help-27

[sage kernel]

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[restive river]

Hello everyone. At the very last step, I don’t see how those two expressions equal to each other, can anyone help me out with this?

[devout snow]

@restive river Has your question been resolved?

[restive river]

<@&286206848099549185>

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@restive river Has your question been resolved?

[restive river]

<@&286206848099549185> <@&286206848099549185> <@&286206848099549185>

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[vestal granite]

is it possible that the foci of an ellipse is more farther than the vertices? asking for a friend

[vestal granite]

feel free to check if i had any miscalculations

thanks!

<@&286206848099549185>

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[cobalt flint]

Ive been using the Arrhenius equation but my prof got a different answer than me

Im doing (ln(20))/((1/293.15-1/313.15)(8.3145)) = H

Now the answer is supposed to be 61.4kJ but I get 1.653

[devout snow]

@cobalt flint Has your question been resolved?

[cobalt flint]

<@&286206848099549185> , would you guys know of a chemistry channel I could get help for this question from?

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[pallid otter]

Would I integrate the function, find the roots and take it away from each other?

[devout snow]

Please don't occupy multiple help channels.

[pallid otter]

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[tepid wind]

Person A pays 21$
Tax - 5%
Discount - 20%
The answer sheet says the answer is 25$
25x.2 = 5 > discount % calc
25-5 = 20 > subtracting discount from answer price
20 x .05 = 1 > tax % price
20 + 1 = 21 > adding tax to the discounted price
however I do not get why I cant do this in reverse
I can get
21/1.05 = 20 > price before tax
but I dont know the final step of how we get the 5 dollars or am i just misunderstanding something here

[amber valley]

You know that 20 is 80% of the total

[tepid wind]

so i am an idiot

alright thanks

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[narrow thunder]

I have no clue for this question

the only thing I can think of rn is x = t^2 and y = t

but otherwise im lost

[devout snow]

@narrow thunder Has your question been resolved?

[devout snow]

@narrow thunder Has your question been resolved?

[analog trellis]

Use Stokes's theorem.

[narrow thunder]

Is the vector field just the expressions before dx dy and dz?

And then I would get the bounds from the boundary given right?

[analog trellis]

Write it as

$\vec{F} \cdot \dd{\vec{r}}$.

[woven radish]

stabulo

[analog trellis]

Then Curl(F) = <0, 0, 1>.

Or just use Green's theorem.

[narrow thunder]

Okay I'll try that, thank you!

[analog trellis]

Basically the line integral equals the area of the region bounded by the closed curve in this case.

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@narrow thunder Has your question been resolved?

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[tiny flume]

what is the equation of the line through (4,-1) and whose segment intercepted between the axes in the fourth quadrant is equal to 2sqrt17?

[restive river]

I don't really understand what you mean in the second half of that

[dire palm]

I think she meant a segment of either x or y axis

[proud perch]

Its linear equations with a bit of trig attached

Can you draw a triangle in the 4th quadrant whose legs are on the axes

[dire palm]

You need two equations one is
$x_{0}y_{0}=2√17$ and $\frac{y_0}{x_0}=-4$

[woven radish]

Mushfiqur

[tiny flume]

where did 4 came from

[dire palm]

The slope, it will be -1/4

[tiny flume]

i dont get it T_T

[devout snow]

@tiny flume Has your question been resolved?

[tiny flume]

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[tiny rain]

hai, can someone explain the working here

@arctic field

[arctic field]

[tiny rain]

hello my saviour

[arctic field]

orthogonal decomposition

you need projections ig

much more annoying in infinite dimensional

[tiny rain]

hm wait but

the answer i worte

is from the ans key

confused

how does it mak sense

[arctic field]

so like

[tiny rain]

[arctic field]

Av is in the column space of A

[tiny rain]

yes

[arctic field]

and i guess v - Av should be in the null space of A

oh wait

i didnt see the first line

A^2 = A okay

so A is a projection

[tiny rain]

yes

wut

[arctic field]

okay so basically

[tiny rain]

ye

[arctic field]

how is null space and column space usually denoted

[tiny rain]

wait ur asking me

[arctic field]

well have you seen any common notations for it

cuz i know a few

but

you might not have seen them

[tiny rain]

Av = 0 nullspace

Av = B

columnspace

[arctic field]

i meant like

im(A) and ker(A)

or something

[tiny rain]

o

um

nullspace(A) columnspace(A)

XDDDDD

[arctic field]

okay sure

[tiny rain]

yes

[arctic field]

the first one should be clear

the second one might not be

so we should show that

[tiny rain]

first one yes

wait just checking

Av = 0 is also in the col space right?

[arctic field]

uh

0 is in the col space

because A0 = 0

[tiny rain]

yes

[arctic field]

theyre both subspaces

so they gotta include 0

anyway so

[arctic field]

so for x = v - Av to be in the null space we just gotta show that Ax = A(v - Av) = 0

[tiny rain]

yes

[arctic field]

okay so

you just compute

[
A \parens {v - Av} = Av - A^2 v
]

[arctic field]

then because A = A^2

aaa wtf

[tiny rain]

where did the cat come from

[arctic field]

random sticker

[tiny rain]

[arctic field]

okay so

[tiny rain]

hm

[arctic field]

its 0

[tiny rain]

wait lemme

work it out

[arctic field]

yes

oh hm

they wrote v1 is in nullspace v2 is in column space

same same

[tiny rain]

hm

wait

im

lost

am i supposed to write like

v - Av_1 + Av_2

or just Av

[arctic field]

no its supposed to be v

like

[tiny rain]

OH

OKAY

lai

WATS NEXT

no caps

sorr

[arctic field]

uh

and then

[arctic field]

kinda by definition or whatever

[tiny rain]

yes

[arctic field]

and then

[arctic field]

so thats part (a) done

[tiny rain]

yes

[arctic field]

now for part (b)

[tiny rain]

wait

so like

lets say

v

i want to know if v is in the nullspace

i can show

Av = 0

right

[arctic field]

yes

[tiny rain]

if i wanna show if its in the col space

its like

Av = anyting

[arctic field]

yes

well

uh

no

[tiny rain]

wot

[arctic field]

thats not exactly accurate

[tiny rain]

o

wait

why is it like that tho

[arctic field]

uh

thats just definition

like

colspace(A) is the set of vectors in the image of A

and nullspace(A) is the set of vectors sent to 0 by A

and then theres that

rank nullity theorem

[tiny rain]

o

okay

make sense

makes

okay

lai

part ii

b

[arctic field]

basically it goes like

if a vector is in both the colspace and nullspace of A then it must be 0

we gotta prove that ig

so like

[tiny rain]

hm

[arctic field]

so like

the way you do that is to basically check definitions

[arctic field]

maybe i shouldnt use quote

meh

now we need to show that w = 0

[tiny rain]

wait so like the vector exists in both null and col space yes

so it must be 0

MUSTTT

[arctic field]

we have to prove that

probably

at least your writing proved it

so

lets

[tiny rain]

smol

but i zoom

yes

[arctic field]

and then

[tiny rain]

yes

OH

wait

a sec

wait a sec

i dont get the

Aw = A(Av)

[tiny rain]

cough

OKAY

I UNDERSTAND

THANK YOU

[arctic field]

wait we arent done

lmfao

we just proved that colspace intersect nullspace = 0

now we need to use that result

[tiny rain]

wait at

i tot we had to prove that

oh wait

nvm

lmao

[arctic field]

no we have to prove that the decomposition is unique

okay so

not completely sure what you've written in your thing

but

the way im thinking rn

is say you have two decompositions of v

[tiny rain]

hyes

[arctic field]

not necessarily different actually

we're gonna show theyre the same

[tiny rain]

i nid to sowt hat v_1 = v1'

[arctic field]

yes

[tiny rain]

hmmmmmmmmmmmmmmmm

[arctic field]

cant quite follow your notes

but

if you take the difference

you get

[tiny rain]

hm

what does that prove

i dunsee it

[arctic field]

nothing yet

[tiny rain]

o

[arctic field]

but now

because both colspace(A) and nullspace(A) are subspaces

[arctic field]

in fact these are easy to check even if you dont know theyre subspaces

[tiny rain]

yes

[arctic field]

we just multiply this whole thing by A

[tiny rain]

yes

[arctic field]

good

so

i think i got it the wrong way round

oh well

[tiny rain]

actually

do u mind like

[arctic field]

just pretend here its switched

lmao

[tiny rain]

typign it together

cus its all apart

abit

confuse

[arctic field]

[tiny rain]

[arctic field]

lets see

gimme a bit ig

[tiny rain]

yesmam

[arctic field]

something crashed

[tiny rain]

[arctic field]

gotta restart computer

[tiny rain]

wait

so u lost

progress

[arctic field]

nah

[tiny rain]

😮

[arctic field]

just

[tiny rain]

o

[arctic field]

brb

[tiny rain]

yesmaam

[tiny rain]

omg

thats so formal

and long

lemme see

[arctic field]

#❓how-to-get-help

[tiny rain]

#❓how-to-get-help

[tight quail]

Ty

[tiny rain]

hm

@arctic field hi

i understand

u r the best

[arctic field]

[tiny rain]

wheres that sticker from

[arctic field]

hw help server

[tiny rain]

o no

but i cant use

sadge

[arctic field]

[tiny rain]

wow flex

oh wait

[arctic field]

we can all be sad together

[tiny rain]

no

u must

happy

u are snow

[arctic field]

we can also be happy together

[tiny rain]

yes

i am sad because i suck at meth

XD

ok

i shall go

[arctic field]

[tiny rain]

tysm madam once again

[arctic field]

okay

[tiny rain]

.close

[devout snow]

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[fast helm]

an oil company wishes to run a pipe from point A to point B. they are position across a riverbank 500m wide and point b is 5 km to the right of the point directly across a. the pipe is 200$ to be run through the water and 100$ to be run through land. what is the expression for the amount of piping to be run into the water? what is the expression for the amount of piping to be run into land? show that the total cost, C = 200* sqrt(500^2 + x^2) + 100*(5000-x) . what is the value of x for which cost is minimum? what is the minimum cost?

[fast helm]

i also dont understand this really

i graphed it

but i dont know how to rearrange into that formula

[devout snow]

@fast helm Has your question been resolved?

[devout snow]

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[craggy pumice]

I have a mechanism that can move in two oposing axies in 3d space as shown in the image, and I know the rotation/ angle of both axies and want to find a formula for calculating a coordinate point on a line that extends from the mechanism.

[craggy pumice]

It can rotate a total of 180 degrees for each mechanism, and the top mechanism is connected to the end point of the stick on the bottom mechanism

heres a video of an actual model of it

the grey piece that i point to is the point im trying to find a formula for

[wooden veldt]

Sounds like inverse kinematics

[craggy pumice]

I personally am taking geometry currently so if you could help me figure out the exact formula, it would really help

[wooden veldt]

Google inverse kinematics it's pretty much this exact problem

[craggy pumice]

ok

i did

ill try to figure it out

thank you

.close

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[restive river]

Can anyone help me with this question I always get confused

[restive river]

Number 4

Like ik it's not hard but

I'm thinking it's A, C and E?

But I really forgot what a reflection and rotation is

I think reflecting it doesn't change the shape right?

But it moves it

I'm so confused

[tame palm]

Reflection folds the image across the designated axis.

[restive river]

So it would be halves?

[tame palm]

So the first option states to "reflect across the line x=3/2.

You can mathematically show that the line x=3/2 crosses the center of the rectangle.

[restive river]

Oh I see it on the paper

But

It's -3,-2

But when it's reflected the signs switch correct?

[tame palm]

How would you mathematically evaluate the reflection across the line x = 3/2?

[restive river]

By flipping it?

[tame palm]

Yes, but how would you calculate where (-3,-2) ends up by folding across the line x=3/2?

[restive river]

By going 90 degrees?

[tame palm]

That would be a rotation.

[restive river]

oh right

So I gotta go clockwise

or

[tame palm]

This might be easier to understand using the second option.

If you flip the point (-3,4) across the line y=3/2 x, how would you calculate where it ends up at?

[restive river]

I would see -3, 4 becoming 3,4

or 3,-4

Since flippin it would change the signs

[tame palm]

How would you calculate the new point of the corner (-3,4)?

Not sure?

[restive river]

idk

[tame palm]

I'm going to use a tick mark to indicate the new position of the point, x' and y'.

When evaluating the transformation, you replace one of the variables in the line of reflection.

[restive river]

Right

The x

[tame palm]

\begin{align*}
y' &= \frac{3}{2}x\
y' &= \frac{3}{2}(-3)\
y' &= -\frac{9}{2}
\end{align*}

[woven radish]

Kookiemon

[tame palm]

And vice-versa for x' and y.

[restive river]

And divide -9/2?

[tame palm]

No, that will be the y-component of the translated position.

[restive river]

Oh

[tame palm]

$(x,y) \to (x',y')$

[woven radish]

Kookiemon

[restive river]

So they both became positive?

[tame palm]

And you can solve for x' vice-versa.

$y = \frac{3}{2}x'$

[woven radish]

Kookiemon

[tame palm]

And using y=4.

[restive river]

3/2x = 4?

[tame palm]

3/2 x' = 4

You want to make sure you differentiate the original values from the new values.

[restive river]

Right

[tame palm]

\begin{align*}
y' &= \frac{3}{2}x\
x' &= \frac{2}{3}y
\end{align*}

[woven radish]

Kookiemon

[restive river]

So both A and B?

[tame palm]

This is the second option, reflection across the line y=3/2x. Does that look like it reflects back onto itself?

[restive river]

Yea

[tame palm]

By reflect back onto itself, the question is asking if the image remains the same.

[restive river]

Yea bc they fold onto each other?

Wait no

Bc the age changes

Image "

[tame palm]

Exactly.

[restive river]

So B is eliminated

[tame palm]

Correct.

[restive river]

Now C

A clockwise rotation

Like a clock so

The image would stay the same

Just a different way

[tame palm]

Correct.

[restive river]

So that's an answer

A C

And D would also be a correct one

Nope nvm

Bc it's gone change the Y

[tame palm]

👍

[restive river]

So the answers are

A C E

[tame palm]

Double-check E.

[restive river]

or

Lemme see

Nvm

Just A and C

Because it's doing a translation in E

[tame palm]

What point is it rotating around?

[restive river]

6,-2

[tame palm]

If you rotate around the point (6,-2) by 180 degrees, you get this.

And if you then move it 9 units to the left, will it end up back where it started?

[restive river]

Nope

It would be correct

If it didn't move 9 units left

So the answers is A C

[tame palm]

👍

[restive river]

So one more question and I know that I'm correct

Number 3

Now I'm pretty sure it's X= 4

[tame palm]

Correct.

[restive river]

okay just wanted to make sure

And number 10

Ik sas

I think it's AB = CB

Bc if ab and cb are equal then that's all that is needed to be proved

[tame palm]

The question says what information do you need to prove the triangles are congruent using SAS(side-angle-side).

That means the information you need are the length of a side, an angle, and then another side length; in that order.

[restive river]

Oh I get it now

No I don't

Bc wouldn't c and d be correct?

[tame palm]

The two triangles share one side, BD.

[restive river]

Right

Oh so I gotta prove

[tame palm]

You are given an angle, CDB and conversely ADB, as being right angles.

[restive river]

Ad and cd are equal

[tame palm]

👍

[restive river]

Thanks for the knowledge

[tame palm]

yw

[restive river]

wait can you guide me through a few more

If you got time

I'm trying to get information for the state text next week

Tryna study this study guide teacher gave ke

Me**

[tame palm]

Ask away.

[restive river]

Number 9

Wait

Let me look at it

Okay i looked and

I think it's D

The areas are congruent

[tame palm]

Hmm.

[restive river]

Wait

Its B

COB = AOD

[tame palm]

Sounds good.

[restive river]

I'm right?

[tame palm]

Yes.

[restive river]

I need help with all 3

but I don't understand 17 the most

[tame palm]

Do you understand what the slope of a line is and how to find it?

[restive river]

Hm

It changes

[tame palm]

The slope of a line gives an indication of how slanted a line is.

More specifically, it is a ratio of the change in the y value divided by the change in x value.

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

[woven radish]

Kookiemon

[restive river]

Right

[tame palm]

For linear equations, ie. a line, in the form y = mx+b, the slope is m.

A perpendicular line has a slope equal to -1/m.

[restive river]

Right

[tame palm]

$\perp m = -\frac{1}{m}$

[woven radish]

Kookiemon

[tame palm]

So if you have the line y = -2/3 x +5, find the slope and then calculate the slope of the perpendicular line.

[restive river]

-2 is x

3 is y?

[tame palm]

$y = \underbrace{-\frac{2}{3}}_{m}x + 5$

[woven radish]

Kookiemon

[restive river]

Ohh

So 5 becomes -5

[tame palm]

The equation is already in the form y = mx + b.

So now you just need to find the slope of the perpendicular line using

[restive river]

Hm

And it has to pass through (0, -2)

[tame palm]

Yes. To find the equation of the line, use the Point-Slope formula.

$y - y_{1} = m(x - x_{1})$

[woven radish]

Kookiemon

[restive river]

And plug them in

[tame palm]

Correct.

If you have any interest in the STEM field, remember the Point-Slope formula. It is used a lot in mathematics in one form or another.

[restive river]

Brainfart

I'm lost

[tame palm]

What is the perpendicular slope? You know m = -2/3.

[restive river]

5?

[tame palm]

Just invert the fraction and then negate that value.

[restive river]

3,-2?

[tame palm]

3/2

[restive river]

Ohh

So any negative answers are eliminated

[tame palm]

Yes.

[restive river]

So it's D

[tame palm]

Plug in the values of the point it needs to go through.

[restive river]

Okay

5 goes through 0,-2

So it changes?

[tame palm]

One moment ...

[restive river]

Okay

Okay

I got my answer

C

[tame palm]

https://www.geogebra.org/classic/duxp8sfp

There are an infinite number of perpendicular lines to the line y = -2/3 x + 5 and the question asks you for a specific line that goes through the point (0,-2).

If you find the perpendicular slope and use the Point-Slope formula, you can calculate that specific line.

[restive river]

I see

Can you help with 18 now

[tame palm]

Use the same method as before.

Find the slope of the original equation, then calculate the perpendicular slope.

[restive river]

Alright

[tame palm]

This one should be rather straight-forward as there is only one solution with the correct slope.

[restive river]

D

[tame palm]

No.

What is the slope of the given equation?

[restive river]

The slope is

-5, -3

[tame palm]

That is the point the question is asking you to move the line through.

[restive river]

Oh right

Okay and now

[restive river]

Where it go

Oh

[tame palm]

And the perpendicular slope would be?

[restive river]

7/5?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

Channel closed

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Available help channel!

Send your question here to claim the channel.

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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lethal osprey]

how do i solve this problem

[long kettle]

What have you tried

[lethal osprey]

i tried doing implicit differenciation

but i dont really know what im doing

[long kettle]

Show your work

[lethal osprey]

im just plugging in formulas

[long kettle]

d/dt (3x) ≠ 3

[grizzled shoal]

dde

dude

[silent estuary]

can i try my math bot

[grizzled shoal]

you r wrong

[lethal osprey]

is it 3 * dx/dt?

[silent estuary]

i have made a math bot in python

[long kettle]

Yes

[grizzled shoal]

lemme solve it

🍺 hold my beer

[long kettle]

Ask in #discussion, not someone else's help channel

[long kettle]

It's not your problem to solve

[silent estuary]

but i wanna help this person

[long kettle]

I mean, do it on your own, I guess

[long kettle]

You don't need a bot for that

[silent estuary]

i do

because im not that advanced

[lethal osprey]

ok so i got the answer

but i still dont really know what im doing

[long kettle]

If you can't help, then dont

It's just the chain rule

[silent estuary]

@lethal osprey do you want me to paste my bot’s answer

[long kettle]

Do not just give away answers

[silent estuary]

it has explanations

[long kettle]

Don't care

[silent estuary]

i can cover the final answer

[silent estuary]

then how am i supposed to answer??

[long kettle]

d/dt g(f(t)) = g'(f(t)) * f'(t)

You get that, right?

[long kettle]

Answer what?

[silent estuary]

his question

[long kettle]

You're not supposed to answer it

[lethal osprey]

yeah

[long kettle]

You're supposed to help OP find the answer

[silent estuary]

yes as i said it has explanations

[long kettle]

Let's say you wanted to find d/dt x²

x, in this scenario, is a function of t

[lethal osprey]

its fine bro i figured it out but you can still send it so i can take a look and maybe see what i can find helpful for myself

[silent estuary]

alr bro one sec

[long kettle]

So x² is just (x(t))²

[silent estuary]

To find the vertical velocity of the particle, we need to take the derivative of the function y = x^3 + 3x + 1 with respect to time. Since we know that the horizontal velocity of the particle is constant at 2 cm/s, we can use the chain rule to express the derivative of y with respect to time as follows:

dy/dt = (dy/dx)*(dx/dt)

Since we know that dx/dt is constant at 2 cm/s, we can plug this value into the equation above to get:

dy/dt = (dy/dx)*2

To find the value of dy/dx, we need to take the derivative of y = x^3 + 3x + 1 with respect to x. Using the power rule, we can write:

dy/dx = 3x^2 + 3

Now we can plug this value into our previous equation to get:

dy/dt = (3x^2 + 3)*2

Since we are looking for the vertical velocity at the point (2, 15), we can plug in x = 2 to get:

dy/dt = (3*2^2 + 3)*2 = (12+3)*2 = 30 cm/s

Therefore, the vertical velocity of the particle at the point (2, 15) is 30 cm/s.

idk if its right, @long kettle could you check for me

[long kettle]

-_-

[silent estuary]

yea or nah

simple question simple answer

[lethal osprey]

wdym by (x(t))^2 could you maybe put it in the math form

[lethal osprey]

is this solely from a bot itself?

[long kettle]

x(t) is just a function, like f(t)

If you wanted d/dt (f(t))², would you understand that it's 2f(t) * f'(t)?

[silent estuary]

the bot is chatgpt

made by openai

[long kettle]

This is not how we help people in this channel. Giving all the steps, with explanations or no, is not how this server runs

[silent estuary]

bro

why u so triggered

[silent estuary]

read this

the client is always right

[lethal osprey]

yeah i was thinking that it looked like chatgpt but when i tried typing in the same question it didnt give the same answer

[silent estuary]

A particle moves along the path y =x^3+3x+1 where units are in centimetres. If the horizontal velocity Vx = dx/dt is constant at 2 cm/s, find the vertical velocity Vy =
dy/dt of the
particle at the point (2, 15).

i asked this

[lethal osprey]

aight chill out now i mean its still helping me one way or another all help is appreciated

[silent estuary]

yes

smh

[long kettle]

Do you understand this

[lethal osprey]

yeah so i do the the first derivative but the f'(t) is undefined or something like that?

[long kettle]

Wdym undefined?

It's just the chain rule

g(t) = t², f(t) = ... f(t)

(f(t))² = g(f(t))

[lethal osprey]

yeah i mean for the du/dx its usually not there and an actual number but in this case i can only put it in f'(t)

[long kettle]

Technically, it's always there

d/dx x² can be written 2x * dx/dx

But dx/dx = 1

Again, it's just an application of the chain rule

[lethal osprey]

ah

[long kettle]

d/dx (f(x))^n = n(f(x))^(n - 1) * f'(x)

[lethal osprey]

yeah

[devout snow]

@lethal osprey Has your question been resolved?

[devout snow]

Channel closed

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Available help channel!

Send your question here to claim the channel.

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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[random pendant]

How to solve first using Z subistion

[random pendant]

Substitution

[sonic smelt]

Let z = x^2 + 3

[random pendant]

Okay and then I got the derivative

How do I transfer

Dz/dx=2x

Which one goes other side

[sonic smelt]

3x(x^2 + 3)^4dx becomes 3x z^4 dz/2x

x's cancel out

[random pendant]

Huh

Wh dz/2x

Why

[sonic smelt]

dz/dx = 2x
dz = 2x dx
dx = dz/2x

[random pendant]

How about x2

How can i know its value

[sonic smelt]

?

You don't have to

[random pendant]

Like

Don't Don't need to make x²=z-3

And know value of x

The

X.z⁴.dz/2x

[sonic smelt]

No

[random pendant]

How do I integrate it then

[sonic smelt]

3x (x^2 + 3)^4 dx = 3x z^4 dz/2x = 3/2 * z^4 dz

Now you just have to integrate z^4

[random pendant]

How about the x

How do i do x z⁴ dZ/2x

[devout snow]

@random pendant Has your question been resolved?

[random pendant]

<@&286206848099549185>

[restive river]

Any problem@random pendant ?

[restive river]

can you simplify (x*z^4)/(2x)?

@restive river hey how can i become a helper?

[random pendant]

Hm

[restive river]

go to info and it lets you self-assign roles

[random pendant]

Why do we have

All that over 2x

[restive river]

@random pendant give the question please

[random pendant]

Main question is 3x(x²+3)⁴dx

Integrating it I would get 3 out integral and let z = x²+3

So I end up with x.z⁴.dx

What is next step

[restive river]

Your missing 3

ah not quite because you divide by 2x since dx/dz = 1/2x

3x.z⁴.dx

[random pendant]

It is out the integral

[restive river]

@restive river hey give me the way to info for being a helper

https://discord.com/channels/268882317391429632/525440994242461702

[random pendant]

Ok so basically dx=dz/2x

What's next

I got x z⁴ dz/2x

[restive river]

yep

[random pendant]

What do I do with the x

[restive river]

so you have (x*z^4)/2x dz

[random pendant]

What

How?

[restive river]

or you can rewrite this as (x/(2x))*z^4 dz

by * I mean multipliy

I would write it out nicely but the latex bot isn't working

[random pendant]

I don't understand the part of

Why did we remove the 2x from the sz

Dz

[restive river]

because the 1/2x is actually inside the integral

[random pendant]

Wait wait

Is dz/2x same as 1/2x dz

[restive river]

yes

[random pendant]

Ohhhh

I didn't know that

So now I can have

X*z⁴/2x

[restive river]

yep

[random pendant]

Can I cancel x with x

[restive river]

exactly

[random pendant]

Is the answer gonna be

3/10*(x²+3)⁵+c

[restive river]

that's correct

you could also try differentiating to check

[random pendant]

Uhhhhhhhh

The differentiation would be

3x(x²+3)⁴

Wow

That's the same

[restive river]

👌

[random pendant]

Thanks alot

Can I just multiply the 2nd bracket with 2 in number 3

[devout snow]

@random pendant Has your question been resolved?

Channel closed

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fringe olive]

just need help with part a and b

[devout snow]

@fringe olive Has your question been resolved?

[devout snow]

@fringe olive Has your question been resolved?

[devout snow]

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Send your question here to claim the channel.

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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[restive river]

whats an example of an anti symmetric relation

[pine fox]

divisibility

can you tell me why it's an anti-symmetric relation?

[restive river]

i only really understand these relations on sets

hi?

open another channel

pls

[wooden wraith]

You already have a channel open. Stop posting in other people's channels

[restive river]

i am barely passing this concepts class

i doubt i can help

[devout snow]

@restive river Has your question been resolved?

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Available help channel!

Send your question here to claim the channel.

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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vapid lotus]

stuck on the whole thing.

[untold ore]

Rise -1

Run 8

Your first point is on the origin

[celest bone]

Hi

How could I unlock the abstract álgebra chat

?

[vapid lotus]

whats rise and run ive never heard those terms before

[untold ore]

So -1/8x is the slope of this line

In order to graph this line, people say rise/ run

You rise the amount of squares in the numerator, and then run the number of squares in the denominator

In this case, the numerator is negative is negative, so we rise, or count down negative one

[untold ore]

Then you run, or count eight square to the right. And that is where your point will be placed

[vapid lotus]

could u sketch how it has to be graphed..

im so sorry i love how ur explaining it im just way too dumb

😭😭

[untold ore]

Desmos.com

Go to that website and type in the equation

[vapid lotus]

is it this?

[vapid lotus]

okay

[ocean holly]

your slope is going up

[ocean holly]

since its negative, it should be decreasing

[vapid lotus]

im confused why is it just at 0

[untold ore]

Your first point will be placed at the origin

[ocean holly]

because if you plug in 0 in x, you get y = 0

plus, since your graph does not have a b, your y intercept is at 0

[vapid lotus]

are u saying its 0, 0?

[ocean holly]

you can look up some videos on "y = kx" if you need more resources

for your origin point, yes.

[celest bone]

Fk

I just want to chat in the abstract álgebra channel

Idk how

[vapid lotus]

can anyone just write where to put the dots

😭😭💔

[ocean holly]

its an open channel

[celest bone]

It always send me to another channels

[ocean holly]

#get-advanced-access

please read that

[celest bone]

I have done that

And I choose 8

And 1

[vapid lotus]

boy

[celest bone]

?

[ocean holly]

desmos is your answer key

[devout snow]

@vapid lotus Has your question been resolved?

[devout snow]

@vapid lotus Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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Available help channel!

Send your question here to claim the channel.

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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[restive river]

how do i find these two?

.close

[devout snow]

Channel closed

Closed by @stable stump

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[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[haughty jolt]

I’m doing a project where I find data for a table (yellow paper). From this I have to plot the data and create a y=sin(x) equation. I’m currently stuck because I can’t figure out the equation

[supple knot]

jesus christ

[haughty jolt]

are the images bad? I can try to take better ones

[supple knot]

maybe try it in some graphing software

https://www.youtube.com/watch?v=CgWypDdAC4Q

you just need to figure out 4 parameters in the sine model

https://www.maa.org/sites/default/files/images/upload_library/3/osslets/100multiParameterAnimation/sine.html

you should be able to figure out B and A from the heights

[haughty jolt]

I solved it using desmos, however I don’t know how to solve it using algebra

$$y=-4.4407sin\pi/12(x-h)+12.2332$$

[woven radish]

JollySaintQuinnichalos

[haughty jolt]

I put in the point (1,16.5639)

$$16.5639=-4.4407sin\pi/12(1-h)+12.2332$$

[woven radish]

JollySaintQuinnichalos

[haughty jolt]

I don’t know how to solve from here

[devout snow]

@haughty jolt Has your question been resolved?

[haughty jolt]

<@&286206848099549185>

[devout snow]

@haughty jolt Has your question been resolved?

[haughty jolt]

<@&286206848099549185>

[haughty jolt]

.close

[devout snow]

Channel closed

Closed by @haughty jolt

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Send your question here to claim the channel.

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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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[safe sun]

Can anyone help me

[amber valley]

[tender saddle]

with???

[safe sun]

I’ll send a picture

I tried it myself multiple times

It keeps showing as incorrect

[amber valley]

What did you get?

[safe sun]

Those were my answers

[amber valley]

You're supposed to substitute x in the equation with the values on the left

[safe sun]

So how do i do it

[amber valley]

So for x=1, y=25-2(1)=23

[safe sun]

So 1 is 23?

Whats the first one

[amber valley]

That's the first

[safe sun]

Okay second one

[amber valley]

Give it a try, show your work

[safe sun]

It moved me on to the next question but it was incorrect again

[amber valley]

I meant just write it here and we could check

[safe sun]

This is the new question

[amber valley]

Ok, what do you get for x=1?

[safe sun]

Would it be 7 because at the question above it says 1+6?

[amber valley]

Exactly

[safe sun]

Ok what about the second one

3

[amber valley]

How did you get 3?

[safe sun]

No i’m saying 3 is the x

For the second one

[amber valley]

Ah my bad, yes

[safe sun]

Would it be 14

3=14

[amber valley]

That's not how you write it, but how do you get 14?

[safe sun]

Because for the first one it was 7

So do i just multiply 7 14 21 28

[amber valley]

No, you're supposed to substitute each value of x in the equation

[safe sun]

So what would the second one be

[amber valley]

1+6*3

[safe sun]

Would the second one be 4

[amber valley]

,calc 1+6*3

[woven radish]

Result:

19

[safe sun]

Ok what about the third one

8

Is the x

[amber valley]

How would you get it?

[safe sun]

Would it be 31

[amber valley]

Bro, I feel like you're trying things at random

[safe sun]

What do you mean

[amber valley]

How did you get 31?

[safe sun]

Uh 19-7 and than 19+12

[amber valley]

Isn't that random?

[amber valley]

^

[safe sun]

I’m just trying my best

[amber valley]

Ok sorry

[safe sun]

Can you explain it to me clearly

[amber valley]

The equation says y=1+6x

[safe sun]

At the same time i feel sleepy and having anxiety so my bad if i say something stupid

[amber valley]

It's easy

The table gives values x=1, x=3, x=8 and so on

You substitute x in the equation and solve

[safe sun]

It can be easy but i’m just slow meaning it takes a while for me to understand

[amber valley]

Notice, for the first we put the first value of x in the equation and got 7

[safe sun]

Yea cause i said 1+6

[amber valley]

For the second we put the second value on the equation and got 19

[safe sun]

Would it be 26 for the third one

[amber valley]

How?

[safe sun]

Ok so remember how i said 1+6 so do i just add 7+19?

[amber valley]

Again, you're supposed to change x with 8 and solve

You don't sum the values of y, or the values of x, or anything else

You're supposed to change x with the value it's given and solve for y

[safe sun]

Do you think you can do it for me and see if i understand better that way or do you think i should try still solving it

[amber valley]

Ok, so in this case x=8 right?