help-27

[crystal token]

How do I factor out the expression?

or explain how I should do it in the begining

<@&286206848099549185>

[crystal token]

<@&286206848099549185>

[last holly]

difference of 2 suqares on the denominator gives $(\frac{\sin v}{\cos v}+\frac{\cos v}{\sin v})(\frac{\sin v}{\cos v}-\frac{\cos v}{\sin v})$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

this cancels with the numerator, giving the whole expression as $\frac{1}{\frac{\sin v}{\cos v}+\frac{\cos v}{\sin v}}$

[woven radish]

mygenderisanonnewtonianfluid

[crystal token]

So I convert my image to what you wrote of the difference of 2squares on the denominator

[last holly]

yea show me when ur done

cuz the next step should be clear but i'll help you out if you need it

i just realized that sounds very insulting

i'm sorry

that was not my intention

[crystal token]

Its ok 👍

[last holly]

cool

[crystal token]

I very much need help

[last holly]

ok

so we are trying to prove now that $\frac{1}{\frac{\sin v}{\cos v}+\frac{\cos v}{\sin v}}=\sin v\cos v$

[woven radish]

mygenderisanonnewtonianfluid

[crystal token]

It looks like a fundamental identity , the image above

[last holly]

so we're going to now multiply both sides by $\frac{1}{\sin v\cos v}$ to get $\frac{1}{\sin^2 v+ \cos^2 v}=1$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

it's the first pythagorean identity

[crystal token]

Yup

[last holly]

I can help you with writing the proof, too if you want

[crystal token]

Yes please I apprecaite it

[last holly]

Ok. So we're trying to prove that $\frac{\tan v-\cot v}{\tan^2 v-\cot^2 v}=\sin v\cos v \forall v\in\mathbb{R}$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

this should be the first line of the proof.

And it's easier to do the difference of 2 squares step here, so for the second line, we say that this is equivalent to $\frac{\tan v-\cot v}{(\tan v+\cot v)(\tan v-\cot v)}=\sin v\cos v \forall v\in\mathbb{R}$

[woven radish]

mygenderisanonnewtonianfluid

[crystal token]

Ohhhh I should've done that instead

So many identities and formulas

[last holly]

and we now expand using the definitions of tan and cot: $\frac{\frac{\sin v}{\cos v}-\frac{\cos v}{\sin v}}{(\frac{\sin v}{\cos v}+\frac{\cos v}{\sin v})(\frac{\sin v}{\cos v}-\frac{\cos v}{\sin v})}=\sin v\cos v\forall v\in\mathbb{R}$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

this is the third line

and by cancellation, we see that this is equivalent to $\frac{1}{\frac{\sin v}{\cos v}+\frac{\cos v}{\sin v}}=\sin v\cos v\forall v\in\mathbb{R}$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

this is the fourth line

and now we multiply both sides by $\frac{1}{\sin v\cos v}$, we get $\frac{1}{\sin^2 v+\cos^2 v}=1\forall v\in\mathbb{R}$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

this is the fifth line

and we know that $\frac{1}{\sin^2 v+\cos^2 v}=1\forall v\in\mathbb{R}$. And we've shown that $\frac{\tan v-\cot v}{\tan^2 v-\cot^2 v}=\sin v\cos v \forall v\in\mathbb{R}\Leftrightarrow\frac{1}{\sin^2 v+\cos^2 v}=1\forall v\in\mathbb{R}$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

therefore, $\frac{\tan v-\cot v}{\tan^2 v-\cot^2 v}=\sin v\cos v\forall v\in\mathbb{R}$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

and that's the proof

👍

do you have any further questions?

if not, please close the question

[crystal token]

No , no questions I just want to say thank you for helping me your way of doing the work is sooo much better than how my teacher did it, your an awesome person and thank you for your time

[last holly]

no problem

thank you

[crystal token]

.close

[devout snow]

Channel closed

Closed by @crystal token

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.

[calm belfry]

i need help with finding y

[last holly]

what exactly are you asking?

are you asking for y where x=0?

[calm belfry]

i need help finding x i mean

[last holly]

cuz u have that filled in

ok

x where y=0?

[calm belfry]

yeah

[last holly]

so the way i like to do this is by defining the inverse function

but im self taught so im not sure how teachers typically introduce this

does ur teacher have a specific way they want you to do this?

[calm belfry]

ion think it matters as long as i show how i got it

[last holly]

ok

so we have x defined as a function of y, and to find y for some x value, we can define y as a function of x

we have $y=-5\cos(2x-\frac{2}{3}x)$ and we can transform this into $\cos^{-1}(-\frac{y}{5})=(2-\frac{2}{3})x$

[woven radish]

mygenderisanonnewtonianfluid

[calm belfry]

dat shit looks more complicated lol

[last holly]

it'll all be easier i promise

we can then divide both sides by $1+\frac{1}{3}$ to get $\frac{1}{1+\frac{1}{3}}\cos^{-1}(-\frac{y}{5})=x$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

we now have x as a function of y

and we evaluate $\frac{1}{1+\frac{1}{3}}cos^{-1}(-\frac{y}{5})$ at $y=0$ to get $x$ when $y=0$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

this is also just $\frac{3}{4}cos^{-1}(-\frac{y}{5})$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

this yields $\frac{3\pi}{4}$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

which is obviously wrong

i did something wrong

im sorry

i was thinking that $\cos^{-1}(0)=\pi$ but it's $\frac{\pi}{2}$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

the real answer is $\frac{3\pi}{8}$

[woven radish]

mygenderisanonnewtonianfluid

[last holly]

which is also wrong

i messed up somewhere

[calm belfry]

.close

[devout snow]

Channel closed

Closed by @calm belfry

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.

[restive river]

I have a question. I've written my equation for a degree as Sin(2/3pi(t))+1 and Sin(120)+1 I believe the ground level would be the radius under the water.

[timber pebble]

its hard to tell but i think by "above or below water" they mean that the water surface is at 1 meter of the ground

[restive river]

Would the mid-line also be 1 meter than?

[timber pebble]

yea, thats kind of how im reading it

[restive river]

Thanks Jan.

I appreciate it.

[timber pebble]

[devout snow]

@restive river Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.

[maiden zephyr]

help

[maiden zephyr]

alright guys

who can help me

word problem problem rite

how

[restive river]

r(x) represents revenue you want to find the x values that will result in the revenue that you want

For example you are trying to find what value of x would give you 14000 as the revenue

[maiden zephyr]

ok thnx

/close

.close

[devout snow]

Channel closed

Closed by @maiden zephyr

Use .reopen if this was a mistake.

[devout snow]

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.

[snow sentinel]

I have 4 digits,
for instance:
1234

How can I calculate how many combinations of such digits there are?

For example:
combinations for 1234:

1234
1,234
12,34
123,4
1,2,34
1,23,4
12,3,4
1,2,3,4

(8 combinations)

[devout snow]

@snow sentinel Has your question been resolved?

[stone stump]

combination is the wrong word

I am actually not exactly sure what you want

it seems slightly more like partitions but for that you would also have stuff like 13,24

do you just want to know in how many ways you can place commas between the numbers?

if yes, there are 3 places for a comma and each comma can be there or not. so 2^3 options

[snow sentinel]

👍

That's what I wanted thanks

[devout snow]

@snow sentinel Has your question been resolved?

[devout snow]

Channel closed

Closed by @snow sentinel

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.

[rapid latch]

s

[rapid latch]

How do you find the x intercept of this quadratic function?

[dense jay]

for that one

quadratic formula would be easiest probably

[rapid latch]

But we have to determine the properties of the function

like the vertex, y int, x int, AoS, orientation

[dense jay]

so?

use the quadratic formula to get the x ints

use vertex form for the vertex and Aos

[rapid latch]

oh wait u right

my mistake

got a lil confused

can u solve it?

[prisma snow]

no you can group this

much easier

[rapid latch]

show

[urban harbor]

remember that x-intercept are just points where y = 0, so that's just another word for solutions / roots of the equation

[prisma snow]

nvm grouping is harder

didn’t see the negative

[rapid latch]

oh damn

wait how do u convert it into vertex form?

[prisma snow]

complete the square

factor out -2

then you can start completing the sqauew

[rapid latch]

wait i think im dumb

i am not a mathematicallly inclined individual

idk if this is right or not

[prisma snow]

you do -2(x^2 + 8x -5/2)

then start completing the square

[rapid latch]

ohhh

thank you

ahhhhh

ummm

now what

i think i made a mistake

[prisma snow]

i would do

-2(x^2 + 8x -5/2)
-2(x^2 + 8x + 16 - 16 - 5/2)
-2([x+4]^2 - 37/2)

-2(x+4)^2 + 37 = 0

[devout snow]

@rapid latch Has your question been resolved?

Channel closed

Closed by @rapid latch

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.

[mortal merlin]

So i have been doing this math exercise and the awnser is y=6 but i have found 4y=6 and cant figure out my mistake can anyone help?

[untold lodge]

there is no way the answer is y = 6

you can check this by subsituting y = 6 in the equation

you will get something like this:
2 - 2 = 3 - 5

and 0 is not equal to -2

[mortal merlin]

Oh so my awnser is correct?

[untold lodge]

check?

i dont know 🙂

[mortal merlin]

Thats what i am doing right now

Math just aint mathing

💀

[devout snow]

@mortal merlin Has your question been resolved?

Channel closed

Closed by @mortal merlin

Use .reopen if this was a mistake.

[devout snow]

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.

[high pewter]

ello. have a calculus quiz in about an hour and while i don’t expect this to be on it, i don’t quite see where i’m going wrong

[high pewter]

i’m finding the second derivative of this to be

but putting using points but those just gives me solid negatives all the way across

[high pewter]

i really just want to know where i’m going wrong and why i’m ending up with a negative consistently

[winter patrol]

fked up the multiplication here

[high pewter]

wooo

woop *

well

actually i think i thought ahead there and i still treat it as a 16

or else i wouldn’t have ended up with -8x

[winter patrol]

ok, then the next error is that you didn't factor out the - sign properly

$-8x^2 + 28 \redneq -4(2x^2 + 7)$

$\frac{-a+b}{c} = -\frac{a-b}{c} \redneq -\frac{a+b}{c}$

[woven radish]

ℝαμΩℕωⅤ

[sullen island]

\redneq lmao

[high pewter]

i see i see

[woven radish]

ℝαμΩℕωⅤ

[high pewter]

that leaves me at a loss with what to do with the (2x^2+7)^2 then

[winter patrol]

you can just leave stuff as is,

[high pewter]

oh wait yeah

[winter patrol]

don't try to forcefully reducing the expression by illegally erasing stuff

if there isn't anything meaningful to be done, don't do anything

[high pewter]

how would i end up with the square root in that case?

[winter patrol]

solve for when f''(x) = 0

and determine whether those candidates are locations of inflection (just solving for f''(x) = 0 is insufficient)

[high pewter]

okokok i get it now

thanks a bunch

.close

[devout snow]

Channel closed

Closed by @high pewter

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.

[calm nest]

hey

[calm nest]

Problem description:
A thief stole a necklace at 9:00, and shortly after threw it somewhere in a dock. The waterlevels in the dock change in accordance to the formula: y = 0.75 + 1.5sin(π(x+3)/6). Y = waterlevels in meters. X = time in hours starting from midnight.

Multiple people visit the dock throughout the day. Which person or persons will find the necklace?
a) Charlie passes by at 11:00
b) Jack looks at the boats between 12:00 and 13:00.
c) The thief returns to find the necklace at 15:00.
d) Molly and her friends come to fish between 16:00 and 18:00
e) Emma watches the sunfall between 21:00 and 22:00
f) workers scout the dock at 23:00

My work:

is this correct?

i think this is how i am supposed to solve it

<@&286206848099549185>

[devout snow]

@calm nest Has your question been resolved?

[devout snow]

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.

[alpine tapir]

Could someone give me a curve sketching problem to help me study (no exponential or ln functions)

[sweet heath]

try sketch x^3 + 2x^2 + 3x +4=0

btw what do you mean by " curve sketching problem"?

[alpine tapir]

To sketch any equation

On a graph

[devout snow]

@alpine tapir Has your question been resolved?

[devout snow]

@alpine tapir Has your question been resolved?

[devout snow]

Channel closed

Closed by @alpine tapir

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.

[rugged raven]

Can anyone help me out on how to solve the task? I'm desperate
Stochastics / University-Level

Task:
The following is known about the value of three shares: Each of the three shares currently costs 1 €.

The value of share 1 rises with probability 0.61 in one year to 1.50 € and falls to 0.50 € with a probability of 0.39.
Share 2 rises in the same period with a probability of 0.24 to 1.60 € and falls to 0.40 € with a probability of 0.76.
Share 3 is worth 1.70 € in one year with a probability of 0.45 and is still worth 0.30 € with a probability of 0.55.
A trader randomly selects two of the three shares and buys one each at the current price of current price of 1 euro.

a) What is the probability that the trader will make a profit with this portfolio within one year? make a profit?
(b) What is the probability that his portfolio consists of shares 1 and 2 if the trader has made a profit?

[devout snow]

@rugged raven Has your question been resolved?

[devout snow]

@rugged raven Has your question been resolved?

[devout snow]

@rugged raven Has your question been resolved?

[devout snow]

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.

[fervent jewel]

So I need to show that $p(x) = x^n + a_{n-1}x^{n-1} + \cdots + a_0$ where n is odd has $a$ and $b$ such that $p(a) < 0 < p(b)$.

[woven radish]

WhoTao

[fervent jewel]

Here is a outline of what I have done.

Ive shown that $\lim_{x \to \infty} p(x) = \infty$ and $\lim_{x \to -\infty} p(x) = -\infty$

[woven radish]

WhoTao

[fervent jewel]

Then I claim that there exists $a$ and $b$ such that $p(a) < 0 < p(b)$.

[woven radish]

WhoTao

[fervent jewel]

Is that a valid argument?

[dense jay]

you may need to show its continuous, thats the only thing i can think of

or actually

no you dont

i think thats fine

[fervent jewel]

I kind of use that is is continuous within the proof.

To use the algebraic continuity theorem

But that is fine, since I've shown that polynomials in general are continuous in a previous assignment.

SO I can just site it

ty

.close

[devout snow]

Channel closed

Closed by @fervent jewel

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.

[vapid summit]

I’m not sure if my set up is correct. I’m only getting 0 for my answer and that’s not right

[devout snow]

@vapid summit Has your question been resolved?

[vapid summit]

<@&286206848099549185>

.close

[devout snow]

Channel closed

Closed by @vapid summit

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.

[cold hornet]

engineering help?

[dense jay]

maybe

just ask and we'll see

[cold hornet]

Your fourth task is to identify the extent of the turbulent mixing region from your plot any idea?

I understand this is a maths server but i decided to go for it

[dense jay]

im clueless, i think there is an engineering server in #old-network might be a better shot

[cold hornet]

ah okay i didn't know thanks i appreciate it

.close

[devout snow]

Channel closed

Closed by @cold hornet

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.

[sleek wind]

how to do this?

[lusty sapphire]

Synthetic division and setting the remainder to zero is my first guess

[sleek wind]

wut?

[fast ruin]

@sleek wind do yk sum and product of roots formulas

[sleek wind]

(x-α)(x-β)(x-γ)and roots r like α+β+γ αβ+αγ+βγand αβγ no?

[fast ruin]

no like r1 + r2 + r3 = -b/a, r1*r2 + r2*r3 + r3*r1 = c/a, r1*r2*r3 = -d/a

oh eyah

yeah

mb

[sleek wind]

yh

[fast ruin]

so if u write those out

and plug in the alpha and 1/alpha

[sleek wind]

wut does it mean by α, 1/α

[fast ruin]

like

one of the roots is

1/3

the other is 3

or like 7 and 1/7

[sleek wind]

-1/3, no?

[fast ruin]

no reciprocal roots just means taht they are reciprocals of each other

a and 1/a type stuff

[sleek wind]

im confused

[sleek wind]

where do i plug it?

[fast ruin]

in the α+β+γ αβ+αγ+βγ αβγ equations

see what you get

[sleek wind]

wym?

can u give me an example of wut i do?

[fast ruin]

like α+β+γ = -b/a

[sleek wind]

yh

[fast ruin]

but γ = 1/α

so it rly is α+β+1/α = -b/a

[sleek wind]

how u know that?

[fast ruin]

cause they said taht theres a pair of reciprocal roots

so one of them will be 1/α

[sleek wind]

can beta be 1/α or no?

[fast ruin]

yea

it doesnt matter which one

[sleek wind]

oh alr

then wut do u do after u plug it in α+β+γ αβ+αγ+βγ αβγ

[fast ruin]

youll have 3 equations

cause also αβγ

[sleek wind]

yh

[fast ruin]

and u could prolly do sm from there

[sleek wind]

wut?

bro i hate this topic so much, y not just stick to α β γ, how cruel

[fast ruin]

ikr its annoying

ok write out the 3 equations and send them

[sleek wind]

β = 1/α
α + (1/α) + γ 1 + αγ + (1/a)(γ) γ, is it this?

[fast ruin]

u set beta as 1/alpha right

[sleek wind]

yh

[fast ruin]

yea and then the equations

since α+β+γ = -b/a, αβ+ βγ+ γβ = c/a etc

[sleek wind]

yh...?

[fast ruin]

and then yk gamma in terms of c and a

so u can manipulate the first 2 equations to get an equation in terms of a,b,c,d

instead of alpha and gamma

[sleek wind]

wym?

im a bit confused again

[devout snow]

@sleek wind Has your question been resolved?

[devout snow]

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.

[rancid canyon]

help me i need help understanding integrals and memorising since i have hard time memorising stuff

[rancid canyon]

i am taking calculus 3 and its not been easy to me

[dense jay]

what kind of integrals are you working with?

[rancid canyon]

ill show

i have to solve all of this test

[dense jay]

screenshots please

[rancid canyon]

and it has not been easy fr

[rancid canyon]

sure

supposed to use riemann sums

[rancid canyon]

i dont know how to use it

[dense jay]

riemann sums are things such as the rectangle rule, trapezium rule etc
you would be applying these rules with a limit as n -> infinity where n is the number of 'strips' or partitions, youd end up with something like this

[rancid canyon]

okay...

mind explaining?

[rancid canyon]

dude mind explaining?

[dense jay]

https://youtu.be/F0uuW-I6icY?si=Bvrkhwjakr94HKt3

if you watch this from around 00:23:00

ish it gives a general idea

[rancid canyon]

oo allright

thanks alot

as of for the rest of the testt?

like 1st quesion? im really lost

[dense jay]

https://youtu.be/gFpHHTxsDkI?si=y5ZbZ7ZXyr5nuiDQ
this one seems to have a more specific example that might help you out seeing it in practice

if you have to use riemann sums this is basically what youll be doing

[devout snow]

@rancid canyon Has your question been resolved?

[devout snow]

@rancid canyon Has your question been resolved?

[devout snow]

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.

[haughty pendant]

Hi

[haughty pendant]

I understand that one to one is for every x there’s a 1 corresponding y but in terms of this question idk where to start

[woven radish]

$Pure$

[prime egret]

So start from f(x1) = f(x2) deduce that x1 = x2 to show injectivity

[devout snow]

@haughty pendant Has your question been resolved?

[haughty pendant]

But what do I put for the left side of the equation? (3x-1)/x?

[devout snow]

@haughty pendant Has your question been resolved?

[devout snow]

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.

[carmine swallow]

how do I solve this

[dense jay]

first find g'(x) as an equation

in terms of x, f(x) and f'(x)

[small raptor]

might want to use the product rule

[carmine swallow]

how...

imma go shower rq

[soft stump]

well

product rule is h(x) * p'(x) + h'(x) * p(x)

you would have to do that with the x and the f(x) that you are givin in the function g(x)

[devout snow]

@carmine swallow Has your question been resolved?

[carmine swallow]

so what functions would I put for h and p

[soft stump]

well these

[carmine swallow]

so -1 and f of -1

oh wait

do I do like

nvm idk

can you show me the equation

[soft stump]

well this is the equation

[carmine swallow]

so what do I do with that

.close

[devout snow]

Channel closed

Closed by @carmine swallow

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.

[coral wraith]

im confused on what to do for the height

[coral wraith]

anyone?

pleaseee

kysefkjfhdjsk\

ddadfd

ds

[vapid summit]

what do you have set up so far?

[devout snow]

@coral wraith Has your question been resolved?

[coral wraith]

2x*x*??=26

[vapid summit]

that's right

so 2xxheight=26

do you have a cost equation set up?

[coral wraith]

10*2x^2+2*7*x*height+2*7*2x*height

@vapid summit

[vapid summit]

ok good

so basically you can solve the volume equation to get h in terms of x

[coral wraith]

Wdym?

[vapid summit]

rearrange the equation you got for volume to have height by itself on one side

you just divide both sides of the equation by 2xx

[coral wraith]

Right

h=26/2x^2

[vapid summit]

yes

so now you can plug that in for height in the cost equation

that gives you only one variable so you can take the derivative

[coral wraith]

Oh

[vapid summit]

do you understand now?

[coral wraith]

Yes

I get x=cuberoot(273/20)

[vapid summit]

oops i forgot to actually solve it

give me one minute

ok that's what i got too

[coral wraith]

So I just plug it in

[vapid summit]

yes

[coral wraith]

Nice it’s right!

Thanks!

.close

[devout snow]

Channel closed

Closed by @coral wraith

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.

[thick dust]

How to measure area because theres a curve. I need to measure the blue part. Thank you

[dense jay]

!original

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

@thick dust Has your question been resolved?

[thick dust]

Oh this isnt mine, its my sister’s sorry 😅

Im not able to get the full question from her because of some problems, but this is what she is trying to figure out

[dense jay]

its just, i cant really do much with only what you gave me
id like to assume that curved bit is the segment of a circle but i cant say for sure

[thick dust]

Oh ok i understand, and thank you very much

[devout snow]

@thick dust Has your question been resolved?

Channel closed

Closed by @thick dust

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.

[pure drum]

I need help finding the area of the blue shaded side. I don't know where to start!

[supple knot]

Show the entire question

[lusty sapphire]

My guess is 18 is the length of the blue triangle base

[pure drum]

yea I think so

[devout snow]

@pure drum Has your question been resolved?

[pure drum]

.close

[devout snow]

Channel closed

Closed by @pure drum

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.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.

[spiral cape]

Is the z-y plane including the space under the circle

[devout snow]

@spiral cape Has your question been resolved?

[spiral cape]

.close

[devout snow]

Channel closed

Closed by @spiral cape

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.

[brazen dome]

I've solved AC using the law of cosine, but I don't know how to find the radius of O. Any clue?

[devout snow]

@brazen dome Has your question been resolved?

[brazen dome]

<@&286206848099549185>

[dry flume]

The circumscribed circle of quadrangle ABCD and the circumscribed circle of △ABC is the same
So you can use the law of sine to solve it

[devout snow]

@brazen dome Has your question been resolved?

[brazen dome]

Why you can decide that it's the same?

[dry flume]

Because point A、B、C and D are all on the circle O

So OA=OB=OC=OD
O is the outer center of △ABC

[brazen dome]

I see. Then, which side of the triangle(?) Should I use the law of sine?

[dry flume]

AC because we already know ∠ABC

It is easier to compute
You can also use another angle
But you need more computation

[brazen dome]

Then sinABC/AC, right? after that? Sorry I still do not fully understand

[dry flume]

AC/sin∠ABC=AB/sin∠ACB=BC/sin∠BAC=2r
r is the radius of circumscribed circle

This is law of sine

[brazen dome]

I see, I've never heard that it's equal to 2R

Alright, I've found the answer. Thanks @dry flume

.close

[devout snow]

Channel closed

Closed by @brazen dome

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.

[urban aurora]

Surely there must be a link between this and calculus? What is it?

[devout snow]

@urban aurora Has your question been resolved?

[prisma snow]

i don’t see a link, calculus is about rate of change and area under a curve

odd numbers are in the form of 2k + 1 where k is an integer

the difference between odd numbers always is a multiple of 2n, where n is a positive integer or 0

[urban aurora]

The pink equation is the change in the black equation
The blue is the change in the pink
Also the black equation is the sum of the pink (Like an integral is the sum of the changes)

[prisma snow]

does the brown text have a significance?

a+b+c, 3a+b, and 2a?

[urban aurora]

the a,b and c values are the values for: ax^2 + bx + c

Which is another thing. Notice how the black one is a quadratic, the pink one is linear and the blue one is constant

[prisma snow]

ax^2 + bx + c
3ax^2 + bx
2ax^2

like that?

[urban aurora]

Not exactly. In that example we find a by saying 2a = 2 therefore a = 1
Then 3a+b = 5 therefore b = 2
Then a + b + c = 6 therefore c = 3
Therefore we have x^2 + 2x + 3 (Which is the equation that describes the black equation)

[prisma snow]

why is 3a + b = 5 and not 7, 9 or so on?

[urban aurora]

Because 5 is the first change. We consider this diagonal of numbers

[finite briar]

2nd difference implies that second derivative remain constant, ithink

[urban aurora]

Is there some way I can use calculus to derive the formulas? I have tried, but gotten the wrong answer

[finite briar]

I dont exactly understand the question

What are a,b,c?

is it used in the formula that determines the sequence?

so something like $ax^2 + bx + c$?

[urban aurora]

ax^2 + bx + c is the formula that determines the sequence

[woven radish]

ItzKraken

[urban aurora]

yes

[finite briar]

okay

[finite briar]

By this, if you differentiate the the formula for the sequence twice and set it equal to 2, what do u get?

[urban aurora]

x^2 + 2x + 3 (This describes the formula)
2x + 2 (This is off by 1 for some reason?)
2 (This describes the second difference)

[finite briar]

x^2 + 2x + 3 is given..??

okay god am so confused

[finite briar]

are we given this

or x^2 + 2x + 3

[urban aurora]

Just copying the image to bring it back

[prisma snow]

so:
x^2 + 2x + 3
3x^2 + 2x
2x^2

[urban aurora]

In that example we find a by saying 2a = 2 therefore a = 1
Then 3a+b = 5 therefore b = 2
Then a + b + c = 6 therefore c = 3
Therefore we have x^2 + 2x + 3 (Which is the equation that describes the black equation)

The a, b, and c are only used for the quadratic

[finite briar]

oh thats what u meant

so ur asking if its possible to solve this using calculus only?

[urban aurora]

Yes

[prisma snow]

i feel like you are just differentiating each level

there is a pattern use power rule

[finite briar]

not really what he did

[prisma snow]

according to this

[urban aurora]

As mentioned there. The first derivative does not describe the first difference for some reason? It is off by exactly 1.

[prisma snow]

why do you assume it’s meant to be in a parabolic form?

why not ax^2 + bx^1.0382

(these are abitrary values)

[urban aurora]

Good point. We did these things in highschool though, and someone was asking me about it. It has been years since I have done it and I forgot how to so I wanted to use calculus to do it. Anyway, the reason I assume it is parabolic is because that is what I was taught years ago. Another way of thinking about it I guess is the fact that the first difference is changing by a constant amount (Just as a parabola has a derivative that changes by a constant amount)

[prisma snow]

here’s why it can’t work if you assume it’s parabolic:
we are given a function which provides an odd number (pink)
f’(x) = |2x| + 5 (assuming 5 is the starting value, or 0th term)
and we are given a function which produces 2 (blue)
f’’(x) = 2
and we want to find f’(x), integrating f’’(x), so
f’(x) = 2x + c where c is a real number
if we sub in (0,5)
c = 5
hence f’(x) = 2x + 5
integrating f’(x) give us
f(x) = x^2 + 5x + d where d is a real number
subbing in (0,6) yields d = 6
hence f(x) = x^2 + 5x + 6
let’s sub in values and see if this works:
f(0) = 6 (works)
f(1) = 12 (doesn’t work)
hence this is just a recurrence relation in the form of T(n) = 5 + T(n-1) where T(0) = 6

[urban aurora]

But x^2 + 2x + 3 accurately describes the black equation if you start at n = 1

Also because it is quadratic, this T(n) = 5 + T(n-1) should be T(n) = 2n + 5 + T(n-1)
As T(1) = 2(n-1) + 5 + (6) = 11 (Expected result if starting at 0)
T(2) = 2*1 + 5 + (11) = 16 (Expected result)

[devout snow]

@urban aurora Has your question been resolved?

[prisma snow]

you cannot obtain this through calculus

[urban aurora]

Another thing that makes me think there surely must be a link though, is the fact that this is just a discrete version of what we do in calculus (which is continuous)

[urban aurora]

.close

[devout snow]

Channel closed

Closed by @urban aurora

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.

[sleek wind]

how to do this?

[stuck field]

Well do you know what the product of roots is going to be?

[sudden harness]

seems like an interesting problem regarding roots of a cubic eq

[sleek wind]

Yh

[empty yoke]

Write ax^3 + bx^2 + cx + d = 0 as x^3 + (b/a) x^2 + (c/a) x + (d/a) = 0

Now assume roots to be alpha, 1/alpha, beta

[sleek wind]

Can beta be gamma?

[empty yoke]

Now - b/a = sum of roots, c/a = pairwise multiplication and sum of root (like 2.3 + 3.4 +2.4) and - d/a as product of roots

[empty yoke]

Yeah sure it's just a variable

[sleek wind]

Oh ok

[empty yoke]

Take it whatever you want

[empty yoke]

Then you'll have 3 equations solve for it u will have the identity above

[sleek wind]

I understand this part

[sleek wind]

Ah Yh I got that

[empty yoke]

Like this now solve for this

U will get the relation, first eliminate beta/gamma by putting - d/a

Since roots are reciprocal last equation is just beta/gamma

[sleek wind]

In those 2 equations?

[empty yoke]

Yup

[sleek wind]

Now wut?

I’m on mobile it’s hard to type wut i got

[empty yoke]

Ok let me write it down

Ignore bottom left scribble

First u put value of Beta in first equation, u will get value for (alpha + 1/alpha) = d/a - b/a

Then put beta and value of this in second equation

It will become c/a = 1 +(-d/a) (d/a-b/a)

c/a = 1 - d(d-b)/(a^2)

ca = a^2 - d^2 +db

ca-db=a^2-d^2

Hence verified

Im just substituting roots with a, b, c, d terms

[devout snow]

@sleek wind Has your question been resolved?

[sleek wind]

Mb for taking so long to reply

[empty yoke]

No problem, so makes sense?

[sleek wind]

Yh

Then how do you do the 2nd part?

Do I just substitute the numbers?

[empty yoke]

Yup try to remove roots from equations

Get answer in terms of abcd

[sleek wind]

Ah alr

Tysm

.close

[devout snow]

Channel closed

Closed by @sleek wind

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.

[thorny pawn]

I’m looking at this

I’m looking at this but then what if c=1

Then isn’t |1-c| = 0 so for any epsilon it’s less than epsilon.

[empty yoke]

Then try from left hand side

It still would be discontinuous

[thorny pawn]

Right but can I somehow modify the solution?

I want to just use the negation of epsilon delta

Oh I see what you mean

[empty yoke]

Yup

-1

[thorny pawn]

Like if x<0 then we have |-1 - c|

[empty yoke]

Yup

[thorny pawn]

Yeah

[empty yoke]

So |1+c| > epsilon for many epsilon

Either way discontinuous

[thorny pawn]

|1+c|?

Oh yeah okay

Got it

[empty yoke]

Yup

If you take c<0

Then for other side

[thorny pawn]

So how can I write this formally in the proof

Do I do two classes?

Cases

[empty yoke]

|1-c| > epsilon

[empty yoke]

you know the definition right epsilon-delta

Negate it

[thorny pawn]

Well just the case when c=1

Then my epsilon is 0

But isn’t epsilon supposed to be greated than 0

[empty yoke]

Look x/|x| € {-1,1} right

So, u must prove that to show continuity

|1-c| < epsilon and |1+c| < epsilon

Which is not possible and discontinuous

[thorny pawn]

I can prove the left limit is -1 and right limit is 1

But can I also do it this way?

[empty yoke]

Yess

True

If left hand limit =/= right hand limit

Then discontinuous

You can prove it that way too

[thorny pawn]

No I mean I just want to do it with the negation

Should setting epsilon = |1-c| covers most cases

Except when c=1

[empty yoke]

This fucntion is piecewise continuous, i mean if you just take x>0 then just choose c something like 0.9999 or 1 which will prove its continuous when x>0

And when x<0, choose c = - 0.9999 or - 1 which would prove epsilon delta for it but not on whole domain

Let me post the graph of it

You get it?

[thorny pawn]

Right yeah I get that so can’t I say if c is = 1 look at x<0 then it’s not continuous there

Well I suppose we come back to |1+c| < epsilon and |1-c|<epsilon

[empty yoke]

Exactly it discontinuous

Basically you cant close the gap at x= 0 for f(x)

Its 2 units wide

1-(-1)=2

[thorny pawn]

Yeah But I’m not quite sure how to write this proof formally

Maybe I can choose epsilon to be the max[ |1-c|, |1+c| ]

Because then we have a counter example for either case

[thorny pawn]

Can anyone verify if this works because I think it does

[empty yoke]

Yess you can choose max

It will work by being bigger than minimum ond

One

[thorny pawn]

Yeah I think this is the way to go

[empty yoke]

If epsilon = max(|1-c|, |1+c|) = |1+c|

[thorny pawn]

Then we look at x<0

[empty yoke]

Oh wait not max but min

[thorny pawn]

Oh

[empty yoke]

Then epsilon < max

Lol a blunder

Or u can take

Half of |1+c|

And epsilon < |1+c|

[thorny pawn]

Oh Hm but if we choose epsilon to be min then epsilon can be 0 no?

Say c=1

Then we have epsilon is max(2,0)

Choose 2 then look at x<0

|1+1|=|2|=epsilon

[empty yoke]

We are trying to prove discontinuity right?

[thorny pawn]

Yes

So prove there’s an epsilon for any delta such that |f(x) - c|>=epsilon for some x

[empty yoke]

Yup and when we take min

Okay

The the other side would be greater than epsilon

Since we took min of them

[thorny pawn]

But then epsilon can be 0 no?

[empty yoke]

Like min(2,0) = epsilon okay and 2 is for lets say x> 0, then |1-c|> 0 so no such epsilon can be given for both

[empty yoke]

Yup so be it we are making sure that it will fail

[thorny pawn]

I’m not folllowing sorry

How did I get this?

[empty yoke]

Fk typing let me write it on paper

Yeah min it is

So we found one such epsilon by using min

Also c = 1 is arbitrary so it should work for all

[thorny pawn]

But my confusion is then epsilon is 0 which contradicts the assumption of epsilon greater than 0 no?

[empty yoke]

Oh that just exclude then 1 and - 1

For c

Its giving 0 at 1,-1 because actually function is continuous on x>0, and x<0

So basically you doing is

Limit f(x) - 1

And limit f(x) = 1 at x>0

Or lets choose some other epsilon

[thorny pawn]

Right okay

[empty yoke]

Ohh nvm

When negating

It becomes

|fx - c| >= epsilon

[thorny pawn]

Yeah

Wait I’m still not sure why it’s min and not max

If it’s max then isn’t it guaranteed that epsilon will be equal to at least one of |fx -c|

Either when x<0 or x>0

[empty yoke]

If it is max then it would be bigger than other one, so it would not work since its an AND

[thorny pawn]

No it should be an or right

We’re saying there exists some x

That this epsilon doesn’t work

[empty yoke]

We are finding epsilon which should not work at x=0

And function take value c at x=0

If we put c=0, then epsilon = 1/2 would have worked

[thorny pawn]

Right yeah

1>1/2

[empty yoke]

Yeah

[thorny pawn]

But say c is 1 then if I choose epsilon to be 2 it should work? Because if we look at x<0 then |1+c| = 2 = epsilon

It doesn’t matter than |1-1| =0 < epsilon

Or am I misunderstanding the definition here

For c=1?

if x>0 we have |-1-c| right

So it’s |1+c| >= epsilon

[empty yoke]

If we have x>0 its 1-c

[thorny pawn]

Yeah I meant x<0 sorry

[empty yoke]

Here

[empty yoke]

Yup

[thorny pawn]

So max should work?

Since we only need to find some epsilon that for at least 1 x it doesn’t work?

[empty yoke]

They have pretty much done the same, chosen e for one side then proved that it is smaller for other

We have to make cases

[thorny pawn]

Okay let me rewrite this

Choose epsilon to be max[|1-c|,|1+c|] then,
If epsilon = |1-c| > 0 look at x>0, we have |f(x) - c| = |1-c| = epsilon
If epsilon = |1+c| > 0 look at x<0 we have |f(x) -c| = |-1-c| = |1+c| = epsilon
So we’re done

[thorny pawn]

Is this right?

[empty yoke]

Both works lol

For min u can do this

The thing is u take max u compare it to same side

U take min u compare it to other

I think you should look up if it needs to AND or OR

[thorny pawn]

No but if u take min then epsilon can be 0 tho isn’t that a problem

I’m fairly sure it’s meant to be or

The negation of for all x is there’s some x it doesn’t work

I’ve read this in spivak calculus

[empty yoke]

Yup right

[empty yoke]

I think this should just work fine

[thorny pawn]

Yeah I think so too

I’ll stick with this

[empty yoke]

Signum is actually neither continuous nor discontinuous

[thorny pawn]

Thanks so much @empty yoke and @modern frost I’ll go have lunch now

[empty yoke]

Np

[thorny pawn]

I only have 1 right now but if I get another I’ll send here

[empty yoke]

Analysis by tao

[devout snow]

@thorny pawn Has your question been resolved?

Channel closed

Closed by @thorny pawn

Use .reopen if this was a mistake.

[devout snow]

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.

[solar yoke]

How would I do this

[old tusk]

Showork

[alpine tapir]

First one you can do it with pythag

[old tusk]

!status

[devout snow]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@solar yoke Has your question been resolved?

[solar yoke]

How would you do that with pythag theroem?

I’ve only seen pythag theroem done with measures so im confused

[devout snow]

@solar yoke Has your question been resolved?

[devout snow]

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.

[brisk hare]

Integrate (a^2 - x^2)^1/2 where the limit is from 0 to a

[worthy talon]

trig sub

If you do x=asint, dx=acostdt youll have a²-a²sin²t under the root which becomes √a²cos²t acost dt or acos²tdt which you can easily solve using power reduction formula

Remember to change limits of integration when subbing

[devout snow]

@brisk hare Has your question been resolved?

[devout snow]

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.

[sweet elk]

What does diagram look like and how to get T

[devout snow]

@sweet elk Has your question been resolved?

[devout snow]

@sweet elk Has your question been resolved?

[sweet elk]

Wut

[devout snow]

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.

[alpine forge]

??????

[devout snow]

@alpine forge Has your question been resolved?

[alpine forge]

oh cuz f_xy and not w or some other variable

?

[dry flume]

The denominator is ∂y∂x
For most functions,change the order of variable which we take partial derivative with,the result is still the same
But there are some exceptions

[alpine forge]

but isnt this the derivative wrt x then wrt y

[dry flume]

fxy means doing partial derivative of x first then doing partial derivative of y

[alpine forge]

yeah

then why cant the denominator be dxdy

[dry flume]

And the sequence of the variable is from back to front in ∂f/∂... notation

So the correct sequence is ∂y∂x

[alpine forge]

ah so it's backwards

alright tahnks

thanks

.close

[devout snow]

Channel closed

Closed by @alpine forge

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.

[balmy dove]

how is this 1/a

this is the final step

I understand that when x => inf
the whole thing becomes 0

but why does it become 1/a (positive) when x = 0

[acoustic leaf]

you subtract the lower bound so the negatives cancel out

[balmy dove]

oh shoot

thanks man

.close

[devout snow]

Channel closed

Closed by @balmy dove

Use .reopen if this was a mistake.

[devout snow]

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.

[zinc pecan]

Pl i need help in this ( generalite sur les fonction

[tender lotus]

!status

[devout snow]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@zinc pecan Has your question been resolved?

[zinc pecan]

1

i dont have any idea on how to solve it

i did question 1 but others idk

[devout snow]

@zinc pecan Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.

[pliant wind]

Is anyone here familiar with cournot?

[pliant wind]

game theory?

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[devout snow]

@pliant wind Has your question been resolved?

[devout snow]

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.

[cursive thicket]

Just want to double check

Both of these notations mean i first differentiate wrt to y and then second derivtive wrt x right?

[wooden veldt]

yes, they are annoyingly opposite (as in the letters are in opposite order)

[cursive thicket]

Thanks

.close

[devout snow]

Channel closed

Closed by @cursive thicket

Use .reopen if this was a mistake.

[cursive thicket]

.reopen

[devout snow]

✅

[cursive thicket]

Wait

The second one is not read from right to left right?

[wooden veldt]

it is not, correct

[cursive thicket]

Okay thanks

.close

[devout snow]

Channel closed

Closed by @cursive thicket

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.

[obsidian wasp]

.

[devout snow]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.

[cursive thicket]

at the end i get b + 5 = a - 1

is there anything else i have to do?

or is it already continous?

or do i just express a and b and say those are the required parameters?

[winter patrol]

simplify the equation i suppose

not much else to do other than that

[winter patrol]

was there anything else in the question?

[cursive thicket]

nope

[winter patrol]

that's pretty much all that you can do then

[cursive thicket]

oh also

just to make sure

when i write lim x->1

its the same limit approaching 1 from negative side is equal to limit approaching 1 from positive side?

[winter patrol]

can you reword that

[cursive thicket]

wait

[winter patrol]

there are slight issues with the notation in your work though

$\lim_{x\to 1^-} = \red{\lim_{x\to 1^-}}(x^2+ax-2) = 1 + a - 2 \
\lim_{x\to 1^+} = \red{\lim_{x\to 1^+}}(bx^3++5) = b+5$

[woven radish]

ℝαμΩℕωⅤ

[cursive thicket]

Ment to say that

[winter patrol]

$\lim_{x\to a} f(x) = \lim_{x\to a^-} f(x) = \lim_{x\to a^+} f(x)$ if $\lim_{x\to a^-} f(x) = \lim_{x\to a^+} f(x)$

[woven radish]

ℝαμΩℕωⅤ

[cursive thicket]

thank you for this, will make sure to write it properly next time

in the context of continuous functions do i have to write the if?

[winter patrol]

for continuity you want
$$\lim_{x\to a^-} f(x) = \lim_{x\to a^+} f(x) = f(a)$$

[woven radish]

ℝαμΩℕωⅤ

[winter patrol]

(given you can approach from both sides of a)

[cursive thicket]

but its the same if i write as x tends to a, no?

[winter patrol]

wdym

[winter patrol]

if you want

[cursive thicket]

just making sure its not a mistake to write it that way

[winter patrol]

well

the whole thing i wrote would essentially be required, just stating that isn't very good

you'd want to determine whether lim as x→a f(x) exists

and to do that, you'd need to consider the one sided limits and see if they're the same

[cursive thicket]

okay

thanks for the help

much appreciated

.close

[devout snow]

Channel closed

Closed by @cursive thicket

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.

[night depot]

how would one isolate x in this equation?

[frigid merlin]

how do you find factors of a number?

[night depot]

uh

[frigid merlin]

am i supposed to send a pic

[dry oxide]

open a new channel

[night depot]

check #❓how-to-get-help

[frigid merlin]

oops

[night depot]

im trying to make it so that if i have the varriables a t and p i can find the value for x

though im not sure how to find the equation

[devout snow]

@night depot Has your question been resolved?

[devout snow]

@night depot Has your question been resolved?

[night depot]

seems like no one can / wants to do my question so ill close it after next

[devout snow]

@night depot Has your question been resolved?

[night depot]

no

[devout snow]

Channel closed

Closed by @night depot

Use .reopen if this was a mistake.

[devout snow]

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.

[kind cedar]

is there any way to do this without solving every option?

[vapid nest]

maybe...

but it depends

are you trying to be lazy here or do you want to find a better solution

[kind cedar]

i want to find a way to take any polynomial into its matrix form

[vapid nest]

so write it out

so first of all we know that $x^T(Ax)$ = $x * (Ax)$

[woven radish]

nosqldb

[kind cedar]

yeah

[vapid nest]

yeah and I'd just keep it like this and solve

[kind cedar]

sorry i dont get it...

[vapid nest]

like since A keeps changing

I wouldn't bother with altering it

if A was the same and x was changing, I'd tell you to figure out the inner product or sm

[kind cedar]

nvm i got it

.close

[devout snow]

Channel closed

Closed by @kind cedar

Use .reopen if this was a mistake.

[devout snow]

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.

[hidden dragon]

If in indefinite integration, a constant is always added, why do we say in physics, indefinite integration of dv gives v(velocity) and not v+c?

[toxic flower]

well its actually v+C used

[hidden dragon]

There was a equation I saw and in that it was not used

[toxic flower]

can you share?

[stone stump]

we hopefully have some initial velocity to figure out which C it is

[toxic flower]

yeh exactly

[hidden dragon]

Yeah it was a question like that

The equation was integration of dv = integration of f(t)dt
On rhs a constant was added but on LHS no constant was added

[toxic flower]

lets say a constant is also added on lhs named c1, and on rhs c2

[hidden dragon]

Ok

[toxic flower]

thn you can subtract c1 from both the sides

[hidden dragon]

OHh!

[toxic flower]

now on rhs you will get c2-c1=C

[hidden dragon]

Yes I understand now

[toxic flower]

which is counted as a single constant

[hidden dragon]

But did they skip that step though?

[toxic flower]

hm yeah

[hidden dragon]

Ohk

[toxic flower]

usually that step is skipped

[hidden dragon]

I see

Thank u!

[toxic flower]

if you solve LDE then also this step is skipped

[hidden dragon]

LDE?

[toxic flower]

[toxic flower]

linear differential equations

[hidden dragon]

Oh Kay!

I'll close the channel then 👍

.close

[devout snow]

Channel closed

Closed by @hidden dragon

Use .reopen if this was a mistake.

[devout snow]

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.

[gilded coyote]

I feel like this is a stupid question. We define a circle with 360 degrees as 2pi. But this obviously means that 2pi/2 = pi. 360/2 is 180 degrees. Making pi = 180 degrees.

Mathematically, it all makes sense, but my head gets jumbled up with the geometry. I guess because Pi is typically the ratio of the circumference and diameter, my brain doesn't like it being a half-circle. My brain still wants to associate pi with the whole circle.

When I ignore the 2 and just make pi the ratio of the circumference to the radius, all of the issues go away.

When we're talking about the degrees of a circle, does pi cease to represent a full circle?

[gilded coyote]

And secondly, is there any inherent problem with just ignoring pi altogether and just making it the ratio of the radius to the circumference when I'm working with trig?

Because then I get pi = 360 degrees. pi/2 = 180 degrees., etc. The fractions make more sense to me.

1 radian becomes 360/pi

[drifting sierra]

You can just consider 2pi as a single thing