help-0

[heady egret]

wait am i right

wait

we have (2,5)

left by 2

we have (0,5)

up by 4

we have (0,9)

g(0) = 9

?

but what does he want from us

[dense blaze]

It’s called graph transformation
Graph compression means 2/5g(x)
Shift left means g(x+2)
Shift up means g(x) + 4

[heady egret]

g(x):g(x) = 1 lol

Isn't it meaningless or i dont know

what is g(x):g(x)

[dense blaze]

That’s the notation for equation for g(x)

It’s not the ratio

[summer shore]

@dense blaze so is it 2/5(x+2)+4? also how would i know the slope of the slope of the line and vertical intercept

[dense blaze]

you got g(x) to be y = mx + c form

gradient/ slope is m

y intercept is c

[summer shore]

oh

ok thank you mr pikachu

.close

[lone heart]

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[tardy raft]

I don’t remember how to do this exactly but from what I think I remember I got 8

[tardy raft]

Is that correct and if not can someone help me

[waxen flame]

Looks good.

[tardy raft]

Actually?

Yo be clear how did you solve it?

[waxen flame]

Used ratio of similar triangles.

[tardy raft]

Yup ok

Ima keep this help chat open as I might need help later on

Is this correct?

[waxen flame]

No.

[tardy raft]

How not?

Opposite to it is the shortest angle

[tardy raft]

???

[waxen flame]

You need to estimate the values of all the line segments.

[tardy raft]

Wdym?

[waxen flame]

Assign a value to any one of the sides opposite a given angle measure and use that to calculate the lengths of the other sides.

[tardy raft]

Isn’t it simply smallest angles opposite is the smallest side

[waxen flame]

No.

[tardy raft]

I’m sry but I don’t get it all can you show me what you mean on one line v

[brittle lava]

use a ruler

[tardy raft]

??

[waxen flame]

Are you familiar with the Law of Sines?

[tardy raft]

Yes

[waxen flame]

Set BD equal to 1 and use the Law of Sines to calculate the lengths of every other line segment.

[waxen flame]

While true for one triangle, there are two triangles in the question.

[tardy raft]

Can’t we do each seprratley?

And choose the shortest angle

[waxen flame]

For triangle ABD, you can use that rule to determine that BD is the shortest side for triangle ABD, that does not necessarily hold for both triangles ABD and ACD.

[tardy raft]

Ohhh ok

Is it dc?

[waxen flame]

What makes you say that?

[tardy raft]

Nothing I don’t know how to do sine thing you said

Doesn’t it use sides?

[tardy raft]

BC?

[tardy raft]

It has to be according to this

[waxen flame]

How would you mathematically prove that?

[tardy raft]

I did the sine stuff

Land it was the smallest

And*

[waxen flame]

👍

[tardy raft]

It’s correct?

Please say yes

[waxen flame]

Yes.

[tardy raft]

Ok thanks

What about this question?

I think it’s c

I just don’t get the radius part

Only one with -7 and -3

[waxen flame]

Correct.

[tardy raft]

What would the concept for this be?

Like last one was sines

[brittle lava]

construct lines OA, OB, those are of length r, use the arc's length (120) to find the angle theta AOB, arc=radius * theta
(theta is just the angle)
consider the triangle AOB construct its height which corresponds to the distance from AB to the origin of the circle, use trig to find the height

also notice that triangle AOB is isosceles because AO and OB are the same length r, that means that the height meets the chord AB in a point M, such that AM = MB

[tardy raft]

How do I find ab though

I mean ob

Or is

Oa*

[brittle lava]

actually, mAB=120 means that the angle AOB is 120

[tardy raft]

Oh

Does that mean we divide it in half for two triangles?

Or no?

[tardy raft]

?

[brittle lava]

that's right, angle AOB = 120°, but now that you've constructed its height, how many degrees is angle AOM?

[tardy raft]

60!

?*

[brittle lava]

it is correct but why would you say that?

[tardy raft]

Bisecting

So half

[brittle lava]

angle AMO, how many degrees is that?

[tardy raft]

60

90*

[brittle lava]

ok, so now what do you do to find AO?

[tardy raft]

Sine?

[brittle lava]

notice that the triangle AOM is right and AO is its hypothenuse

[tardy raft]

Pythagorean theorem

But idk the value of no

Mo*

[brittle lava]

exactly, so you can't use pythagorean theorem

cosine and sine will work

[tardy raft]

Wait how though

Like what just simply cos sin and tan

Like x/5

[brittle lava]

consider angle AOM, it is 60°, now, cosine of angle AOM, what is that exactly, you know the cosine of an angle in a right triangle is the ratio of two sides, which?

[tardy raft]

Huh

[brittle lava]

one is always the hypothenuse

[tardy raft]

Yes and one is

Adjacent

[brittle lava]

so in triangle AOM, what is the cosine of angle AOM?

[tardy raft]

X/c

Cosine using sides no?

X/x*

Or angles?

[brittle lava]

in this picture, cosine of angle A, what is that?

[tardy raft]

B/c

b*

[outer phoenix]

b/c

[brittle lava]

that's right, so in our triangle AOM, cosine of AOM, would that be also the same ?

but our b and c are names differently

[tardy raft]

Oh you want the names

Mo/ao

[brittle lava]

yes!

but both are unknown, so try with the sine of the same angle

[tardy raft]

Ok

Am/ao

5/x

??

[brittle lava]

yes

sine(60°) = sqrt3/2

so sqrt3/2 = 5/x

find x

[tardy raft]

5.763502692

So 10sqrt(3)/3

[tardy raft]

Right?

[brittle lava]

yup, so now to find OM, you either do pythagoras or cosine of the angle again

[tardy raft]

Ummm so 5.76 is ao?

[brittle lava]

yeah

[tardy raft]

I got 8.33333333 for om

[brittle lava]

yeah that's wrong

[tardy raft]

Oof

[brittle lava]

what you do

[tardy raft]

Took square of 5.76 and minutes 25 by it

For got sort

[brittle lava]

you forgot to sqrt everything

[tardy raft]

Answ we is B

Thanks

5sqrt(3)/3

Right v

[brittle lava]

yeah, and for next time you could've also used tan of angle AOM

[tardy raft]

Oh ok

[brittle lava]

👍

[tardy raft]

This is 74 right?

We can do 360-280-106 or no?

[brittle lava]

explain your steps

[tardy raft]

Umm

Those were my steps above?

360-106-180

[tardy raft]

Yup

[brittle lava]

that way you find angle APC

[tardy raft]

So how would we go about this?

[brittle lava]

triangle ABP

is, once again, isosceles

[tardy raft]

Yes

Is angle sob 106

It’s 37!

[tardy raft]

The answer?

[brittle lava]

37

[tardy raft]

The answer is 27 right

37*

[tardy raft]

I’ll take that as a yes

[brittle lava]

yes

[tardy raft]

Ok nice

[tardy raft]

You there?

[brittle lava]

yeah

more geometry?

[tardy raft]

I have. a few questions left

And then I’ll be done hopefully

[tardy raft]

Ye

So for the question above we have one common angle

And parallel sides

[brittle lava]

the angle in common is?

[tardy raft]

C

[brittle lava]

ACB and ECD you mean

[tardy raft]

Yea mb

[brittle lava]

so they share an angle

now use the fact that AB // ED

[tardy raft]

Yea

Is it aa theorem?

[brittle lava]

Idk about the names tbh, but they share angles, 2 of them are needed for them to be similar

[tardy raft]

That’s what aa is angle angle

So?

Another problem?

[tardy raft]

?

[brittle lava]

construct AD, CE

prove the triangle similar to find BC's length

[lone heart]

@tardy raft Has your question been resolved?

[tardy raft]

One second ok

Hi ownthpugh

How though

Idk where to go from what you said at all

[brittle lava]

what have you done already?

[tardy raft]

Creates the lines

Only that

[brittle lava]

notice ABD and CBE are congruent

[tardy raft]

Yes I noticed

[brittle lava]

notice also that DAE and DCE, look at the same arc DE, meaning angle DAB is congruent to angle BCE

two angles, similarity

find ratios between them now

[tardy raft]

Rations between the angles?

[brittle lava]

no sides

the angles are all equal

the sides of similar triangles are proportional

[tardy raft]

I give up on this question

I will go to it later

How would I do this I’ve drawn the diagram?

[brittle lava]

euclid's 2nd theorem

have you studied it?

[tardy raft]

I think I can’t remember

That wasn’t the name though

[brittle lava]

in a right triangle the square of the height relative to the hypothenuse is the product of the projections of the other sides of the triangle to the hypothenuse

DC^2 = BD•DA

[tardy raft]

Ok

How do I go about this?

[lone heart]

@tardy raft Has your question been resolved?

[lone heart]

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[median oar]

Let me see if I understand LU vs PLU.
For any given (square) matrix, we can suppose it can be factorised into a lower and upper triangular matrix, multiplied together, and solve the system of equations given by that statement.

[median oar]

Now we end up with a system of equations to solve for to find out what the L and U are exactly

Then as with all linear systems we can either have no solutions, a unique solution or infinite solutions

So for any arbitrary A, we can have either of these cases

[median oar]

LU decomp can be done when this has a unique or infinite solution set

[median oar]

PLU is needed when the solution set doesn’t exist

And both methods are numerically unstable?

[naive valley]

this all sounds correct up to the last sentence, i'm not sure about numerical stability although wikipedia claims that LUP is numerically stable "in practice" if you use partial pivoting, so presumably the same is true of PLU

[median oar]

Hmm

I’m not too sure how exactly pivoting helps the numerical stability

[lone heart]

@median oar Has your question been resolved?

[lone heart]

@median oar Has your question been resolved?

[lone heart]

@median oar Has your question been resolved?

[vapid shuttle]

.coose

[median oar]

.close

[lone heart]

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[surreal meadow]

--prune

[vale wigeon]

and so the saga ends

[lone heart]

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[vale wigeon]

. hold on, green names can prune???

. then what did maximo just do

[pale kestrel]

what he did was troll u

[pale kestrel]

.close

[lone heart]

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[young finch]

celos

[sly mantle]

shuri needs help

[pale kestrel]

yeah i dont wanna get up

[surreal meadow]

ann i just wrote prune after roketto did it lol

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[alpine sable]

Where do I start?

[young finch]

wouldnt you just find the taylor series?

[near apex]

Write it in form of infinite degree polynomial. Then do what is asked.

Although i don't really know what is the radius of convergence so i dunno about that.

[young finch]

RoC is solved after you have the summation

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

I found the taylor series but I have no idea what to do next

[young finch]

send the taylor series

[alpine sable]

its alternating so I think we use (-1)^n+1

[young finch]

yeah

any other patterns?

you dont have to expand the factorial

keep it as n!

or whatever it was

[lone heart]

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[young finch]

thatll make it easier to find the pattern that the derivative gives

.reopen

[alpine sable]

.reopen

[lone heart]

✅

[alpine sable]

x^n-1 ?

[young finch]

doesnt summation start at 0

[alpine sable]

x^n

[young finch]

yeah

[young finch]

^

send it with the factorial not simplified

[young finch]

dont see any pattern

try to expand it to the 6th or 7th degree at least for the derivative component to see if there is a pattern

[alpine sable]

(-45/8)/(5!) x^5 + (315/16)/(6!) x^6

[young finch]

i feel like theres a very obscure pattern

[alpine sable]

something to do with a multiple of 3

and 8

[earnest dune]

How do I solve this?

[alpine sable]

read #❓how-to-get-help

[earnest dune]

Ohh I'm soo sorry

[alpine sable]

16 + 8(3(n+2))?

[young finch]

multiplies: 1,1.5,2,2.5,3,7

[alpine sable]

nvm

[young finch]

how would it be that the 1st and 2nd are the exact same

the 7 throws me off

are you sire its 315

oh

wait its 16

ok so its just 3.5

@alpine sableyeah thats your pattern

trying to figure out how to implement the same term from 1 to 2

itll be something like 1/4(0.5n+1)

no it wouldnt

its like we need a half factorial

cause we will want 1*1.5*2*2.5*3...

[lone heart]

@alpine sable Has your question been resolved?

[modern sedge]

this "half factorial" could be calculated as n!/2^n if I'm not mistaken

[young finch]

oh youre a genius

@alpine sable

[alpine sable]

?

[young finch]

^

we would have to shift it forward one though

so (n+1)!/4*2^(n+1)

that might not actually work thought because we would have the right first term

[modern sedge]

are u finding taylor around x=0?

[young finch]

yeah

think so

needs a formula and a RoC

[modern sedge]

this should be sequence of derivatives, analyzing what you do at each step it seems like nth derivative evaluated at 0 is simply n! / (-2)^(n+1)

I'd recommend you analyze the process of making taylor series, instead of analyzing the taylor series itself

[modern sedge]

Spotting pattern in this is much easier, at each step you increase power by 1, change sign and multiply by n

so you can find general expression for derivative

and then make taylor

[young finch]

ah

i just told op to make the taylor series and look for a pattern

lol this would have helped a whole lot

[modern sedge]

Oh wait, I started with inital expression, so (n-1)th derivaitve is n! / (-2)^(n+1)

[lone heart]

@alpine sable Has your question been resolved?

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[lone heart]

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[fallen estuary]

can someone help me with this?

[fallen estuary]

I formed the equation 1 * e^(3t/4) = 0.64

but that doesn't give me the right answer

oh i fucked the equation

hold on

[barren portal]

[young finch]

[fallen estuary]

oops

its 1 * (3/4)^t yes

[young finch]

1 isnt necessary

why use t

[fallen estuary]

yeah

[young finch]

not wrong but weird variable for distance

[fallen estuary]

t is just what we have been using for these types of quetsions

[fallen estuary]

what is that

the top equation i get

[young finch]

bottom equation is what you wrote

[fallen estuary]

o

oops

well thanks for offering to help

.close

[lone heart]

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[opal herald]

Help

[opal herald]

its easy but tripping me tf out

[zealous lichen]

Try calculating the combination of getting both winning tickets

It should be easier than calculating its probability

[opal herald]

Wouldnt the combination of winning 2 tickets jujst be 2/250?

[zealous lichen]

I mean the combination of getting the winning tickets when buying 10 tickets from 250

[opal herald]

Oh

alr I got it thx

.close

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[lone heart]

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[fair osprey]

So I want to calculate the area, and diameter of the smaller circle for a project but I don’t know how i would go about this, the measurements are 110mm x 110mm for the outer circle but I need to know the smaller one.

[fair osprey]

I don’t understand 😭

I’m in the 8th grade…

[vale wigeon]

please open your own channel. #❓how-to-get-help

[buoyant storm]

post in your own channel

[limpid spade]

barev

[frigid basin]

I don't think the circle problem is solvable with your information

[vale wigeon]

so you are asked to calculate the area of the small circle, but you aren't told any info about the smaller circle?

[fair osprey]

nope

[vale wigeon]

then it is impossible.

[fair osprey]

oh

is there any way?

Like a close measurement?

[limpid spade]

is there a picture?

[echo socket]

Idk get your ruler I guess

[fair osprey]

I took it off Google

It’s a basic wheel for a children’s scooter

idk I tried searching for the exact measurements in Google but I wasn’t able to find any so if someone has luck help me out lol

[limpid spade]

you want to find the white circle?

[fair osprey]

Yes

[limpid spade]

we cant help

[fair osprey]

damn

[fickle sentinel]

i think he's trying to buy a scooter? that website just sells scooters

[fair osprey]

I’m not trying to buy one

I just went in it randomly searching for the measurements

[limpid spade]

i would guess around 25 mm or whatever

[fair osprey]

In diameter?

[fickle sentinel]

ok but you can only find the area of the white circle provided a radius of either circle / difference in radius

[fair osprey]

idk

I just searched it up

[limpid spade]

whats the project about

building a game?

[fair osprey]

Building a electric scooter

I’m making one myself

[limpid spade]

so youre buying wheels?

well buy them, then measure the diameter or radius of the white circle in real life xd

[lone heart]

@fair osprey Has your question been resolved?

[lone heart]

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[patent bluff]

how do i separate the a?

i need the y and the constant a to be separated from the x for integration

kinda like y=a(x)

so that after i integrate the x, i can just multiply the constant a back in

i need a process sorta like this

[mortal trellis]

just split it into two integrals?

a^2x^2 and -x^4

[patent bluff]

wdym?

can u explain that step by step?

[mortal trellis]

$\int x^2(a^2-x^2) dx = \int a^2x^2 - x^4 dx = \int a^2 x^2 dx - \int x^4 dx$ and then you can just integrate

[ocean seal]

Denascite

[patent bluff]

okay

but what about the y?

hold on

[mortal trellis]

this feels like an XY problem

can you give the whole original problem statement

[patent bluff]

i need to find the area bounded by that

considering a^2y^2, would it then look like this?

[patent bluff]

It's just "find the area bounded by the given curves and lines" and this is one of the items

[mortal trellis]

take roots and consider both the positive and the negative

a sketch of the situation might also help

[patent bluff]

good so far?

the thing changed, it's not considering the bottom half anymore.. hmm..

[mortal trellis]

the bottom corresponds to y=-sqrt(...)

[patent bluff]

oh okay,

[patent bluff]

where do i go from here?

[mortal trellis]

well now you have two functions

f(x) = -sqrt(...)

and g(x)= sqrt(...)

and you have to find the area between them

thats something you should know how to do

[patent bluff]

i just integrate this? the constant is still there

[mortal trellis]

and?

would it be a problem if the constant was a 2?

or a 17?

[patent bluff]

well that's the thing, it can't be integrated if it's an unknown constant

[mortal trellis]

why not

just solve it in terms of the constant

[patent bluff]

i need it to kinda be like this where i just integrate the x's

[mortal trellis]

for what

there is no problem with having constants inside the integral

[patent bluff]

there is for unknown constants

like what if i wanted to graph the equation first

manually

[mortal trellis]

well then you would pick some a like you did above

but that has nothing to do with solving the integral

you are solving it in general

for all a at the same time

[patent bluff]

picking a value for a isn't supposed to be part of the process, i just did that to see what the graph would look like and to make sure my algebra is all correct

[mortal trellis]

well it is for graphing

but not for solving the problem

[patent bluff]

you're not getting what i mean, i'm just gonna close, thanks for the time

.close

[lone heart]

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[fickle sentinel]

proportion question

radius of cylinder 1 : radius of cylinder 2 should just give the answer

[queen jay]

is it 3:4

[fickle sentinel]

yes it is

[queen jay]

yayy

thanks

[fickle sentinel]

sqrt81 : sqrt144
9 : 12
3 : 4

np

[queen jay]

❤️

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[ruby mist]

81 pi = 2 pi r1h1, 144 pi = 2 pi r2 h2, as they are similar, ri:r2=hi:h2, on simplifying u get 81:144 = (h1 square):(h2 square) so h1:h2 = 3:4

,reopen

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[ruby mist]

81 pi = 2 pi r1h1, 144 pi = 2 pi r2 h2, as they are similar, ri:r2=hi:h2, on simplifying u get 81:144 = (h1 square):(h2 square) so h1:h2 = 3:4

[ruby mist]

,close

[tardy stag]

.close

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[mint matrix]

Six people want to take a seat
at a round table. Two tables are different if and only if
at least two guests are neighbors at a table but not at the other.
What is the number of different tables?

I am failing to have insight on this problem

[mental flame]

Open a new channel, this one is claimed already

[mint matrix]

How to vizualise it properly

[mental flame]

!status

[lone heart]

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

[honest vigil]

Hv no idea on how to form the quadratic functions

Couldnt interpret the question

[mental flame]

What have you tried thus far?

Can I see your work

[honest vigil]

No work currently since I couldnt form an equation out of the question. Trying to figure out how I can put them all tgt 👀

[mental flame]

Ok well let's first form the equation for "300 can be produced by a machine that operates at a rate of x packages for every minute"

[median oar]

300 packages can be produced when a packaging machine operates at a rate of x packages per minute. A study found out that when the rate of operation of the machine is increased to (x + 3) packages per minute, the time saved is 5 minutes for 300 packages. Determine the new operating rate of the machine.

go wild

[zealous lichen]

calculate the minutes needed for 300 packages for both rates

And set their difference to 5

[honest vigil]

x * t = 300?

[mental flame]

Yep

Now let's go for the second part. Do you know how to form an equation from " A study found out that when the rate of operation of the machine is increased to (x + 3) packages per minute, the time saved is 5 minutes for 300 packages. "?

[honest vigil]

(x+3)(t-5)=300?

[mental flame]

Let's stick with the varible t, but yes that is correct

[honest vigil]

Typo sorry

[mental flame]

Np 👍

Now you have a system of equations

I gtg rn but feel free to ping helpers now

[honest vigil]

x = 25
Rate/min = 28?

Oh alright thanks for helping out

[honest vigil]

Sorry for the ping but if u could help me check my answers

[lone heart]

@honest vigil Has your question been resolved?

[mental flame]

Ok I'm back for a bit. Could I see your work?

[honest vigil]

x=-20*

[mental flame]

Ok were going to ignore the negative value because thatcwould make no sense in this context. I see you solved for t here correct?

[honest vigil]

Yeah

Ohh

Messed up x and t

[honest vigil]

Got the answers thanks alot 🙏

[mental flame]

Np :)

[honest vigil]

.close

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[primal warren]

local max and min

[zealous lichen]

!status

[lone heart]

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

[primal warren]

i take the partial derivatives, i get fx = e^(-2x^2-2y^2) - (4x^2)(e^(-2x^2-2y^2) and fy = (-4yx)(e^(-2x^2-2y^2), set them both equal to zero

the e term is never going to be equal zero

so with the second equation -4yx = 0

i dont know how to proceed from this point

[tardy stag]

for fx = 0 it's pretty similar

[primal warren]

this is what im thinking, the first equation 4x^2 needs to be equal 1 so that both terms subtract each other

so 4x^2 = 1 ---> x = 1/2

so i just plug the x in the second equation?

-4y*1/2 = 0 ?

[tardy stag]

this is not the only solution

[primal warren]

yeah

[zealous lichen]

Shouldn't it be 4x^3=1

Oh wait nvm

[tardy stag]

no

[zealous lichen]

I made a mistake

[tardy stag]

yes

[primal warren]

but thats not the only critical point? (1/2, 0)

[tardy stag]

quadratics have two solutions in general...

[primal warren]

oh...

oh...

thanks

the second derivative test is brutal

.close

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[warm flame]

The point (0, 0) would be a boundary point?

[zealous lichen]

yes

[warm flame]

okay just wanted to make sure

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[empty flare]

Can someone explain to me why it's not the other way around? k = z, j = y FYI

To me it should be: 1200 ( -Cos (30) k+Sin (30) j)

[lone heart]

@empty flare Has your question been resolved?

[ancient saddle]

Hello! Notice that 30° is the angle it makes with the vertical line

so -sin(30°) is correct in this case

if it was the angle it made with the horizontal line, it would be -cos(30°)

[empty flare]

oh ok

thanks

bit confusing picture then

[lone heart]

@empty flare Has your question been resolved?

[lone heart]

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[lean wraith]

Could someone show me how to finish out this Laplace equation question

[zealous lichen]

what's going on here

what is the question

[lean wraith]

I think it is a fourier series expansion of the function f(x) to find the appropriate values of Bn.

I think I have it actually. Thanks

[zealous lichen]

what is the summation thing

ok

[lean wraith]

.close

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[fervent ferry]

hello
I don't understand why the general solution to linear diff equation have this C

[zealous lichen]

when you integrate you get constant

c

[fervent ferry]

in the course i'm following they always says you can get rid of constants of integrations

"you just need one"

so im a bit lost

[zealous lichen]

when integrating you get 1 constant at the end

but when solving a differential equation you might integrate multiple times

giving you multiple constants

[fervent ferry]

i got it

equation 2 is the homog.

i dont understand why they omit the constant

it's this right?

they say the solution is just the part without the scalar

[zealous lichen]

what scalar?

[vale crag]

no

what they're saying is, if you take x_h as some non-zero solution to the DE (for example 1/2*e^(-int...) would work), then any solution of the DE can be written as C * x_h for some constant C
if you take x_h = 0, ofc you're screwed, C * 0 = 0 for any C

x_h is just some solution you use to express all the others in their thing, doesn't have to be e^(-int...) specifically

but yeah I don't really see why that's an interesting observation either

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[queen jay]

is this correct?

[thorny patio]

Yes it looks good to me

Its reflected over that vertical line

[queen jay]

yay

thanks

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[queen jay]

its B or C

and i think its B

but im not sure

[obtuse folio]

oh

[queen jay]

oh wait

this one was already claimed

mb

[queen jay]

idk

[obtuse folio]

plug 15 in your equation

also I think you guys have to take another channel

my work so far, are you allowed to bring (n+2)(n+1) out of the integral?

[mental flame]

Open your own help channel. See #❓how-to-get-help for directions.

[lone heart]

@obtuse folio Has your question been resolved?

[obtuse folio]

.close

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[wise dirge]

what would the adjacent of this triangle be?

[dense acorn]

what rules do you know to relate sides and angles

[wise dirge]

sin rule

[wise dirge]

like trig ratios?

[dense acorn]

things like sine and cosine rule

[wise dirge]

i know the sine rule

[dense acorn]

I think this can be done with just sine rule but it's a bit long

[wise dirge]

what would be the better approach?

[dense acorn]

you're given two sides and an angle, cosine rule relates 3 sides and an angle, so you can solve for the unknown side length

[wise dirge]

like the base?

[dense acorn]

it's much more immediate

[dense acorn]

yes, I assume that's the adjacent we're looking for here

[wise dirge]

so what is the cosine rule?

[dense acorn]

,w cosine rule

hmm not helpful

https://image3.slideserve.com/6482242/the-cosine-rule-l.jpg

lowercase letters here are side lengths and uppercase are angles

the choice of c and b are arbitrary, what matters is the angle and opposite side

can do this question with sine rule instead if you'd like

[wise dirge]

what would the adjacent of angle 'A' be?

like a?

[dense acorn]

either b or c

9cm would be a if you're applying the rule here, since you only know the angle opposite it

notice how C and B don't show up in the cosine rule

[wise dirge]

so we only need angle A and the length of two sides?

to use cosine rule?

it's pretty much like sine rule

.close

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[hazy rune]

hello what is the fastest/easiest way to factor quadratics. Like how do I factor $2b^4 - 7b^2 - 4$ into $(2b^2 + 1)(b^2 - 4)$

[ocean seal]

GamingGods

[tepid drum]

hello

simply use the quadratic formula to get the roots

[hazy rune]

I can only get the roots from the quadratic formula

Im trying to factor

[tepid drum]

after getting the roots you can get the factored form directly

if the leading coefficient of the quadratic polynomial is a , and the roots of this polynomial are x_1 and x_2 . then the factorized form of this polynomial is a(x-x_1)(x-x_2)

[hazy rune]

but sometimes the quadratic formula wont work

like in this case its being negative and you cant have a square root of a negative number

so Ill have to bring in "i" and everything

[tepid drum]

for example if you want to factor $x^2+3x-4$ you first find the roots which are $x_1=1 and x_2=-4$ and $a=1$ here then the factorization of this polynomial is $(x-1)(x+4)$

[ocean seal]

calculus is fun

[tepid drum]

if the roots are complex then the polynmial can't be factored in terms of real numbers

but you can still factor it using the roots and its factorization will be complex not real

for example if you want to factorize $x^2+1$ then using the quadratic formula the roots are i and -i and the leading coefficient is 1 which leads to the factorization $(x-i)(x+i)$

[ocean seal]

calculus is fun

[hazy rune]

$2b^4 -7b^2 -4$ factored is $(2b^2 + 1)(b + 2)(b -2)$ but, if you solve it using quadratic formula, you will get an awnser that has an "i" in it.

[ocean seal]

GamingGods

[tepid drum]

wait a sec

[ocean seal]

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

[hazy rune]

?

[tepid drum]

you dont hve to get the values of b which give the zeros of this polynomial

you just have to get b^2

use the quadratic formula for b^2

you can get the values of b and it will still be true

the values of b that you will get are $sqrt(i)/2,-sqrt(i)/2,2 and -2$

[ocean seal]

calculus is fun

[tepid drum]

with the leading coefficient being 2

[hazy rune]

This is too hard for me. Im trying to figure out how they went from $2y^2 - 7y -4$ to $(2y+1)(y-4)$ in one step. They first tried to find multiples of 8 which were 2,4 and 1,8. They circled 1,8.

[ocean seal]

GamingGods

[hazy rune]

thank you so much, @tepid drum

[tepid drum]

wait i made a miscalculation here

[tepid drum]

np let's work this step by step

[hazy rune]

no, ill figure it on my own. thanks though

.close

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[tepid drum]

the values of b that you will get are $\sqrt(i)/2,-\sqrt(i)/2,2 and -2$

[ocean seal]

calculus is fun

[lone heart]

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[ionic moat]

I'm currently struggling with making an equation or function of some sort

I have T, as in time, which ranges from 0 to 750 (with the step being 1)
And I need it to return Y
Y should be -160 at T = 0
Y should be -360 at T = 375
Y should be -300 at T = 750

I don't really have the knowledge to do this so if you can direct me it'd be great

[ashen palm]

what kind of behavior do you want the function to have?

[ionic moat]

Can you list some?

I don't know the names

[ashen palm]

well uh

1 second

lemme make one

[ionic moat]

Aight

[ashen palm]

ok so the quadratic equation going through those points isn't very nice

0.00092444444444444x^{2}-0.88x-160

[ionic moat]

Planning to implement this into javascript and the previous attempts were not to liking at all

[ashen palm]

do the values of Y need to be integers?

I mean ig you could always just take a floor

[ionic moat]

Doesn't have to be

[ashen palm]

Ok

[ionic moat]

(Prefer floats)

[ashen palm]

hm

[ionic moat]

Avoid big nums pretty please though

[ashen palm]

26/28125*x^2-8/9*x-160 seems to be want you'd want, anything else is going to get pretty annoying to figure out

and it doesn't get too big

here's a graph in desmos

messy numbers but it hits all the points you wanted

[ionic moat]

yeah seems about right

[ashen palm]

if you don't want as big of decimals you could always round

[ionic moat]

No need

I'll check it real quick

[ashen palm]

ok

uh wait

i messed smth up

give me a second lol

26/28125*x^2-22/25*x-160 here's the right one

[ionic moat]

Is it possible for you to last minute change T = 750 to -160?

@ashen palm

[ashen palm]

ok

gimme a sec

8/5625*x^2-16/15*x-160

@ionic moat

[ionic moat]

Thanks

Different topic

I happen to get this issue a lot

Like, I want to make e.g 0 - 500, 0 - 1
250 being 0.5 etc

How would you do that?

[ashen palm]

wait what?

OH

just divide by 500?

[ionic moat]

aaaa

And what about

0 - 750 becoming 0.5 - 0.7

0 = 0.5
375 = 0.6
750 = 0.7

[ashen palm]

divide by 3750 and add 0.5

[ionic moat]

375~0~ ah yes

checking it 😩

375 or 3750?

just making sure

[ashen palm]

3750

[ionic moat]

Interesting

Thanks

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[dreamy kelp]

I need some help making a linear system for question 10

[dreamy kelp]

I got x+y=13 for one but u can't get the other one

[gray isle]

use info in the first line

total distance of 25km

[dreamy kelp]

So I have to subtract 25km?

[gray isle]

no

write the equation what represents:
total distance travelled is 25

(looking at the diagram only and nothing else)

[dreamy kelp]

It wants the distance from home to cabin one

[gray isle]

I know

[dreamy kelp]

And cabin 1 to cabin 2 wich I got x+y=13

[gray isle]

and to find that ideally you set up equations representing what you have

(looking at the diagram only and nothing else)

[dreamy kelp]

K

[gray isle]

forget about what you just got

[dreamy kelp]

So I need it to =25

[gray isle]

focus on doing ONLY

write the equation what represents:
total distance travelled is 25

according to the diagram and I repeat ONLY the diagram,
what's the expression for the distance travelled

[dreamy kelp]

2y+x=25?

[gray isle]

no

[dreamy kelp]

The 5 tho

OH

Do I need to subtract the 5 since I have it already

[gray isle]

overthinking

[dreamy kelp]

I'm so confused 😭

[gray isle]

also trying to jump ahead

you're trying to do other things

[dreamy kelp]

O

[gray isle]

do exactly as I've asked and nothing else

[dreamy kelp]

How do I write that equation again

[gray isle]

according to the diagram and I repeat ONLY the diagram,
what's the expression for the distance travelled

[dreamy kelp]

We just learned it today in class so I'm confused

[gray isle]

how much from
home to 1
1 to 2
2 to 3
3 back to home

[dreamy kelp]

Home to 1 is x
1 to 2 is y
2 to 3 is y and 3 to home is 5

[gray isle]

yes

the sum is just those four things added together

[dreamy kelp]

X+2y+5?

[gray isle]

lowercase X but yes

[dreamy kelp]

O ya mb

[gray isle]

and you are told that's equal to 25

[dreamy kelp]

Yes

[gray isle]

though unsimplified all I wanted from you was the equation
x + 2y + 5 = 25

[dreamy kelp]

O 😭

What next

[gray isle]

you can simplify that setting that up, apply the basic principle first

you now have a system of equations which you could proceed to solve with substitution or elimination

[dreamy kelp]

Haven't learned that yet

We learning tmrw

He just wants use to use the valyes

Values*

So do I do that

For the solutions

[proven leaf]

Ramonov is saying you can get another equation by summing the distance from home to cabin 1 then from cabin 1 to cabin 2

this distance is given in the problem

use the picture and the given number :)

[gray isle]

if you want to check with option is correct, then just substitute

check whether
the x + y is actually 13
AND whether
x + 2y + 5 is 25 (or x + 2y is 20)

[lone heart]

@dreamy kelp Has your question been resolved?

[lone heart]

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[craggy spire]

Help!

[frigid hatch]

11-5 to find 6

then 6:?=11:22

the pic is confusing tho, what are those blue lengths?

[craggy spire]

I assume the total length of all of the side hingys

12

[frigid hatch]

look into thales' theorem

yes should be correct

[craggy spire]

this i would also need help with please

[frigid hatch]

try first

[craggy spire]

okay

im not really sure on how i should start with this

[lone heart]

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[ivory merlin]

Hello. i just want to know if I am correct. I did some mapping notation.
f(x)=3(-x+2)^2+2

[ivory merlin]

(x, y) → (−x-2,3y+2)

is this correct?

[foggy current]

What do you mean?

[ivory merlin]

transformation shifts the graph horizontally by 2 units to the right.
transformation stretches the graph vertically by a factor of 3.
transformation shifts the graph vertically by 2 units upward
Reflection across the x-axis

[foggy current]

Uhhh

I don't get it

Oh wait

I think I get it...

[ivory merlin]

like, how f(x)=3(-x+2)^2+2 modifies (x, y)

[mental flame]

do you mean how f(x)=3(-x+2)^2+2 relates to its parent function x^2?

[ivory merlin]

yes, thats what i mean

[mental flame]

ok, is f(x)=3(-x+2)^2+2 a function you came up with trying to map these transformations?

[ivory merlin]

no, vice versa.

[mental flame]

ohhh ok

[ivory merlin]

i got this from the equation

[mental flame]

in that case you hit all the marks but there is one transformation you shouldn't have

[ivory merlin]

uummm...

idk which one it is though.
f(x)=3(-x+2)^2+2
it shipts up 2 units and 2 right

streched vertically by factor of 3 and it is reflected

[mental flame]

what makes you think its reflected?

[ivory merlin]

f(x)=3(**-**x+2)^2+2
the - that is in front of x

[foggy current]

Isn't it reflected?

[mental flame]

if it was reflected there would be a - distributed to the whole equation. not just the x

[ivory merlin]

oh crap, i need to factor that one out dont i?

[mental flame]

i graphed it so it doesnt appear to be

[ivory merlin]

so what would that '-' mean

[mental flame]

well id imagine it was placed there to trick you

[ivory merlin]

i graphed it with desmos,

when i erase the '-', it relfects over the y-axis

i got confused 😅

[mental flame]

you cant just "erase" the -

[ivory merlin]

i did it to see what changed in the graph

[mental flame]

ohh nvm

[ivory merlin]

so it is relfected horizontally then?

[foggy current]

Yeah

[mental flame]

nope

[ivory merlin]

🤔

[mental flame]

like i said you cant just erase a - without making the equation change

[ivory merlin]

it is still the same equation. the '-' in f(x)=3(-x+2)^2+2 is not affecting the whole equation as you said

[mental flame]

here, think of it this way, gimme a min

[ivory merlin]

👍

[mental flame]

ok we have $3\left(-x+2\right)^{2}+2$ lets factor out a -1 from $(-x+2)$

[ocean seal]

Judgemental Snail

[mental flame]

if we do so we get $3\left(\left(-1\right)\left(x-2\right)\right)^{2}+2$

[ocean seal]

Judgemental Snail

[foggy current]

Oh you did it that way

Ok I get it

[mental flame]

lets distribute the ^2 to both multiples

we get $3\left(\left(-1\right)^{2}\left(x-2\right)^{2}\right)+2$

[ocean seal]

Judgemental Snail

[mental flame]

-1^2 is just 1

so we get $3\left(\left(1\right)\left(x-2\right)\right)^{2}+2$

[ocean seal]

Judgemental Snail

[mental flame]

which is literally just $3\left(x-2\right)^{2}+2$

[ocean seal]

Judgemental Snail

[mental flame]

now if you want to map the transformation now it would be less confusing considering the - is gone :)

[ivory merlin]

oh, ok

[mental flame]

does that clear things up for you?

[mental flame]

im glad :)

[ivory merlin]

i get it now

thanks

[mental flame]

np :D

[ivory merlin]

.close

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[mental geyser]

whats the equation for a and b

[gray isle]

differentiate and then evaluate at the specified value

[mental geyser]

wdym differentiate

[gray isle]

find the derivative

[mental geyser]

what abt for b

[sage marten]

e=mcsquared

[lone heart]

@mental geyser Has your question been resolved?

[gray isle]

same

only extra part is determining
when the ball hits the ground

[lone heart]

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[queen jay]

arent all of the construction marks part of the construction of the perpindicular bisector?

[gray isle]

no

[queen jay]

oh

is it 1 and 3 then

[gray isle]

yes

[queen jay]

yay

thanks ❤️

.close

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[hard aspen]

hey, can someone go through my work?

better quality

[lone heart]

@hard aspen Has your question been resolved?

[fair garden]

@hard aspen I think it can be done in a much easier way. Here is a hint - Any square of an integer is either of the form 4k or 4k+1 where k is any integer. Find a contradiction using this.

[hard aspen]

hm

would we still have to prove (x,y) = 1?

[fair garden]

Don't think so

[hard aspen]

im stuck

we'd get 8k = 3z^2

which seems to be possible

[lone heart]

@hard aspen Has your question been resolved?

[naive crystal]

This might be it....|| RHS is the multiple of 3 where as LHS is not ||

[hard aspen]

hmmm? p = 3n?

[hard aspen]

i did something similiar here tho, expressing perfect squares as 3m or 3m+1

[ocean seal]

_basudev

[hard aspen]

however, (x,y) = 1. so it cannot be 3k

[hard aspen]

i proved it here though i have no idea if its correct

[naive crystal]

I don't think greatest common divisor has a roll over here

I tried something

but I don't know if this is helpful or not

[hard aspen]

that does seem correct

this is the solution provided. i cant make heads or tails of it tho

[lone heart]

@hard aspen Has your question been resolved?

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@hard aspen Has your question been resolved?