help-13

[tight cove]

The sheet says to “Graph then state whether the following relations are functions” but I’m not sure how to do this one

[sage badge]

Find y by itself

[surreal cave]

solve for y

[tight cove]

Would it be x = y2

[surreal cave]

Solve for $y$ in $3x+2y=10$

[wraith dagger]

XxMrFancyu2xX

[tight cove]

Idk

Class hasn’t taught us that yet

This was supposed to be given as an example

[surreal cave]

Ok, instead how about try to pick point values $x$ and $y$ that $3x+2y=10$ for example $x=2$ and $y=2$ works

[wraith dagger]

XxMrFancyu2xX

[surreal cave]

can you try to find any other points that work?

[tight cove]

x = 1 and y = 3.5

[neon moon]

Non-integer points are tough to be drawn. Consider we have a 3x term on LHS and a 10 on RHS, we may not want x to be odd number.

Some suggested points for you will be (-2, ?), (0, ?), (2, ?), (4, ?), etc, in which those ? can be found by solving equation with the preset x value.

[tight cove]

LHS?

RHS?

[odd remnant]

left hand side

[odd remnant]

right hand side

[neon moon]

In case you need any help on the vocabulary.

[tight cove]

Brain hurt

[tight cove]

This is supposed to just be an example all I need is an answer

[cedar kiln]

@tight cove Has your question been resolved?

[tight cove]

Bruh

.close

[cedar kiln]

Channel closed

Closed by @tight cove

Use .reopen if this was a mistake.

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.

[lunar flare]

Hi! Could someone help me understand what I'm doing wrong in this question? I tried differentiating f(x,y) and multiplying fx by va and fy by vb, but that didn't work.

[neon moon]

Hint: What is the sign of dx/dt and dy/dt?

[lunar flare]

I got it. Thanks 😄

.close

[cedar kiln]

Channel closed

Closed by @lunar flare

Use .reopen if this was a mistake.

[cedar kiln]

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.

[crimson sedge]

7p^2- 38p - 24 = 0 i want to check my answers with someone for my vertex i got (19/7, -529/7), for my roots i got (-4/7,0) and (6,0) i got my parabola is upwards and a minimum, my y int is -24, for my aos i got 19/7. If someone could check these id be really happy cause im stressing about this project due tmmr that determines if i take the final exam

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

.close

[cedar kiln]

Channel closed

Closed by @runic gust

Use .reopen if this was a mistake.

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.

[simple breach]

how do I know if the sequence (6n^3-2n)/(3n^2+2) converges or diverges?
I tried dividing all the terms of the numerator and denominator by n^3 first:
for the numerator, I got 6- 2/n^2, which evaluates to 6 as n approaches infinity
for the denominator, the function I was trying to evaluate was 3/n + 2/n^3. When I try to evaluate it as n approaches infinity I got 0. I'm not sure what to do from here, since the denominator's limit is 0 so I can't divide the limits

[dire geode]

Don't divide by the highest term in the numerator. Divide by the highest term in the denominator

[simple breach]

ok I see, so since the numerator 6n- 2/n will evaluate to infinity, then the whole fraction will evaluate to infinity and thus the sequence diverges?

.close

[cedar kiln]

Channel closed

Closed by @simple breach

Use .reopen if this was a mistake.

[cedar kiln]

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.

[rain vine]

The process I did:
$$ (1-4x)^{-1} \geq 7 $$
$$ \frac {1}{1-4x} \geq 7 $$
$$ 1 \geq 7 - 28x $$
$$ 28x + 1 \geq 7 $$
$$ 28x \geq 6 $$
$$ x \geq \frac {6} {28} $$
$$ x \geq \frac {3} {14} $$
but the answer is $\left[\frac {3} {14}, \frac 1 4\right) $

[wraith dagger]

JXHN

[neon moon]

Hint: 1 - 4x has to be greater than 0, but why?

[rain vine]

reciporcal property of inequalities i know that but there is not zero here

[neon moon]

Or let’s put it this way, your step 2 to step 3 is wrong, since you don’t know what os the sign of 1 - 4x, you cannot just multiply that denominator to the other side and pretend the inequality direction remains unchanged

[rain vine]

oh okay then can i take 7 to left hand side in step 2 then?

[neon moon]

A better way would be to do it like this,
$$ (1-4x)^{-1} \geq 7 $$
$$ \frac {1}{1-4x} \geq 7 $$
$$ \frac {1}{1-4x} \cdot (1 - 4x)^2 \geq 7 (1 - 4x)^2 \text{ and } 1 - 4x \neq 0 $$
$$ \dots $$

[wraith dagger]

jimmy1234

[rain vine]

i don't understand i understand the process but i don't understand the concept

[rain vine]

this would just make the question in quadratic equation

from that we get two values?

for x?

[neon moon]

You are right it makes it a quadratics, but then we can make the "move-denominator-to-the-other-side" step legit.

Method 2 is to consider the question case by case. It applies whenever you have variable in denominators.

Case 1, 1 - 4x > 0, then should you change sign in step 3 or not

Case 2. 1 - 4x < 0, then you should again think about sign change at that step and so on.

[cedar kiln]

@rain vine Has your question been resolved?

[rain vine]

@neon moon sorry I was afk.
I understand why (1-4x)^2 makes the denoinators moves since a^2 >= 0.
so I just have to solve the quadratic equation after that right?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[crimson sedge]

Consider an elastic string whose ends are held fixed ($u(0,t) = 0 = u(L,t)$). The string is set in motion from its equilibrium position with an initial velocity $u_t(x,0) = g(x)$, where $g(x)$ is $f(x)$ from Exercise 2.

$f(x) = \begin{cases}
\frac{4x}{L} & 0 \le x \le \frac{L}{4} \
1 & \frac{L}{4} < x < \frac{3L}{4} \
\frac{4(L-x)}{L} & \frac{3L}{4} \le x \le L
\end{cases}$

a) Find the displacement $u(x,t)$ for $g(x)$ as given by $f(x)$ above. \
b) Plot $u(x,t)$ vs $x$ for $0 \le x \le 10$ and for several values of $t$ for $0 \le t \le 20$. \
c) Plot $u(x,t)$ vs $t$ for $0 \le t \le 20$ and for several values of $x$. \
d) Describe the motion of the string.

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

I've solved a similar problem to this before except $f(x)$ and $g(x)$ were swapped.
Now that $f(x) = 0$ and $g(x) = u_t(x,0)$, what do I do here?

[wraith dagger]

CrimsonDevil_Rias

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

can anyone help me?

[crimson sedge]

Uh

Were no help channels available?

1170

Ratio of savings to spending is 9 to 4

Thus, 9/13 out of 1170 is used for saving and 4/13 out of 1170 is used for spending

Therefore, 810 is saved and 360 is spent

95

Ratio of comedy to action to horror is 6 to 8 to 5

Total number is 19

Thus 6/19 out of 95 is comedy
8/19 out of 95 is action
5/19 out of 95 is horror

Arthur owns 40 action movies, 30 comedy movies, and 25 horror movies

You're welcome

I answered your question, now someone please come help me answer mine

Lest I get the process out of Quizlet

@crimson sedge I hope my explanation helped you

If you are dealing with ratios, add all of the numbers up. That's your denominator. The individual numbers each serve as the numerator of said category

If the ratio is 9:4 like in this example, then 13 is your denominator

Thus, one part is 9/13 and the other is 4/13

Same applies with n-category ratios

n1 : n2 : n3 : n4 : ...
The distribution of is as follows:

n1/(n1 + n2 + n3 + n4 + ...), n2/(n1 + n2 + n3 + n4 + ...), n3/(n1 + n2 + n3 + n4 + ...), n4/(n1 + n2 + n3 + n4 + ...),

[crimson sedge]

Tysm @crimson sedge

appreciate it alot

[crimson sedge]

<@&286206848099549185>

[torpid shard]

@crimson sedge don't tag without any need

[crimson sedge]

Bruh

[crimson sedge]

Did you even read the question?

[torpid shard]

Where's the question?

[crimson sedge]

Pinned message

[torpid shard]

Last question was DarkAmber's

[crimson sedge]

Don't question for question now.

If you can try, do try the problem.

Thank you.

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

They posted their question in this channel because they thought my own question had been resolved

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

@crimson sedge

You should ask the question in the physics server as well

#old-network

[crimson sedge]

I left that server

This question is more directed towards Fourier series

I see

[crimson sedge]

I already have part a) solved. Parts b) and c) require me to just plot graphs and stuff Part d) asks me to describe the motion of the string

[crimson sedge]

Find the amplitude of the resulting wave

Basically find maximum of X(x) and T(t)

Answer= ||A^2||

Weird that nobody helped u

Isn't that difficult

[crimson sedge]

@crimson sedge

[crimson sedge]

Um

That's not exactly the right way to go

[crimson sedge]

https://media.discordapp.net/attachments/903430334681608232/1110090718946537503/899874619996114944.png

To find the Fourier series of the function, you must first set up eigenvalue problems involving X and T

$\alpha^2 u_{xx} = u_{tt}$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

If $u(x,t)$ be written as $X(x)T(t)$, then the above becomes the following

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

$\alpha^2 X''T = XT''$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

Use separation of variables

$\alpha^2 \frac{X''}{X} = \frac{T''}{T}$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

Since these are to be turned into eigenvalue problems, we need to equate them to a certain constant

We call this constant -λ

Thus we have

$\alpha^2 \frac{X''}{X} = -\lambda$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

And

$\frac{T''}{T} = -\lambda$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

Both of these are second order differential equations

$\alpha^2 X'' + X \lambda= 0 \
T'' + T\lambda = 0$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

Use the method of characteristic equations to solve for X(x) and T(t)

$\alpha^2 r^2 + \lambda = 0$ for $X(x)$ \
$r^2 + \lambda = 0$ for $T(t)$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

Solve for $r$ in each characteristic equation

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

$X(x) : r = \pm \frac{i\sqrt{\lambda}}{\alpha} \
T(t) : r = \pm i\sqrt{\lambda}$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

The general solutions for each differential equation are given as follows

$X(x) : c_1e^{\frac{i\sqrt{\lambda}}{\alpha}} + c_2e^{-\frac{i\sqrt{\lambda}}{\alpha}} = 0 \
T(t) : c_1e^{i\sqrt{\lambda}} + c_2e^{-i\sqrt{\lambda}} = 0$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

Use Euler's identity

$X(x) : c_1 \left(\cos{\frac{\sqrt{\lambda}}{\alpha}} + i \sin{\frac{\sqrt{\lambda}}{\alpha}}\right) + c_2 \left(\cos{\frac{i\sqrt{\lambda}}{\alpha}} - i \sin{\frac{\sqrt{\lambda}}{\alpha}}\right) = 0 \
T(t) : c_1 (\cos{\sqrt{\lambda}} + i \sin{\sqrt{\lambda}}) + c_2 (\cos{\sqrt{\lambda}} - i \sin{\sqrt{\lambda}}) = 0$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

Distributive property gives us

[crimson sedge]

$X(x) : k_1 \cos{\frac{\sqrt{\lambda}}{\alpha}} + k_2 \sin{\frac{\sqrt{\lambda}}{\alpha}} = 0 \
T(t) : k_1 \cos{\sqrt{\lambda}} + k_2 \sin{\sqrt{\lambda}} = 0$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

Now that we have $X(x)$ and $T(t)$, we need to impose our boundary conditions

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

The string of length $L$ is held fixed at its ends

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

Which means the boundary conditions are

$u(0,t) = 0 = u(L,t)$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

And the initial condition is

$u_t(x,0) = g(x)$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

Now do you understand where this is going?

When all of the conditions are satisfied, you will be left with something resembling a Fourier series

That means

$u(x,t) = \sum_{n = 1}^\infty u_n(x,t) \cdot c_n$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

Where

$u_n(x,t)$ are your eigenfunctions

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

And in those eigenfunctions,

$\lambda_n$ are your eigenvalues $\forall n \in \mathbb{N}$

[wraith dagger]

CrimsonDevil_Rias

[crimson sedge]

This
This right here is exactly why I said this is leaning more towards Fourier series than complex physics

[sonic thistle]

Rias>Akeno

[livid tusk]

@crimson sedge easier to set it up this way

$$X''+\Lm X=0$$
$$T''+\a^2\Lm T=0$$

[wraith dagger]

nilpotent nix (nix)

[livid tusk]

just makes everything come out nicer

since you need $X(0)=X(L)=0$ then you know $X_n(x)=\sin\paren{\frac{n\pi x}{L}}$

so $\Lm=\paren{\frac{n\pi}{L}}^2$

it's been a bit since i've done PDEs so does that sound about right

[wraith dagger]

nilpotent nix (nix)

[livid tusk]

then that means $T_n(t)=a_n\cos\paren{\frac{n\a\pi x}{L}}+b_n\sin\paren{\frac{n\a\pi x}{L}}$

[wraith dagger]

nilpotent nix (nix)

[livid tusk]

is this all ringing a bell

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[muted nest]

hi

[muted nest]

I need some help

@cedar kiln

[runic garnet]

The bot is no longer sentient sorry

But just ask ur question

@muted nest

[cedar kiln]

@muted nest Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[inland fossil]

how in the world is this -6

im getting 18 using stokes

[cedar kiln]

@inland fossil Has your question been resolved?

[cedar kiln]

@inland fossil Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[solemn basin]

the question is find the equation of a cruve with derivitive 10e^2-(3/2)x dx and passes through the origin. I integrated it to get the answer of -2e^-5x-1 but it has a +2/e

[solemn basin]

how do you get that part?

[worthy cairn]

Is the derivative $10e^2- \frac{3}{2} x$ or $10e^{2-(3/2)x}$? Either way, that integral looks wrong

[wraith dagger]

catGPT

[solemn basin]

sorry i got the derivitive wrong

its 10e^(-5x-1)

[worthy cairn]

Ok so then your integral is $y = -2e^{-5x-1}+c$. You need the +c because it's an indefinite integral. Then you use the condition they give you to find c

[wraith dagger]

catGPT

[worthy cairn]

They say it goes through the origin, so plug in the coordinates of the origin into the integral and find c

[solemn basin]

ok thank you

.close

[cedar kiln]

Channel closed

Closed by @solemn basin

Use .reopen if this was a mistake.

[cedar kiln]

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.

[native blaze]

Given any function f : R → (0, +∞) we define a new function ∆f : R → R
per:
∆f(x) = f(x + 1) − f(x).
Define ∆2f(x) := ∆(∆f)(x) and, given any n ∈ N, define ∆nf(x) = ∆(∆n−1f(x)).

1.Prove that ∆(f + g)(x) = ∆f(x) + ∆g(x).
2.Prove that ∆(f · g)(x) = f(x + 1)∆g(x) + g(x)∆f(x).
3.Prove that ∆(f/g)(x) = (g(x) · ∆f(x) − f(x)∆g(x))/(g(x)g(x + 1)).
4.Find a function h(x) that satisfies:
∆h(x) = h(x).

[cedar kiln]

@native blaze Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[wraith dagger]

actually legend

actually legend

[atomic ember]

just for clarification, the . is multiplication operator right?

[wraith dagger]

actually legend

[atomic ember]

nw :)

[wraith dagger]

actually legend

actually legend

[atomic ember]

hmm from what i could observe is that one possible solution for x here would be to try to get both then numerator and denominator equal so u can have 1 + 1 = 2, so x in this case will be -23*10^8

[wraith dagger]

actually legend

[atomic ember]

im trying to think, i dont know if i have enough experience/knowledge to help but ill try 😅

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[oak beacon]

So I have got a problem solving this. The electron numbers of Nitrogen and oxygen in there last shells are 5 and 6 respectively. The last shell contains 4 orbitals and each orbital can hold up to 2 electrons. Now how many ways can we arrange N and O's last electron configuration? ( assuming they will create a bond by sharing single or multiple electrons but we won't consider it's chemical properties here)

[dire geode]

#old-network for physics or chemistry server

[cedar kiln]

@oak beacon Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[tawdry summit]

How do i write the decimal value of a binary number?

[carmine bronze]

https://www.youtube.com/watch?v=VLflTjd3lWA

Seems like you have already done the first two, what are you having difficulty with?

[rain drift]

You're on the right track for the first two.

Every digit to the left is a new power of 2. If it has a 1 in the slot then you count it.

So for example if you had 11111111, that would be 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1+ 2^0 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255

[tawdry summit]

dont wory

the vid was super helpful

i understand it now

tysm

.close

[cedar kiln]

Channel closed

Closed by @tawdry summit

Use .reopen if this was a mistake.

[cedar kiln]

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.

[mighty mortar]

Is this correct, specially 169/36 in the second step.

[cedar kiln]

@mighty mortar Has your question been resolved?

[molten compass]

I know this doesn’t directly answer your question but have you tried using partial fractions

There seems to be a lot of algebra mess that could be avoided with partial fractions

Also your second line seems to work

Your 5th to 6th line doesn’t seem to work

I don’t know how you got log in one step

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[uneven iron]

Do you see something similar to the derivative of ln(2x+1) there?

Yes

Yes

Think about a way to eliminate the 2 in the denominator

Integrals are the anitderivatives

The result of the integral is a function which derivative is the function you already integrated

[sand cradle]

This has been asked on Math StackExchange before:
https://math.stackexchange.com/questions/770792/how-to-integrate-int-frac112xdx?noredirect=1
https://math.stackexchange.com/questions/2188691/can-you-solve-int-frac12x1-dx-without-substitution?noredirect=1

[uneven iron]

$$\int{f(x)} = F(x)$$
$$F'(x) = f(x)$$

[wraith dagger]

Rub05

[uneven iron]

Yes, but is a longer method

Yes

[sand cradle]

Np, I just wanted to point out that it has already been solved on MSE, google sometimes doesn't find LaTeX code

[uneven iron]

What's that website?

[sand cradle]

Math StackExchange. It's a math forum

[uneven iron]

1/2 ln|1+2x|...

It's just one step if you know derivatives and chain rule

Do you know how to differentiate?

[uneven iron]

.

Now that makes sense

What's your first language?

Hm... I'll just put and example of chain rule

$$f(x) = \ln(2x +1)$$
$$ f'(x) = \frac{1}{2x + 1} \times 2$$

[wraith dagger]

Rub05

[uneven iron]

If you want the function that's inside the integral you have to remove the 2, so divide the function by 2 and you have it

$$f(x) = \frac{\ln(2x+1)}{2}$$
$$f'(x) = \frac{1}{2} \times \frac{1}{2x+1} \times 2 = \frac{1}{2x +1}$$

[wraith dagger]

Rub05

[uneven iron]

Correct

It's more mechanical

But you should learn that method too

There are other integral that can be solved by parts

And sometimes, that method is really long

But sometimes, doing the method I told you (it's not even a method), you can do it in seconds

That method is not always useful

You have to see first if the function has the form of the derivative of a ln, a arctan or a chain rule

Not really

U-Sub doesn't work always

Integration is hard, don't worry

Nop

It's been a while since I don't use U-Sub

Maybe because your integrals are built for that method

Did you learn by parts or partial fractions?

$\int{\sqrt{9-x^2}dx}$

[wraith dagger]

Rub05

[uneven iron]

You need u-sub for that

That's the question

I know you said u = 9 - x²

Nope

You would make a harder integral

[short blade]

have you heard of trigonometric substitutions?

[uneven iron]

I don't think so

[short blade]

im not sure, but trigonometric subs work

let $x = 3\sin\theta$

[wraith dagger]

maximo

[short blade]

well let's work it out

first of all, we find dx in terms of dtheta

so $dx = 3\cos\theta , d\theta$

[wraith dagger]

maximo

[short blade]

you'll see

now we can sub in

$\int 3\sqrt{9 - (3\sin\theta)^2}\cos\theta ,d\theta$

[wraith dagger]

maximo

[short blade]

it works out nicely

you can simplify the square root

what is (3sin(theta))^2

$\sqrt{9-(3\sin\theta)^2} = \sqrt{9 - 9\sin^2\theta} = \sqrt{9\cdot(1-\sin^2\theta)}$

yes

[wraith dagger]

maximo

[short blade]

and what is 1-sin^2theta?

[ember mesa]

$cos^{2}(θ)$

[wraith dagger]

Zouni

[short blade]

no spoilers

right

so we get $\sqrt{9\cos^2\theta}$

[wraith dagger]

maximo

[short blade]

yes

[short blade]

and this simplifies nicely

to $3|\cos\theta|$

[wraith dagger]

maximo

[short blade]

but we usually forget the absolute value for integrals

so we just express it as $3\cos\theta$

[wraith dagger]

maximo

[short blade]

you can, but this is standard

[ember mesa]

it's called theta

[short blade]

theta is a very common letter for variable angles

[uneven iron]

$\alpha$ enjoyer

[ember mesa]

you can use phi, might look nicer

[wraith dagger]

Rub05

[ember mesa]

$φ$

[wraith dagger]

Zouni

[dreamy sleet]

x is already taken

[short blade]

i'll use u

so our integral simplifeis to $$\int 3\cdot 3\cos u \cdot \cos u , du$$

[wraith dagger]

maximo

[short blade]

yes

$\int 9 \cos^2 u , du$

[wraith dagger]

maximo

[short blade]

doesn't that look nice?

[ember mesa]

let me guess, gcse?

[short blade]

trigonometric integrals are relatively easy

there's an identity here which is particularly handy

$\cos^2 u = \frac{1+\cos 2u}{2}$

[wraith dagger]

maximo

[short blade]

so we just substitute

no

integrating this is far easier

we have cos now instead of cos^2

[short blade]

this holds every time yes

anyhow

now we get to $9\int\frac{1+\cos 2u}{2}, du$

[wraith dagger]

maximo

[short blade]

and using linearity $\frac{9}{2}\int 1, du + \frac{9}{2}\int \cos 2u, du$

[wraith dagger]

maximo

[ember mesa]

well you technically could just learn integration by parts and skip the substitution

have you done integration by parts

yeah you could technically just use that and not do substitution

but substitution is nicer

no

[short blade]

are you asking how i got here @low lake

[ember mesa]

when you get 9cos^2u

[short blade]

$9\int\frac{1+\cos 2u}{2}, du = \frac{9}{2}\int 1, du + \frac{9}{2}\int \cos 2u, du$

[wraith dagger]

maximo

[short blade]

i pulled out the 2 in the bottom

and split the integral

now

what is the integral of 1?

u in our case

but yes

and the integral of cos(2u)?

it'll matter here

let's do a u sub then

let $v = 2u$

[wraith dagger]

maximo

[short blade]

yes

why not?

$dv = 2du$

[wraith dagger]

maximo

[short blade]

so we get

$\frac{9}{2}\int 1, du + \frac{9}{2}\int \cos 2u, du = \frac{9}{2}u + \frac{9}{2}\int \cos v\cdot \frac{1}{2}, dv$

what is the integral of cos(v)?

whoops

hold on

no i did

[wraith dagger]

maximo

[short blade]

dv = 2du

so du = dv/2

[ember mesa]

$S (\omega)=\frac{\alpha g^2}{\omega^5} ,
e ^{[-0.74\scaleleftright[.7ex]{{}{\frac{\omega U_\omega 19.5}{g}}{}}^{-4}]}$

[wraith dagger]

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

[ember mesa]

use gobbler formula to soolve

you need this formula for your exam

[short blade]

are you following up to here temmie

[ember mesa]

it is very important

[short blade]

it's just a bigger formula, don't worry about it

you don't need to know it

yes

that's not going to show up

no, but im like 99% sure

[ember mesa]

gobbler formula is very important

@short blade I think you have overcomplicated the question a little bit

[short blade]

how so

[ember mesa]

if someone isn't strong at maths, show the most algorithmic approach

[short blade]

the dv will go away relatively quickly

[ember mesa]

so trig sub then integratin by parts

[short blade]

i beg to differ, i think this is fine

[ember mesa]

I agree with you

[ember mesa]

might be complicated to someone not familiar with substitution

[short blade]

yup

so let's write it in

$\frac{9}{2}u + \frac{9}{2}\int \cos v\cdot \frac{1}{2}, dv = \frac{9}{2}u + \frac{9}{4}\sin v + C$

[wraith dagger]

maximo

[short blade]

and what did we say v was?

$\frac{9}{2}u + \frac{9}{4}\sin v + C = \frac{9}{2}u + \frac{9}{4}\sin 2u + C$

[wraith dagger]

maximo

[short blade]

and what was u?

well

we said

x = 3sin(u)

can you solve for u here?

[ember mesa]

hint: gobbler formula

[short blade]

yes

[ember mesa]

yes

find the inverse: x = 3sin(u)

[short blade]

close

we start with $\frac{x}{3} = \sin(u)$

[wraith dagger]

maximo

[short blade]

so what is u?

yes

plugging in

$\frac{9}{2}u + \frac{9}{4}\sin 2u + C = \frac{9}{2}\sin^{-1} \frac{x}{3} + \frac{9}{4}\sin(2\sin^{-1} \frac{x}{3}) + C$

[wraith dagger]

maximo

[ember mesa]

how are you that fast at typing laytex

[short blade]

the good thing is that we're done (barring some simplifying)

[short blade]

copy paste

yes

we can simplify some

but it still isn't super pretty

[dreamy sleet]

is there a way to simplify $$ \sin (2 \arcsin \frac x3) $$ here

[wraith dagger]

l33t_syncopations

[short blade]

yes

[ember mesa]

yes

[short blade]

it should be 2x * sqrt(9-x^2) / 9

as to how, you use a right triangle

i would show you but i think that's something you learnt in trig and not really the point

[ember mesa]

actually can you simplify that

wouldn't you run into domain problems @short blade

[short blade]

we just assume the domain works

the questions aren't really about trig

[ember mesa]

right

[short blade]

it's about integration, but you're right

we'd have to specify domains

the domain for x

[ember mesa]

dw

[short blade]

yeah dw

yes im sure

it's

so we can simplify $\sqrt{9-x^2}$

[wraith dagger]

maximo

[short blade]

suppose we said $x = \cos u$

[wraith dagger]

maximo

[short blade]

experience

[short blade]

so

[ember mesa]

the trig sub comes from $sin^{2}x + cos^{2}x = 1$

[wraith dagger]

Zouni

[short blade]

$\sqrt{9 - \cos^2 u}$

[wraith dagger]

maximo

[short blade]

now we can't use $1 - \cos^2 u = \sin^2 u$

[wraith dagger]

maximo

[short blade]

we needed a 9 in front of the cos^2

yeah pretty sure

let's try something

$\int \sqrt{9-x^2}, dx$

[wraith dagger]

maximo

[short blade]

and we integrate by parts

[ember mesa]

what was the original integral

[short blade]

what i wrote

[ember mesa]

oh my f** god are you serious

[short blade]

$u = \sqrt{9-x^2}, dv = 1$

[wraith dagger]

maximo

[ember mesa]

no you don;t need trig sub

[short blade]

what would you suggest?

[ember mesa]

i thought it was 1/

$(9-x^{2})^{\frac{1}{2}}$

[wraith dagger]

Zouni

[ember mesa]

and then apply taylor series

and integrate

no you do need trig sub im just smooth brained

my bad

no you do need trig sub

well technically you don't but trig sub is the easiest way

I saw the $(9-x^{2})^{\frac{1}{2}}$ and thought of derivative for some reason

[wraith dagger]

Zouni

[ember mesa]

@short blade will you ever forgive me?

[short blade]

yes lol it's nbd

when i saw what you were doing i thought it might have worked too

but you get to x = sqrt{u - 9}

[ember mesa]

ah

[dreamy sleet]

this?

[short blade]

or + 9

[ember mesa]

?

you need to use trig sub

[short blade]

trig sub is the way here

it's quite an important topic

if you haven't discussed it in your class, don't worry about it (yet)

but it does show up

are you sure it will show up?

have you seen the syllabus for it?

i mean

it depends

[ember mesa]

if it's uni level it will 100% show up

[short blade]

why would they put something uni level on an entrance exam?

isn't that why you go to uni

[ember mesa]

scholarship

[short blade]

i think the right course of action is consulting the materials you have about what can be on the exam

[ember mesa]

or if it's jeet/gaokao related

[short blade]

speculation doesn't help

[ember mesa]

hmm

not that hard to learn. my opinion, learn it

you'll have to learn it eventually regardless

[short blade]

if the concern right now is university entrance, i think they should prioritize what they need to learn

[ember mesa]

trig sub takes like one poop worth of time to learn the basics of

do you mind sharing the list

it's probably implied in calculus

[short blade]

can you share the list?

[ember mesa]

that's fine

yeah

[short blade]

how do you know we don't speak romanian?

[ember mesa]

try me

not sharing the list is a pretty Hungarian thing to do if you ask me @short blade

[fair geyser]

just german things

[ember mesa]

ok

bro it's in Romanian I can't read that

joke*

canned laughter

list seems pretty short, I think you'll be fine if it's in 2 months

[short blade]

this one doesn't have any mentions of integration or trig integrals

[dreamy sleet]

this formula might help $S (\omega)=\frac{\alpha g^2}{\omega^5} ,
e ^{[-0.74\scaleleftright[.7ex]{{}{\frac{\omega U_\omega 19.5}{g}}{}}^{-4}]}$

[short blade]

so it should be good

[wraith dagger]

l33t_syncopations
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[short blade]

this also doesn't seem to include trig sub

are you familiar with group theory and analysis?

that should be your main concern before studying trig subs

[ember mesa]

do you know romanina

[short blade]

pretty easy to see what it says

straight trig though

not in an integral

[ember mesa]

what tf

[short blade]

"integrarea prin schimbare de variablila"

[ember mesa]

one hundred and eighty intelligence quotient moment

[short blade]

this is change of variables right?

[ember mesa]

finally

[short blade]

and the one after is partial fraction decomposition right?

"integrarea prin metoda descompunerii in fractii simple"

[ember mesa]

bro what

[short blade]

either way, it seems to me that the most they'll give you is a trig integral, not a trig sub

and i want to restate that analysis and group theory are far more difficult than integration

might fuck around, learn romanian

[dreamy sleet]

the first thing on this picture you sent

[short blade]

the "grupuri si izomorfisme de grupuri" section

[ember mesa]

math major moment

[short blade]

seems pretty straightforward lol

[dreamy sleet]

yes not hard to see roughly what that means

[ember mesa]

uhh

[short blade]

also have a friend that speaks romanian

[ember mesa]

not to scare you, but group theory looks like this

[short blade]

so it would be cool to speak with him

[ember mesa]

http://abstract.ups.edu/aata/ssets-ection-sets-and-equivalence-relations.html

that would be cool

[dreamy sleet]

is “corpuri” a field? if you just need to know definition and example then it’s fine

[short blade]

tbf it looks like they're only asking for basic applications/definitions of groups, subgroups, homo/isomorphisms

so not that bad

[ember mesa]

probably region blocked

ah ok then

weird to not know trig-sub but know discrete

what

[short blade]

i'm surprised integrals gave you such a hard time haha

[ember mesa]

are you sure?

[dreamy sleet]

groups are baby stuff?

[short blade]

i mean fair enough

group theory isn't crazy

it's when you get to the advanced stuff that it's more challenging

[ember mesa]

it's very left field for 99% of people

[short blade]

good on the romanian education system, or wherever you're at

[short blade]

they learn it young though

so it makes sense for it to click more easily

[ember mesa]

I suppose

[short blade]

younger peeps absorb info like sponges

[dreamy sleet]

where does it get challenging

[ember mesa]

"come on class, say isomorphism"

lmao

[short blade]

izomorfisme!

[dreamy sleet]

when do they learn group theory?

[short blade]

it's pretty similar to english, i'm surprised

[ember mesa]

theres no way you absorbed vocabulary that quickly

[short blade]

don't be afraid to send stuff in romanian here btw, it's quite easy to tell what it's saying

[short blade]

nah i scrolled back up

but tbf

[ember mesa]

de ce îmi miros farturile

[short blade]

it's like a mix of italian and english

[dreamy sleet]

only the vocabulary

[ember mesa]

ah ok if you speak italian then fair

[short blade]

nah spanish

but close enough eh?

[ember mesa]

ah

lol

nononono

[short blade]

im doing french rn. i don't have the will to learn a new alphabet

[ember mesa]

languages should stop at 1 alphabet

[dreamy sleet]

did you learn about groups in primary school or something?

[ember mesa]

it's all roman

wtf

cracked education system

[dreamy sleet]

did you get to isomorphisms?

[ember mesa]

did you get to homo erectus?

everyone learns about homo erectus in group theory, come on

[short blade]

everything is romanian in disguise

[ember mesa]

means upright man in latin

I don't know if you would've learned group theory from just reading a book as a kid

no

do you know what a relation is

no

[dreamy sleet]

sometimes you can have sqrt(x) or sqrt(9-x)

for those you don’t need trig sub

[ember mesa]

if you see something that kind of looks like pythagorean identity, use strig sub

$sin^{2} + cos^{2} = 1$

[wraith dagger]

Zouni

[ember mesa]

or if you see things that could be this identity

hmm

[dreamy sleet]

or like $$ a - a \cos^2 x = a \sin^2 x $$

[wraith dagger]

l33t_syncopations

[dreamy sleet]

sure

what is the question asking?

for those n, n will probably be around sqrt(2022)

which is around 45

this comes from minimizing x + 2022/x

by differentiating it

by computing d/dx (x + 2022/x)

[ember mesa]

yes

@low lake you have to be screwing with people lol

finding the stationary points of the derivative and then find the minimum stat point

-_-

[dreamy sleet]

you’ll need to learn about this before taking that entrance exam

alternative notation

then set it to 0 to find the minimum

[ember mesa]

set that equal to 0 and solve the quadratic using quadratic formula

[dreamy sleet]

you may want to review taking stationary points with differentiation

so that means the minimum numbers for your original function f(n) will be close

so you can try values near 45 like 44, 46, and see which ones give the minimum for f

trial and error in this case is simple, so it can be tried first

[ember mesa]

well you got +- sqrt(2022)

so two points

[dreamy sleet]

but the function is from N, so only nonnegative integers

you can use a calculator

or you can notice that 45^2 = 2025

which is very close to 2022

again, the domain is N, which should mean the natural numbers

so the least values should be 45 or 44 or 46

and also there’s a floor function, which may change things a bit

find f(44), f(45), and f(46)

and also try f(43) and f(47) just to be sure

if no calculator allowed, you can do long division with 2022 / 45

looks like there are 3 answers then

from the derivative earlier, the smallest has to be around 45, so there are only 3

see the derivative earlier: from that, we know the minimum must be near 45, as the floor function changes things, but not by much

if you like, you can check 42 and 48 too

so it doesn’t go down

this is an application of it

optimization of functions

gradient descent in multivariable calculus

linearization of a function/taylor series

what do you mean?

where

[cedar kiln]

Channel closed

Closed by @low lake

Use .reopen if this was a mistake.

[dreamy sleet]

no, that was because they misread it

[cedar kiln]

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.

[safe dragon]

how do i solve

[idle cedar]

any progress so far ?

or any idea

[stable edge]

,rotate

[idle cedar]

thanks I was rotating my head like an idiot right now sitting in the library lol

[cedar kiln]

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

@safe dragon Has your question been resolved?

[safe dragon]

1

[stable edge]

I guess you could just try listing them

[safe dragon]

Okay

[stable edge]

there's nine possible results, but some of them will get you the same sum

[inland roost]

isn’t there 6

[stable edge]

there's nine ways to spin the wheel

there might be 6 different money sums

idk i didn't count them

[cedar kiln]

@safe dragon Has your question been resolved?

[safe dragon]

How do i do 1

Idk how to start

<@&286206848099549185>

[pulsar garden]

Omds

That’s pretty easy imo

[safe dragon]

bro

that’s not helpful

[hazy escarp]

thats great well done

so what do you know

[safe dragon]

idk how to do it at all

[hazy escarp]

so do you know what an x-intercept is?

do you know what a y-intercept is?

or how to find it?

[torpid shard]

I think he got discouraged

[cedar kiln]

@safe dragon Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[rich yew]

need some help here

[tropic oxide]

!status

[cedar kiln]

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

[rich yew]

2

[tropic oxide]

show current progress

[rich yew]

well 1 and 2

[tropic oxide]

[rich yew]

tried splitting it into different right angled triangles

but got nowhere

[tropic oxide]

splitting how?

do you have a diagram?

[rich yew]

made a 2 by 3m triangle in the middle

obviously didnt work

[tropic oxide]

ok so you do not have a diagram

[rich yew]

nope

[rich yew]

i think i know how to do it now

i'm a little off

nvm i got it

thanks👍

.close

[cedar kiln]

Channel closed

Closed by @rich yew

Use .reopen if this was a mistake.

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.

[gentle perch]

Need. Some help

I don’t know what this is

Like what is this

Is it like -gx +2

[dire geode]

https://www.onlinemathlearning.com/function-transformation-hsf-bf3.html

[cedar kiln]

@gentle perch Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[plucky carbon]

Is this a separable form for a differential equation? I was told you had to have the Y and X terms separate

but the definition is written as multiplication, this is subtraction.

[cedar kiln]

@plucky carbon Has your question been resolved?

[plucky carbon]

.close

[cedar kiln]

Channel closed

Closed by @plucky carbon

Use .reopen if this was a mistake.

[cedar kiln]

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.

[light pine]

im rly stuck here

idk what to use as my parameters not my limits

this is all ive done so far

[cedar kiln]

@light pine Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[lime wagon]

How can I find the upper and lower bounds of each integral, and have I sketched it correctly?

[lime wagon]

It seems I can find the bounds from the given formulae

Is that correct?

Taking the integrals is actually really easy. What is difficult is finding the correct bounds. Having wrong bounds yields 0 points in the exam. So if someone can explain to me how to find the correct bounds for these 3 integrals I would be very appreciative!!

Pls someone

[dire geode]

the question is... very small

[lime wagon]

Wait..what?

Oh

I guess you see it in worse quality than me in the chat

Okay so

I have the solutions

And I can calculate the integrals no problem when I have the bounds

But I wouldn’t have figured the bounds out myself

So I need help with that

[cedar kiln]

@lime wagon Has your question been resolved?

[lime wagon]

@dire geode how would you get your boundaries for this problem if I may ask?

[dire geode]

i usually just draw the domain in a plane

[lime wagon]

It’s hard to do that..

With such domains

[dire geode]

sorry, one plane at a time

x=0 plane, z=0 plane, y=0 plane

[lime wagon]

So you draw 3 2D plots?

[dire geode]

yea

[lime wagon]

Uuuu

That actually makes so much sense

Thanks lol

That was rlly helpful idk why I didn’t think of that

.close

[cedar kiln]

Channel closed

Closed by @lime wagon

Use .reopen if this was a mistake.

[dire geode]

"shadow method" here is pretty similar
https://mathinsight.org/triple_integral_shadow_method

and here
https://tutorial.math.lamar.edu/classes/calciii/tripleintegrals.aspx

[cedar kiln]

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.

[lime wagon]

Also, is there a latex converter in this discord?

[lime wagon]

Where I can put stuff like (9x+3^y) and it converts it into latex?

[dire geode]

See #latex-help

#latex-testing

[cedar kiln]

@lime wagon Has your question been resolved?

Channel closed

Closed by @lime wagon

Use .reopen if this was a mistake.

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.

[tall grotto]

i think ik how to do it, but not sure

should i be just plugging in t=8 and 11, and see if D(t) increased?

like D(11)>D(8)

seems too simple which is y im not sure

[ancient lodge]

It says per hour

So see if [D(11)-D(8)]/3=0.15

[tall grotto]

i got 6.7902 for D(11) and 6.7964 for D(8)

so it was overall decreasing?

which automatically makes Jaya's claim incorrect then

[ancient lodge]

I misread the question earlier, see the edits

but I'm still pretty sure Jayla is incorrect

[tall grotto]

oh

why is it /3?

[ancient lodge]

per hour

and 3 hours have passed from 8 to 11

[tall grotto]

ohhh

so d11-d8 would be

-.002 per 3 hours

[ancient lodge]

I trust you can use a calculator

[tall grotto]

so then divide by 3 would be __ per hour

got it thx

[ancient lodge]

👍

[tall grotto]

i have two more questions if u have the time?

i feel like im supposed to use identities somewhere, but i can't find them lol

i know i should probably move the root2cosx over to make +2cosx on the right

[tall grotto]

wait, if D(11)-D(8) was /3h, shouldn't we multiply by 3 instead of divide?

shouldn't change the final answer though but is this step correct?

[ancient lodge]

(change in tide)/(hours) = change in height/hr

and I don't rlly have time to help with your eq.

srry

[tall grotto]

its ok np

[tall grotto]

but i still dont understand this

would the units for d(11)-d(8) be m/3h?

[cedar kiln]

@tall grotto Has your question been resolved?

[tall grotto]

<@&286206848099549185>

just need clarification for this question and one more

[tall grotto]

.close

[cedar kiln]

Channel closed

Closed by @tall grotto

Use .reopen if this was a mistake.

[cedar kiln]

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.

[clear sage]

bacteria in a culture increased from 4 to 80 in 2 hours

[clear sage]

assuming that the rate of increase is directly proportional to the number present

determine the time from now at which the population will reach 500

[violet flume]

differential equations?

what class is it for?

[clear sage]

calc

[violet flume]

okay

create a differential equation

"the rate of increase is directly proportional to the number present"

you need to write out using calculus:

• the rate of increase

• directly proportional

• the number present

say y(t) gives the number of bacteria present

can you complete the other two and give a differential equation?

[clear sage]

hmm would i be able to write that dp/dt=kp

[violet flume]

p?

population?

[clear sage]

yh

[violet flume]

works for me

okay, solve for p(t)

[clear sage]

.close

[cedar kiln]

Channel closed

Closed by @clear sage

Use .reopen if this was a mistake.

[violet flume]

everything okay?

[cedar kiln]

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.

[tulip pecan]

8th question, dunno what to do after this

[cedar kiln]

@tulip pecan Has your question been resolved?

[tulip pecan]

.close

[cedar kiln]

Channel closed

Closed by @tulip pecan

Use .reopen if this was a mistake.

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.

[crimson sedge]

i got stuck at finding the values for c1 and c2

[foggy merlin]

what are c1 and c2 ?

[livid hound]

probably the constants of integration

can you show what you've tried

[brisk dirge]

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

yes it is the constant of integration

[crimson sedge]

the final function i got is -ln(x)+c1x+c2

using the power rule f'(x)=-1/x

[livid hound]

use f(1) = 0, f(4) = 0
and solve a system of equations

[crimson sedge]

I tried but i end up with 2 constants of integration

[livid hound]

show work

[crimson sedge]

That's what i was able to do the only question i did that is similar to this one i was able to get rid of c1 to find c2 but now i don't know if the antiderivative is correct in the first place

[livid hound]

don't use a calculator for the ln(4)

your antiderivative is correct

use f(1) = 0, f(4) = 0
and solve a system of equations

$\begin{cases} c_1 + c_2 = 0 \
-\ln(4) + 4c_1 + c_2 = 0 \end{cases}$

[wraith dagger]

ℝamonov

[livid hound]

ln(4) is just a number,
use substitution/elimination like you would any other linear system

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

I'm not sure how or what is a linear system could you show me how i would do it and what is a linear system?

I'm bad at math 🙂

[livid hound]

have you ever solved system of equations before

aka simultaneous equations

[crimson sedge]

It's a miracle i made it to calc 1

[livid hound]

this is something you should've done well before calc 1

[crimson sedge]

No

[livid hound]

look up systems of equations

[crimson sedge]

Is c2=ln4?

[crimson sedge]

My bad i did study it but it's been a while i never really used in calculus

[livid hound]

algebra is used continuously throughout math
earlier concepts/ideas/principles are applicable to more complex problems

how are you getting c_2 = ln4

[crimson sedge]

Idk

[livid hound]

wdym you don't know

did you do any work for it

[crimson sedge]

I'm just multplied by - 4 so that i could get rid of c1

I'm lost

[livid hound]

did you look up a video guide

can you show the work you're doing

[crimson sedge]

Yes

[livid hound]

show, not tell /give vague descriptions

what did you have after multiplying by -4
and what did you do after that
that led to getting what you got

[livid hound]

work is messy,
but result is ok

[crimson sedge]

So it's correct?

[livid hound]

but result is ok

[crimson sedge]

Ok thanks

Appreciated

[livid hound]

the ln(4) can be simplified though
(and no i don't mean use a calculator)

[crimson sedge]

How?

[livid hound]

power rule for log

these are also things you should know (along with exponent laws)

[crimson sedge]

Is this the one where you bring the power to front?

[crimson sedge]

This?

[livid hound]

yeh

[crimson sedge]

?

[livid hound]

that goes in the opposite intended direction

i said ln(4) itself could be simplified

[crimson sedge]

ln2^2?

[crimson sedge]

2ln2?

[livid hound]

yes

[crimson sedge]

Ok thank you

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[short vapor]

This might be something real trivial (idk anything about proofs just done basic eng major requirement math) but I just watched this veritasium video (https://www.youtube.com/watch?v=HeQX2HjkcNo @ around 4:30) and he's talking about how Cantor proves the number of reals between 0 and 1 is greater than the number of natural numbers. I understand his argument that once you've listed out and matched all the reals and natural numbers you can generate another real by adding 1 along a diagonal, but why is it that you can't add 1 to every number in the list of natural numbers all the way to the "last" natural number, shift everything down, and match 1 (since now the list starts with 2) with the new real? I know my reasoning is flawed I just don't understand why you can't do this as well

[crimson delta]

there is no "last" natural number

the problem isnt really that you cant find a matching that also includes the new number

the problem is that for every matching you will find such a new number

no matter what you do, there will always be a number that you miss

[short vapor]

My bad computer died lol