help-17

[twin horizon]

Write this as (3/12)÷(1÷(3/8))

[vast shale]

or else im just confused

HOWWW

[vast shale]

okay

[vocal sleet]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[vast shale]

@twin horizon

[twin horizon]

Yes simplify the right abracket

1÷(3/8)

This part

[vast shale]

2.6666666666666667

@twin horizon

[twin horizon]

Or preferably 8/3

Because when a 1 is divided by a fraction the position of the denominator and numerator switch

[vast shale]

oooh

i see

so like this?

[twin horizon]

Then you get (3/12)÷(8/3)

[twin horizon]

No

[vast shale]

okok

[twin horizon]

1÷(a/b)=b/a

[twin horizon]

b ≠ 0

[twin horizon]

Yes

[vast shale]

this can be shortned to 1/4 right?

[twin horizon]

you know that division is multiplication by 1/the divisor

[twin horizon]

No

[twin horizon]

3/12 can be shortened to 1/4 not the whole thing

[vast shale]

not like that

like

[twin horizon]

You get 3/12 x 3/8

[vast shale]

not like this??

[vast shale]

so i gotta multiply them?

[twin horizon]

This is unnecessary but it is correct

[twin horizon]

Yes do you know why?

[vast shale]

no???

why

[twin horizon]

a/b÷c/d=a/b*d/c

[vast shale]

oooh

yeah

[twin horizon]

Because #help-17 message

[vast shale]

multiply with oppisate= division

[twin horizon]

Yes multiply is the opposite of Divide

[twin horizon]

You can take it from there

[vast shale]

like this

right?

@twin horizon

[twin horizon]

Yes

Then multiply them

[vast shale]

then divede by 3

[twin horizon]

Yes

[twin horizon]

Yes

[vast shale]

okay

thanks alot

how do i explain this part tho

how does the 1 disappear

whats it called?

[twin horizon]

#help-17 message

#help-17 message

[vocal sleet]

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[glad pewter]

Where am i going wrong with finding the range of this function?

[glad pewter]

This is a graph of the function, and becuase it goes to negative infinity, has a horizontal asymptote and then continues to infinity, i dont see why my answer is wrong.

[woeful igloo]

Hmm, can you tell when it has value say -5/32?

[glad pewter]

you think that could be a problem?

[glad pewter]

im a little confused by this

like if i plug that number in for X

[quaint lance]

Have you had differentiation yet?

[glad pewter]

no not yet

im in the first days of calculus

[woeful igloo]

for y or g(x)

whats the value for x if y is -5/32

[glad pewter]

there is no value the fucntion doesnt reach that

-5/32 is -0.16

the function reaches to 0.3

[woeful igloo]

so what about the range? is it still what you said?

[glad pewter]

No, it should be

[glad pewter]

like this

ignore that i put a U instead of the union symbol

[woeful igloo]

Yep thats it

Actually, that -5/16 should have a square bracket

btw, your range also included the interval (-5/16, 0) which is not there

[glad pewter]

wait im confused by this

i thought that space was empty

[woeful igloo]

yes it is empty

[vast shale]

yall crying rn all the ais gave up on me please please help me missing number is 3 <@&286206848099549185>

[woeful igloo]

but in the answer (which i assume you wrote in the image) it is included

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[glad pewter]

Thank you for your help

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[livid prairie]

the inscribed angle is half the measure of the intercepted arc

[twin horizon]

Use x/360 x 2πr = 2/5(2πr)

[nimble vector]

got it yea tyty

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[grand linden]

$y'' - 2y' + y = xe^{2x}$

[twin meteor]

Baby Einstein

Baby Einstein

Baby Einstein

Baby Einstein

Baby Einstein

[raven merlin]

"Baby Einstein"?

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[novel iris]

I have the function
$g(t-t') = \begin{cases} \frac{e^{-0.4 (t-t')}}{\sqrt{3^2-0.4^2}}\sin{(\sqrt{3^2-0.4^2}(t-t'))} & t> t' \ 0 & t\leq t' \end{cases}$
And I'm trying to take its convolution with some arbitrary function $f(t)$
so I reached
$\int_{-\infty}^{\infty}g(t-t')f(t')dt'$. Because $g$ is 0 for all times prior to $t'$ does that mean I'm allowed to change the limits from $t'$ to $t$?

[twin meteor]

KySquared

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[novel iris]

<@&286206848099549185>

[novel iris]

Nvm I got it

.close

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[warm vector]

I'm doing some statistic for sports outcomes and want to make sure what I'm doing is correct. Let's say two teams are playing each other. One team wins 80% of their games. The other only 10%. You could say that team one has an 80% chance of winning this game because that is their record so far. But what is their chance of winning the game vs team 2? I would assume that you take team 1 chance of winning and multiply it by team 2 chance of losing. So that would be (.8 * .9) = .72. So does this mean that team one has a 72% chance of beating team 2? If so, why is their chance lower than their overall win percentage when the team they're playing against is so bad?

[dense cedar]

80 + 10 doesn't sums up to 100% , so 10 % draw ?

Oh wait i understand*

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[warm vector]

nO

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[dire torrent]

Having some trouble with this one

[dire torrent]

The multiplication of z by e^-iφ should map the point to one belonging to the line rotated by a value of -φ, since that's the angle it forms with the real axis, shouldn't the resulting line be contained within the real axis?

And, thus, wouldn't its distance be precisely the real part of ze^-iφ?

<@&286206848099549185>

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[surreal basin]

3. d = |Im(e^(-i phi) z)|

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[placid totem]

can someone explain what's happening in this?

I know I need to get it to sin theta/theta so the limit = 1 * 3/4

[kind light]

what do you not understand here exactly?

like the transformation to get from the left to the right? or why they did that? or something else?

[placid totem]

I guess the transformation

[kind light]

take out 4 from the denominator, then multiply numerator and denominator by 3
do you get this?

[placid totem]

when you say take out 4 from the denominator, I don't get that.

what happens to the numerator if you do that

[kind light]

$$\lim_{y\to0}\frac{sin 3y}{4y}$$
$$\lim_{y\to0}\frac{1}{4}\cdot\frac{sin 3y}{y}$$
$$\frac{1}{4}\lim_{y\to0}\frac{sin 3y}{y}$$

[placid totem]

ohhh okay

[twin meteor]

Skill_Issue

[placid totem]

that makes sense

and then you're just moving that new 3 in the numerator over to the 1/4

that way it's sin 3y/3y

okay I understand now

thanks!

[kind light]

np!

[placid totem]

.close

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[cunning beacon]

part c

[cunning beacon]

i'm having a difficult time visualizing this

and don't really know how to approach this

[waxen hawk]

Hello

Put them into a matrix then take the discriminant

[cunning beacon]

for part c

[waxen hawk]

It is the angle between the normal vector and the vector

[cunning beacon]

what do i put in a matrix

[waxen hawk]

What

[vocal sleet]

@cunning beacon Has your question been resolved?

[cunning beacon]

do i put all vectors in a matrix

because i thought that would just be doing scalar triple product

which would find the volume of the shape

u • (v x w)

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@cunning beacon Has your question been resolved?

[cunning beacon]

<@&286206848099549185>

[lone ocean]

Yes

[cunning beacon]

wouldn't finding the discriminant of that just give the volume?

[lone ocean]

Dude u can think of triple product as basically dotting the normal vector with another vector

Divide by their magnitudes

[cunning beacon]

can you maybe write it out?

i'm having trouble following

[lone ocean]

See v x w will give u the normal vector

And dot this with the other vector

And divide by magnitudes

[cunning beacon]

divide by the magnitudes of v x w and u?

[lone ocean]

Yeah

[cunning beacon]

why tho

what does that leave you with

[lone ocean]

Angle

[cunning beacon]

how

[lone ocean]

U get cos theta

Wait I'll do it for u

@cunning beacon

[cunning beacon]

i understand what you're doing, (U • N)/(|U| |N|) gives us cos of the angle between U and N, but N is orthogonal to the plane so i'm not seeing how that gives us the angle between U and the plane

is that how you're supposed to find the angle between a vector and a plane?

by finding the angle between that vector and a vector orthogonal to the plane?

[vocal sleet]

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@cunning beacon Has your question been resolved?

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[bleak prawn]

https://imgur.com/dIPbtIt

[bleak prawn]

WRA says ln(x^2) = 2ln(x) is 'True' but it shows they have 2 different graphs?

Also I thought a negative number for x in ln(x^2) is valid but a negative number for x in 2ln(x) isnt?

So are they equal or not?

[magic wasp]

The domain of 2ln(x) is the positive real numbers

On that domain, they are indeed equal

[bleak prawn]

Ah oke

Makes sense

Thank you!

❤️

.close

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[warped osprey]

did up to this step but idk if its right

[woeful stream]

you basically just need the $x^0, x^1, x^2$ coefficients

[twin meteor]

Element118

[warped osprey]

the thing is, wudnt there be like multiple r values for the x=0, 1 and 2 coefficients

unless i did smth wrong in my expansion

[woeful stream]

the only way you can get a coefficient in that range is r=0,1,2

so you might as well just write the first few terms of $(1+x)^{13}$

and multiply out

[woeful stream]

probably some mistakes here

[twin meteor]

Element118

[warped osprey]

oh ok lemme do that

[warped osprey]

so are the possible terms 2(13x)+2+2(78x^2)+ax(13x)+bx^2

alr i got it tyvm

.close

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[mild trench]

ok so

[mild trench]

wait lemme finish from what I know

[kind light]

!original

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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[dense cedar]

!xy

[vocal sleet]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[mild trench]

find the values of X in x^2 - 3x = x^2 - x^3

[dense cedar]

You have solved it correctly

[mild trench]

thanks

[outer warren]

you have a stray - sign there

[dense cedar]

💀

[sterile island]

@everyone if x =2 .find the the value of y=x+10

[vast shale]

that's ur doubt??

[hushed agate]

This guy had been posting trolls in various help forums

[mild trench]

oops

ty

.solved

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[short shuttle]

deriving a general expression for the no of ways a composite no can be expressed as a product of its co prime factors

[vocal sleet]

Please don't occupy multiple help channels.

[short shuttle]

.close

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[neat gazelle]

i didn't think there would be a math server tbh

[neat gazelle]

hold on

[dense cedar]

Huh!?

[fervent wasp]

Do you have a question?

[neat gazelle]

yep

just give me a sec

Given log2 3 = p and log3 7 = q. Express log42 63 in terms of p and q

i have 0 clue how to do this question

my first thought was to change 42 but im not sure how

[dense cedar]

ln 3/ln 2 = p , ln 7/ln 3 = q
ln 63/ln 42 =. (ln 7 + 2ln3 )/[ln7 + ln 2 + ln 3]

[neat gazelle]

does ln mean it doesn't have a base?

[dense cedar]

ln means base e

[neat gazelle]

oh right

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[tired pagoda]

I forgot how to turn the second length into a positive because their side lengths of a rectangle. What do i do to change it into a positive?

[soft walrus]

nope, you are actually solving just for l in that quadratic

and becasue negative side lengths make zero sense we actually discount those in the context of Geometry

so we know our rectangle has a length of 45, and the -5 answer is called extraneous

[tired pagoda]

is there a way to get both sides positive using this method?

[pine hull]

Nooo, you might get both positive, both negative, one positive one negative. That's how quadratic equations works

[tired pagoda]

sure thx

[pine hull]

As it is related to length of an object, you need to consider the positive one only

[tired pagoda]

ok

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[tropic hull]

How can I prove

[gentle thicket]

open a new help channel

[twin horizon]

Rationalizing

[gentle thicket]

this has been closed

[velvet zephyr]

this is easy

[vast shale]

make a triangle

the easiest way

or if you know the half angle formula for cos2a

its a piece of cake

[velvet zephyr]

multiply by 1-cos theta

[twin horizon]

I did this in 2 years ago

[velvet zephyr]

I mean 1+cos theta

or anything

[vast shale]

why

make a triangle

lol

[velvet zephyr]

Okay. So?

[twin horizon]

It was fun doing trig identities for the first time

[velvet zephyr]

Bro has experienced life

[gentle thicket]

y'all trying to help
and the OP posted the question in closed channel and left

[tropic hull]

Thankyou all

[velvet zephyr]

if you're done do .close

[peak matrix]

hypothesis rejected

[peak matrix]

not gonna work lol

[twin horizon]

[velvet zephyr]

or i'll call the mods

[gentle thicket]

but still it's a closed channel

[velvet zephyr]

Ok, you can go

[peak matrix]

still, not A -> not (A and B)

[tropic hull]

.close

[peak matrix]

It's okay, it's already closed

[velvet zephyr]

<@&268886789983436800>

.

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[velvet zephyr]

. I did actually

After this I should be given the honourable role

[velvet zephyr]

.close

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[fathom roost]

I don't I know where I went wrong

for the x value asymptotes

Omd

nvm

im reading the answer wrong

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[jagged swallow]

help k i hhh

[jagged swallow]

with a

sintheta x 1/tantheta

then what

[ornate ember]

try instead to turn cot(x) into cos(x)/sin(x) instead of 1/tan(x)

[jagged swallow]

oh valid

[ornate ember]

it should simplify nicely 🙂

[jagged swallow]

hey thx s omu ch mwah

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[whole geode]

i’m trying to solve these system of linear equations and i’ve already tried using the substitution and elimination method and i got (31/6, -8/9) but this thing is saying im wrong and i don’t know what i’m doing wrong. if anybody could help walk me through this i would appreciate it. also i’m so sorry my handwriting is terrible and you can tell i erased this 448927284 times

[white hearth]

ah first step you could eliminate the denominators

because if you have 1/2 x = 5 its the same as 1x = 10

[velvet zephyr]

you have drawn in the third line a 'ण' .

but forgot to put a horizontal terminated line

[white hearth]

and then you have it easier with calculating

[drifting jackal]

What does the instructions say?

[drifting jackal]

I mean your solution is correct

[whole geode]

yeah, i don’t know why it’s saying i’m wrong i re-entered it 3 times

[drifting jackal]

The format could be wrong?

[whole geode]

i was thinking that the -1/3 is supposed to have an x infront of it in the problem but idk, i might just have to email my professor or something

[drifting jackal]

If you press the "practice another", the practice is similar to the original, see if there is an x in front or not

Or solve the practice and see what it expects

[whole geode]

oh thanks i didn’t think of that, it gives me the same kind of problem but ill try solving it and see

bro i’m definitely doing something wrong here, the answer is 8, -3 and im getting these big fractions. like im jusy following the elimination method so i dont know

[drifting jackal]

Lol it is missing the x

It's -(1/4)x

[whole geode]

dude, this is so annoying lol. hold on i’m going to try to solve the other one with an x and see if i finally get the answer

finally

.close

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[drifting jackal]

You should report that to your professor

[whole geode]

yeah i’m going to email her loll

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[cobalt pilot]

anyone know what to do for this? lim x -> pi/4 tan(x) - 1 / cos(X) - sin(x)

[somber portal]

have you tried separating it in two fractions?

[worn bobcat]

where are the parenthesis?

I would probably write tan(x) - 1 as (sin(x)-cos(x))/cos(x)

And then in the denominator you get a sin(x)cos(x), which you can simplify using sin(2x)=2sin(x)cos(x)

[dim pumice]

where do you get a sin(x)cos(x)

[dim pumice]

$\frac{\tan(x)-1}{\cos(x)-\sin(x)}$

[twin meteor]

rbit

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[uncut mist]

so i did the problem and for some reason the website i entered it into is saying its wrong but idk what i did wrong

@tired kelp idk if ur still here

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[uncut mist]

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[sinful ermine]

Doing pre-questions going into college this fall. Am curious how one would solve this:

[worn bobcat]

@sinful ermine Can you tell me what the set A x B is?

[sacred remnant]

now i'm interested too

[sinful ermine]

If I were to go about making it in my mind it would be the set of ordered points from A and B

[worn bobcat]

how many elements are there in A x B? do you want to list them out?

[sinful ermine]

So like: (2,1), (2,3), (2,5), (4,1) , (4,3) , (4,5)

[worn bobcat]

Excellent!

So some of those elements are gonna belong to U and some of them are gonna belong to V and some of them are gonna belong to W (although that one's pretty easy)

Do you understand what the blue condition is saying?

like what it means for a pair to be in U

(hint: a pair is in U if the second number is ... than the first number)

[sinful ermine]

Does a air being in U mean it satisfied the function?

*pair

[worn bobcat]

short answer: yes. long answer: you should call it a condition, not a function. but yes.

[sinful ermine]

Yes I see because it is an inequality

[worn bobcat]

yes exactly

[sinful ermine]

So V would be the only function

[worn bobcat]

and strictly speaking there is no such thing as "satisfies a function", although sometimes people say that when they mean "this value is a zero of the function"

[sinful ermine]

Okay I will keep that in mind

So far, are a) and b) answered?

What is an arrow diagram as asked for in c)?

[worn bobcat]

Yes, indeed. Why is U not a function?

Do you know the precise definition of a function?

[sinful ermine]

Off my mind, a relationship of taking an independent variable to output a dependent one

[worn bobcat]

yup, more or less

you noted that W is a function, why is that?

[sinful ermine]

Did I? I see it as a set

[worn bobcat]

yeah so I actually was a little quick to conclude that you got part b) right

So the crazy thing about functions is that they're actually relations, and relations are actually just sets

[sinful ermine]

Okay. I saw this online and I thought the problem was more complicated than it seemed

[worn bobcat]

so therefore functions are technically just sets

[sinful ermine]

That is interesting

[worn bobcat]

maybe we should actually do part c) and do part b) last because the diagram that you draw in part c) will help illustrate part b) pretty nicely

[sinful ermine]

Yes relations are sets since they are like grouping of objects of the sort

Yes, what is an arrow diagram?

[worn bobcat]

this is the arrow diagram for the relation W

[sinful ermine]

Aww I see

[worn bobcat]

so basically you draw the two sets, and any time the first element is related to the second element, you draw an arrow going from the first element to the second element

And some arrow diagrams induce a function in the sense that elements from the first set get mapped to elements in the second set as indicated by the arrows

However, W doesn't form a function because the number 2 can't simultaneously get mapped to 3 and 5

[sinful ermine]

Makes sense

[worn bobcat]

cool!

Do you think you have enough tools to solve the rest of the problem?

[sinful ermine]

So for c) I need to make sure the conditions line up as described

As per condition or function in U, V or W

[worn bobcat]

Yeah, so if for example (2, 5) is in U then you draw an arrow going from 2 to 5

[sinful ermine]

Okay so c) is just drawing it out got it

Thanks I think that’s all

Thought it was much harder than it seemed at first glance

[worn bobcat]

Haha no worries! I think it's a fun exercise because it really makes you think about what a function actually is

and just to clarify, a function f is a subset of A x B such that for every single a in A, there exists some (a, b) in f for some b in B

so every element in the domain gets mapped to some element of the codomain

and (that's not all)

if (a, b) is in f and (a, b') is in f, then b = b'

So in other words a value cannot get mapped to two different elements of the codomain, that would not be allowed

[sinful ermine]

Does A x B always form like a plane? What about (a, b, c)?

Or is not regarded geometrically like that

[worn bobcat]

If A and B are both the set of real numbers from 0 to 1, then in that case you can interpret A x B as the set of coordinates that lie inside a 1 by 1 square in euclidean coordinates

however, if A is the set of capital cities in the world and B is the set of words in the Cambridge English dictionary that start with the letter E then in that case the set A x B has no apparent geometric meaning

in that case (Canberra, elephant) would be an element of that set

[sinful ermine]

Okay I got a better idea now

Guess I’ll close this with .close thanks again!

[worn bobcat]

No problem! Keep having fun with math :)

[sinful ermine]

.close

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[austere swift]

what specific things should i point out about the boxplot when answering question d

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[hazy bone]

What does it mean to differentiate with respect to something other than x

[hazy bone]

Like $\frac{d}{d2x}(sin(x^2))$

[twin meteor]

PianoDolphin

[hazy bone]

Here I want you to differentiate with respect to 2x

What doest that mean?

Like if I am saying $\frac{d}{dx}(sin(x))$ it is asking that if I change the value of x a little bit, how does that affect the value of the sin(x), or more accurately, 'how many times' is that change bigger than the change in input, ie x.

[twin meteor]

PianoDolphin

[hazy bone]

But what does it mean to differentiate two functions with respect to each other?

Is it still related to the rate of change? or is it "if you change the value of x a little bit, 2x will change, and sin(x2) will change, but how many times is the change in sin (x2) bigger than the change in 2x?"

Is this the meaning, that we are comparing the rate of changes of two functions with respect to each othe?

and if so, the way to do it would be to first find the derivative of the upper function and divide it by the derivative of the lower function wrt x.

[edgy sapphire]

it's a parametric derivative yea

[hazy bone]

Like $\frac{\frac{d}{dx}(sin(x))}{\frac{d}{dx}(2x)}$

[twin meteor]

PianoDolphin

[hazy bone]

you sure?

[edgy sapphire]

yea like replace t with x here

it's like thinking of (2x) as the variable instead of x like you usually would

[hazy bone]

but 2x is not really a variable

I mean it is

I think it makes more scence to think of 2x as it's range

so 2x is just all the possible values in range of the function f(x) = 2x

The chain rules says $\frac{d}{dx}(h(g(x)) = \frac{dh(x)}{dg(x)} \times \frac{dg(x)}{dx}$

[twin meteor]

PianoDolphin

[hazy bone]

right?

[hazy bone]

so when we say that we are differentiating dh(x) wrt g(x), is it the same thing as this?

[hazy bone]

does this also come under parametric diffrentiation

how come we solve $\frac{dh(x)}{dg(x)}$ as h'(g(x))

[twin meteor]

PianoDolphin

[hazy bone]

that is suppoed be a dah

dash*

prime notation

[edgy sapphire]

it's h(x) up top but it could be in terms of anything right

and to do the d/dg(x) you'd want it in terms of g(x)

so it's more like dh(g(x))/dg(x)

[hazy bone]

oh, so this is the more correct way to write it?

and here we are not doing parametric differentiation?

[edgy sapphire]

they're both ways of looking at this so either way

parametric or chain rule

[hazy bone]

ok so then if I were to go $\frac{d}{dg(x)}h(x) = \frac{\frac{d}{dx}h(x)}{\frac{d}{dx}g(x)}$ will that be correct?

[twin meteor]

PianoDolphin

[edgy sapphire]

yea that's correct

main idea is that the (x) part isn't that important, like how you express the function

[hazy bone]

so the opposite then must also be true right $\frac{d}{d(2x)}sinx^2 = sin`((2x)^2)$ ?

[twin meteor]

PianoDolphin

[edgy sapphire]

something looks backwards, writing sin(x^2) in terms of u=2x would look like sin(1/4u^2)

[hazy bone]

Well I think if you use the chain rule you would also have to multiply sin`(4x^2) with 2x

[edgy sapphire]

uhh not sure, either way d/d2x should be smaller than d/dx

[hazy bone]

k

np

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[distant lark]

How do I find a vector perpendicular to two lines given their parametric equations?

[civic otter]

Take advantage of the cross product

[distant lark]

Is the vector the component multiplied by the parameter?

eg
r(t) = (0,0,1) + t(1,1,1)
Do i take the (1,1,1)?

[civic otter]

Yep

[distant lark]

After doing that, I graphed it in desmos. When I made the vector a line, it doesn't intersect both lines.

Am I misunderstanding what "vector perpendicular to two lines" is or did I make a mistake?

Oh nevermind I see now

doesnt have to intersect 🤦‍♂️

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[hybrid flicker]

you mean the De Morgan Laws here

well yeah, they have the same truth tables

so they're equivalent

Idk what you mean by distributive property

this is equivalent

to this

because they have the same truth table

and works for any statements P, Q

[loud walrus]

I think you are missreading

[hybrid flicker]

This is a mathematical property, not a "trick"

[loud walrus]

There is no trick there, you are confusing trick with assumption.

They told you that is true, right?

So you assume it, you don’t know why, but you assume it is true.

Later you can find the proof

But it is not a trick.

It is like saying (a+b)^2 = a^2+b^2+2ab is a trick

It is not, maybe u dont know why

But it is not a trick

[hybrid flicker]

that is a different property entirely

this comes from the total order over the real numbers

you're either <, = or > compared to another real number

i'm just saying this is entirely different

from this

here it's perfectly valid, it's called De Morgan's law

https://en.wikipedia.org/wiki/De_Morgan's_laws

here the 'distribution' is not one

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[amber knoll]

need help with calc

[amber knoll]

question is here

a cannot equal 0, find the lim as x is approaching a of x^2-a^2/x^4-a^4

i understand the factoring

so where i am is 1 over x^2+a^2

and i know thhe answer

dont know where the 2 is from

becauser the answer

is

1 over 2a^2

yes

i belive

a cannot equal 0

finding the lim of x approaching a

where a cannot equal 0

and if a were to equal 0 the lim DNE

yes

but where is 2 coming from

that what i dont get

kind of?

here

ill send the problem

83

i understand the process

like i know how to do the math

but what i dont get is if a can = 6 then why isnt the answer c

because you said a can equal any number correct?

or did i missread

.close

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[amber knoll]

thanks for the help btw

ur the goat

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[scenic latch]

Hello everyone

[scenic latch]

So basically, I wrote 10 because he put it to the side, then 15(4) = t, is that correct?

So 10+15(4) = t

So 70 = t

Was there a better way to write that?

[wide gull]

yup thats correct]

[scenic latch]

Okay thanks, could you help with this one also?

I have no idea where to even start on that one 😔

Is it like 71 = -1 + h or something?

[ornate ember]

Almost

consider the twice his height

[scenic latch]

Uhhh

[wide gull]

first we can say his height at age 2 is h

[scenic latch]

71(2) -1 = h?

Am I cooking?

[wide gull]

😭 😭 😭

close

[ornate ember]

Ok this is great place to stop and think for a second

basically what you said here is theat the height would be 142-1 = h = 141

So then Micah would be 141 inches as a 2 year old

That's almost 12 ft

that's a tall ass baby

[scenic latch]

Well that can't be right

Okay let me lock in

71 -1 = 2h

I actually turned the stove on this time

🔥🔥

[ornate ember]

Ooof you're so close!

remember it's "1 less than twice the height"

so it should be 71 = 2h - 1

[scenic latch]

🌝

[scenic latch]

Ion get it

Why is the -1 there

[ornate ember]

"Micah's adult height is one less than twice his height as age 2"

As another example, What if I said "you have 1 less than 3 times as many apples than me and I have 2 apples!"

So then they would have 3x as many apples as me (3 x 2 =6), and one less than that (6 - 1 = 5). So then they would have 5 apples

[scenic latch]

Does "is" mean a equal sign?

[ornate ember]

yeah pretty much

[scenic latch]

Booyah!

Thanks 😼

[ornate ember]

yep np!

[scenic latch]

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[timber badge]

Hey

[timber badge]

What exactly is poison distribution

Can anyone help me figure it out

[lavish river]

poisson

not poison

what do u want to know about it

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@timber badge Has your question been resolved?

[bronze osprey]

why don't you Google your questions

[timber badge]

Oh I did

Didn’t helped

That’s why here

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[hardy citrus]

for A why do we use the blue equation and not the purple

[hardy citrus]

sorry

not the purple but the one next to the purple

[novel wedge]

wdym

oh purple

because as the limit approaches 3 f(x) is approaching 4

[hardy citrus]

not the purple

what i meant to say was why we dont use the blue

[novel wedge]

wait use that for what

[hardy citrus]

for A

sorry if im confusing you

[novel wedge]

oh because its g(-x)

subbing -x into g(x)

[hardy citrus]

ooohh

i see

[novel wedge]

when x = 3 -> x becomes -3

[hardy citrus]

tysm

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[grim crane]

could somebody help me with this

[novel wedge]

did u plot at least 3 points to find the direction of motion?

[grim crane]

yea i think it is counterclockwise isnt it

[novel wedge]

lemme check

[novel wedge]

which points did u choose?

im getting clockwise

[grim crane]

oh

wait iam dumb

[novel wedge]

,rotate

[grim crane]

thx i neglect the 8 theta

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@grim crane Has your question been resolved?

[fervent wasp]

找到屬於你的浪漫～

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[sinful surge]

Hello how do I solve this question?

[sinful surge]

Linear algebra

[wraith moth]

row reduce until you find an equation/s with 0 on the left hand side

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@sinful surge Has your question been resolved?

[sly sierra]

there's one obvious answer

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[wheat wasp]

I am struggling to understand how to simplify square roots it also has made me realize im unsure how to multiple big numbers correctly and in a way that I can understand. I have tried to look up videos but they arnt helping much. Ive failed to remove all perfect squares from inside the square roots. For the square root of 450, 20, and 12. Im unable to do it for any though seeing as I simply don't understand it. Im currently on Khan Academy. I wish I could explain how I am stuck but it feels as though numbers are coming from the cosmos and I just don't understand how to find these numbers

[wheat wasp]

even with examples like this I still don't understand

[kind light]

what do you not understand?

[wheat wasp]

How I find the numbers inside of the square root

how did they begin to solve this

[kind light]

prime factorization

[wheat wasp]

Should I learn that first then

[kind light]

you havent?

like 12=2^2×3

[wheat wasp]

no I havnt had to do math since before covid

[kind light]

90=2×3^2×5

wtf you should, prime factorization is basically the base of this

[wheat wasp]

thank you

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[smoky pebble]

why cant we directly consider the case where just 2,3,4,5,6 cards are de arranged

[smoky pebble]

why exclusively single out 2 also in 1

question

kinda got it but id appreciate

an answer tbh

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[forest olive]

i have this probabilities question:
a teacher prepared 2 different set of questions for exam
the first set has 20 copy of it
the 2nd set has 30 copy of it
what is the chance that the first student and the 2nd student both of them get the first set of exam ?

[forest olive]

now i have the answer for this question

but i wanna ask how can i draw it in venn diagram or in idk squares

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[chrome marten]

What do you mean by diagram or square ?

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[vocal sleet]

@whole vigil Has your question been resolved?

[sullen sierra]

WHAT

USE At ai

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[muted charm]

how t is there is eqn of weighing machine

[vapid quail]

https://youtu.be/26ZMgnVKS0c?si=KNTIVzdYNkvCDKNo

[muted charm]

?

[cursive turret]

he is just spamming.

[muted charm]

.

[gentle thicket]

wdym?

can you elaborate your query

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[coarse python]

12x-3=-x² Solve by completing the square

[woeful stream]

What have you tried so far

[coarse python]

Quadratic equation in standard form

I just need the confirmation for the answer

Would this be Right good sir?

[woeful stream]

you can always try the other methods of solving to double check your work

[coarse python]

Already did

But would that be the right answer?

[woeful stream]

If all methods of solving agree, then there's good reason to think you got the right answer.

Wonder if Wolfram alpha also works

,w Solve 12x-3=-x^2

[twin meteor]

Results provided by WolframAlpha

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

Requested by element118

[coarse python]

Yup

It is

Thx

Can u close this?

[woeful stream]

refer

[coarse python]

.close

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[vast shale]

@gentle thicket

[vast shale]

what exactly is the question here…?

[gentle thicket]

seems like I am a question for him

[vast shale]

lol

[glossy maple]

,w 77^2

[twin meteor]

Results provided by WolframAlpha

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Requested by redstoneplayz09

[glossy maple]

Here is your answer

[vast shale]

fr

[gentle thicket]

frfr

[vast shale]

oh my bad ill send it

Im thinking its increasing from (18,∞)

[gentle thicket]

where's W?

oh nvm saw it

I'm blind

[vast shale]

yea w is the graph itself

[peak matrix]

Literally the whole graph 💀

[gentle thicket]

there are more than one

[vast shale]

these are the answer options

[peak matrix]

keep in mind that it has to be increasing and concave up

[vast shale]

hm

[gentle thicket]

oh okok then that should be it

[vast shale]

okay gotcha

[vast shale]

is it not increasing and concave up from (18,∞)?

[gentle thicket]

It is increasing from (3,6) I think but not concave up

[vast shale]

yea option B would have to be correct then

[gentle thicket]

yup

[vast shale]

mind if i send some other ones?

[gentle thicket]

ones😶

okay ig

[vast shale]

i appreciate it man lmao

[vast shale]

would it be A to B?

[gentle thicket]

they're looking for decreasing not increasing

[vast shale]

oh then B to C

[gentle thicket]

yeah

[vast shale]

the options btw

cool cool

[velvet zephyr]

he don't know you lil bro

[gentle thicket]

bro sent me a DM and friend request before pinging here☠️

[velvet zephyr]

💀 🙏

[vast shale]

wru

[vast shale]

wouldnt the highest roc of the temp be at may?

[gentle thicket]

uhm yeah

[vast shale]

alright, now with this one im a bit confused

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[worthy tiger]

helo

[worthy tiger]

could anyone provide me with a BPT/thales theorem question from triangles chapter class 10 cbse with the diagram

example question like thing

[thin jay]

whaat

[vast shale]

B TO C AND C TO D

[thin jay]

do you want prrof

??

[thin jay]

??? do u want proof

[worthy tiger]

yes

[thin jay]

this is the proof

ok @worthy tiger ?

[worthy tiger]

okay

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[tacit axle]

whats the fastest way to learn trig identities, verifying trig identities, double angle and half angle identities, and just solving trig equations overall? i have a test in two days. i know everything about precalc level trig besides the above. i do know some of the identities like pythagorean identities and i know the sum and difference identities.

[flat whale]

do a lot of problems you don't already know

[tacit axle]

whats a good source for that

[flat whale]

the book your teacher assigned

[tacit axle]

fair enough lmao

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[placid wharf]

Hello, I am struggling to understand where the form of the factor comes from as x^k * y^n and why it’s desired to make the equation an exact equation. Could somebody please help me understand where it comes from?

[flat whale]

it's just a trick you memorize

introduce variables k and n in the exponents, then work backwards to determine what they need to be to be exact

[placid wharf]

Okay I see, we are multiplying by those to introduce two functions of x and y, how are the differentials of x/y and xy acting in the equation as when I have seen the form for exact its
f(x,y)dx + g(x,y)dy = 0
however here we have
f(x,y)d(x/y) + g(x,y)d(xy)

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[acoustic grove]

maybe a stupid question but - can someone help me understand why that when he cancelled out 3 and sqrt x+3, when he wrote the question again later it is 3-sqrt x+3? I thought when u cancel out stuff it becomes 1

[vocal sleet]

@acoustic grove Has your question been resolved?

[acoustic grove]

<@&286206848099549185>

[visual coral]

Okay so first of all

When you distribute the 3sqrt(x-3) over the numerator, what do you get?

[acoustic grove]

the numerator of the original question?

[visual coral]

Yep

[acoustic grove]

so, what you mean is that
1

wait omg

[visual coral]

Did you realize it

[acoustic grove]

is this whats happening?

and since its multiplied by 1, 3sqrt(x-3) doesnt change?

okay if this is the case then i also have another question

[visual coral]

One of the fractions cancels the square root and one cancels the three

So yeah

[acoustic grove]

huhhh ok, also my 2nd question

this -1, where did it come from?

ignore the underlined 9 and -3 thats from the video

[visual coral]

Assuming he didn't change the denominator, let's just look at the numerator here

[acoustic grove]

yeah he didnt i just stopped mid video quickly

[visual coral]

What is (-1)(x-6)?

[visual coral]

Thought so just wanted to make sure

[acoustic grove]

-1x * 6?

[visual coral]

Yep

Which is the same numerator as before

[acoustic grove]

oh so did he like cancel it out and then had -1 left?

[visual coral]

He factored the -1 out basically

[acoustic grove]

huh ok, what im really asking is why did he "take out a -1" (he says this in the video) or like even know how to do that, is there a rule for this?

sorry for my dumb questions i have the math knowledge of a tenth grader

[visual coral]

Or you can think of it as him multiplying rhe numerator terms by -1 and multiplying by -1 again to cancel out

[visual coral]

No it's okay!

It's so he can pair these

My bad for the shitty drawing BTW lmfal

[acoustic grove]

but couldnt it already have been paired? you just rewrite it as x-6

[acoustic grove]

npnp

[visual coral]

Yeah that's what he just did

He rewrote it so it's obvious they're the same term, just one is negative

[acoustic grove]

huh, so could i skip that -1 part and still end up with the same answer as him? i dont understand why he did that

[acoustic grove]

ohhh i see

test stuff

[visual coral]

Yeah

[acoustic grove]

oh wait i also realize

in 6-x x is negative and the denominator x-6 its -6

so would that cause some issues if we didnt rewrite it and cancelled it straight away?

[visual coral]

Yeah!

[acoustic grove]

like from my profs pov, would he be like wth is going on here this chick tryna cancel 6-x with x-6

[visual coral]

You could just cancel it, but you need to remember that 6-x = (-1)(x-6)

[acoustic grove]

ahhh ok

[visual coral]

So when you divide them, you're left with -1

[acoustic grove]

so if i ever need to rewrite an equation similar like this i "pull out a -1"?

[acoustic grove]

aaaaaaaaaaaaaaa

okkkkk

big bran

help

*brain

thank you sm

[visual coral]

Np!

Good luck on your studying

[acoustic grove]

thank you!

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[main sierra]

No way bro

Ban this guy

[limber falcon]

dealt with

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[opal crow]

Can someone quickly check if this solution is correct

Wait so is it right

Then can you write it on somewhere

And take a pic

Yea I dont

[warm flame]

...

[opal crow]

I’m unsure if a meme of horse sitting on its balls is against the guidelines or nah but hell I wanna get this hw done

[warm flame]

dude what is that image..

[opal crow]

Exactly

Wow

[warm flame]

So uh

Can I get help?

Its a pretty hard issue

please..??

[opal crow]

Sure

[warm flame]

k

So

Im drawing a character and need to accurately redraw his height

I was hoping so 5 '5

Now a head is just the characters head then you measure how many makes up the body

His head is 1 and a half inches with a ruler

Hes 6 heads tall

So how do I transfer his head into like, real inches in height

Originally I determined his head is 11 inches tall

11 x 6 = 66 then divided by 12, it equaled 5.5

which I thought was 5 '5

But i was told somethings wrong so..

yeah

[opal crow]

I have no idea dude wait

Maybe ill try

Wait so is his head now 11 inches 1 and a half inches

[warm flame]

Using a ruler, 1 and half

[opal crow]

Do you have something that can measure with your character in your frawing’s scale

[warm flame]

My guess for real life is 11

[warm flame]

I used a ruler, got 1 and half for his head

[opal crow]

Because if you are drawing on paper I don’t think it mattered you just need something that has a set height to just compare it with

Like a can

[warm flame]

i just need to know his IRL height