help-28

[fast marlin]

new one aint too bad

it'll get the answers wrong but the reasoning is right

just because its a language model so it needs to put the right numbers down, and doesnt really have a calculator

[lean rock]

have you tried to visualise it?

[full forum]

@lean rock Has your question been resolved?

[lean rock]

one idea is that it is the heights of a bouncing projectile

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[torn jolt]

Can we write basis for column space from reduced echelon form? Or we always have to write it from original matrix please help

[spice orchid]

from the original matrix

echelon form tells you which columns of the original matrix you pick for the basis

[normal thicket]

Can you give an example?@spice orchid

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[trail igloo]

Guys help me with this

Can someone help

[near mirage]

The second one is

$e^{i (\frac{5\pi}{4}) 44i} = e^{A\pi + Bi}$

Therefore

$e^{-55\pi} = e^{A\pi + Bi}$

$-55\pi = A\pi + Bi$

$A = -55, B = 0$

[trail igloo]

Please

[glossy valve]

Oğuzhan

[trail igloo]

Can you solve the others

And I really appreciate it @near mirage

[near mirage]

$\int_{imln2}^0 sin(\frac{z}{144}) dz$

$u = \frac{z}{144}$

$\frac{du}{144} = dx$

$\frac{1}{144} \int_{imln2}^0 sin(u) du$

$= \frac{1}{144} (sin(0) - sin(iln2))$

$= -\frac{sin(iln(2))}{144}$

[glossy valve]

Oğuzhan

[near mirage]

Using the identity

$sinh(x) = -i sin(ix)$

$\frac{i \cdot isin(iln(2))}{144} = \frac{sinh(ln(2))}{144}$

[glossy valve]

Oğuzhan

[trail igloo]

Thank you 🙏🏽

[near mirage]

My pleasure

Please tell me if you don't understand something

[trail igloo]

What about the others ? Is it okay if u explain to me

[near mirage]

Which part?

[near mirage]

Only the last one is left

[trail igloo]

This one

[near mirage]

Which is just

$\frac{2 - \frac{1}{2}}{2 \cdot 144} = \frac{3}{576}$

[glossy valve]

Oğuzhan

[trail igloo]

No I’m talking abt the other question 😅

[near mirage]

Yeah I just simplified the first one

[near mirage]

What does it mean by C to nothing?

[trail igloo]

I have no clue unfortunately

😪

What abt this ?

@near mirage u there ?

[near mirage]

Think this as

$e^{i\theta} = cos(\theta) + isin(\theta)$

[glossy valve]

Oğuzhan

[near mirage]

Which I think you know?

Right?

Because these question require Euler's formula

[trail igloo]

Yea but the question needs more simplification

But it’s okay I’ll figure it out

[near mirage]

So $cos(\theta) = -\frac{1}{2}, sin(\theta) = \frac{\sqrt3}{2}$

[glossy valve]

Oğuzhan

[near mirage]

So theta is in the second quadrant

So we get that it's 180 - 60 = 120 degrees

So it's $e^{i\frac{2\pi}{3}}$

[glossy valve]

Oğuzhan

[near mirage]

The rest is easy

[trail igloo]

Thank uuu

[normal thicket]

But it's e^z/m@near mirage

What can we do this?

Z/m = i2pie/3 ??

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@trail igloo Has your question been resolved?

[normal thicket]

@near mirage

Here

Please look into it

[near mirage]

Where z = A pi i

The question states this*

[normal thicket]

Here

You find out value of e^i thita...but it's asking about e^z/m

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[torn jolt]

Hi

[torn jolt]

Can anyone figure out what substitution was used here?

[shrewd hamlet]

Hmm

Perhaps they did

$\frac {1}{(x^{\frac 34}) (1 + x^{\frac 14})}$

[glossy valve]

Stephen

[vast fossil]

Yeah

[shrewd hamlet]

And then they did the sub $u = x^ {\frac 14}$

[glossy valve]

Stephen

[torn jolt]

ohhh I see how that would work out damn good thinking

but wouldn't the 4 be in the denominator?

[glossy valve]

Stephen

[shrewd hamlet]

Hmm

[torn jolt]

dx = 4 / x^(-3/4) du

so no

ah I see

Okay that makes sense

Thanks alot both of you!

Wouldn't have figured that out myself

yea that stumped me, the factoring was rly neat

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[autumn mason]

Trying to obtain t from y=y0+vxt+1/2gt^2, Basically im trying to graph a ball over time but I dont know what t is.

[light sonnet]

It's a time v position graph, meaning that time is the x axis

[autumn mason]

yes

so how would I make that into a calculation

t=final x or something

[light sonnet]

What do you mean by calculation?

[autumn mason]

so im plotting a graph into a coding program, and I need to work out t, in other words i need to find y with respect to t (need to find the roots of a quadratic of y)

[light sonnet]

If you know the quadratic formula, you can use that to solve for t

[autumn mason]

Hm, still not sure how to get t, thanks anyway

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[void crane]

I’m supposed to use a limit comparison test for this, but I’m not sure what to compare it to.

[stiff musk]

can you show that 4^n > n^4 for all n > 4?

[void crane]

I'm not sure how to do that.

[stiff musk]

maybe show that it's true for n=5, and also show that 4^n has a larger derivative than n^4 for n>=5

[void crane]

Would that be a limit comparison, though? I'm supposed to use that for this problem. D:

[stiff musk]

yea, if you can show that 4^n > n^4 for large enough n, then that means your summand is >= 1/3

and you know the series whose terms are 1/3 diverges

(the terms don't even go to zero)

[void crane]

nth-term test?

[stiff musk]

yea

so you are then doing limit comparison with the series $\sum_{n=1}^{\infty}\frac{1}{3}$

[glossy valve]

Bungo

[void crane]

My homework is for the limit comparison test, though. The instructions say, "Use the limit comparison test to determine the convergence or divergence of the series." Is there a way to do this with that?

[stiff musk]

yea that's what i said in my last comment

comparing with the series with constant terms equal to 1/3

[void crane]

Ohh

[stiff musk]

your series is bigger than that one

and that one diverges

[void crane]

Would I have to use a calculator to show that term-by-term?

[stiff musk]

i think it suffices to show it for just n=5, and then argue using derivatives that 4^n has a larger derivative than n^4, for n >= 5

(pretending that n is a continuous variable when you take the derivative)

or you could probably show it by induction as well

[void crane]

Okay, I'll try that. Thank you. :D

[stiff musk]

sure, gl!

[void crane]

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[torn jolt]

please help me with this geomertry

.

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@torn jolt Has your question been resolved?

[torn jolt]

NO

i need help please

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@torn jolt Has your question been resolved?

[torn jolt]

fuck this

no one is even helping and this stupid bot asking stupid question ever

NO ITS NOT HAS BEEN RESOLVED

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[late zodiac]

Help pls

[hushed palm]

Assuming that its a right triangle
just use one of the trigonometric functions(sin, cos, tan)

specifically tan is fastest

[late zodiac]

Is it like this?
h/sin(48)=12/sin (42)

[onyx glen]

no need to assume, you know the third angle is 90°

[onyx glen]

you could do that but it is kind of excessive

[hushed palm]

its a valid way

but you have faster ways to do it

and simpler

[late zodiac]

oh alr

[hushed palm]

just use tan 48° = h/12

and find h

[late zodiac]

I am only allowed to use "Law of Sines"

[hushed palm]

wait whato

then move with your method

[late zodiac]

This is the answer I got bytw:
AB/Sin(ACB)=AC/sin(ABC)

h/sin(48)=12/sin (42)

h=13.327 ft

[hushed palm]

looks about right

[late zodiac]

So my answer is correct?

[hushed palm]

idk i dont have a calculator with me

[late zodiac]

oh alr

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[crude monolith]

In an isosceles triangle with vertex angle 110 degrees and the corresponding side equal to 14.5, determine the perimeter of the triangle.

[crude monolith]

I need help with this problem here.

[hushed palm]

wdym by corresponding side

[crude monolith]

I honestly dont get that part, thats why im here

im guessing its not one of the equal sides

[hushed palm]

no pictures?

[crude monolith]

nope

this is confusing lol

[hushed palm]

wow

im going to assume that its the opposite side

[crude monolith]

yeah

same

[hushed palm]

so this triangle will have sides a, a, 14.5

and we dont know what a is

so we will use the law of cosines

[crude monolith]

yeah

okay

c^2 = a^2+b^2-2abcos(c) correct?

[hushed palm]

you will have to do some quadratic stuff

thats correct

14.5 will be c

[crude monolith]

ok

[hushed palm]

and 110 will be the little c in the cos(c)

[crude monolith]

ok

i will plug in this info now

[hushed palm]

idk what the answer should be

i dont have a calculator with me

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[rare quartz]

i know i'm supposed to use the ratio test but i'm wondering if somebody can show me how that looks. i know i'll end up with lim n->inf |((-4x-5)^n+1(n+1)!)/((-4x-5)^n*(n!))|

[rare quartz]

but i'm not sure what the rest of the reasoning looks like

[gritty rose]

Simplify by using definition of factorial and exponent rules

[rare quartz]

wouldnt it just be lim n->inf |-4x-5| ?

that seems so wrong

[gritty rose]

Nope

Do you know what (n+1)! / n! = ?

[rare quartz]

i guess not :C

n+1?

[gritty rose]

Yes

[rare quartz]

so its lim n->inf |(n+1)(-4x-5)|

but if this is the case it's also where i'm stuck.

i'm not sure what comes after

because thats just inf(-4x-5), right?

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@rare quartz Has your question been resolved?

[stiff musk]

consider two cases:
(1) -4x-5 = 0
(2) -4x-5 is some nonzero constant

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[tacit oar]

Hello, I have a question regarding Riemann sums
https://www.youtube.com/watch?v=F0uuW-I6icY&list=PLqxPTlfRXFzZoRSzf44Huziq0mxXtZuSX&index=3&ab_channel=ProfessorLeonard
Here is the video that I learned from professor leonard^

at minute 1:11:33, it says that Xn/Ck = a + k . Δx

However, on minute 1:33:13, it magically changes to = a+(k-1)Δx

What's going on here?

[tacit oar]

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[fluid adder]

what shape is this

[fluid adder]

I forgor

I have concluded it is called a curve

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[dark escarp]

Is this correct?

[dark escarp]

Normalized form: .2347*10^11

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@dark escarp Has your question been resolved?

[elfin stream]

Yeah

[dark escarp]

Thanks @elfin stream 👍

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[tacit eagle]

hi. why is my answer wrong?

[tacit eagle]

I added together: 2, .5, 2/9, 1/8, 2/25, am i suppose to multiply by 2 first?

<@&286206848099549185>

[hot herald]

why are you adding 2/25

[tacit eagle]

thats point number 5

[hot herald]

so what

[tacit eagle]

@hot herald

so we dont add it?

1-5

is 5 points

[hot herald]

how is that related to the area of those yellow rectangles

[tacit eagle]

true

ur right

so

dont inglude

5

but

do multiply

by 2

to each term

or can i do that at the end

[hot herald]

why are you multiplying by 2

recall the formula for area of a rectangle

[tacit eagle]

1/2 bh?

so onl multiply by 1.5?

@hot herald

do i multiply by 1.5?

or .5?

or what lol

[hot herald]

1/2 bh?
NO

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[tacit eagle]

what do i multiply it y then

lol

rfecangle

b*h

[tacit eagle]

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[edgy cypress]

i need help integrating that

[rapid rain]

Try to find the best substitution possible

for example, maybe x = cos(t) or x = sin(t)...

One of them will work, but can you see which one?

[edgy cypress]

yeah ill try

[torn jolt]

Cube ABCD.A'B'C'D'. Vecto AB equals vecto a, vecto AD equals vecto b, vecto AA' equals vecto c. Demonstrate vecto AC, vecto B'D', vecto BD', vecto DB', vecto BC' and vecto AD' according to vecto a, vecto b and vecto c.

I need help guys

[edgy cypress]

um this is an occupied channel

<@&268886789983436800>

[torn jolt]

I know but noone's at my channel

[winged geyser]

please be patient and stick to your channel

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[runic spruce]

for this negation is fine but

[runic spruce]

can i set n =4k or n=4m +1 then sub into that

and disprove assumption

or is that wrong

[stable plover]

well contradiction would mean you assume that n^2 - 2 is divisible by 4 for some integer n

[runic spruce]

are u allowed to say 'this is two less than a multiple of 4 therefore not divisible by four'

or does that not make sense

nvm thats a shit method

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[torn jolt]

?

[shrewd hamlet]

What have u tried

Maypul Seerup

@torn jolt

[torn jolt]

no worries i got it

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[runic spruce]

tried calculating distance but quadratic i got has no solutions

[strong crystal]

Could you show your work?

Just so i can see what you got?

[runic spruce]

,rotate

[nova wing]

that has a root

maybe you just typo'd it if you used your calculators equation solver

b^2 - 4ac : (-8)^2 - 4(4)(4) = 64 - 64 = 0 = 1 root 🙂

[runic spruce]

i get imaginary numbers

[nova wing]

t = 1?

[strong crystal]

B=-8,c=20

[nova wing]

oh am i looking at the wrong quadratic

i'm looking at the one on the left 🙂

[runic spruce]

is my method wrong

i assumed it was

[nova wing]

assuming the quadratic is correct my intuition is maybe you don't want the roots but the minimum point of the graph?

[runic spruce]

yeah the question is asking 'shortest distance'

[strong crystal]

Wait

Yeah

Why roots?

We just want the smallest value

Not roots

Minimum

Aka

Vertex of parabola

y coordinate

Make sense?

That line is the distance

[runic spruce]

right so once yo get it into this form you know its a quadratic

because looking at the question my mind does not go straight to that

[strong crystal]

Distance cannot be negative or you did something wrong, itll only be 0 what they reach the same point

So thats why the quadratic has no real roots

Yeah

[strong crystal]

Do you know derivatives?

[runic spruce]

lol yah

so once u havve minimum point

[strong crystal]

Just find the critical point

Yeah

[nova wing]

or you can complete the square 🙂

[strong crystal]

Thats the distance

[runic spruce]

then pythagoras for distance?

[runic spruce]

yeah

[strong crystal]

Its already in the root

The sqrt term tells you the distance

We just want the min

Because distance is defined to be the shortest

Make sense?

[runic spruce]

Oh I see

I think it’s the wording that confused me😭

Thanks

[strong crystal]

Dw i was also confused at first then i realized

Happens to the best of us

[runic spruce]

Yeah lol thanks

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[strong crystal]

Np

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[inland fjord]

this is my work so far

I think I must've done something wrong bc I'm not sure how to approx arccot(3/4)

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[inland fjord]

<@&286206848099549185>

[inland fjord]

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[grizzled lion]

how would I approximate $\sqrt{20}$ without a calculator?

[glossy valve]

Price

[grizzled lion]

i think i am supposed to use linear approximation but idk how to do that

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[dense edge]

left side is incorrect?

I checked with differentiation rules and got a different answer

oh

I see what I did now

denominator lol

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[dense edge]

how would I get my left side answer to match with the right side?

without using l'hopital's rule

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[spice orchid]

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[keen shoal]

sqrt(1)?

where’d you get that from

[spice orchid]

for some reason you turned 2x into zero

[keen shoal]

recheck 3rd last step

[dense edge]

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[grizzled lion]

could anyone help me revise this explanation for linearization?

[grizzled lion]

i tried to keep it simple to understand

but i think i phrased things poorly

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[pulsar gale]

@grizzled lionits not simple

you dont linearize sqrt(20) that makes no sense

you could linearize y = sqrt(x) and approximate at x = 20 using the tangent line

[grizzled lion]

ah thank you i should make that clarification

[grizzled lion]

is this better?

[pulsar gale]

yea but it’s not just “plug into this formula”

You should have a graph

And you should explain that it comes from the tangent line at that point

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[celest fulcrum]

Hi, for the limit comparison test how do you find what to compare the original series to

[celest fulcrum]

like for this question

[distant plume]

@celest fulcrum

[celest fulcrum]

hi

[distant plume]

My strategy is to make summands that look similar that are either greater or lesser than

[celest fulcrum]

Yeah I understand that, but does it matter what u choose

like for this expression

[distant plume]

And I do this without knowing ahead of time

I do not yet know if a newly made series will be a convergent and useful as some upper bound to squish our given series into convergence

But I first try to draft a new series of similar form

Then, attempt to show that series to be convergent.

But there is some risk taking.

You can try to walk through your idea with me.

And we'll see if it works

[celest fulcrum]

I just compared it to a differnt sum and it worked which is how i got it right

but I was wondering how they got this series or if it matters if I have the same one

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[dire flame]

where did i go wrong 😦

[gritty rose]

Can't read the question

[dire flame]

i didnt rewrite the integral so it might be a little hard to follow

im looking at my teachers work but i dont understand how sin(theta) disappeared

[gritty rose]

They made a mistake

[dire flame]

there is like 50 mistakes

i keep getting 0 as my final answer though

[gritty rose]

Yea 0 seems right

Anything you integrate 0 to 2pi of sin(theta) is gonna be 0

Since r and z don't have any theta in them, whatever they integrate to will just be a constant to the theta integral

[dire flame]

are my bounds wrong?

This is a strange answer

[gritty rose]

Pretty typical actually

There are problems like this in every multivariate calc book

[dire flame]

ohh okay ty 🙂

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[dreamy tapir]

hiii pls help its Ho: u = 1 vs H1: u =/ 1

please

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[shell glen]

Problem 9. One or more options may be correct.

How do I do this.

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[viral zenith]

Hello!

[viral zenith]

This is my question

El cheapo Symbolab says to change the order of integration, I'm not exactly sure what I have to do to change the limits...

[vast fossil]

A good way to get the intuition for that is to draw the region

[viral zenith]

I still don't see it...

[vast fossil]

Try typing sqrt(y) < x < 2 {0 < y < 4}

Okay just sqrt(y) < x < 2 is enough

[viral zenith]

Okay it's given me this

So the upper limit was 2 before and now it corresponds to 3?

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[torn jolt]

Hey

[torn jolt]

How do you find principle angle

I’m still stuck on the question

[onyx glen]

$\mathrm{ref}(\theta) = \begin{cases} \theta & \theta \in [0, \pi/2) \ \pi - \theta & \theta \in [\pi/2, \pi) \ \theta - \pi & \theta \in [\pi, 3\pi/2) \ 2\pi - \theta & \theta \in [3\pi/2, 2\pi) \end{cases}$

[glossy valve]

Ann

[torn jolt]

-42pi/15 @onyx glen how would I get the principle angle

[onyx glen]

add a multiple of 2pi to it first to get the angle between 0 and 2pi coterminal to it

in so doing, also determine its quadrant

then act accordingly

[torn jolt]

Why do you add 2pi

@onyx glen I don’t understand why you add 2pi, sorry

Wouldn’t you add 2pi, and minus 2pi

Cause isn’t there 2 answers

I may be wrong tho @onyx glen

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[onyx glen]

.reopen

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✅

[onyx glen]

sorry, had to go sort sth out irl

[onyx glen]

i said to add a multiple of 2pi to it. in geometric terms this means finding its coterminal between 0 and 2pi

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[torn jolt]

Okay, so you always add 2pi? @onyx glen

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[radiant nebula]

Let ABC be a triangle, I the midpoint of [BC]. Show that the set of points M satisfying MB² + MC² = 2MA² is the line (AI).

you can use scalar product.

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[brittle steeple]

well you figured out f(5)

what's f(0.5)

so you have a linear function

and you know two points that it goes through

[opal pewter]

Just calculate the whole function

2 eqn 2 variable

Umm
Do u know the general form of linear function ?

Yep that only

y=mx+b

So (x,y)=(.5,0)
So 0=0.5m+b is one equation

Similarly form the other eqn

Yep

Wlc

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[earnest badger]

Could anyone recommend me what sort of statistical tests I could employ to compare my data? I am looking at total greenhouse emissions (dependent variable) vs GDP per capita growth. Specifically, I am currently looking at the data for lower v higher income countries, is there any statistical test that could maybe tell me if one of the two groups respond differently to changes to the dependent variable, or would simple linear regression be fine for that

[ember shadow]

linear regression should be fine, although a generalized linear model is probably more appropriate since your dependent variable is (I assume) nonnegative

[earnest badger]

Thanks 👍🏻

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[normal thicket]

https://math.stackexchange.com/questions/1368003/number-of-60th-primitive-roots-of-1

[normal thicket]

Can anyone help me with this explanation

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[lusty steeple]

How do i solve this? Number 3.

[lusty steeple]

Im supposed to find the measure of each anglr indicated

.

Welp time to bomb the math tests

[light sonnet]

Same side interior angles

[lusty steeple]

Thank you!

How to solve number 10?

7y+78=180 ?

Then i figure out what goes into y that makes 180

[ember shadow]

it's just regular algebra then

[lusty steeple]

Huh

[ember shadow]

7y + 78 = 180. just a regular algebra problem

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[teal thicket]

how would i calculate the reflected point of B using this formula | ux + vx + w| / √(u²+v²) ?

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[marble viper]

What generalized equations could I use to graph the probability curve of rolling multiple dice?

[marble viper]

I wanted to program something which would show the mean of a set of dice rolls, but I quickly realized that using a brute-force method to get every permutation of dice roll would be straining on my computer, to say the least

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[ember shadow]

maybe look into the multinomial distribution

[marble viper]

Lemme wikipedia that

huh, interesting

Alright well I at least know where to start looking, thanks

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[abstract quartz]

do you have to change the n = 0 or n = 1 under the ∑ whenever you dy/dx or ∫ ? and which change happens for which

[spice orchid]

the reason you are changing it here is because the n=0 zero term would just be 0, so you can omit it

[abstract quartz]

so i just consider this for both cases?

[spice orchid]

if you integrate you dont lose any terms

[abstract quartz]

one more thing

the final answer is x^n+1 / n+1

with ∑ n = 0

is it changed just to make it look better?

[spice orchid]

thats just reindexing, to make the sum start at 0 for whatever reason

[abstract quartz]

thank you for the help

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[signal solar]

isnt the first linear and the second component form

[nocturne kettle]

correct

[signal solar]

do i divide the first vector by 2?

since its 2v

so like

v: <-5, -2>

idk im confused

[nocturne kettle]

i believe the yellow boxes aren't for you to solve

[signal solar]

yeah but if i multiply it by 3 would it give me 3v

[nocturne kettle]

oh

thats what you mean

yes thats right then

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[signal solar]

wait so did they just give me v-u?

[signal solar]

how do i solve that

[nocturne kettle]

lmao i guess they did

not sure what that's about

[signal solar]

me neither lol

how do i do this?

oh fuck

i get it

it goes horizontally

yep

[nocturne kettle]

hmm

[signal solar]

i think its a dot product

[nocturne kettle]

i think when they asked v-u they meant -u

then you could use that here

although you can just do that now too

[ember shadow]

looks like it should be dot product

[signal solar]

so (5*-10) + -4 times 27

-158

[ember shadow]

what is -2u? and what is v?

[signal solar]

oh wait i used 2v

[signal solar]

they give 2v and v-u nvm

so

[nocturne kettle]

yea set up an equation to solve for u

then you can plug in and find dot product

[ember shadow]

you don't need to "set up an equation"

[signal solar]

v is <-5,-2>

what should i do to solve for -2u then

[nocturne kettle]

well

you can set up an equation

but apparently "you don't need to"

[ember shadow]

are you not given u = <9, 7>

[nocturne kettle]

basically v - u is given

that's a different problem

[signal solar]

oh thats a diff

yep

[signal solar]

how can i set it up

[nocturne kettle]

you know v

v - u = <5, -27>

plug in v and solve for u

[signal solar]

omg yes thats much easier than what i was thinking

<-10, 25> = u?

[nocturne kettle]

that's what i got

[signal solar]

ok got it

i need to finish 5 asap XD

wait we're already doing it

i was doing other problems got distracted

okok

[nocturne kettle]

haha

[signal solar]

so

<-20,50> = 2u

[nocturne kettle]

correct

[signal solar]

-20 * -5 , -2*50

<100, -100>

0

so

orthogonal right

[ember shadow]

did you make sure to take the dot product of -2u and v?

[nocturne kettle]

yes i believe that was -2u

[nocturne kettle]

i also got that

nice

[signal solar]

perfect

ok i got them right

teamwork XD

[nocturne kettle]

lmao

power of friendship pulled us through

[signal solar]

for sure lol

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[faint hill]

how do i do this

[rain plinth]

do they show the points generally increasing, generally decreasing, or neither

(as you go from left to right)

[faint hill]

neither

[rain plinth]

depends on the graph

[faint hill]

what is correlation

[rain plinth]

correlation means that generally as one variable goes up, does the other go up, or down, or do something crazy

[faint hill]

ok

[signal solar]

its basically how much the points align

the more linear the higher correlated it is

[faint hill]

what is number 3

[rain plinth]

(if the line has a positive slope, that is)

[signal solar]

well if it has a negative its still gonna be linear and more correlated

[rain plinth]

ig

[faint hill]

is number 3 positive

[signal solar]

so basically if its going up its positive if its going down its negative and if it seems to be going nowhere its not correlated at all

or if it makes a weird shape

[rain plinth]

hexagon

[signal solar]

the more linear it is the stronger the correlation
correlations are between -1 and 1

-1 being a perfect negative line of points and +1 being a perfect positive line of points

the strength depends on how much it resembles that line

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[sly marten]

need help

[signal solar]

,w rotate

[glossy valve]

Results provided by WolframAlpha

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

Requested by nino#6114

[signal solar]

rip thats not it

[signal solar]

,rotate

[signal solar]

...L

[light sonnet]

Just copy and paste the image again

[sly marten]

sorry

[light sonnet]

The bot takes the latest image

[signal solar]

do you know the midpoint formula?

yeah rip

[sly marten]

x + x/2 , y+y/2 ???

[signal solar]

oh wait i read the problem differently

E isnt the midpoint

well we know D to E is 2x

and EF is 3x

also note how DE +EF is DEF

so what do you think we should do

@sly marten

[sly marten]

add 3+2

[signal solar]

x*

but yes

which equals

[sly marten]

uhhh

4?

nah jk

5

[signal solar]

xD

5x yep

remember that x is there though

but anyway

so now find the distance between 1 and 16

do you know how to do that

[sly marten]

nah bro

[signal solar]

max x value minus min x value

so 16-1 is the distance

thats the distance of DEF

so now

[signal solar]

remember that this is also the distance of DEF

[signal solar]

recall

so now we can solve for x

do you know how to do that

[rain sundial]

Use section formula

[rain sundial]

Wtf. You can't solve for x

Ratio is 2:3

[signal solar]

5x=15 then he can solve

[sly marten]

no

[sly marten]

ok

[rain sundial]

E= ( (2×16+3×1)/2 + (3×9+2×17)/2))

[sly marten]

x=3?

[signal solar]

yep

now plug in x

[sly marten]

what lmao

[sly marten]

k

6 and 9

[signal solar]

yep

so D to E is 6

E to F is 9

[sly marten]

is E (7,10) ?

[rain sundial]

Section formula lol

[signal solar]

so now just add 1+6 and thats the x coordinate of E

[sly marten]

i did

is E (7,10) ?

[rain sundial]

Bruh this wrong. You can't find x

[sly marten]

dont tell me man

im following the other guy

please inform me on how to do this correctly

[rain sundial]

Use the Section formula.

[sly marten]

bro

what is that

[signal solar]

some_21

give me ur answer

[rain sundial]

https://www.cuemath.com/geometry/section-formula/

[sly marten]

never learned that lol

this is geometry bro

[rain sundial]

This is also of coordinate geometry. This is basics

Use this formula

[sly marten]

u took some different geometry man

[signal solar]

oh

[signal solar]

you wrote this wrong

[rain sundial]

Ik

/5

[signal solar]

;-;

anyway the way im teaching him doesnt require the formula

its easier for him than to just memorize and plug in

i was gonna get to the formula later so that he knows where it comes from

anyway he got the same answer

what we're doing is not wrong

the x coordinate is still 7

[signal solar]

for the y coordinate you did it wrong

because remember we only calculated the x-coordinate

its only the first section that you need because

remember that you're going from D to E

so basically you're adding that distance

you're traveling that 6

but you start at 1

so 1+6 = the coordinate of E = 7

for y you have to set it up again

instead 2y and 3y

the formula also works

@sly marten try it and ask me if you need help

you can ping me

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@sly marten Has your question been resolved?

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[gray roost]

help

[gray roost]

I need a refresher on how to do this problem please.. if someone could do just 1 with me i’d be set to begin my unit test✨

[nocturne kettle]

you are given three side lengths of two different triangles

what is the only viable way to prove they are similar with the given information?

[gray roost]

don’t you like multiply each side by longest to longest shortest to shortest and middle to middle

iykwim

[nocturne kettle]

you divide, yes

and see if the ratios are the same for each

[gray roost]

so would it be like 122*59?

for ex

[nocturne kettle]

no, i said divide

[gray roost]

oh

[nocturne kettle]

also the longest side of the bottom one is 66

[gray roost]

divide what though..

[nocturne kettle]

122/66

[gray roost]

okay then 56/59?

[nocturne kettle]

since i put the side length of the bigger triangle on top here, you want to do the same for all three

flip the numbers

um sorry

56 and 59 should not be paired together

[gray roost]

😭

[nocturne kettle]

you want to pair the two longest, two middle length, and two smallest with each other

[gray roost]

OH WAIT 56 AND 30?

Then 110 and 59

[nocturne kettle]

yes

[gray roost]

so then do i divide all of them and then what

[nocturne kettle]

you do 56/30, 110/59, 122/66, if they do not come out as the same value then the triangle is not similar

do you understand why that is?

[gray roost]

wait im getting weird answers

no

sorry

[nocturne kettle]

hm that is a problem

give me a minute i can draw something

here i have two triangles

they are similar

do you see why?

[gray roost]

They can all be divided by those numbers

?

[nocturne kettle]

that reasoning is weak since all numbers can be divided by pretty much every other number

no, notice how the numbers of the top one are the bottom one's times 2

now try doing the ratio thing we were doing

10/5, 6/3, 8/4

what are those?

[gray roost]

Um the ratios from the triangles

[nocturne kettle]

no i mean what number do these spit out when you divide them

[gray roost]

2

[nocturne kettle]

yes

and they are all 2

same with the previous question

[nocturne kettle]

if you divide these values and they do not end up being the same, then these triangles are not similar?

does that make more sense now

[gray roost]

yea

But i kept getting like

crazy decimals

for the ones we sis

did

[nocturne kettle]

yes

[nocturne kettle]

if those decimals are not the same

they are not similar

[gray roost]

okay so i should mark “not similar?”

[nocturne kettle]

yup

[gray roost]

alright.

Could you help me with another one?

😭

sorry

you dont have to

[nocturne kettle]

sure

haha everyone's here to help dont apologize

[gray roost]

This is wacky because they are like connected

its wildin lol

[nocturne kettle]

have you learned the vertical angle theorem?

[gray roost]

no ion think so

[nocturne kettle]

"The vertical angle theorem states that the vertical angles that are formed when two lines intersect are congruent"

meaning

[gray roost]

ooo

[nocturne kettle]

when these two lines intersect those two marked angles are always congruent

[gray roost]

alr

i mean they look congruent but idk how to do the math too check that 🗿

😹

[nocturne kettle]

well theres no math involved

[nocturne kettle]

where do you see vertical angles here?

[gray roost]

<T

[nocturne kettle]

yup

so that is one piece of information down

we need two more pieces of information to prove congruency

[nocturne kettle]

notice each triangle has two side lengths as well

so now do the ratios again and if the dividing comes out to the same value, you can prove congruency by....

sorry

*similarity

not congruency

[gray roost]

44/33 and 56/42?

[nocturne kettle]

correct

[gray roost]

they are

✨✨

[nocturne kettle]

yup

so which option is it?

[gray roost]

would it be an AA?

because they are both angles

right..?

[nocturne kettle]

no

do you know what AA, SAS, SSS, ASA, etc. means?

[gray roost]

wait let me het my notes

🥹

[nocturne kettle]

oof

[gray roost]

SAS?

[nocturne kettle]

yup

[gray roost]

they both have the same little silly half circles

[nocturne kettle]

LMAO

well yes

but you know why its called SAS right?

[gray roost]

twins✨😎

yea because

they have side angle sides 🥸

totally…..

i an so smart

🧠

[nocturne kettle]

well yes that is correct tho

[gray roost]

braining

[nocturne kettle]

just wanted to make sure you knew that

not just the

silly little half circles

😅

[gray roost]

they are goofy

[nocturne kettle]

mhm

[gray roost]

now i gotta do more 💔💔

ty for your help

[nocturne kettle]

np, good luck

[gray roost]

THERES ONE WITH NO NUMBERS

GOOD LAWD

OKAY

[gray roost]

ty

.close ✨

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Closed by @gray roost

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

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[bold jungle]

hi how do i find the sides of the triangle?

[brittle steeple]

It tells you?

ah

Pythagorean theorem, for the other 2 sides

[bold jungle]

oh ok thanks, so a^2+b^2=6^2?

[brittle steeple]

no, the original triangle isn't a right triangle

they draw the line for you to make it right triangles