(-1) = -n

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so they have the same sign

nimble coral Sep 20, 2023, 10:50 PM

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Oh right sorry

normal sigil Sep 20, 2023, 10:51 PM

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m + n = -15
4m + n = 0

nimble coral Sep 20, 2023, 10:51 PM

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-m-n=15

normal sigil Sep 20, 2023, 10:51 PM

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normal sigil m + n = -15 4m + n = 0

So these are our two equations

nimble coral Sep 20, 2023, 10:51 PM

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And you switch the signs

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Yes

normal sigil Sep 20, 2023, 10:52 PM

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normal sigil So these are our two equations

What do we do now? We can subtract them!

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Observe: m - 4m + n - n = -15 - 0

nimble coral Sep 20, 2023, 10:53 PM

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normal sigil Sep 20, 2023, 10:53 PM

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Good, so m = 5

nimble coral Sep 20, 2023, 10:53 PM

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normal sigil Sep 20, 2023, 10:54 PM

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Why is 5 + n = 0?

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Use the equations.

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m + n = -15

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5 + n = -15

nimble coral Sep 20, 2023, 10:55 PM

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Oh

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N=-10

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Let me check if it fits

normal sigil Sep 20, 2023, 10:56 PM

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nimble coral N=-10

Check again?

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Minus 5 from both sides

nimble coral Sep 20, 2023, 10:56 PM

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Ohhhhh

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-20

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Aghhhh

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Idk why i make so many mistakes

normal sigil Sep 20, 2023, 10:56 PM

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Practice makes perfect

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Right, I recommend you try some simultaneous equation problems online

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That can be quite key so it’s really important you have that skill

nimble coral Sep 20, 2023, 10:57 PM

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Yeah

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I need a lot more practices

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It is just lately i have picked up math again

normal sigil Sep 20, 2023, 10:58 PM

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🕺 It will pay off

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Are we all done?

nimble coral Sep 20, 2023, 10:58 PM

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Can i check?

normal sigil Sep 20, 2023, 10:58 PM

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Go for it

nimble coral Sep 20, 2023, 10:59 PM

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👍 yup it is right

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Thank you very much

normal sigil Sep 20, 2023, 11:00 PM

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🕺

nimble coral Sep 20, 2023, 11:00 PM

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I need a lot more practices

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Thank you🥹 bye

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.close

pearl pondBOT Sep 20, 2023, 11:01 PM

#

Channel closed

Closed by @nimble coral

Use .reopen if this was a mistake.

pearl pondBOT Sep 20, 2023, 11:43 PM

#

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winter rain Sep 21, 2023, 12:09 AM

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Hi, I need help with part A and B of this question. How do I show that a = 2 and b = -4? I'm not sure where to start about this

pearl pondBOT Sep 21, 2023, 12:09 AM

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winter rain Hi, I need help with part A and B of this question. How do I show that a = 2 and...

winter rain Sep 21, 2023, 12:20 AM

#

#

Bad picture but this is what he showed for part a in class, can't seem to wrap my head around how he answers it

pearl pondBOT Sep 21, 2023, 12:35 AM

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@winter rain Has your question been resolved?

winter rain Sep 21, 2023, 12:45 AM

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For A, i see the factors in the denominator, is that all that's necessary to answer the question? Given the vertical asymptotes and the hole/removable discontinuity?

#

For B, i was not sure how to come up with proper work to show how i got my answer

my teacher is really keen on showing our work, making sure it's very sound, so this is as far as I can get (B): since there's a r.d. at x=-2, (x+2) must be at the top of the numerator. then I just tried what values i could multiply (x+2) with to get -5x^2+cx. But how would I write this on paper??? and is this valid?

winter rain Sep 21, 2023, 1:13 AM

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I think i got it im going to bed

pearl pondBOT Sep 21, 2023, 1:43 AM

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@winter rain Has your question been resolved?

pearl pondBOT Sep 21, 2023, 2:13 AM

#

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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

ivory ridge Sep 21, 2023, 2:15 AM

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helloo! pls help meeee

pearl pondBOT Sep 21, 2023, 2:15 AM

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ivory ridge helloo! pls help meeee

ivory ridge Sep 21, 2023, 2:15 AM

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for 7. e, is there any other shorter way to do it??

plush bramble Sep 21, 2023, 2:17 AM

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ivory ridge for 7. e, is there any other shorter way to do it??

Find the complement

ivory ridge Sep 21, 2023, 2:17 AM

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what do you mean?

plush bramble Sep 21, 2023, 2:17 AM

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Complement set

ivory ridge Sep 21, 2023, 2:17 AM

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how would i do that with this quesiton

plush bramble Sep 21, 2023, 2:17 AM

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Negate "at least 2 red cards"

ivory ridge Sep 21, 2023, 2:18 AM

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uhm

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sorry can you explain it in steps?

plush bramble Sep 21, 2023, 2:20 AM

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ivory ridge sorry can you explain it in steps?

Do you know what negate means?

ivory ridge Sep 21, 2023, 2:20 AM

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to like remove?

plush bramble Sep 21, 2023, 2:20 AM

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No

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What's the opposite of "at least two red cards" in words?

ivory ridge Sep 21, 2023, 2:20 AM

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2 red cards max

plush bramble Sep 21, 2023, 2:21 AM

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No

ivory ridge Sep 21, 2023, 2:22 AM

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oh so just no restrictions?

plush bramble Sep 21, 2023, 2:22 AM

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ivory ridge oh so just no restrictions?

Also no

ivory ridge Sep 21, 2023, 2:23 AM

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idk im rly confused

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2 black cards?

plush bramble Sep 21, 2023, 2:23 AM

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Is 2 red cards part of your question or part of the negation?

ivory ridge Sep 21, 2023, 2:24 AM

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part of the question

plush bramble Sep 21, 2023, 2:25 AM

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ivory ridge 2 red cards max

So adjust this

ivory ridge Sep 21, 2023, 2:26 AM

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less than 2 red cards

plush bramble Sep 21, 2023, 2:26 AM

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Yea find that

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Then subtract that from the total number of hands

ivory ridge Sep 21, 2023, 2:27 AM

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lemme try

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so i would do

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10400600

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minus the ways it can be for 2 red cards and 1 red card?

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wait

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is the answer 6.3x10^11?

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@plush bramble

plush bramble Sep 21, 2023, 2:36 AM

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ivory ridge 10400600

Where did this come from

plush bramble Sep 21, 2023, 2:36 AM

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ivory ridge minus the ways it can be for 2 red cards and 1 red card?

Why 2 red cards

plush bramble Sep 21, 2023, 2:36 AM

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ivory ridge less than 2 red cards

You had this right

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"less than 2" means 0 or 1

ivory ridge Sep 21, 2023, 2:37 AM

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oh wait ignore the number

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so first total ways is 52C13 and then minus (ways with 0 reds + ways with 1 red)

plush bramble Sep 21, 2023, 2:39 AM

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Yup

ivory ridge Sep 21, 2023, 2:39 AM

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yEUH

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so it would be 6.3 x10^11 right?

pearl pondBOT Sep 21, 2023, 2:54 AM

#

@ivory ridge Has your question been resolved?

#

Channel closed

Closed by @ivory ridge

Use .reopen if this was a mistake.

#

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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

wanton thunder Sep 21, 2023, 3:34 AM

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?claim

pearl pondBOT Sep 21, 2023, 3:34 AM

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wanton thunder ?claim

wanton thunder Sep 21, 2023, 3:34 AM

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hey

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cna someone send a guide

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a youtube video or a book pcitures

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on how to solve quadratic equations by ,completing the squares, extracting the squares, factoring, using quadratic formula

#

pleasee ty

analog topaz Sep 21, 2023, 3:42 AM

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Here use this for quadratic formula

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https://youtu.be/C206SNAXDGE?si=AeZQkSWLPuBpYF3N

YouTube

The Organic Chemistry Tutor

Completing The Square Method and Solving Quadratic Equations - Alge...

This algebra 2 video tutorial shows you how to complete the square to solve quadratic equations. This video is for high school students taking algebra 1 & 2 and college students taking introductory or college algebra. This video contains plenty of examples and practice problems with solutions / answers that can help you with your next workshee...

▶ Play video

analog topaz Sep 21, 2023, 3:44 AM

#

analog topaz https://youtu.be/C206SNAXDGE?si=AeZQkSWLPuBpYF3N

This is for completeing the square

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https://www.youtube.com/watch?v=t7-JCa7phCQ&pp=ygUfZmFjdG9yaW5nIHVzaW5nIGdyb3VwaW5nIG1ldGhvZA%3D%3D

YouTube

The Organic Chemistry Tutor

Factor By Grouping Polynomials - 4 Terms, Trinomials - 3 Terms, Alg...

This algebra 2 video tutorial explains how to factor by grouping. It contains examples of factoring polynomials with 4 terms and factoring trinomials with 3 terms. This video contains plenty of practice problems for you to finish your next worksheet assignment.

Algebra Review: https://www.video-tutor.net/algebra-for-beginners-bas...

▶ Play video

analog topaz Sep 21, 2023, 3:45 AM

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analog topaz https://www.youtube.com/watch?v=t7-JCa7phCQ&pp=ygUfZmFjdG9yaW5nIHVzaW5nIGdyb3Vwa...

And thats for factoring

wanton thunder Sep 21, 2023, 3:48 AM

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can i learn all dat in 30 mins

analog topaz Sep 21, 2023, 3:52 AM

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wanton thunder can i learn all dat in 30 mins

You could

pearl pondBOT Sep 21, 2023, 4:03 AM

#

@wanton thunder Has your question been resolved?

pearl pondBOT Sep 21, 2023, 4:18 AM

#

Channel closed

Closed due to timeout

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#

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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.

oblique reef Sep 21, 2023, 4:31 AM

#

24acbe8bbc1e43e2b85e8f43d494eb2dtplv-ejcjvp0zxf-webp-scale425415.png