precalculus

[rugged wigeon]

do u know which one?

[viscid thistle]

i mean when you are finding $\lim_{x\to 2}x^3=8$ you are essentially doing this

[obsidian monolith]

Al𝟛dium

[viscid thistle]

if $\lim_{x\to a}f(x)=L$ and $\lim_{x\to a}g(x)=M$ then $\ \lim_{x\to a}(f(x)+g(x))=\lim_{x\to a}f(x)+\lim_{x\to a}g(x)=L+M$

[obsidian monolith]

Al𝟛dium

[rugged wigeon]

ohh so theyre using that property

[viscid thistle]

yeah

well

it's not addition at the numerator but yeah same thing essentially

[rugged wigeon]

ok thank you! ill keep looking into it

[viscid thistle]

you're welcome

[rugged wigeon]

so does that mean x^2 is L and 9 is M

EPICCCC

[viscid thistle]

well

L=9 on this case

because L=lim x->-3 x^2=(-3)^2=9

i spoke too quickly

[rugged wigeon]

ohh okok

thanks

[viscid thistle]

and this is why the numerator equals 0, L=9 and M=9, so L-M=0

np

[bold meadow]

graded hw

[steel venture]

,rccw

[steel venture]

do you still need help?

[elfin oasis]

hello

can you help me in my activity?

tips or formulas would do, thank you so much!

[sterile wedge]

can someone help me with this problem please

[rare pagoda]

Find the slope

Then use point slope form for some point in the graph

[dark sky]

is part a (15,4)?

b is (9,-1)?
and c is (7,11)?

[umbral cloud]

How to turn integral into sum?

[copper vigil]

@umbral cloud do you have a specific problem?

[umbral cloud]

Yupp

While Ik is the limit of Fk(X)

Montrer que= prove that...
I just need a hint to understand the problem

That's the function f(t)

[viscid thistle]

all of them are correct

[urban geyser]

how would I graph these?

[sick steppe]

what's x| representing?

[urban geyser]

computer error

supposed to be just x

[sick steppe]

Do you know what |x| looks like?

?

[urban geyser]

yes, ik what |x| looks like

[sick steppe]

Ok so you can either draw |x| and x on the same axes, then add ordinates
or you can break |x| into the piecewise definition and add the functions together, then graph

[stray hedge]

Can someone help with A pls

[sick steppe]

$b'(x) = 0$

[obsidian monolith]

moshill1

[urban geyser]

ok thx

[hoary bluff]

pls help me..

[lethal oracle]

@robust star Are you asking for help with that?

[robust star]

Yes

[lethal oracle]

factor all of it

[robust star]

Ok

for the excluded values I got -4,2, and 5 but it's asking for two excluded values only

[lethal oracle]

one sec

[night glacier]

how is B 110?

isn't B the interior angle of 70° + 90°

180= 70°+90°- angle

[robust star]

Isn't B 180-70?

[blazing parrot]

what do you mean by interior angle of 70 + 90

[winged quartz]

Hey so I'm taking accel precalc and this is the closest channel related to precalc. I'm kind of having trouble solving this. Can anyone help?

[blazing parrot]

try having u = sin(x)

[winged quartz]

well I haven't learned using u

[potent creek]

i believe he means just subbing sin with u to simplify it. And then factor or something like that -- not 100% sure ngl

[winged quartz]

I see what you mean, but I have everything down till here and I'm guessing that I'm supposed to move the entire left-hand side onto the right hand side and from there it says to factor.but I don't see anything that could be factorable..

[potent creek]

ok to factor i think you make it 2-2u^2 = 4-5u. Then you bring to one side and factor. Then after you factor, sub the u's back with sin. Also, im not 100% sure so yea

[winged quartz]

ok then that puts me at -2u^(2)-5u+2 or -2sin^(2)-5sin+2

Some way I need to get to this tho

[potent creek]

wait

are you proving this identity?

or somethign like that

[winged quartz]

i think so

[potent creek]

ok mb.

[winged quartz]

its not simplifying, thats for sure so the only other thing is verifying the equation

[potent creek]

you cant manipulate both sides then

yea ok

[winged quartz]

mhm

I mean it never says it's verifying either... just says to solf it

[potent creek]

dude im sorry idk what to do. I tested values and they were different ¯_(ツ)_/¯

[winged quartz]

yeah no, its fine thanks for the help

[night glacier]

i can't understand what to do here?

I have my own calculations but

I don't believe they're right.

Can anyone give me the answer + an explanation?

@potent creek

<@&286206848099549185>

[potent creek]

?

whats that mean?

[night glacier]

sorry for ping bro

[potent creek]

np lol

[night glacier]

it wants me to find the C'C

so i guess the length from C to C'

[pure vessel]

f(x)=x^2-2x Find the zeros of the function

[velvet granite]

@pure vessel set it equal to zero

x^2-2x=0

you can factor an x out and get

$x(x-2)=0$

[obsidian monolith]

ICHIROfan51

[velvet granite]

now you get two zeroes

[night glacier]

<@&286206848099549185>

[lethal oracle]

@night glacier

[cursive birch]

im confused on how to do this :<

[bold meadow]

5 points.

[cursive birch]

?

you gonna explain what you mean by that orr

[trim hemlock]

it means you are probably working on some kind of test

[cursive birch]

blackboard hw actually

[random perch]

does anyone know what i’m supposed to do here?

[viscid thistle]

It's written below.

Get the equation of line and then.

[trim hemlock]

You dont really need the equation

You just need the slope

[quartz lance]

log3(x-2) = -1
not so sure what i do with the brackets :/

[trim hemlock]

Just raise 3 to that power

[quartz lance]

sorry my bad its base 4

*3

[trim hemlock]

Yeah, still same stuff

[quartz lance]

so it would look like this Log(x-2)^3?

or have i completely messed that up XD

[random perch]

yeah idk how they got that 1.6875 ??

[proper pilot]

yooo, Good afternoon people, I would like to ask, is the amplitude none, undefined or smth else. I got a graph like this, it's all about trigonometric functions

y = 1/2 tan 2x

like I know that its absolute value of a

but isnt the amplitude the highest point

plz send help

[full pagoda]

there is no amplitude of a tangent graph

[proper pilot]

oh, I forgotabout that

thanks

[wispy aurora]

is x^2* sin(1/x) differentiable at x =0? How about x^2 * cos(1/x)?

[sick steppe]

Well neither of them exist at x=0

so no, they arent

[obtuse cloud]

well, try differentiating x^2*sin(1/x), you get 2x*sin(1/x)-*cos(1/x), now try finding the the value at x=0, you can try using the squeeze theorem and get that the limit is between -1 and 1, but it can't be determined, similar for x^2*cos(1/x)

[rapid lance]

could someone help find the 'criteria' an ellipse needs to follow such that it has integer solutions/natural solutions

[glass dagger]

does anyone want to mentor a self taught leanrer?

[north pagoda]

How do i find the inverse of this funciton

[lilac storm]

so i have started off the question and part (a) is really simple and i found the derivative.

these are the graphs i got when inserting the eqs into geogebra

i want to ask that are these graphs correct, like have i inserted them correctly?

for (c) what i did was insert 10 into the real eq and for (d) i inserted 10 into the derivative eq

what i need help with is part (e), how do i calculate part (d) and can someone also tell me that the graphs and eqs are correct in the geobebra picture that is above.

[sick steppe]

d is just P'(10)

e is what happens as time goes on and on

[lilac storm]

yes i got (d) but what do insert in (e) and into which eq, the original one or the derivative one.

is it plugging in infinity into the x's so the x's turn into 0 and then just solve the eq?

are you there?

are you there?

[sick steppe]

you dont plug anything into e

what's the mathematical way of writing about what happens at the extremes of a function?

[lilac storm]

can't remember?

[sick steppe]

do you know what a limit is?

[lilac storm]

yes

[sick steppe]

ok so how do you express time going forward forever?

[lilac storm]

as infinity?

[sick steppe]

yes

[lilac storm]

so the population is infinity in the long run?

[sick steppe]

No

[lilac storm]

oh

[sick steppe]

$\lim_{t \to \infty} P(t)$

[obsidian monolith]

moshill1

[lilac storm]

yeah so i insert infinity into t.

[sick steppe]

No

infinity isnt a number

[lilac storm]

oh, ok

[sick steppe]

P is a rational function, so what does a rational function tend toward at the extremes

[lilac storm]

i don't know why i don't know this or maybe can't remember.

[sick steppe]

do you know what a horizontal asymptote is?

[lilac storm]

yes

[sick steppe]

Horizontal asymptotes are the limits for infinity of a rational function.

[lilac storm]

uh, ok

so what does this mean in like simple words?

[sick steppe]

find the horizontal asymptote

[lilac storm]

oh

so the horizontal asymptote is 25, right?

[sick steppe]

yes

[lilac storm]

so does that mean that the population will be 25000 in the long run since 25 is the horizontal asymptote and the question is asking the population in thousands so the population will be 25000 in the long run, right?

ok, thank you so much for your time and help.

[lilac storm]

so i just want to ask that what would be t at the beginning of 2008?

[uncut mulch]

0

the beginning of 2008 is 0 months after the beginning of 2008

[lilac storm]

ok, and i just want to make sure that in a i am going to do f(0) meaning i will sub 0 into the original eq and in b i will take the derivative and plug in 24 into the derivative eq, right?

[uncut mulch]

yes

[lilac storm]

ok, thank you so much

[viscid thistle]

Hi i need some help with this one

Im not sure how they got the answer 2.23 meters

Thanks!

[white vault]

can someone solve this please

[tender lotus]

I can't figure this out

[fallow slate]

Oh this one is simple. You multiply the denominator by its conjugate, which is (root t + 2)

You know what a conjugate is?

[tender lotus]

the same as denominator right?

oh its num

[fallow slate]

no its actually the same as the numerator

yeah nice

[tender lotus]

i get those mixed up im trying right now

[fallow slate]

because that makes "t" rationalized

i think you got it

[tender lotus]

thanks

[fallow slate]

np

[tender lotus]

alot! lol

still got it wrong

for the numeator i got root t +2 ^2

denominator t-4

[fallow slate]

ok let me see

yes you should get a radical in your numerator

but its important that the denominator is rationalized

which is correct

[tender lotus]

im not sure why the system is marking it wrong

[fallow slate]

the system?

[mild swan]

numerator should be (√t + 2)^2

[tender lotus]

its hw

[mild swan]

or expanded

[fallow slate]

ah yeah

[mild swan]

denom = t - 4

[fallow slate]

maybe you need to expand the numerator

?

[mild swan]

^^

[fallow slate]

im not sure

[mild swan]

There's no other possibility

Yea - expand the numerator

👍

That SHOULD get you to where you need to go

,w simplify (sqrt(t) + 2)^2/(t-4)

bruv

it did the opposite lol

[mild swan]

👀

[tender lotus]

oh no lol

[obsidian monolith]

Something went wrong!

An unexpected error occurred while processing your command!
The error has been reported and should be fixed soon.
If the error persists, please contact our friendly support team at our support guild!

Exception

aiohttp.client_exceptions.ClientOSError: [Errno 104] Connection reset by peer

[tender lotus]

I'm going to have to ask the professor why its wrong, i hate web assign

[fallow slate]

haha yeah you should

[tender lotus]

for this, same thing right?

[fallow slate]

yeah you multiply the numerator by (root a + root b)

[mild swan]

(the conjugate)

careful when simplifying though

[fallow slate]

For this question you need to use the change of base formula and power rules to simplify. It also helps you make the bases equal. If you still need help I can show you some work for it

yeah no problem give me a second

[fallow slate]

So basically, you did all your math correct except that you forgot to square the pi as well.

Yeah no problem!

[viscid thistle]

@fallow slate tysm!

[faint dagger]

I was about to say that

[arctic kestrel]

can someone help me solve for those^^

i go the first image wrong but this one is similiar

[velvet granite]

Id probably start with the individual triangles that give you 2 sides

this way you can use SOH CAH TOA

[arctic kestrel]

i was thinking about that but then got totally lost

[velvet granite]

So that bottom triangle has all 3 sides

the middle triangle has 3

[arctic kestrel]

yeah

and then what?

[velvet granite]

Do some trig kid

[arctic kestrel]

<@&286206848099549185>

[sterile wedge]

Can someone help me please. I think (a) is [-4,4] I feel like that is wrong. (B) i got -3 which I think is right (C) i got -3 (d) I am unsure how to do

[thorn lily]

I keep getting this question wrong - I can’t figure it out. If the period is 8pi, wouldn’t b be 1/4 because 2pi/(1/4) = 8pi ?

I don’t understand how I got this one wrong either, can someone help?

[uncut mulch]

you seemed to have disregarded that cot(theta) < 0

[terse ivy]

A sphere has radius 4cm and a different one has radius 8cm. How much bigger is the biggest sphere in comparison of the smallest?

[echo wagon]

In terms of volume?

Take the ratio of the volumes

[terse ivy]

How do I take the ratio of the volumes

[echo wagon]

Put the one in the numerator and the other one in the denominator of a fraction

And simplify

[terse ivy]

hmmm

so I should give as an answer that the biggest sphere is twice as big

haha jesus this seems like kindergarten math, but I

don't get it

[echo wagon]

Well, twice as big is wrong

Show your work

[terse ivy]

It's in norwegian so it would be no point'

[echo wagon]

I didn't ask to see the question

But your answer

[terse ivy]

I have not given any answer yet

[echo wagon]

You said it's twice as big

How did you get that?

[terse ivy]

Just an assumption since 4 is 1/2 of 8

[echo wagon]

Sure, but look at the ratio of the volumes

Because the radius is cubed in the volume formula

[terse ivy]

V(r) = 4/3pi r^2

[echo wagon]

^3

[terse ivy]

yeah 3* my bad

4/3 * 3.14 44*4 is what i should do to get the volume of the sphere with ratio 4 then?

4/3 * 3.14 444

wtf

4/3 * 3.14 4 * 4 * 4

4/3 * 3.14 * 4 * 4 * 4

never mind I got it

[viscid thistle]

anyone a genius with calculus? dm me I need help

[untold whale]

Is this true for any complex numbers: $2|\alpha_1||\alpha_2|\leq|\alpha_1|^2+|\alpha_2|^2$?

[obsidian monolith]

emphatic_wax

[echo wagon]

(|α1| - |α2|)^2 >= 0. Expand this.

[untold whale]

nice haha thank you

[swift flume]

does anyone know why the graph of this kind of dips down through 5/3 on the left side, then rises back up and infinitely approaches 5/3, as x approaches negative infinity?

it makes sense to me that it approaches 5/3

but why does it go through

then back up

[viscid thistle]

anyone good with calculus? dm me I need help

[mild swan]

@viscid thistle don't ask to ask, just ask in a channel

[lilac storm]

to find the average cost function, is the formula C(x)/x?

if so then for a, is the function (5000+2x)/x?

are these two statements correct that i wrote?

ok, so i am good with a and b so can anyone help me with c?

[lilac storm]

anyone there to help?

[round yarrow]

Hey guys, please solve the qotd in MODS...

[odd abyss]

can anyone help question 5

[odd abyss]

can someone look at question 5 again pls?

[uncut mulch]

what's question 5

[odd abyss]

in the discord

@uncut mulch

[lilac storm]

can anyone please help me with (b)?

[uncut mulch]

seems like just entering a command into geogebra

what's your issue with it?

[lilac storm]

yeah, i don't know maybe i'm making a mistake entering the command into geogebra because it is not working.

do you want me to post the geogebra picture as well?

[uncut mulch]

yes

[lilac storm]

ok, just a moment.

like, there's no graph

did i enter it wrong?

[uncut mulch]

get rid of the f

and read the insturctions

written

[lilac storm]

yes i got the derivative eq underneath it, so does that mean that there is no graph?

[uncut mulch]

from just what you're asking it to do, no

[lilac storm]

oh, ok.

thank you so much for your help.

[arctic kestrel]

can anyone help with this one...

I've been trying at it using some basic trig and geo concepts

but i can't crack it

[copper vigil]

@arctic kestrel law of cosines?

[tough hemlock]

Can anyone help me with this problem

[sick steppe]

those are functions

[ornate lintel]

systeme of equation

solve for x

(:

[lilac storm]

can anyone help me with this question?

[sleek socket]

<@&286206848099549185>

[umbral cloud]

Guyq

How to prove this

[sick steppe]

what's the notation?

[glass breach]

explain

[viscid thistle]

hi I was wondering

how did the teacher solve this

like did he root of the 1/2 of the other side?

i get the first 2 lines

[inland anchor]

can someone check answers for me?

we'll have to go in vc tho if thats ok

[uncut mulch]

from the 2nd to 3rd line,
they squared both sides

[inland anchor]

actually nvm i can send pic

did i answer this correctly/

[uncut mulch]

no

[inland anchor]

whats the right way to do it?

[uncut mulch]

add integer multiples of 2pi

[inland anchor]

so just add 2 pi?

[uncut mulch]

that will get you one of the acceptable angles

[inland anchor]

would one be 11pi/6

[uncut mulch]

yes

[inland anchor]

what abt the negative

[uncut mulch]

add integer multiples of 2pi

[inland anchor]

aanswer

[uncut mulch]

(there are negative integers too)

[inland anchor]

could i add -2 maybe??

dumb question

[viscid thistle]

Ramonov

They squared it? why

isnt squaring it the same as taking 1/2 root of x

[uncut mulch]

-2 is not an integer multiple of 2pi

"1/2 root" is uncommon wording

[viscid thistle]

I dont know what ti call it

its obv not square root

[uncut mulch]

$\br{x_1^{1/2}}^2 = \br{4x_2^{-1/2}}^2$

[obsidian monolith]

ℝamonov

[uncut mulch]

raise the the power of 2, "squaring" is the most concise way to describe it

[viscid thistle]

if it was x^2, i thought to isolate it we would have to take square root of both sides

[inland anchor]

would -13pi/6 be good?

[uncut mulch]

would -13pi/6 be good?
yes

if it was x^2, i thought to isolate it we would have to take square root of both sides
but you don't have x^2 here

[viscid thistle]

but wouldn't i be 1/2suqre root

nvm I'm confused

lol

[uncut mulch]

$a^{1/2} = \sqrt{a}$

[obsidian monolith]

ℝamonov

[viscid thistle]

I thought

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

[obsidian monolith]

JuicerSeducer

[uncut mulch]

nope

that's completely wrong

$a^{\frac 1n} = \sqrt[n]{a}$

[obsidian monolith]

ℝamonov

[naive dragon]

I was talking with someone who has a math degree about holes in asymptote/function graphs, and she said that the way we're being taught is incorrect. In a function with more than one x= statement in the denominator (eg. [(x - 2)(x + 3)]/[(x + 5)(x - 2)]), there's no reason to represent a hole on a graph, since the potentially erroneous statement (x - 2) can just be cancelled out.

Is she correct?

$eg. [(x - 2)(x + 3)]/[(x + 5)(x - 2)]$

[obsidian monolith]

Goldra

[uncut mulch]

no

$\frac{(x - 2)(x + 3)}{(x + 5)(x - 2)}$ behaves like $\frac{(x + 3)}{(x + 5)}$ except at $x=2$ where it will be undefined.

[obsidian monolith]

ℝamonov

[uncut mulch]

and in your graph you can't just imply that it's defined there.

someone with a math major degree shouldn't be making such a claim,
are you quoting exactly what they're saying word for word?

[faint nest]

Im confused on these kind of problems can someone help cuz my whole hw is like this

[naive dragon]

I am paraphrasing

[uncut mulch]

yeh, that's an issue. gonna need exactly what they said

what you paraphrased is incorrect, their initial claim is probably good and you most likely misinterpreted it

[naive dragon]

I'm getting some of their messages, give me a second

[naive dragon]

Would you mind if I dmed you them? Took screenshots of their messages so idk if I want an entire server seeing those

[uncut mulch]

up to her whether you can publicise here messages here. as long as its math related its fine.

[naive dragon]

She's on dnd right now so I'm not comfortable messaging her about that

[uncut mulch]

fine dm me

but i'll respond here if i need to use the bot

[faint nest]

@uncut mulch are u free to help me with that question real quick

[uncut mulch]

use reference angles,
use given information to identify the quadrant theta is in

[faint nest]

its in quadrant 3

but idk where to go from there

[uncut mulch]

draw a triangle and/or apply pythagorean trig identities

[faint nest]

im still lost.

i found the missing side as root 77

with pythagorean

and my answer of 9/root 77 was wrong

[uncut mulch]

you messed up your ratio for cos

[sage flame]

can someone help me with this one?

[kindred wave]

What's the problem here?

[viscid thistle]

is 3 the correct answer

@kindred wave

[kindred wave]

,w diff 8x^(3/4) ,x=16

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by vampy#5136

[lilac storm]

so i have defined C(t) and C'(t) according to the first instruction.

Then i used the solve command to find the critical points

can anyone help me with step 3 and 4

and also why aren't there any critical points showing if i have entered the solve command?

[lilac storm]

anyone there to help?

[lilac storm]

is anyone there that can help me with this question?

[fiery creek]

@lilac storm you want to find critical points of C(t)?

also if you want to find where it is increasing or decreasing

can't you just use the graph of the function

[lilac storm]

yeah so i know how to find them but how do i find them on geogebra, like what do i type in so it shows and tells the critical points. Like for example, when you type derivative and the function, it automatically gives you the derivative function so how do i do it for the other 2 things?

[fiery creek]

i'm not sure

just find the critical points by hand

do you know how?

[lilac storm]

oh, ok

yes of course

[fiery creek]

ok

do you need help with the other two

[lilac storm]

yeah so i just want to make sure that why is it saying use the solve command for finding the critical points, meaning that there is a command that i can enter to find the critical points.

[fiery creek]

alright

[lilac storm]

yeah so i just want to ask that do you like know how would i type that command in, like for example step 1 is easy which is defining C(t) and C'(t) so you just basically type the original eq and for the derivative eq, you enter derivative (f(x)), so basically this is my question with the critical points that do you know how to like it says to use the solve command to find the critical points because of course i know how to find all these things by hand but this question is solely on geogebra, locating the important things on geogebra

are you there?

are you there?

[bronze sandal]

hi, can the summation $\sum_{i=0}^{n} \frac{(n-i)^2}{2}$ be simplified?

[obsidian monolith]

yesfood

[gusty geyser]

by simplified do you mean the summand or like

the whole thing

,tex bc you basically have \begin{align*}
\sum_{i=0}^n \frac{(n-i)^2}{2} &= \frac{1}{2} \sum_{i=0}^n (n-i)^2 \
&= \frac{1}{2}\left(n^2 + (n-1)^2 + (n-2)^2 + \cdots + (1)^2 + 0\right)
\end{align*}
do you know how to simplify the inside?

[obsidian monolith]

ciceronii

[bronze sandal]

I meant the whole thing

sorry that summation was actually slightly incorrect, I'm trying to simplify $\sum_{i=0}^{\frac{n}{2}} \frac{(n-i)^2}{2}$

[obsidian monolith]

yesfood

[bronze sandal]

the only reason i want to simplify it is because im trying to find its time complexity and the summation was the exact worst case, but apparently it's the same as O(n^2)?? sorry not exactly precalc but i wasnt sure where else to post this and ii would still like to know how to simplify this if possible

oh and sorry to be more clear, yeah i do mean to simplify it so i dont have infinite terms lol

[iron bane]

Could someone help me out?

[iron bane]

<@&286206848099549185>

[lilac storm]

can anyone please help me with c?

[lilac storm]

anyone there that can help me with part c of this question?

[sick steppe]

the amount made between 11 and 10 will be the amount at 11 - the amount at 10

[lilac storm]

yes, i have tried that but the answer in the back of my textbook is different from what i get doing this

[sick steppe]

what does the book say?

[lilac storm]

26

[sick steppe]

Ask your teacher then, cause I'd think it's N(3)-N(2)

[lilac storm]

like is that the only way to solve this question or there is another way that's why the answer says 26, because i tried multiple times but i just don't get 26

[sick steppe]

Either the book is wrong or im smooth braining it

[lilac storm]

oh, ok then i believe in your way so you said subtracting N(3)-N(2)?

[lilac storm]

so i have defined C(t) and C'(t)

i just need help on how do you use the solve command to find the critical points?

and by the way moshill1, you were absolutely correct on the previous one. I was being so stupid and kept on subtracting N'(3)-N'(2), no wonder I would've gotten the right answer. N(3)-N(2) is correct because you do get 26 which is the correct way you told me

sorry about the previous one

but i do now need help with step 2 on how to use the solve command to find the critical points on geogebra?

[lilac storm]

anyone there to help?

[pulsar raven]

Third step "löse" means "solve" in english @lilac storm

[proper pilot]

What are real life examples on Cosine Trigonometric functions, like why is it so important that we need to ''understand'' those waves?

[hexed ermine]

Its a big part of physics, an example might be with sound

Sound is composed of different frequencies and amplitudes

Which is connected to sinusoidal waves

@proper pilot

Another example is with projectile motion, splitting an objects path into its x and y components at each point along the trajectory

both dealing with cosine and sine waves

[proper pilot]

Damn, thanks man

[upper kite]

Hey, not sure if that's the right place to post, since this is from the "Get ready for Pre-Calculus" category on Khan Academy, and not actual pre-calculus, but well, here's the problem :
Am I just being dumb here and not being able to do basic algebra ? Or is something wrong here ? Because to me this arithmetic sequence makes sense except for the first two terms.
4 - 1/5 is not equal to 3(4/5), right ? Or am I just being dumb ?

[pulsar raven]

@upper kite it is a mixed number

so it means $3+\frac{3}{5}$

[obsidian monolith]

KingIbr16

[upper kite]

This is literally the first time I hear of that, why did I have to google it, why on earth have I never been taught those in school

[pulsar raven]

but now i think it makes more sense to you right?

[upper kite]

Right, so this is basically 19/5 which is what I've been getting as an answer but written in a different way

Thank you for your help by the way ^^

[pulsar raven]

wait i did a mistake

it is $3+\frac{4}{5}$

[obsidian monolith]

KingIbr16

[pulsar raven]

yes you´re right

[upper kite]

Haha yeah I was wondering, but don't worry, I figured it out ^^

[pulsar raven]

[limpid rampart]

guys, if you add 2 other data points to a set, and the median increases but the mean stays the same

can u conclude that the data points were greater than the original median

[proper pilot]

hello if anyone have time, can someone pls check if we did it right, pls help

[viscid thistle]

How would I find the x intercepts of quadratic function that can’t be factored?

[pliant locust]

Do you have Any example?Usually just completing the square works

[viscid thistle]

Yeah the example is y=3x^2+30x-78

And I don’t know what to do since it won’t factor

I gotta find the x intercepts

[pliant locust]

Can you show your current work?
You can factor out 3 and then complete the square, it wont be fully factorized but it will be sufficient for finding the x intercept

[obsidian monolith]

rts

[pliant locust]

Usually when you cant fully factorize, you try to factorize as good as you can, it leave you with one term and you start to analyze when the expression is 0 and you then see that the 3 as coeffeicient has no impact, but that it is rather 0 if and only if the factorized term equals the negative of the other term.

$$3x^2 + 30x - 78 = 3(x^2 + 10x - 26) $$
$$x^2 + 10x - 26 = x^2 +10x +5^2 - 5^2 -26 = (x+5)^2 - 51$$
According to second equation:
$$3x^2 + 30x - 78 = 3((x+5)^2 - 51)$$
Which equals to 0 when:
$$(x+5)^2 = 51$$
$$x_{1} = \sqrt{51} -5$$
$$x_{2} = -\sqrt{51} -5$$

[obsidian monolith]

rts

[pliant locust]

There, i had a minor mistake

[viscid thistle]

I’m just confused about the second step where you got the two 5^2 from to get the new equation

[pliant locust]

So i was looking at the polynomial $x^2 + 10x - 26 $ which cant be factorized using quadratic formula, so what i did is completing the square,
My goal is to rewrite a polynomial as a perfect square, which is in the following form
$$(x+a)^2$$
When you expand a perfect square you get:
$$x^2 + 2ax + a^2 $$

and

[obsidian monolith]

rts

[pliant locust]

when you look at $x^2 + 10x -26 =x^2 + 2*5x -26$ you can notice that it is almost an expanded perfect square

[obsidian monolith]

rts

[pliant locust]

What you see is missing is a^2, which in this case is 5^2, so what you do to the expression is that you add 5^2 while at the same time you remove it. This is what completing the square is

so, here i will add $5^2$ while also subtracting it, because adding something and removing it at the same time doesnt change the expression
$$x^2 + 2*5x -26 = x^2 + 2*5x + 5^2 - 5^2 - 26$$

[obsidian monolith]

rts

[pliant locust]

If i have for example the expression $1 - x$, adding and subtracting 5 at the same time doesnt change the expression, it is just rewritten.
$$1 -x = 1 -x +5 -5$$

[obsidian monolith]

rts

[viscid thistle]

Ok that makes sense, how did you get the 51 though?

[pliant locust]

Well, that is the remains after completing the square, when i factorized the terms into a perfect square what was left was -5^2 -26

-25 -26 = -51

I think your textbook explains how to complete a square better than me but i am happy to answer more questions

[viscid thistle]

Thank you, you gave good explanations I just need more practice with it so I fully understand it

[pliant locust]

oh i notice that it says 25x everywhere because discord, it should say 2*5x

[viscid thistle]

Ohhhhhh

[obsidian monolith]

rts

[pliant locust]

What you see is missing is a^2, which in this case is 5^2, so what you do to the expression is that you add 5^2 while at the same time you remove it. This is what completing the square is

What you see is missing is a^2, which in this case is 5^2, so what you do to the expression is that you add 5^2 while at the same time you remove it. This is what completing the square is

[obsidian monolith]

rts

[viscid thistle]

Thank you, I was lookinng at some other problems and it’s making sense to me

How do you Find the axis of symmetry with a table

[pliant locust]

Try drawing a graph first to see the x-interceptions

[viscid thistle]

Thank you

[round quest]

y=-4 sec 2(x+pi )-5

how do i find the period for this

[ornate lintel]

$$y=-4sec 2(x+/pi)-5$$

^^

$$f(x)=-4\cdot sec 2(x+\pi)-5$$

[obsidian monolith]

lebedevhツ

[night isle]

Differentiate both terms and use product rule

[dark sky]

so i found the factors of x^2-4x+5, which are : x=2+i. 2-i

how would i write it in factored form

?

[sick steppe]

a(x-r)(x-s) is factored form

[lilac storm]

i need help with step 2, how do you use the solve command on geogebra to find the critical points?

[lilac storm]

anyone there to help?

[gritty wing]

I'd google it ¯_(ツ)_/¯

https://wiki.geogebra.org/en/Solve_Command

[lilac storm]

yes, i googled it multiple times and i have also tried multiple times, but i'm not getting anything. like you can see the first step which defining C(t) and C'(t), i simply enter it and i get it but i don't know why this solve command is not working?

i also have this with the question if this helps

do you know how to use the solve command to find the critical points?

are you there?

are you there?

anyone there?

[lilac storm]

anyone there to help?

[normal night]

No one is here to help

[viscid thistle]

Hello

I have a question

Where can I go for help

[uncut mulch]

can't you just do
solve C'(t) = 0

[valid estuary]

Could someone explain to me how jump discontinuites form

Like fundamentally how do you get two different y values here from a single x

[uncut mulch]

jump discontinuities arise in stuff like piecewise functions

also you don't get 2 different y values here

[valid estuary]

One is undefined

[uncut mulch]

the open circle there is to explicitly indicate that point isn't part of the curve

when x=1, y~1.8 (or w/e that value is supposed to be ONLY)

[valid estuary]

Ohhh I get it now

Ok so then how do discontinuites like these form:

Just at that particular x value the function doesn't work, but the rest is continuous?

[uncut mulch]

the function isn't continuous at x_0
however it is still defined there as indicated by the closed circle
f(x_0) = 0

[valid estuary]

Yeah ok that makes sense thanks

[pulsar raven]

@lilac storm here my solution again:
löse means solve.
$f^\prime (x)=g(x)$

[obsidian monolith]

KingIbr16

[frank rivet]

help needed

[trim hemlock]

is there any more info, especially one that specifies what f(x) might be?

[frank rivet]

nope

[trim hemlock]

hmm

[frank rivet]

i dont quite get how to do it

[trim hemlock]

then i guess you can draw anything that fits the condition

[frank rivet]

like ik what it asks for

[trim hemlock]

ok lets try the first one

[frank rivet]

but its hard to satisfy all the needs

[trim hemlock]

limit as x approaches to 1 and f(1) does not have the same value

so what impression can you get from that?

have you thought of something like a piecewise function?

[frank rivet]

no

[trim hemlock]

right? because theres is no function that can act so, just piecewise functions

so the first one seems to fit into a piecewise function kind

now how do you graph it?

just think of a simple graph

[frank rivet]

could yo u help me in making it @stuck mountain also needs help with it

[trim hemlock]

maybe a line? or a curve if you like, approaching to y=2 as x->1

[frank rivet]

we both stuck on same question on the practice sheet

[trim hemlock]

i cant give out answers

[frank rivet]

yeah i understand

[trim hemlock]

so just play around a bit

[frank rivet]

yeahh

[trim hemlock]

a line/curve , increasing/decreasing to y=2 as x goes to 1 from both side

[frank rivet]

could this work,

?*

[trim hemlock]

you are misinterpretating it

2 is the y-axis value

not the x

[frank rivet]

ahh i get it

[viscid thistle]

can someone check my answer?

[lime sequoia]

Yeah you're good

Applied power rule and chain rule

[zenith turret]

nvm

[fringe dome]

note that you can make such a function continuous

[fringe dome]

replace t by its value

compute

fill

3 steps

do for each column

[noble harness]

Hello there!

[grave tartan]

Recall properties of logs

[mild swan]

^^

or compute the thing

[bold lintel]

What do I need to do to (x^2-9i^2) in order to solve my function? I have to have 34x in my final answer and this way is not giving it

[uncut mulch]

i^2 = -1
introduce a scaling factor like a
f(x) = a(x^2-10x+25)(x^2+9)

[lilac storm]

just need help in b, how to find the local extrema

i have calculated the second derivative, i am done a and c but i'm just stuck on how to find the local extrema

to find the local extrema, do you plug in the value that you find by doing f''(x)=0 into the original eq?

anyone there to help?

[sick steppe]

2nd deriv test says that if f''(a) > 0 at critical point x=a, then x=a is a min and f''(a)<0 means max

[lilac storm]

is that what a local extrema is?

ok, thanks for your help.

[jolly spoke]

where are the y coords coming from??

etc (6, 1)

[uncut mulch]

they chose values of x where log_5(x-1) is easy to calculate

f(6) = 1

results in the point (6,1)

[glass owl]

How do I write an equation to match this function? I thought of putting this function in fractional form, and placed the equation of the slant asymptote, y=x+1, at the front, then added a fraction x in the numerator (since the x-intercept is 0), and put (x-1) in the denominator for the vertical asymptote. I don't understand what I'm doing wrong here- I can see if I remove the +1 in x+1, the equation matches the graph, but why? I thought fractional form placed the equation of the slant asymptote first, and then a fraction.

[uncut mulch]

your fraction had x in the numerator

it should've been 1 (or a different constant if the conditions were slightly different)

@glass owl

[dark sky]

does (x^2+1) and (x+1)^2 have the same multiplicity?

[sick steppe]

multiplicity of roots?

[plain abyss]

So for a what's the best first step in order to graph

Oh and Amp is 4

[dark sky]

how to find a function that represents this graph

[sick steppe]

You know the roots and the lowest multiplicity they can have

[dark sky]

yus but idk how to make the dips go low

this is what i got its got same shape and root but the dips are different

[sick steppe]

the scaling factor

[dark sky]

cute thx

for this function, does the root 0 have a multiplicity of 2?

[sick steppe]

yes x=0 has multi. 2

[pastel carbon]

Possible if I can get help with my question?

I have to find the solution to |3x+2| +5 ≥ 18 and put the answer in interval notation

I got [11/3,5]

but wouldn't it be a union interval since the sign in the question is greater than or equal to?

or am I wrong?

[sick steppe]

,w solve |3x+2|+5 >= 18

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by moshill1#9771

[pastel carbon]

thank you

,w solve |5-2x|+7<14

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Suikae#5524

[cunning raptor]

Hello there, I am very new to calc and we are currently learning the derivatives rules. I ran into this question and i tried the product rule but i didnt get the right answer. (We didn't learn the quotient rule yet).

Ans:

[full pagoda]

you can't use the product rule on a quotient

[cunning raptor]

hmm we havent got to the quotient yet, thats what i am confused about

this is listed as a practice before the quotient rule lesson

[full pagoda]

if you really want, you can write the x in the denominator as a negative exponent and then do the product rule

[cunning raptor]

thats what i did

i didnt get this:

[full pagoda]

one second

[cunning raptor]

okay

[full pagoda]

sorry i had to restart my internet

[full pagoda]

what exactly are you doing?

can you show me your steps?

[cunning raptor]

okay so

f'(x-1)g(x^-1) + f(x-1)g'(x^-1)

[full pagoda]

that notation is a bit funky but i understand what you mean

so far so good

[cunning raptor]

= (1) (x^-1) + (x-1)(-x^-2)

= (x^-1) + (x-1)(-x^-2)

[full pagoda]

still good so far

[cunning raptor]

= (x^-1) + (-1/x + 1/x^2)

[full pagoda]

i lost ya there

[cunning raptor]

= let me take out brackets

= x^-1 -1/x + 1/x^2

wait

[full pagoda]

yeah i'm not sure what you did to the right side

[cunning raptor]

brah

-1/x is

-x^-1

so they cancel out

and you're left with 1/x^2

which is the ans

[full pagoda]

oh you split the fraction

[cunning raptor]

yea i got it right?

[full pagoda]

sorry the way i thought about it, you just write it as (-x+1)/x^2, get a common denominator, the x's cancel and you're left with 1/x^2

splitting the fraction works as well though

that just wasn't my way of thinking so i was confused when you did that lol

[cunning raptor]

okay! i got it 🙂

thank you

[willow valve]

why is it that the integral can be without the dx

[vestal thorn]

What did I do wrong?

[elfin anvil]

having trouble understanding dot/cross products

can anyone help

[river patio]

https://gyazo.com/bb36344e2836cd65a3a5b797be24da43?token=c96f452313da52759dfbc43a9397218e

help

[graceful cypress]

I have a notation question. Part of why it is "difficult" to grasp certain concepts, is because of the seemingly counterintuitive ways in which things are written.

Take this for example:

why isn't it f (3x, 2y) ?

how can the first part "equate" = the second part?

x2 = 2^2 = 4

makes sense to me

but not the f (x, y) = [3x, 2y ]

[feral crater]

i might be miss understanding your question but isn't this just a question about how mathematicians decided to "write" maths? i mean f(x)=2x you wouldn't write that as f(2x). it's just how people decided that maths was suppose to be written.

one upside with the current system is that you can nest functions inside each other with an easy notation.

f(x)=2x
g(y)=3y
=> f(g(y))=2(g(y))=2(3y)

[graceful cypress]

@feral crater, thanks for replying. It is indeed a matter of convention as you put it. However, just with all symbols, I cannot imagine there being no rhyme or reason involved. f(x) = 2x

the equation just confuses me, since how can f(x) < which contains no mention of 2

equal 2x

[sick steppe]

Cause that's how the function is defined..

f(x) is analogous to y

[feral crater]

f(x) is basically a name. for the function.
we call it f(x) just to name it so that we can recall it later.

[graceful cypress]

Cause that's how the function is defined.. < oke, kind of understand where you are coming from (programmer by profession)

[sick steppe]

Nah i hate programming

[graceful cypress]

This was really helpful guys

Felt like a weird mental blockade

[feral crater]

i would say a function from programming make sence 🙂

[graceful cypress]

It is actually quite cool

f(x) can now function as a reference

for 2x right ?

[feral crater]

yepp 🙂

[graceful cypress]

f(x) = 2x

f(x) + sqrt (z)

can you compose stuff like this?

g (x) = f(x) + sqrt(x)

or better yet g (x, z) = f(x) + sqrt(z)

[sick steppe]

this is the generally accepted notation for multi-variable functions

[graceful cypress]

awesomeeee

[feral crater]

well technically but usally we tend to keep f(x) notation separate from normal.

so we usally write f(x)=2x
g(x,z)=2x+ sqrt(z)
or

f(x)=2x
h(z)=sqrt(z)
g(x,z)=f(x)+h(z)

[graceful cypress]

weird how things swing around and suddenly make sense

[feral crater]

but i think that's just random prefrence

[sick steppe]

f(variable1,variable2) = g(variable1)+h(variable2)

[feral crater]

but yeah programming is just maths logic in disguise

[sick steppe]

$V(x,y,z)=\frac{by}{a^2+y^2}$ example from my physics assignment

[obsidian monolith]

moshill1

[sick steppe]

b and a are constants not variables, so we dont write them in the function notation. Also note that x and z dont actually appear in the function

That's just because it's talking about R^3 space so you generally be consistent and write all 3 spatial dimensions

[graceful cypress]

Yeah, very good point. Sometimes I complicate stuff, because I expect them to be wholly unknown to me and hence in need of another approach or framing. However, then I suddenly realise, no: you are already familiar with this.

[graceful cypress]

Very fascinating about the constants!

[viscid thistle]

can someone explain to me how to solve this problem cuz i dont understand my teacher's logic

[pliant locust]

Use a graphing calculator or desmos.com to graph the two functions, the solutions are the points where the graphs intercept

[viscid thistle]

oh ok. My teacher only drew one graph and came up with the answer so i was confused

thanks

[vale urchin]

Here I am not certain what to do

Is Q (3, -1) and P (-1, -4)?

would it be 4, 3?

[feral crater]

almost

[vale urchin]

because it travels upward

the vector

4 over to the right

up 3?

or am I missing something

[feral crater]

sorry, yes PQ is 4,3

it's me being blind

[vale urchin]

okay I didnt see it either no worries

so thats the vector

<4,3>

[feral crater]

but really is there vectors in precalc? it's been a while for me.
yes 🙂

[vale urchin]

yes this is toward the end of the quarter though

so what happens when they dont give the graph to easily count

they just give initial point P as (-4,4) and Q = (-3, -1)

[feral crater]

you just need to calculate the diffrance

[vale urchin]

no graph

-7, 3

Im making things harder than they need to be

[feral crater]

P as (-1,-4) and Q = (-3, -1)

was the points ^^'

[vale urchin]

oh sorry im talking about a diff problem now

[feral crater]

ahh okay but yeah just calculate the diffrances in x value and y value

[vale urchin]

but it said wrong unless im being really dumb rn

op

yep

I am

[feral crater]

you got it?

[vale urchin]

no I messed it up

they said it was 1, -5

[feral crater]

okay so just take [(X1 - X2) , (Y1-Y2) ]

[vale urchin]

I did that

they said it was wrong 😦

nvm I just flip them

because terminal and initial

so x1 is actually -4

got it right thannk you

[feral crater]

yeah it's a bit confusing ^^'

hope you smash the next test and good luck mate

[vale urchin]

thanks king, I hope so

[pliant locust]

I recommend just sketching the vectors whenever you are unsure

[vale urchin]

ty

[tall basin]

any clue?

[sick steppe]

solve for when the slope of y is 3, then find the points of tangency

[tall basin]

yeah i just got the answer, it was so simple but my brain couldnt process it for some reason lol, thank you though!

[bold lintel]

I'm determined that this is just a computer thing and not my answer being incorrect

[uncut mulch]

your x-intercepts are very wrong

you aren't setting up the correct equation to determine the x-intercept

[steep nebula]

Does anyone know how to find the alternative derivative for this?

[uncut mulch]

x=-5 is NOT a solution to 0=5

[bold lintel]

I forgot what to do with that outside number after it all got factored but I think it clicked

I know I wouldnt plug that 1 back in but just to check for the 5 i guess? I forget this zero property since the last time you explained it

[uncut mulch]

you don't have to do anything with it

x=-1 is the only solution to tht equation

if you don't like the presence of that 5, you could divide both sides of the equation by 5

@bold lintel

[acoustic leaf]

Where should I start learning calculus

[vale urchin]

I think 2,2?

hmmm

2 to the right

3 upward

2, 3

4, 6

wrong?

9, -6 and -6, 2

but then add

so 3

and -4

okay okay wow good

how?

-1, 2 v

find vectort U + V

1, 1 is u

but another graph shows up

-5, 1

it goes up sorry

I am not sure

wait yes I think so

thats what its asking

so substitution

v-5 = u

so -1=2v + 1(v-5)

3v=4

okay ty

got it wrong

[vale urchin]

<@&286206848099549185>

[stuck lark]

@vale urchin stop repeatedly pinging helpers

[barren sphinx]

whats ur question

[vale urchin]

-1, 2 is v

1, 1 is u

-5, 1 is the bottom graph

[vale urchin]

And from there 0.75 as v and 0.5 as u didnt work

[vale urchin]

So my question is what do I do now?

<@&286206848099549185>

[stuck lark]

@vale urchin i asked you to stop repeatedly pinging helpers

[vale urchin]

it been 15 min

or 30 now

but 15 since last ping

[stuck lark]

no, i saw your message history, you've pinged and deleted those pings at least 5 times in the span of 10 minutes. that's a blatant abuse of the helper ping

[vale urchin]

Yes that was before though

I stopped until after 15 min

[stuck lark]

no, you can ping helpers ONCE after waiting 15min

[vale urchin]

wait what?

Is that new?

[stuck lark]

no

[vale urchin]

but what if the helpers see it and dont do anything ?

[stuck lark]

this server isn't like 24/7 customer service, there isn't a helper guaranteed to be available and willing to help every second that you're here. if absolutely no one's around to help, then too bad. you can ask again, maybe several hours from now, when there are likely more helpers around

[vale urchin]

just like I cant stare at a screen for a constant hour as well. Imposter here asked for the question, didn't help. And I can't ask several hours from now because its due today. I dont expect anyone to answer, but you volunteer to be a helper and obviously there are helpers available.

3/4?

=v

3v=4

oh

what about here -1=2v + 1(v-5)

oh

not divide by 3 on each side?

[stuck lark]

what you need to know is you blatantly abused the helpers ping. i asked you to stop doing that and you didn't listen. abuse the ping like this again and you get a warning

[vale urchin]

I stopped and I said after 15min, I've read the rules plenty, I only remember it being a 15min time limit.

and thanks for the help today

[stuck lark]

pinging after 15min is one thing. pinging several times in the span of 10min is another and is clearly abuse. make sure you understand this

[vale urchin]

I did stop, you gave me my warning, you've helped me a lot today. So thank you.

[uncut mulch]

not divide by 3 on each side?
you could divide both sides by 3 from 3v=4
but doing so does NOT get you v=3/4

[vale urchin]

its 1.3333333333

4/3

but I thought you said it wasnt?

No worries already got it

Thanks for your help, emphasis on help.

[silver musk]

can someone help me find the domain for this function like i can easily find it by using log division and power laws but what about without it?

[trim hemlock]

Think of two things

What cant you have in a fraction

What cant you have in a log

Theres no need for quotient and power rule here

[silver musk]

ah aight i see now

does using the laws change the domain or anything

like is it legal ?

""

[trim hemlock]

No, but its not necessary

[trim hemlock]

No to this i meant

[silver musk]

thanks man

i got another question

like when it comes to finding domains for rational functions, is it always a good habit to try a factorise all components to see if any roots cancel out

that way they may not be a constraint

[trim hemlock]

Can you give a more specific example?

[silver musk]

like for example

or other ways where the numerator is not factorised but the denominator is

[trim hemlock]

So what you meant is you want to factorise the x^2 - 4x + 3 into (x-1)(x-3) and then cancel the x-1 out

The answer is yes, you can do that to find the domain, but you also have to be careful

[silver musk]

yeh idk how that is mathematically allowed

[trim hemlock]

Bevause when x=1, its 0/0

Which is a bad thing

[silver musk]

lol

[trim hemlock]

So when you cancel things out there must be a condition to go with

[silver musk]

so its best to cancel it straight up ?

[trim hemlock]

No

Its best to just leave it as it is

You can cancel it out, but you have do it carefully

[uncut mulch]

when finding domain, you don't factorise to cancel stuff with the numerator
you factorise to easily identify when the denominator is 0 and your expression undefined

[silver musk]

but then how do u explain why theres no asymptote at x=1

cus u got 0/0

?

so it must be a point on the graph

?

[uncut mulch]

(x-1)/(x^2-4x+3) = 1/(x-3) when x \neq 1

[silver musk]

what does the ast part

mean

[uncut mulch]

which last part?

[silver musk]

x/neq 1

[uncut mulch]

when x isn't equal to 1

[silver musk]

ohh

i see

so how do i know wether x =1 is part of the domain

[uncut mulch]

determine whether there are components that will make your expression undefined

if you're dealing with rational functions, you'd only really need to consider the denominator for the domain

[silver musk]

im just confused because upon first glance subbing in 1 into the original provides an error