help-43

[cerulean sinew]

That’s trig sub tho

[brave carbon]

That's the way to do it

[cerulean sinew]

No u sub at all?

[forest token]

What do u mean by u sub then

[cerulean sinew]

Idk I’ve seen someone do it a while ago

Instead of trig sub

[forest token]

🤔

[cerulean sinew]

I can’t find the message unfortunately

But yea

Apparently you can

So I was interested in knowing how

no AI helped me so far except for introduce some overwhelming definition of that integral

[forest token]

What do u mean by u sub bro

x=tan u is a u sub

Do u want to do x=u and come back to where we started

[cerulean sinew]

So then there probably isn’t a u sub approach

[raw furnace]

!noai

[compact pewter]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[raw furnace]

do you know your trig identities for integrals?

[cursive crown]

are you sure it wasn't a different integral?

something like 2x/sqrt(1+x^2)

[compact pewter]

@cerulean sinew Has your question been resolved?

[cerulean sinew]

Yes

I believe so

For this you could do tan^2(θ) = x^2

But then I just don’t know how to integrate the result you get

Like sec^3(θ) in this case

[compact pewter]

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[patent siren]

Someone please help me

[crystal umbra]

the slope of a tangent of a curve at a point is the derivative of the curve at that point, right?

so just differentiate the equation first

[patent siren]

Ohhhhhhh

Tysm

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[native jetty]

Can someone help me with the following problem: Let X be a quotient space obtained from $B^2$ by identifying each point x of $S^1$ with its antipode $-x$. Show that X is homeomorphic to the projective plane $P^2$

[boreal girder]

Surf

[native jetty]

Not really sure where I’d even get started. I have the definition of the projective plane but that’s all I can really think of

[compact pewter]

@native jetty Has your question been resolved?

[thick comet]

What definition do you have for RP^2 and what do you know about it?

[native jetty]

The projective plane $P^2$ is a quotient space obtained from $S^2$ by identifying each point x of $S^2$ with its antipodal point -x.

[boreal girder]

Surf

[native jetty]

I know it’s compact and the quotient map $p: S^2 \rightarrow P^2$ is a covering map. My guess is I want to find a similar quotient map from $q: B^2 \rightarrow S^2$?

[boreal girder]

Surf

[thick comet]

Well using that D^2 is homeomorphic to the upper hemisphere of S^2 may help

Some adapted homeomorphism should show equivalence between S^2 / antipodes and D^2 / antipodes

[native jetty]

Hm. Can I split S^2 into two hemispheres and use the fact that the intersection is S^1?

[thick comet]

Well you could take some equivalence class on S^2/~ (notice that since the antipodes are identified, you have all the "information" on the upper hemisphere) and show some natural way of mapping it to an equivalence class on D^2/~.

[native jetty]

Ah. Each point has one representative in the upper hemisphere, so each element has one representative in it. If it is not, then it’s on the equator and then it is exactly S^1 so we get something like B^2/ x ~ -x on S^1

[thick comet]

Yes

[native jetty]

They are the same equivalence class aren’t they. So it is precisely how we defined P^2 in the first place

Now I just have to show that the quotient map restricted to the upper hemisphere is a homeomorphism right. It’s not enough to show the classes are the same.

Or is it?

[thick comet]

You can just use something like projecting the upper hemisphere reprensentatives x down onto the disk continuously and the identification on D^2 works out inconsistencies that would've arisen normally because of how the equator is identified on S^2/~

[native jetty]

Ah. Sounds good to me

Thanks very much.

.close

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[compact pewter]

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[modern arch]

The question is to solve for x and y

But fir the second line, idk whether to multiply or not

[cyan storm]

this is correct so far

you should simplify the left hand side (think: what is -1 - 2) and then multiply both sides by x to put the variables on one side

also please note that x != 0 (you should write that somewhere to not forget)

so if, when solving, you get the solution x = 0, discard it

[modern arch]

Ok

[modern arch]

Could u explain why

[cyan storm]

which part

[modern arch]

-1-2

Why’s it’s like tht

[cyan storm]

$(x - 1) - 2 = x - 3$, right

[modern arch]

So no multiply

But w hy

[cyan storm]

no after that you get $x - 3 = \frac{4}{x}$

[cyan storm]

then you should multiply by x on both sides

so that all your x's are on the left side

[modern arch]

Ok ty

It looks like I’ll get two x values

[cyan storm]

that's correct

[cyan storm]

yes

do you know how to solve quadratics?

[modern arch]

Yes

[cyan storm]

solve it then :)

[compact pewter]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[near sierra]

dang

bro really gave him the spoilers

and thought he'd look cool

[knotty cloak]

bro im not trying to be cool its easy

[near sierra]

listen ibrahim

everyone in this server knows you can do it, we all know your capability and ability

but our other friend wants some understanding of the problem

so we're helping em

[knotty cloak]

alr

[compact pewter]

@modern arch Has your question been resolved?

[acoustic grove]

I can help everyone with math.

Please send me messages if any help.

[modern arch]

Ok

[acoustic grove]

good

what problem?

[pulsar wagon]

[acoustic grove]

wdym?

[near sierra]

the man is a lil confused but he wants to help

[acoustic grove]

yes

[near sierra]

did you end up solving this quadratic?

[modern arch]

Not yet

I have to shower

[near sierra]

oh okay cook

[modern arch]

Havent done y yet

Can I have tips for solving word problems

I’m rlly bad at them

[near sierra]

is that +1 or -1?

[modern arch]

-1

And 4

As y

[near sierra]

should be a positive one

[modern arch]

Oh

[near sierra]

cuz -4x - x = -5x not -3x

[modern arch]

Ic

[near sierra]

the sum of terms you break should be equal to the original term

[modern arch]

I can’t rlly think right rn

I’m sleepy

[near sierra]

dang

take a break or smth

[modern arch]

I can’t

Test is second period

[near sierra]

damn

[modern arch]

Do u have any tips

I just want to finish sims and be done

Bit I also have to do trig functions

The naming of the equation is hard for me

[modern arch]

I did plus

[near sierra]

oh

what factors did you get

[modern arch]

For?

[near sierra]

after using +1

[modern arch]

Hunt why would it be plus one

Questions

How do I find y

[quartz widget]

,rotate

[boreal girder]

Couldn't find an attached image in the last 10 messages.

Mar 10, 2026, 3:40 AM

[modern arch]

I’m I doing smth wrong?

[quartz widget]

Well this one is correct

[modern arch]

Ty

But could u help me with the second one

I’m struggling with that

But I have to go do something soon

[quartz widget]

Let me see

[modern arch]

Really really soon

[modern arch]

I’m leaving now

[quartz widget]

Squared numbers can't be negative

There is no real solutions

[tranquil mesa]

sub the equation and check the determinant

[modern arch]

Pls explain these terms

[tranquil mesa]

substitute one of the terms out so you have just 1 polynomial, idk if it's a quadratic or not, but then find the determinant to check for the roots, they might not be real (i didn't have time to solve it)

this is a resource you could check out https://en.wikipedia.org/wiki/Discriminant

[modern arch]

After substituting and finding a value

How do I find the next pls

Not In a rude way

Idk which equation IM suppose to put the found value in

[tranquil mesa]

try both and see which is easier to slove

solve

[modern arch]

Can I have tips for word equations

Pls

[tranquil mesa]

ideally try to stay within the second power

[tranquil mesa]

example?

[modern arch]

The second equations

[modern arch]

Like those sentence math questions

I forgot what their called

[tranquil mesa]

in general try to set up equation to make it easier to work with, and list out the facts

[modern arch]

Ok

[tranquil mesa]

solve for one and plug it back to the first, and then solve for the first, if the second is a quadratic then it's easy, just look it up online, other wise try factoring, the rational root theorem can help, and test to find at least one root if you can to build a start

[modern arch]

Can u use an example

Like using equation a and b

That’s sort of thing

[quartz widget]

D>0, there are 2 real solutions

Wait is it

Oh yeah

[strong folio]

you mean word problems?

[compact pewter]

@modern arch Has your question been resolved?

[compact pewter]

Channel closed

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Use .reopen if this was a mistake.

[modern arch]

.reopen

[compact pewter]

✅ Original question: #help-43 message

[modern arch]

Yes

[strong folio]

word problems require familiarity with the terms used in the question, so what kind of word problems do you often face - financial (money-related), physical (physics-related), or some other domain?

[modern arch]

financial and physical

I have some questions

[strong folio]

sure, you can show some of them.

[strong folio]

which one would you like to do first? but from the looks of the paper you have done them all anyway.

[modern arch]

Number a

[modern arch]

I didn’t rlly udneerwgamd, I was copying what my teacher was saying

[strong folio]

right.

[modern arch]

I didn’t want to disturb him bc everyone was following and I couldn’t understand

[strong folio]

personal opinion: ask anyway!

[modern arch]

I’m scared of judgement

Everyone seems smart and it takes me a while to understand math

[strong folio]

that says more about them than about you, OP.

but anyway, so you are given a rectangular room of area 20 sq. meters (sq. = square).
if you let the length of the room be x and the width be y, can you write this out in an equation?

[modern arch]

Er X x Y = 20

[strong folio]

so xy = 20, that is absolutely correct.

your question then says that the length is increased by 3 metres and the width is increased by 1 metre.

[wary wasp]

dang columbina this is fire teaching

like actuallty

explains thru the stuff

[modern arch]

Moving rm, I’m in class

[wary wasp]

even i understood parts when i read

[modern arch]

Brb,

[strong folio]

you know that x was the length. so if the length is increased by 3 meters, what is the new length of the room?

[modern arch]

back

[modern arch]

X+3

[strong folio]

correct!
now, the width is also stated to have increased by 1 meter. what is the new width?

[modern arch]

6+1

[strong folio]

6?

did you mistype the y?

[modern arch]

Y

sorry

[strong folio]

then correct! so the dimensions of the new room are (x+3) metres and (y+1) metres respectively, agreed?

[modern arch]

Yes

[strong folio]

good! you're now told that these two changes double the area of the room.
the old area, as you recall, was 20 sq. metres. what's the new area?

[modern arch]

40

[strong folio]

good! can you now set up the equation for the new room dimensions and area?

[dark snow]

I was gonna send the solution
I noticed there r more

[strong folio]

!nosols please.

[compact pewter]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[dark snow]

Ofc u would 😭

[dark snow]

Ah fair enough mb

[compact pewter]

@modern arch Has your question been resolved?

[modern arch]

No

I don’t understand the second instruction

Oh so we find x and y right

[strong folio]

you know that the new dimensions are (x+3) and (y+1), and the new area is 40.
can you set up another equation with these values?

[modern arch]

Kind of

Doing so no

Know

I was having class and my teacher doesn’t like us with our iPads so I had to go off

[strong folio]

then better finish your class first.

you can come back after your classes are done. besides, it's a little rude to be using devices in classes, in my humble opinion, on top of having your attention split between two places.

[modern arch]

K

Do I expand the brackets

We’re done now

Some of us were sleeping

[strong folio]

I recommend not involving the units at this stage.

[modern arch]

Oh ok

[strong folio]

also, don't use x as a multiplication symbol when the variable x is also present. it's very confusing.

[modern arch]

Class is starting again

Bye and tysm

[strong folio]

sure.

[modern arch]

Next is the test

[modern arch]

I’m sorry

Truly

[strong folio]

you don't have to be! your time first.

[near sierra]

dang this chat is so nice, its giving me butterflies in my stomach

i think i didnt chew em properly 😞

[compact pewter]

@modern arch Has your question been resolved?

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[compact pewter]

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[rapid crescent]

What does the phase plot in the Fourier spectrum mean?

[rapid crescent]

like here

[compact pewter]

@rapid crescent Has your question been resolved?

[rapid crescent]

.close

[compact pewter]

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[untold ether]

Hey I’m doing this function question from a practice test and have no clue how/why it works/how they go the answer

[untold ether]

First pic is the start of the question
Second is what it’s meant to become

[charred finch]

given a function f(x), will you be able to find f(|x|)?

[untold ether]

Yes but I don’t get how the -|x| will turn into that

[charred finch]

so first, what do u do to find f(|x|)?

the method would be similar once u understand

[untold ether]

You just flip the parts that are negative across the x axis

[charred finch]

is this what u mean?

[untold ether]

No

Lemme draw it

[charred finch]

okay..

this?

[untold ether]

Yes

[charred finch]

ahhh

unfortunately that is |f(x)|

not f(|x|)

[charred finch]

for this,

u take the right half of the graph

[untold ether]

Ohhh

[charred finch]

and flip it about the y axis

when it is f(|x|), u take the right half cause |x| is positive

and the right half is positive values of the function

so similarly, for f(-|x|) we take the left half (cause that represents negative values of x) and flip it about the y axis

[charred finch]

hence the 2nd image here

[untold ether]

Ah that makes sense

Ty

[charred finch]

no problem!

[untold ether]

.close

[compact pewter]

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[valid loom]

How can i prove that lines BD and BE are parallel? All i know is that the distance between A and D is a third of the distance between A and C, and that the distance between A and B is half the distance between C and E. My teacher said that it’s possible to solve this by using vectors and algebra, but she also said that there is another way, sadly without specifying this ”other way”.

[elfin finch]

BD and BE arent parallel, i think what you mean is vector BD=k×(vector BE)

[valid loom]

Yea sorry for wording it wrong thats what i meant

[elfin finch]

Are you given any other info?

Or can you show the full question?

[valid loom]

Yea but only that the point C is placed right inbetween Point A and B, but im not sure how that is supposed to help

[elfin finch]

It isnt place between A and B in the picture tho?

[valid loom]

Yea its placed above A and B but the normal from C is between A and B if that makes sense

[elfin finch]

Ye i think i need the full question ngl

[valid loom]

If you draw a line straight down from C it Will land right inbetween

[elfin finch]

So CA=CB?

[valid loom]

Yea

And the size ratio between AD and AC relative to AB and CE is the same also if that makes sense

No sorry AD and CD relative to AB and CE

Since if you multiply AD with two you get the length of CD and if you multiply AB with two you Get CE

So it almost seems as if the triangles ABC and CDE are similar

But i dont know and of the angles so idk how i can prove it

[elfin finch]

Are you given EC=2AB as lengths or as vectors?

[valid loom]

Lengths

Would it help if it were vectors?

She didnt explicitly say that, but maybe we were supposed to assume it?

[elfin finch]

If it were vectors we could actually prove it, without and there isnt enough info

[valid loom]

Yea we got the question orally so im guessing she ment vectors but said the wrong thing

[elfin finch]

Since if we put A,B,C as unchanging point then E could still be anywhere on the circle (C,2AB) (as in C as the center and 2AB as the radius)

[valid loom]

Yea im following

[elfin finch]

Welp ima assume vectors for now then

[valid loom]

Yea i think that would be a smart idea

I dont really see how it Will help tho

[elfin finch]

So do you want to prove it with vector addition or geometrically

[valid loom]

Preferably geometrically

[elfin finch]

Also note that what we're doing is pretty proving E,D,B are collinear, meaning they are all on the same line

[valid loom]

Yea got it

[elfin finch]

If vEC=2vAB, then EC is parallel to AB and EC=2AB (v is short for vector)

[valid loom]

Yea makes sense

Wait question

[elfin finch]

(And also that E and B are on opposite half planes defined with the line AD as the boundary)

[valid loom]

If i draw a line from A to C now and i know EC and AB are parallel can i also know that the size of angle A and angle B are the same?

Angle C*

[elfin finch]

Yes

[valid loom]

Isnt that technically enough to prove that triangles ABD and DCE are similar in form?

Since we know that the size ratio between AD and CD, and AB and CE are the same

[elfin finch]

Oh ye you can

Ye should be easy to prove collinearity from there

[valid loom]

Yea since all angles are the same dont the coherent sides need to be parallel to each other since the angles of the lines are the same?

Lines with the same rate of increase must be either colinear or parallel or something along those lines right?

[elfin finch]

Sure

[valid loom]

Tysm for the help i thought i was cooked when i got this assignment

🙂

[elfin finch]

Do you need help with the vector addition approach or can you do that on your own

[valid loom]

Why tf did it autocorrect to an emoji

[valid loom]

I know that one from before but thx for all the help

[elfin finch]

Np

[valid loom]

.close

[compact pewter]

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[compact pewter]

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[weak trench]

I need help with this. I am confused on how to solve it since there is no volume. A right triangular prism with a right isoceles triangular base is shown. The height of the prism is equal to 9 centimeters (cm), and the base of the right isoceles triangle is equal to 8 cm. What is the volume of the priwsm, rounded to the nearest cubic centimeter?

[trail cave]

no picture to go with it?

[weak trench]

I would send a picture but it is on my chromebook and i am using Discord on my computer

[trail cave]

the volume of any cone or pyramid is 1/3 the prism it was cut from

i.e a prism of its base and height

[weak trench]

I understand

[quartz yoke]

right triangular prism

[quartz yoke]

can you confirm it looks like this

[weak trench]

It's longer

in size

[quartz yoke]

but shape is similar ?

[quartz yoke]

-# another situation to say thats what she said

[weak trench]

Yes it's similar

[quartz yoke]

if you calcuate the area of trianngle and multiply by height you will find the volume

[weak trench]

I'm looking for the volume of it lol

Ah okay

[quartz yoke]

mb volume

[rancid crypt]

The volum it’s Triangle base area*heigh/3. You need to find the triangle area.

😉

[weak trench]

How do you find the area of a triangle

[weak trench]

Why did you wink 😭

[rancid crypt]

B*h/2

[weak trench]

Oh okay

[weak trench]

So 8 multiplied by 9/2?

[rancid crypt]

No, triangle height.

[quartz yoke]

9 is height of the prism not the triangle

[weak trench]

So nine multiplied by 8/2?

[rancid crypt]

No, first of all you need all triangle mesures, then you need to apply pitagoras and find the triangle heigh and then you can do triangle height*8/2

[weak trench]

Oh okay

[weak trench]

So 8^2+9^2?

[trail cave]

It's a right angle isosceles triangle and there's only one triangle like that

[rancid crypt]

No, you need to find your hipotenuse. First.

[trail cave]

the base is the hypotenuse

[rancid crypt]

Right.

[weak trench]

So 9^2+x^2= 8^2?

[weak trench]

?

[quartz yoke]

red is your base of prism

[trail cave]

vro the base of the isosceles triangle is 8

[rancid crypt]

Then apply pitagoras and find hipotenuse.

[weak trench]

I thought the hypotenuse is 8^2

[rancid crypt]

It’s not necessary apply triangle formula for area.

🙂

[quartz yoke]

since the isoceles triangle is a right angled triangle both base and height = 8

[rancid crypt]

Then B*h/2

[weak trench]

I thought the height is 9

[quartz yoke]

look at the left diagram of prism the height of prism is 9

[rancid crypt]

You need the triangle height.

For B*h/2

[weak trench]

So base divided by 2?

[rancid crypt]

Base=8 and triangle height=8. 8*8/2

[quartz yoke]

oh

[weak trench]

35.2?

[rancid crypt]

Yeah this is the triangle area.

Then you need apply de volume formula+Triangle area*height(figure height not triangle)/3

[weak trench]

105.6?

[quartz yoke]

how did you get 35.2?

[weak trench]

I did 8.8*8/2

[rancid crypt]

64/2=32

Apply the formula again with 32. You are doing great.

🙂

[weak trench]

105.6?

[rancid crypt]

(32*9)/3.

[weak trench]

105?

[rancid crypt]

32: triangle area, and 9: height./3

[rancid crypt]

Excuse my error /3

😉

[weak trench]

96

[rancid crypt]

Excuse me it’s a prisme you don’t need divide. Only 32*height.

[quartz yoke]

the height of triangle if you consider the hypotenuse to be 8

[weak trench]

32 multiplied by 9?

[rancid crypt]

@weak trench First we need the triangle alutra making pyramids deaphea we go back to Find the area Finally the volume.

[weak trench]

How do we find the area?

[quartz yoke]

can you confirm what they labelled 8 in the diagram

[weak trench]

I thought it is the base

[quartz yoke]

is this the question?

[weak trench]

Yes

[quartz yoke]

then the length of hypotenuse is 8

[rancid crypt]

The you need to find the triangle height.

[quartz yoke]

do you understand this ?

[weak trench]

How is the hypotenuse 8 though?

[weak trench]

.

[quartz yoke]

the baseof the prism is a right isoceles triangle

[weak trench]

OHH

Okay

What do I do next?

[rancid crypt]

Find the triangle height.

Using Pythagoras.

[quartz yoke]

from here you can see the side opposite to right angle , hypotenuse is 8

[quartz yoke]

please move to #chill for memes

[rancid crypt]

Do you remember how to do Pythagoras @weak trench?

[weak trench]

a^2+b^2=c^2?

[rancid crypt]

And for a catet?

That is for hypotenuse.

[weak trench]

Catet?

[winter fern]

There should be a property for the height of an isosceles triangle

[quartz yoke]

since the triangle isocelese , 8 is the base the other two sides are equal in length, the base angles are equal you can find the base angle

[rancid crypt]

Leg.

[weak trench]

Ah okay

[quartz yoke]

the height of an isoceles triangle drawn to the base side bisects it

[rancid crypt]

Do you remember how to do it?

[winter fern]

Isn't it also equal to half its length

[quartz yoke]

only for right isoceles triangles

[weak trench]

x^2+9^2=8^2?

[rancid crypt]

H^2=8^2-4^2. Because you have another triangle in.

[quartz yoke]

do you understand this, you can find the hieght of triangle from here

[weak trench]

Won't the other side be 45 degrees?

[quartz yoke]

the other angle?

[winter fern]

Yeah that one's right, you don't need any trig

[weak trench]

x?

[winter fern]

Actually you do, I lied

[quartz yoke]

um what is x

do you understand this that the base angles will be 45

[weak trench]

So both of the legs are 45?

[quartz yoke]

not the legs, the angles

[weak trench]

Oh okay

[quartz yoke]

do you understand it

[weak trench]

Why is it 45 though?

[quartz yoke]

hm.. what is an isoceles triangle?

[weak trench]

OH. 2 sides are equal

[quartz yoke]

yes, two sides are equal, along with two sides the angles opposite to the equal sides are equal

[weak trench]

So now what

[quartz yoke]

you know one angle is right angle = 90 can you find other two angles?

[weak trench]

45? 😅

[quartz yoke]

you know because i said earlier xD

[weak trench]

Yeahh

[quartz yoke]

you can use fact that sum of all angles of a triangle = 180
so 90 +x+x -=80
you can find x

[weak trench]

Oh because all triangles = 180

[quartz yoke]

yes

now you know the base angles = 45

[weak trench]

Yeah

[quartz yoke]

now use this fact

[weak trench]

What does bisect mean?

[quartz yoke]

divide into two equal parts

[weak trench]

Oh okay

[weak trench]

So since it bisects it, it splits into two right triangles?

[quartz yoke]

yes

BC was equal to 8cm AD divides BC intotwo parts BD = DC = 4cm

now you have to use trigonometry

[weak trench]

Ohh because half of 8 is 4

[rancid crypt]

AD is the triangle height.

[quartz yoke]

what is tan x

[weak trench]

Do i use Soh Cah Toa?

[quartz yoke]

yeah

use tan to find to AD

[rancid crypt]

Yeah.

[weak trench]

What is the opposite angle?

[quartz yoke]

45 degree

[weak trench]

is the adjacent angle 4?

[quartz yoke]

not angle but side yes 4

[rancid crypt]

4 it’s.

[weak trench]

Oh okay

[weak trench]

Do I multiply them?

[rancid crypt]

Think about the angle that do you have wich leg crate the angle it’s the adyacent.

[weak trench]

Ah I understand

[quartz yoke]

muliply who

[weak trench]

45 and 4

[rancid crypt]

No, you need tan of 45.

Look in tables.

[weak trench]

tables?

[quartz yoke]

you have tan45 = opp/adj = AD/4 so AD = tan45 *4

[rancid crypt]

Or in a calculator.

[weak trench]

So is the answer 4 because I put it in the calculator?

[quartz yoke]

yes 4 coz tan45 =1

[rancid crypt]

Right.

[quartz yoke]

finally you have the height and base

find the area of triangle

[weak trench]

Do I use the Pyhtagoren Theorem or the Triangle formula?

Pythagorean*

[quartz yoke]

Area = base*height/2

[weak trench]

Is it 8?

[quartz yoke]

no

what was your base?

[weak trench]

Wasn't it 4?

[quartz yoke]

4 is the height

[weak trench]

is the base 8?

[quartz yoke]

base was 8

yes

[weak trench]

So 16?

[quartz yoke]

yes

[weak trench]

is that the final answer?

[quartz yoke]

finally multiply area by height of prism

[weak trench]

Alr

[weak trench]

Is it 64?

[quartz yoke]

16*9?

[weak trench]

I thought the height is 4?

[quartz yoke]

oh that was the altitutde of triangle the question has given height of prism

9

[weak trench]

Oh

[weak trench]

144?

[quartz yoke]

yh

[weak trench]

Is that the final answer?

[quartz yoke]

it is

dont forget the units

[weak trench]

Okay, I'll keep that in mind

[weak trench]

i need help with another question also

[quartz yoke]

ic

post it

[weak trench]

A cake pan is in the shape of a right rectangular prism 20 centimeters (cm) long by 20 cm wide by 5 cm high. The pan contains 1,000 cubic centimeters (cm^3) of batter. Approximately how far is the cake batter from the top of the pan? A) 1 cm B) 2.5 cm C) 5 cm or D) 7 cm

[quartz yoke]

what have you tried

[weak trench]

oh I got it right

[quartz yoke]

ic 🎉

[rancid crypt]

[weak trench]

I need help with another question. I've tried it and I got it wrong

[quartz yoke]

mm.. ok post it

[weak trench]

Anya has two different sized cylindrical coffee mugs. The larger mug has an internal height of 15 centimeters (cm), and the smaller mug has an internal height of 10 cm. Both mugs havwe an internal diameter of 8 cm. Which of the following is closest to the difference in cubic centimeters (cm^3) between the internal volume of the larger mug and the internal volume of the smaller mug? A) 63 cm^3 B)251 cm^3 C) 754 cm^3 or D) 1,005 cm^3

I tried C but it is wrong

[quartz yoke]

,w pi165

[quartz yoke]

show your work

what is volume of a cylinder

[weak trench]

I did pi multiplied by 4^2 multiplied by 15 for the big mug. I also did pi multiplied by 4^2 multiplied by 10 for the small mug

[boreal girder]

Results provided by WolframAlpha

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

Requested by mercy075187

[quartz yoke]

ok their difference should be 251

approx

[weak trench]

oh so I was right 😭

[compact pewter]

@weak trench Has your question been resolved?

[weak trench]

I also need help again. I tried 64 but I got it wrong

[empty wadi]

hey do you need any futher help?

[weak trench]

Hi, yes please

[empty wadi]

state your troubles

[weak trench]

I have this word problem. A building contractor has a pickup truck with a rear storage area in the shape of a rectangular prisn. The storage area has a length of 80 inches (in), a width of 60 in, and a height of 44 in. She wants to fill the entire storage area with equal-sized rectangular prism-shaped bricks with lengths of 8 in, widths of 4 in, and heights of 2 in. How many bricks can the contractor fit in the storage area of her truck?

[empty wadi]

okay lets take a moment to see what given data we have

we know shape of the total available storage here is a rectangular prism

so we can find the volume with its given dimensions

[weak trench]

Yeah

[empty wadi]

lets calculate that first

[weak trench]

Is it 64?

[empty wadi]

we have length as 80 inches, width as 60 inches and height as 44,
so the formula for a rectangular prism is l x w x h

its important we use the correct units

volume is always cubed

just multiply 80 with 60 with 44 to get the total volume for rectangular prism

now, we have the dimensions of individual bricks, which is 8 inch, 4inch and 2inch as length width and height respectivelyt

so we can find the individual volumes of each brick

using the same formula,

[weak trench]

Okay thank you

[empty wadi]

so this is the answer you were getting

64 inch^3 is the volume of each brick

the questions asks us how many bricks in total can fit in the storage area

so we divide the bigger volume by each individual brick

[weak trench]

So 211,200 divided by 64?

[empty wadi]

yess!

[weak trench]

3296.875?

[empty wadi]

your answer would be 3300

it divides it completly

you shouldnt get answer in decimal

your answer would be 3300 bricks

[weak trench]

I put it in the calculator

[empty wadi]

that doesnt make sense

the calculator returns the perfect 3300 value

perhaps maybe you messed up the input

?

[weak trench]

I also need help with another question

[empty wadi]

okay sure

[weak trench]

Wilber wants to make the pond in his backyard bigger. It is currently a cone with a radius of 30 meters and a depth of 15 meters. He wants to increase the radius to 40 meters and the depth to 20 meters. How much more water will the pond hold, in thousands of cubic meters? (Round to the nearest thousand cubic meters.)

[empty wadi]

hey awesomeperson i'll just get back to you in a minute oke

[weak trench]

Okay!

[empty wadi]

okay

im here

do you want the solution or an explaination too?

im suggesting the explaination will help you further

in understanding the concept

[weak trench]

Explanation please

[empty wadi]

oke

so we know the shape of the pool is a cone

so

do you know the formula for volume of cone?

or volume of cylinder

[weak trench]

Is the volume of a cone 1/3 multiplied by pi multiplied by r^2 multiplied by height

?

[empty wadi]

yeah

so

we can find the volume of the cones to see how much water they hold

now there's two methods of solving this,

either we can individually find the old volume and new volume
then to find how much MORE water it will hold, we (new volume) - (old volume)

to find the difference

so we can calculate both of these separately or we could take them into one equation and then solve them by substituting the values

which method would you like? or i could show both approaches

[weak trench]

The second method please

[empty wadi]

okay

sorry in image 1, the small h will be 15

[weak trench]

In the first image, is that a r?

[empty wadi]

yes

thats the radius

since the new pool will be bigger, it has a different radius as specified in the question

so we cannot take r and r
we must take r and R

since the values are different

[weak trench]

Is the second image's radius a 40?

[empty wadi]

yes

[weak trench]

What's next?

[empty wadi]

wait up

ill send the whole thing

so its easier to read

[weak trench]

Alr

[empty wadi]

still took more than one image smh

if value of pi isnt given, its easier to take 22/7

if its given, then use the specified value

have you understood it @weak trench

[weak trench]

Is 19000 the answer?

[weak trench]

Why did we subtract the second volume with the first volume?

[empty wadi]

yess, since the question asks us to round the answer to the nearest thousand, it will be 19000

the questions asks us ''HOW MUCH MORE WATER WILL THE POND HOLD"

now

this asks us the difference

how much more

that means

whats the difference between the amount of water it used to hold and the amount of water it holds now

since the new pond holds more water

[weak trench]

The answer is wrong

[empty wadi]

we subtract new volume with old volume

[empty wadi]

what's the answer?

[weak trench]

It doesn't say

[empty wadi]

does it have a specified value for pi?

[weak trench]

Nope

[empty wadi]

19000 what we get after rounding to the nearest thousand

i made no mathematical mistake

[weak trench]

Well idk why it says it's wrong

[empty wadi]

could you screenshot the original question?

[weak trench]

The question is on my chromebook and I'm on computer for Discord

[empty wadi]

uh

oke no worries

do you have options or is it an input integer type software

[weak trench]

Input integer

[empty wadi]

still getting the same result

[weak trench]

Er

[empty wadi]

something may be wrong with either the software or the data may be different

pelase recheck!

[weak trench]

Yeah it's right

[empty wadi]

ah well

[weak trench]

<@&286206848099549185>

.close

[compact pewter]

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[empty wadi]

are you sure mate?

[dense mason]

Nevermind then

[compact pewter]

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[quick magnet]

tt

[quick magnet]

who is arabic here?

[sleek meadow]

#discussion #chill

[compact pewter]

@quick magnet Has your question been resolved?

[dense mason]

!done

[compact pewter]

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[dawn marsh]

Show that if $1, z_{1}, z_{2}, z_{3}, \ldots z_{n}$ are the $(n+1)$-th roots of $1$, then

$$(z-z_{1})(z-z_{2})(z-z_{2}) \cdots(z-z_{n})=1+z+z^{2}+z^{3}+\cdots+z^{n}.$$

[boreal girder]

Halex

[dawn marsh]

I know $z_k = e^{\frac{2k \pi i}{n+1}}$ but not sure how to proceed

[boreal girder]

Halex

[drowsy bough]

here's a small hint: if two polynomials of degree k share k roots, then they are equal up to multiplying by a constant

[compact pewter]

@dawn marsh Has your question been resolved?

[dawn marsh]

Yes, I know that $$1-z^{n+1} = (1-z)(1+z+z^2 + \cdots + z^n)$$ but I'm not sure I can use what you mentioned

[boreal girder]

Halex

[drowsy bough]

i'm pretty sure you can use it because it is a very elementary thing, every time you factor a polynomial by finding its roots you are using it implicitly

[drowsy bough]

but if you don't like it you can also use this: if both polynomials coincide at n+1 different values of z then they must be the same, since their difference is then a polynomial with n+1 different roots but degree at most n (hence the difference is actually zero)

[compact pewter]

@dawn marsh Has your question been resolved?

[compact pewter]

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[haughty smelt]

I keep just getting the start again

[chrome cedar]

What are you trying to prove?

[dense mason]

What are you stuck

[haughty smelt]

I keep getting the same thing as the start

[haughty smelt]

Sinx/1-cosx

[dense mason]

Hmm okay let me see

[chrome cedar]

Use identity for 1-cos^2 x

On line 4

You were almost there

Whats the trig identity which uses cos x and sin x?

[haughty smelt]

Ohh sin^2x

[dense mason]

isnt the denominator you should multiply1+cosx instead?

[haughty smelt]

Whoops yea

Can I simplify this more

[dense mason]

yes you can rewrite this fraction first

[haughty smelt]

I’m not sure how

[dense mason]

it should be sin^2x /sinx(1+cosx)

[haughty smelt]

Yea I fixed it on my paper

[dense mason]

yes correct now

well done

[haughty smelt]

Can I simplify it any more or no?

OH WAIT

[dense mason]

no its equivalent to rhs already

lmao

[haughty smelt]

It’s not that type of question

I’m running on like two hours of sleep lol

and a Dunkin refresher

[dense mason]

look at question 34, what did it ask

[dense mason]

nahhh that is crazy

[haughty smelt]

See I got sleep paralysis

for like the first or second time

So now I’m worried to go to bed

[dense mason]

fried 😭

[haughty smelt]

but

More time to study and watch TikToks

[dense mason]

anyways you finished the question

[haughty smelt]

Yup I’ll be back tho since I have a quiz on Wednesday so today and tommorow I redo all the homework from this unit

Because I love torturing myself

[dense mason]

dawg.

[haughty smelt]

listen it works I have an A

and I’m used to this I got like fifteen disorders and disability’s ( diagnosed ) so I got to work through it somehow 😀

you don’t want to know the way I study for reading chapter quizzes

[dense mason]

damn thats sad, just ask for help if you need help

[strong folio]

instead of redoing the work here, why not find new problems to tackle?

[haughty smelt]

I do have help it’s just the way I do work I guess

[haughty smelt]

I mean I forget the problems by the time I redo them

and It’s easier to ask my teacher questions on certain problems instead of coming with a whole truck load of problems she has not seen

[strong folio]

alright, I won't ask any more. sorry for intruding.

[haughty smelt]

no worries

[compact pewter]

@haughty smelt Has your question been resolved?

[dense mason]

if you finished please type .close, thanks!

[compact pewter]

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[lofty mountain]

Linear algebra...opposite of finding unit vector...but i don't get it

[lofty mountain]

?

yes

(1/||v||)* vector

pyth. thm?

what if the vector is 3 d

i dont get it

ok..

what about this question

[trail cave]

does vro know the distance formula

[pliant scroll]

@lofty mountain are you aware of the formula to calculate the length of a vector

[lofty mountain]

yes

[pliant scroll]

what is it?

[lofty mountain]

Pythagoras theorem

[pliant scroll]

elaborate

just to be sure that you know it

[lofty mountain]

h^2 = p^2 + b^2

[pliant scroll]

... yes

if i have a vector [a, b] what is the length of this vector, then?

using pythagoras

[lofty mountain]

a^2 + b^2

underoot

[boreal girder]

ren

[pliant scroll]

good

[pliant scroll]

do you understand what we have to do here?

[lofty mountain]

no,m

[pliant scroll]

okay. you've been given a vector

they say this vector has length 1

but you have to compute the length and confirm that yes, it actually does have length 1

since you know the distance formula, can you compute the length of the vector for me?

[lofty mountain]

ok

[lofty mountain]

idk the distance formula

i forgot

[pliant scroll]

you literally just

[pliant scroll]

???

[lofty mountain]

oh..that is distance formula

[pliant scroll]

the distance/length formulas are the same thing

[lofty mountain]

okok

then?

[pliant scroll]

once more

[lofty mountain]

h = sq root. of p^2 +b^2

[pliant scroll]

okay

for the last time

i know that you know the distance formula. it is the same thing as the length formula

[lofty mountain]

ok

[pliant scroll]

your question asks you to compute the length of the vector given and confirm that the length is 1.

since you clearly know the formula, please compute the length of the vector

[lofty mountain]

5

[lofty mountain]

?

sq root (3)^2 + (-4)^2

[pliant scroll]

there's a 1/5 outside

[lofty mountain]

what is 1 / 5

[pliant scroll]

...?

what
do you mean

[lofty mountain]

it is outside..but don't know from where it came

[pliant scroll]

what do you mean "from where it came"

[lofty mountain]

if u is a unit vector, then it should follow this formula i.e.
(1/ II v II)* v vector

[pliant scroll]

... yes

[lofty mountain]

continue from there please

[pliant scroll]

ngl i cannot understand what you're saying

i don't think i can get much clearer

[lofty mountain]

(1/ II v II)* v vector = 1

[pliant scroll]

no-

[boreal girder]

ren

[lofty mountain]

oh

now it is clear...

[pliant scroll]

yep

[lofty mountain]

sorry for the issue

[pliant scroll]

no no

it's okay

it's not your fault

sometimes i have trouble understanding what people mean as well, don't worry about it

i'm here to help, so it's my job, don't worry

if you're done, you can close the channel with .close

[lofty mountain]

ok thanks

[pliant scroll]

np

[lofty mountain]

.close

[compact pewter]

Channel closed

Closed by @lofty mountain

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[compact pewter]

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[maiden spear]

I am trying to understand the equations for an inverse kinematics linkage system I found in a documentation. I am already have the solutions however I can't get my head around why these work. I provide the pdf where the full equations are in.

Understanding of first calculation b1: Calculating b1 when X is positive is just 90 - Arctan(X/Y). I understand this like i drew it in the picture. I don't understand the part why you add L3 to X when X is negative. Wouldn't b1 just be adding alpha to 90 when X is negative because the angle is larger than 90 then.

For the equations of c1 and c2 I cannot visually understand what is being done there.

For the other equations I haven't even got there because I struggle to understand even these.

[compact pewter]

@maiden spear Has your question been resolved?

[compact pewter]

@maiden spear Has your question been resolved?

[maiden spear]

<@&286206848099549185> I don't know if such a questions is fitting for the channel or if it is to big. Please let me know then I can search for somehwere else 🙂 Thanks

[dense mason]

Probably most of the members in usa timezone so they might reach in to help soon

This is beyond my knowledge so just be patient for few hours😂

Ping @ helpers may help

[maiden spear]

Ahh okay good to know 😄 Thank you, then I'll just wait a bit!

[dense mason]

No worries!

[compact pewter]

@maiden spear Has your question been resolved?

[past fable]

so hmm

c1 and c2 are the elbow angles and we got tan(90 + b1) which is just -cot(b1)

Ytan(90+b1) is the horizontal reach of the upper arm through b1

subtract l3 for the pivot offset from centerline

divide bby -y, then the arctan is the angle from the pivot to elbow

c1=90-b1 - the angle

what's left is the interior angle at the joint and c2 is the same thing

[maiden spear]

Thank you for your help!
So I am confused are the angles in the graphic not actually what is being calculated? So is the actual c1 like what I drew in the picture the red angle? And the other parts are highlighted in blue and green are these what you meant?

[past fable]

yup

[past fable]

D1&D2 use c1&c2 via sine rule to get the actual distances from bottom pivot to each elbow and then a1/a2 are just law of cosines from there

[compact pewter]

@maiden spear Has your question been resolved?

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[ornate sable]

So I tried 20 a with u sub. I had $u = 2x$ then $\frac{du}{2} = dx$ and $x = \frac{u}{2}$ then if we sub that all in we have $n\int_0^2 \frac{u}{2} f''(u)\frac{du}{2}$ but if I instead do it with theorem 1.19 we have $k = \frac{1}{2}$ and we have $\int_0^2 tf''(t)dt = 2\int_0^1 tf''(2t)dt$ how is this discrepancy happening?

[boreal girder]

BigBen

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[dusty moat]

why is this the case. wouldnt the intergral measure area?

[timber cipher]

Then what would f do?

[dusty moat]

?

[timber cipher]

If the integral measures area of that circle, then how would a choice of f change anything?

[dusty moat]

What?

[timber cipher]

So this is a complex integral. You are integrating over the circle γ which lives in the complex plane.

On every point of the circle, there's a value of the function f(z).

We basically add up what the function is doing on every point of the circle. That's the answer to the integral.

[dusky nymph]

to see that the integral need not have anything to do with area, try f = 0

[dusty moat]

I have no idea how to do that

I dont know what f(z) is

Its just supposed to be some function that gives an in closed space

[timber cipher]

f(z) is not that circle. f(z) is a function that lives on that circle. f(z) can be anything you want! (Kind of.)

f(z) = z² works. If you integrate that over that circle, you get 0.

Are you in a complex analysis course?

[dusty moat]

Not right now im trying to learn complex analysis tho

Can you explain how f(z) could equal z^2 I don't understand

[timber cipher]

f(z) is anything you want. It's a open slot for you to put a function in.

[dusty moat]

Then what does the circle mean

[timber cipher]

That's the space you're integrating over

Note the function exists on every point of the circle, but the function is not the circle itself

[dusty moat]

So it's like if you took a circle chunk out of the graph and looked at the function that was in the circle?

Wait how does it exist on every point of the circle?

Also sorry my phones at 1% lemme get too my computer ill be back in like 4 mins

back

is it every point in the circle or every point on the perimiter

[prisma vapor]

also, the integral sign with circle usually denotes line integral

so it's over only the circle not the whole disk

[dusty moat]

so whats the difference between f(x) and the circle

[prisma vapor]

f(x) is defined on the circle, circle is the domain

it's like defining some function (like x^2) on whole plane and then just looking at the portion of the function restricted to a circle

[dusty moat]

so it would be like 2 points on the circle?

[timber cipher]

In calc 1, you only integrate on the interval (a,b). All integrals are 1D lines, and you can put a function on them.

In complex analysis, you get to integrate over 2D shapes

Usually one takes calc 3 before complex analysis, in which 3 dimensional integrals often happen

[dusty moat]

thats just partial deriviation right?

[prisma vapor]

no, do you know multvariable calculus or have you encountered multivariable functions in the past?

[dusty moat]

idk

[prisma vapor]

like functions defined on plane, not just the real line

(so function with two variables)

[dusty moat]

so just like x+y=z type stuff yeh?

[prisma vapor]

yeah, or f(x, y) = x+y

[timber cipher]

Well, f(z) = x + iy is possible

[prisma vapor]

yeah i'm talking about real functions rn but that would be the complex equivalent

[prisma vapor]

maybe this'll be easier, why do you think it's 2 points?

[dusty moat]

i still dont understand why this would be a higher order intergral? and why its 0

[dusty moat]

cuz a function would go through it at 2 points

to enter

and to leave

or 0 points sometimes

if it doesnt enter at all

or 1

if its tangent

[prisma vapor]

okay, so you're thinking of a line/curve, which would be a function from real line to the space of interest

in this context z is a complex number, so the most natural way to visualize it is on the complex plane

[dusty moat]

yeah

[prisma vapor]

so the function f is NOT a line

[dusty moat]

its a plane right?

[prisma vapor]

not necessarily a plane but a surface

when taken over whole complex plane

and if it's real-valued but let's first just talk about real-valued ones

[dusty moat]

but how would a plane intersect a 2d circle? like i can imagine the z axiss being imaginary but isnt this situation still 2d?

[prisma vapor]

it's not intersecting it

the plane/surface (so the function) is defined on some domain - the set you take input values from

either R^2 or C

the circle is a subset of that domain that carves some portion of the surface

you can imagine a surface floating over the real plane (so it's in the third "dimension")

and then you take a circle out of the real plane and look what shape it traces on the surface floating above it

that trace is the portion of the function defined on the circle, the thing you're integrating

[dusty moat]

wouldent a circle trace out a line on the surface

[prisma vapor]

a curve yes, line no

[dusty moat]

i dont understand

[prisma vapor]

why would it trace a line?

like a straight line

[dusty moat]

yea?

if u have a circle

and u look at it from above

its just a line

[prisma vapor]

you're looking from the wrong "above" tho

the circle is laying on a table

surface is floating above the table

and you look at what portion of the floating surface is directly above the circle

[dusty moat]

so would it be like a circle if u looked at it from above and it would have different hieghts when look at from the side

[prisma vapor]

yup

[dusty moat]

ok that makes sense

[prisma vapor]

idk if the drawing helps but that's what i mean more or less, the arrow in the middle is going "to the back"

yup so that's the f(z) defined on a circle

although it's only the real one

[dusty moat]

so why wouldent the function matter when determining the intergral besides if theres poles

[prisma vapor]

yeah so that's where complex numbers come in

this surface thingie is only the real part

and you have the imaginary part too

which complicates things

[dusty moat]

are you able to draw on the picture u made of what the intergral of that represents

or is it too complicated

[timber cipher]

You're asking for a 4D picture haha.

There's ways that can be done, like using color for the 4th dimension, but it's getting messy