help-13

[bold hinge]

lim h->0 ((x+h)^2 - x^2)/h

Now expand the numerator

[marble bone]

Done

(x^2+h^2+2hx-x^2)

x^2 can cancel out?

(h^2+2hx) / h

Ok then

[bold hinge]

Yep, that simplifies further

[marble bone]

Do it?

and see

h(h+2x) / h if I take h common

[bold hinge]

+2x

[marble bone]

Oh ya

[bold hinge]

Then the h cancels out on top and bottom

[marble bone]

I have h+2x

So now I plug it in?

And get 2x

[bold hinge]

Yep

[marble bone]

Dam

That's nice

But some proofs use h^2=0

As an approximate

Would that mean

Those proofs are wrong

[bold hinge]

Which proofs

[marble bone]

Like what 3b1b showed

In his calc course

I mean series

[silent ledge]

wait i read somewhere, that it's approximations but with a really small error(?)

[marble bone]

@bold hinge s point is also convincing

[silent ledge]

heres the source im not sure since im no mathematician i just wanted to understand this
https://www.askamathematician.com/2014/08/q-since-it-involves-limits-is-calculus-always-an-approximation/#:~:text=Calculus is exact.,always feel a little incomplete.

[silent ledge]

wait which point

[marble bone]

His way of defining derivative as a limit

And solving a limit instead

[silent ledge]

i dont understand what this means

[marble bone]

I think u haven't been taught limits uet

[silent ledge]

yes i jus started this subject T__T

[marble bone]

It's taught later ig

[silent ledge]

wait, what do i need to learn to understand this please

[marble bone]

Limits

[silent ledge]

like...how?

[marble bone]

U need to understand limits which is also a part of calculus

[silent ledge]

alright, what are limits and how do they relate to the question? since all i know is that there's a limit, we have to get as close to it but not actually be the limit(?)

[marble bone]

There are many ways to solve a limit

One way is by factoring

Wait

I am also getting confused

💀

How do we even know that limit isn't a approximation

The moment we cancel out h we know that h=0 and 0 dosent cancel out

How do even show it approaches

Some value

By factoring

[silent ledge]

oof endtimes gotta get back in here

[marble bone]

Ya

[bold hinge]

it's not an approximation because you let the error go to 0. emphasis on "go to" rather than "be equal to"

the whole point of taking the derivative is finding the slope of the tangent line at a given point on a curve

here's an example problem for you:
you are in a car undergoing a constant acceleration. your position as a function of time is x(t) = 5t^2. how fast are you going after 2 seconds?

[marble bone]

its not an approximation because you let the error go to 0

How are we approaching something

When we just factored it

And thought that 0/0=1

Even when we use lhoptal while computing limits as x approaches 0 we compute the function at x very close to 0

Not exactly at 0

We don't approach anything

We just compute at the place closest to 0

Yet not 0

Which again brings back dx

[bold hinge]

we never said that 0/0 = 1

[marble bone]

Then how did we cancel out h

[bold hinge]

because h/h = 1

for nonzero h

[marble bone]

And h=0

[bold hinge]

right, and that's why we have to take the limit

for all h arbitrarily close to 0, h/h = 1

[marble bone]

So ya again "close" To 0

Not 0

?

[bold hinge]

yes

[marble bone]

Which is dx/dx and not 0/0

?

I think I got it in a different way

Nvm

x/x approaches 1 as x approaches 0

This way

Ig

[bold hinge]

yes

[marble bone]

And not because for values "around 0" x/x=1

?

[bold hinge]

that's the same statement

[marble bone]

It's because they approach it

And not close to it

[bold hinge]

lim x->0 x/x = 1, yes

[marble bone]

Yup makes sense

[bold hinge]

when we take limits, we do not care about what the function actually does at that point

it doesn't matter what 0/0 actually is, or whether it is defined

the only thing that matters is the behavior of the function in some arbitrarily small interval surrounding 0, but not at 0 itself

[marble bone]

My point is that " As for values of x very very very close to 0 x/x is 1 " Is not reason the limit is 1 it's because the "x/x approach 1 as x approaches 0"?

And they are different things ig

But ya I am convinced that calculus is exact

[bold hinge]

these both mean the same thing

[marble bone]

No they don't ig

If I think of it very deeply

f(dx) = f(0) [ this is what the first line says ]
While second line says
f(1) = 1
f(0.5) = 1
f(0.25) = 1
.....
Approaches 1

They are totally different

[bold hinge]

f(0) is undefined

you can't just divide 0 by 0

[marble bone]

I mean f(0) should be close to f(dx)

[bold hinge]

f(x) = x/x
we want to find the limit as x approaches 0, so we let x equal 0 and find the limit for some arbitrarily small change in x, dx
f(0+dx) = (0+dx)/(0+dx)
then we have:
lim dx->0 dx/dx

[bold hinge]

this is how we formalize the concept of closeness, by introducing an error term that we make arbitrarily small

you should look at the epsilon delta definition

[marble bone]

And arbitary small brings approximatations

Again

[bold hinge]

right, it does. but as the error in measurement gets smaller, so does the error in the result

[marble bone]

Ya but it will not be 0 or exact

[bold hinge]

but we are still able to get an exact result in this case because the expression simplifies to a simpler one for all x in the neighborhood of 0

look at the epsilon delta definition of the limit

[marble bone]

I am thinking of it in terms of that

[marble bone]

Makes sense thanks for ur time

It's always better to think approach in terms of epsilon and delta

Makes much more sense

[silent ledge]

idk7 can u explain it 4 me TwT i got nothing im too noob

[marble bone]

Wait until someone explains to u limits in terms of epsilon and delta

Then it might make sense

I started making silly blunder when I didn't thought of it in terms of epsilon and delta

[silent ledge]

how far off is epsilon n delta, its not in our syllabus

[marble bone]

https://youtu.be/kfF40MiS7zA this is enough don't watch the lhoptal part

As I doubt u will understand it

[silent ledge]

aight imma watch it

lemme jus ask idk7, is calculus approximate or exact? based on what you got from endtimes?

[marble bone]

Exact

[silent ledge]

aight ill take u guys words 4 it till get on the epsilon thing then imma ask again if i dont get it thanks

i think this worked...

.close

[cedar kiln]

Channel closed

Closed by @silent ledge

Use .reopen if this was a mistake.

[silent ledge]

@bold hinge @marble bone can i dm u guys or smth once i get a higher calc degree to ask abt my question again?

[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.

[feral peak]

do we have to take log in this question?
or else how to calculate since the first 1 was in 12 but thete is no such option

[wispy talon]

You have 2⁵ and 2¹⁰, just check which of the options have both

[feral peak]

oh i guess i know the answer now thanks for the explaination

.close

[cedar kiln]

Channel closed

Closed by @feral peak

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.

[river berry]

hello what is the hight and width of the triangle to get the biggest surface?

[crimson sedge]

count the blocks

[cedar kiln]

@river berry Has your question been resolved?

Channel closed

Closed by @river berry

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.

[coarse hearth]

so we are using binomial theorem here

wat does k denote here

[faint socket]

u are calculating the roots z^1/n so you have n roots, the k is the number of the root

it goes from 0 to n-1 which gives n roots in total

[coarse hearth]

ahhhhh ok ok

thanks man

[faint socket]

you could try it for example for a 4th root, and when you draw it it creats a square inside the trigonometric circle of radius given by the 4th root of the modulus of the original number

and in general it shows as an n-gon, so you are dividing the circle in n parts

[coarse hearth]

ahh so we basically representing many roots in terms of K

.close

[cedar kiln]

Channel closed

Closed by @coarse hearth

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.

[sick crest]

made a tiny mistake somewhere

can somebody help me?

can't find it

[vernal shell]

Hello, I think you forgot the minus sign of u in the first line

[crimson sedge]

well it is there

he has e^ln(u + 1/2)^-1 = 1/(u + 1/2)

it is correct

(that line)

[vernal shell]

look at the line before that

[sick crest]

last line from the first screenshot?

[vernal shell]

yes

it's -u + 1/2

[crimson sedge]

no

properties of logarithms

-1ln(x)

is ln(x)^-1

[sick crest]

yea

[crimson sedge]

n*ln(x) = ln(x)^n

[vernal shell]

$\int \frac{1}{-u+1/2}, du =-\ln |-u+1/2|$

[wraith dagger]

leonardogtf

[sick crest]

i think i made a mistake in the second to last or third to last line in the first screenshot

[crimson sedge]

oh you mean the line before that

[vernal shell]

yes, that's exactly what I said 😅

[crimson sedge]

im sorry

[sick crest]

ohh

now i see it too

ok will fix it and try again. can i leave this thread open or close for now?

[crimson sedge]

you can leave it open if you will try again

just in case

but when you're done, close it

[sick crest]

checked it with a calculator. there is no minus behind the x after integrating. (substitute it with u) <

but i dont get the last step

how do you simplify it like that? 😕

nobody? 😦

<@&286206848099549185>

[ember python]

Rewrite C as ln2 + C, since C is an arbitrary constant, the step is valid

Then combine the logarithms

[sick crest]

okay understood that but does it even matter which one i take?

or is it the same

[livid hound]

wdym by

which one i take

[sick crest]

these two expressions

because it is the same or not?

[livid hound]

ideally you'd simplify as much as possible

[sick crest]

ok will try it with the simplified version

[dire geode]

They explained it here

Valid meaning the two formulas are equal

[sick crest]

ok

still the same result

didn't change anything 😦

[cedar kiln]

@sick crest Has your question been resolved?

[sick crest]

solved it

i wrote -ln(|x+(1/2)|)+C but as you can see from the calculator the right integration is: -ln(|x-(1/2)|)+C

[cedar kiln]

@sick crest Has your question been resolved?

Channel closed

Closed by @sick crest

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.

[deep flicker]

Hi would anyone mind checking my number 6 thank you very much its for my exam in the next few days

[cedar kiln]

@deep flicker Has your question been resolved?

[cedar kiln]

@deep flicker Has your question been resolved?

[cedar kiln]

@deep flicker Has your question been resolved?

[mint sorrel]

Your number 6 is correct.

[cedar kiln]

@deep flicker 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.

[crimson sedge]

can someone check if this proof is good please

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

Channel closed

Closed by @muted obsidian

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.

[eternal comet]

What is your trouble?

[tight herald]

I would just do 4^-x

Or does that have a horizontal

...

[eternal comet]

$\lim_{x\to\infty} 4^{-x} = 0$

[wraith dagger]

Remavas

[tight herald]

Welp

Then I may have to think about this one a bit longer

[eternal comet]

It's quite easy actually, but I'll wait for the op to answer my question.

[eternal comet]

Consider that you need any function with an asymptote at x = -4, and which does not have a finite limit as x goes to infinity

[tight herald]

Hmm

@eternal comet Is it just (x + 4)^x

[eternal comet]

,w plot (x + 4)^x

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Remavas#3737

[tight herald]

Bruuuu

[eternal comet]

Thanks for the amazing bounds wolfram

,w plot (x + 4)^x from -5 to 1

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Remavas#3737

[tight herald]

TF?

[eternal comet]

Seems like it will work

[tight herald]

I guess

Looks awful though

[eternal comet]

A much easier option

[tight herald]

@eternal comet What would be the proper solution

Or easier*

[eternal comet]

I immediately just thought of $\frac{1}{x+4} + x$

[wraith dagger]

Remavas

[mighty drift]

1/(x+4) + x has that same vertical asymptote but no horizontal asymptote

Same

[tight herald]

Hm

[eternal comet]

It behaves as x when x goes to infinity

so no horizontal asymptote

[cedar kiln]

@tulip light 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.

[deep flicker]

Thanks! Sry i was sleeping

[deep flicker]

.close

[cedar kiln]

Channel closed

Closed by @deep flicker

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

Closed due to the original message being deleted

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.

[marble bone]

Say it?

Is it asking the minimum number of members needed for the condition to yield?

I see

Hint :- Just let the number of members needed to be x

And try to see if u can come up with a formula

Like when the costs at both places are equal

That has to be the threshold

[crimson sedge]

Just looking at the ice rink case "Lizzy would pay $40 plus $18.25 per person" what is a very obvious word we can replace with a math symbol such as (+, -, *, /)

[cedar kiln]

@golden lion Has your question been resolved?

[cedar kiln]

@golden lion Has your question been resolved?

[cedar kiln]

@golden lion Has your question been resolved?

[cosmic steppe]

First, Write the equation for the ice skating

@golden lion ^

[cedar kiln]

@golden lion 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.

[deep flicker]

Just a question, if A Cone and A Cylinder were combined into one shape and I was asked for the surface area, it would be (2 x pi x r x h) + (pi x r x l) but if it were only the cylinder and I was asked to find the surface area, it would be 2 x pi x r x h + 2 x pi x r^2 right

[languid ember]

<@&286206848099549185>

[cedar kiln]

@deep flicker Has your question been resolved?

[lethal jackal]

no, if they're combined you still need to add the area of the base that isn't covered by the cone

[deep flicker]

Oh yea I forgot about that thanks!

[glass blade]

Imma do the first for you
You do the rest
f(x) = 9x-3
Let y=f(x)
y=9x-3
y+3 = 9x
(y+3)/9 =x
Thus f-¹(x) = (x+3)/9

[deep flicker]

.closr

.close

[cedar kiln]

Channel closed

Closed by @deep flicker

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.

[rustic sedge]

In -x³ if x=10 do i do it like -(10)³=-(-1000)=1000 or (-10)³=-1000?

[inland quartz]

It will be -1000.
-(10)^3
-(1000)
-1000

[rustic sedge]

Ah i see

Thank youu

.close

[cedar kiln]

Channel closed

Closed by @rustic sedge

Use .reopen if this was a mistake.

[rustic sedge]

A company's profit is determined by the function P(x)=-x(x-10)(x-30) where P=profit x=branches operated

Do i first turn -x(x-10)(x-30) into -x³+40x-300?

If so then if x=10 would the answer be -900 meaning the company lost -900 profit?

[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.

[rustic sedge]

A company's profit is determined by the function P(x)=-x(x-10)(x-30) where P=profit x=branches operated

[rustic sedge]

Do i first turn -x(x-10)(x-30) into -x³+40x-300?

If so then if x=10 would the answer be -900 meaning the company lost -900 profit?

[lethal jackal]

that is not a complete question

you have simply stated something about a company

what problem are you trying to solve?

[rustic sedge]

I believe i sent further message

Do i first turn -x(x-10)(x-30) into -x³+40x-300?

[lethal jackal]

no I saw your message

but here's the thing

[rustic sedge]

Oh

[lethal jackal]

math questions aren't some random language

they're English or whatever native language you want

just stating

A company's profit is determined by the function P(x)=-x(x-10)(x-30) where P=profit x=branches operated
doesn't tell anyone what you're trying to do or why this matters

If someone walked up to you and said "Apple made over $100 billion last year," you'd be like "okay, why are you telling me this?"

the same applies here

[rustic sedge]

Oh

[lethal jackal]

you do mathematical manipulations / mathematical steps to achieve a particular goal

[rustic sedge]

Sorry

[lethal jackal]

not just because they're "correct" or whatever

so is there more to the question?

[rustic sedge]

Do i first turn -x(x-10)(x-30) into -x³+40x-300 so i can find out what the result is if x=10?

Or do i just substitute 10 into -x(x-10)(x-30)

[lethal jackal]

again

you haven't stated a complete math problem

To go back to my example about Apple, what you're doing here is saying something like "Apple made 162.75B in the 12 months of 2021," and then asking, "do I write that number as $162,750,000,000.00 or do I write it in scientific notation, or do I subtract 40% from it?"

[rustic sedge]

A company's profit is determined by the function P(x)=-x(x-10)(x-30) where P=profit x=branches operated

Evaluate the polynomial function for x=10?

[lethal jackal]

what is the actual question being asked

like if you have an actual screenshot of it, it would be much easier

[rustic sedge]

Alright

[lethal jackal]

okay I hope you realize that this bottom part is very important

it tells you what you actually have to do

[rustic sedge]

Yes

I know

[lethal jackal]

just pasting the top part means nothing by itself

would've saved a good 5 minutes if you had pasted the bottom part

[rustic sedge]

Sorry

[lethal jackal]

to do part 1, all you have to do is plug in 10 for x

[rustic sedge]

So no need to turn -x(x-10)(x-30) into x³+40x-300?

If i solve it through plugging in 10 for x in -x(x-10)(x-30) it results in 0?

If i plug in 10 for x in -x³+40x-300 it results in -900?

[lethal jackal]

,w expand -x(x-10)(x-30)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Saccharine#3780

[lethal jackal]

First of all, you have not expanded it correctly

[rustic sedge]

Oh i missed x²

[lethal jackal]

and the x

[rustic sedge]

Ye

Sorry

Lemme solve it really quick

[lethal jackal]

Second, these are two ways of writing the exact same thing

[rustic sedge]

Ah

Sometimes i solve using both so that i can be sure my answer is correct

Its 0?

[lethal jackal]

it is indeed zero

(x-10) = 0 if x = 10

so you get P(10) = (-10)(0)(-40)

[rustic sedge]

So the company doesnt get any profit if they operate 10 branches

[lethal jackal]

yes

[rustic sedge]

And if x=20 its 2000

[lethal jackal]

yeah

[rustic sedge]

And because it says "a company's profit in thousands of pesos..." Its 2,000,000?

Alright thank you

.close

[cedar kiln]

Channel closed

Closed by @rustic sedge

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.

[open moss]

Integration

Just wanted to ask if I actually do this step with log

[upper garnet]

what did u eggen do

even

[open moss]

Like when we intregate nested functions
The derivate of the second one is divided below

🤡

And if we can't whats the reason behind it

Shii

Opposite

[upper garnet]

idu what u mean

[eternal comet]

me neither

[open moss]

Blurred

[eternal comet]

must be a new type of integration

[open moss]

[upper garnet]

u need to use exponential form of trigonometric functions to wovle it

solve

[upper garnet]

then substitution, afterwards ibp, then partial decompision, and then u have to use a special integral

[open moss]

Isnt there a chain rule for intreagation
Can we use it on log like this?

[upper garnet]

no

[eternal comet]

no

[upper garnet]

do u mean integral of logxsinx

[open moss]

Yes

[upper garnet]

because log(sinx) is not an elementary function

[eternal comet]

I assume log(sinx)

Oh wait

Well that explains a lot

[upper garnet]

doesn't have an elementary integral *

use ibp

[open moss]

K thnx for the terms
Will learn about them rn

[eternal comet]

As a side-note, if you mean to logx

write logx

[open moss]

K

[eternal comet]

Just out of curiosity

,w integrate ln(sinx)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Remavas#3737

[upper garnet]

it's big

[eternal comet]

beautiful

[open moss]

F

[upper garnet]

it's doable except first term if u don't know special integral Li

[eternal comet]

Hm, I knew li

but not the polylogarithm

[astral crown]

this one's a famous one tho

you can creatively use the bounds to find the integral

you dont need to do the ususal indefinite integral then plug in bounds

[cedar kiln]

@open moss Has your question been resolved?

[cedar kiln]

@open moss 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.

[coarse hearth]

shoundnt it be (cos 2 pi/n)^2+sin(2 * pi/n)^2

and not whole sqaure

how is it whole square?

.close

[cedar kiln]

Channel closed

Closed by @coarse hearth

Use .reopen if this was a mistake.

[turbid lynx]

try looking up de moivre

[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.

[rugged vine]

hi there i am stuck on proving the statement in blue

i know that for c=1 and n>=5 or 4, the statement is obviously true but how do i rigorously show that?

i tried to work with logarithms but that didn't really lead anywhere

any thoughts?

i looked up a similar proof on mathstackexchange but i am confused by the answer on there

https://math.stackexchange.com/questions/488099/how-to-prove-2n-omega-nk

[crimson tundra]

What about some induction? Show that the statement is true with n+1 by asserting that it is already proven for n, and you can show all of it with just one real calculation.

[rugged vine]

interesting. i didn't consider using induction

actually yeah now that i think about it, this would b easier to prove with induction

but how do i determine when or when not to use induction lmao?

[crimson tundra]

Intuition
If you have some always-repeating thing, like >, so valid "to infinity", induction is usable. No idea when it makes sense/doesn't make sense to use though.

[rugged vine]

lol got it

i was having a real hard time proving this directly. been trying it for more than 50 mins smh

but thanks for clearing up the confusion

.close

[cedar kiln]

Channel closed

Closed by @rugged vine

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.

[coarse hearth]

this is the formula for the sum of n roots?

[eternal comet]

I assume they were referring to this?

[turbid lynx]

that one yes

[coarse hearth]

ahhh

so we jsut used geomtric progression formula and we arrived with this?

cool thanks guys

.close

[cedar kiln]

Channel closed

Closed by @coarse hearth

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.

[ashen olive]

Hey there

[ashen olive]

I have a question in sets theory

It's this one:

"a set A in R will be called bounded if there exists M in R s.t. for every a in A : |a| <= M.

Let B be the set of bounded sets. Prove that B ~ P(P(N))

So using cantor's theorem we have to show 2 one to one functions

one is easy: |B| <= |P(R)|

but the other side.

idk how to do that

[cedar kiln]

@ashen olive 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.

[cedar kiln]

Channel closed

Closed due to the original message being deleted

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.

[elfin trout]

hey can you please help me finding these differential equations

[glossy mist]

Do you know how to solve a first order DE?

And what form you need it in

Qs 2 3 and 4 give you a good hint towards how you need to manipulate Q1

[elfin trout]

unfortunately dunno

[glossy mist]

That seems pretty important knowledge for this piece of homework 🙁

[elfin trout]

should just take integral of it

should I*

[glossy mist]

No

[elfin trout]

can you help me if you have time

[glossy mist]

https://youtu.be/zi2vx-ImISU

I like this series on DEs. Covers everything you would need to know for first order in A-Level Further Maths here in England - should be applicable to yours too

Basically there is a process to follow and it usually just pops out nicely. I'm not going to do your questions for you though, but I am happy to check your work

[elfin trout]

I am watching them now

[glossy mist]

Sounds good

[elfin trout]

so for the firsy q will I take integral of sqrt(1-y^2)/xsqrt(x^2-1)

[cedar kiln]

@elfin trout Has your question been resolved?

[elfin trout]

@glossy mist hey! If you are available can you check my question cause I am still struggling

[cedar kiln]

@elfin trout Has your question been resolved?

[cedar kiln]

@elfin trout Has your question been resolved?

[wicked vector]

Can someone help me with #9

[elfin hemlock]

#❓how-to-get-help

[languid ember]

@elfin hemlock help

[dire geode]

read #❓how-to-get-help

[cedar kiln]

@elfin trout Has your question been resolved?

[dire geode]

.close

[cedar kiln]

Channel closed

Closed by @dire geode

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.

[formal nest]

Hi everyone how do i find the partial derivatives of (-15,30) ?

[tranquil oracle]

that doesn't seem to be something you can find the partial derivative of

you need a function

[formal nest]

can’t i use the definition?

There must be a way since there is an answer

Its 1.3

[tranquil oracle]

it seems they want you to estimate the derivative

[formal nest]

Yea

[tranquil oracle]

so, yeah go to that point and try out the smallest h you can try given your table

[formal nest]

?

What

Would h be an t value for the first one ?

[formal nest]

What does that mean ?

[tranquil oracle]

go to (-15, 30) on your table, that's f(x, y)

find values that are f(x+h, y) for small h that are in your table

[formal nest]

What is h ?

[tranquil oracle]

some number

[formal nest]

I don’t understand

[tranquil oracle]

what values do you have in your table that are f(-15+h, 30) for |h| small?

[formal nest]

-33 ?

Or -20 ?

[formal nest]

Is -33 good ?

[tranquil oracle]

yeah, nearby values are good

[formal nest]

Then what do I do?

[tranquil oracle]

apply the definition

[formal nest]

It gives me 1

[tranquil oracle]

how did you get 1

[formal nest]

-33+26/7

[tranquil oracle]

where did you get 7 from

[formal nest]

Its h

[tranquil oracle]

h is the change in temperature right?

[formal nest]

-33-(-26)

=-7

[formal nest]

Is this right ?

[tranquil oracle]

this isn't the change in temperature, it's the change in the output of the function

[formal nest]

Then how do you find h ?

[tranquil oracle]

h is a change in the input

[formal nest]

Wuuut i rly dont understand

Could you elaborate?

[formal nest]

How do i find the change in inpout

[tranquil oracle]

-33-(-26) is a change in the output of the function

[formal nest]

Whats input ?

[tranquil oracle]

what values you put into the function

[formal nest]

-15,30 ?

-33+26/-5

=1.4 its still not 1.3

[tranquil oracle]

try out the other side

(-10, 30)

[formal nest]

because its smaller ?

[tranquil oracle]

well, it's as far apart as the first one

[formal nest]

6 and not 7 ?

[tranquil oracle]

so maybe it's worth trying out to see as well

(-10, 30) and (-20, 30) are "equally far" from (-15, 30) so maybe both should be used to calculate the result

[formal nest]

Was my calculation good ?

The other gives me 1.2

@tranquil oracle do i make the average?

1.2+1.4/2

[tranquil oracle]

yeah that's reasonable to take an average

yeah that's the main idea

[formal nest]

Ok thanks

[formal nest]

Btw do you know how to solve this limit

do i apply the same strategy?

[tranquil oracle]

well, it depends on how f is defined

[formal nest]

This question is related to the previous

[tranquil oracle]

same f as previous function?

[formal nest]

yes

Wasnt the partial derivative -0,15

[tranquil oracle]

try out those difference quotients for big v

[formal nest]

i did the same as the last problem but got -0,15

[tranquil oracle]

what did you do exactly?

[formal nest]

the answer is 0

[tranquil oracle]

or technically you can argue physically and say that the answer is undefined

[formal nest]

Well last time we dis question a) but we only did half the question only for T

I repeated what u told me and got -0,15 for v

But doesnt f decrease by 0,15 degree for every 1km/h of wind

so why is the answer 0 ?

[tranquil oracle]

okay from a "just try out the table" approach, try doing it for bigger and bigger v

because there's the lim v->infinity

[formal nest]

so i use f(any T, big v) ?

[tranquil oracle]

yeah, try it out

the result should be a function in terms of T

[formal nest]

i still got -0,15

What do i do ?

[tranquil oracle]

where did you try it out?

[formal nest]

On (-15,50)

[tranquil oracle]

try more of it throughout the table

try bigger v

[formal nest]

Ughhhhhhh i hate this problem

ok

I got -0,1

So we assume it decreases to infinity

To 0

[tranquil oracle]

that's what they want you to think

but velocities are capped by the speed of light

so the limit is not defined

[cedar kiln]

@formal nest Has your question been resolved?

Channel closed

Closed by @formal nest

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.

[marble latch]

Der

[marble latch]

For q23 i

b is supposed to be 1, but I got 2 :((((

Nvm

.close

[cedar kiln]

Channel closed

Closed by @marble 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.

[echo oxide]

hello! In the case of the denominators for geometric sequences, you use 1-r in the case that r is greater than one, and r-1 in the case that r is less than negative one? I'm really sorry, but I can't find my notes confirming or denying

[tranquil oracle]

i'm not sure what you are mentioning exactly, are you trying to expand out (1/(1-r)) in powers of 1/r?

[echo oxide]

sorry! to clarify- the sum of geometric sequences

in the formula for that, the denominator?

[tranquil oracle]

the formula can be the same in both cases

$\sum_{i=0}^kr^k=\frac{1-r^{k+1}}{1-r}=\frac{r^{k+1}-1}{r-1}$

[wraith dagger]

Element118

[echo oxide]

wait okay sorry one second just checking bc the answer key alternates using both and I was confused

ohh

okay thank you so much!!

.close

[cedar kiln]

Channel closed

Closed by @echo oxide

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.

[lucid bolt]

Hi, i don't get why these two expressions are the exact same.

[queen horizon]

the result?

[cosmic steppe]

Show the whole graph

[lucid bolt]

The function

[cosmic steppe]

Like the functions it graphs

Unless you're asking if they're the same exact function

[lucid bolt]

They are. I checked on desmos

Gimme a sec

[cosmic steppe]

Well yeah I also graphed it, and I'll tell you why

[queen horizon]

yeah the graphc is same

[cosmic steppe]

Factor out the 2, but because you're factoring from an argument that is being squared, square 2

And you get 4

Esssentially, you're dissecting the function:

(2x - 1)^2 = 2^2 • (x - 1/2)^2

[obsidian coral]

The other thing you can do is, expand each one and you'll see that they are the same

[cosmic steppe]

@lucid bolt you understand exponent properties right

[lucid bolt]

Ohhhhh I see. You factor our the two. But can you write out 2^2 outside the paranthesis?

[queen horizon]

4(-1/2)^2
1^2 = 1

[cosmic steppe]

Yeah

[queen horizon]

just insert any x value

thats why the graph is same

[lucid bolt]

That Also works. Yeah.

Thanks guys. This was very helpful!

[queen horizon]

you can close the channel if you are done

[lucid bolt]

Sure

.close

[cedar kiln]

Channel closed

Closed by @lucid bolt

Use .reopen if this was a mistake.

[cosmic steppe]

No problem

[atomic spoke]

Is this open?

[cosmic steppe]

Yup it should be

Idk why the channel didn't open

Uh

Wait a bit

[atomic spoke]

alr

[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.

[elfin cypress]

I'd like the formula and while im trying to answer it, please let me know if im doing my solution right

[obsidian coral]

There's not really a formula

It's just ratios

[elfin cypress]

yes but i want the formula on how to get the ratio

[obsidian coral]

As I said, it's not a formula

They're ratios

Do you know what a ratio is?

[elfin cypress]

okay im sorry, how do i solve it?

[obsidian coral]

Using ratios

[sick ruin]

@elfin cypress lmao this dude

[elfin cypress]

thats exactly my problem..

[obsidian coral]

As I questioned, do you know what a ratio is?

[elfin cypress]

yes i do but how exactly will you find the height?

[sick ruin]

@obsidian coral knowing what ratios are doesn’t necessarily help

Hmm

[obsidian coral]

You wanna help, feel free. I got stuff to do

[sick ruin]

Ok, lol

Uhhh hm

[elfin cypress]

assuming volume is linear in height and base area, then the ratio FigA:FigB will be 2.1:1 since 42.25/20.25=2.1

so the volume of A if B is 50 is 50*2.1 = 104.3

if volume of A costs 216 then volume B wiill cost 216/2.1 = 102.8

did i get it right?

<@&286206848099549185>

[sick ruin]

Hmm

No no

Let’s do (a) first

It’s actually an interesting question, despite the boring problem context

[elfin cypress]

so i got something wrong?

[sick ruin]

Well yeah but

Actually

[elfin cypress]

enlighten me

[sick ruin]

Honestly I’m not like 100% sure but I’m pretty sure

Okay let’s go on a little side trip

(Gimme a sec)

[elfin cypress]

thank u

[sick ruin]

Let’s say we’ve got two squares here

The small square has a side length of 1, and the big square has a length of 2. So the ratio between these lengths is 2 : 1, or simply 2.

What are the areas of these squares? @elfin cypress

[cedar kiln]

@elfin cypress 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.

[steady salmon]

hello! i don't know why my answer was wrong. please let me know if there's a part of my solution that i should fix (to be fair, it is kinda weird that the volume was 0...)

[cedar kiln]

@steady salmon Has your question been resolved?

[tranquil oracle]

consider 3x+5y+2z for your points

[steady salmon]

wait where do i use this for??

[tranquil oracle]

apply them on P, Q, R, S

what do you notice

[steady salmon]

oh i see lemme check

[steady salmon]

all of them resulted to 5 :0

how did you get that equation??

[tranquil oracle]

well, I tried to figure which plane ax+by+cz=d they all lie on

[steady salmon]

oh gotcha! thank you so much for the help!

.close

[cedar kiln]

Channel closed

Closed by @steady salmon

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.

[tough osprey]

$\int_0^{2\pi}\int_0^{\pi}\int_0^{\infty}r^2(C\frac{r}{a_0} exp(\frac{-r}{4a_0} \cos\theta))^2 \sin\theta dr d\theta d\phi=1$

[wraith dagger]

Trenton

[tough osprey]

I am solving this equation

So normally I will solve the boxed part first :

$\int_0^{2\pi}\int_0^{\pi}\boxed{\int_0^{\infty}r^2(C\frac{r}{a_0} exp(\frac{-r}{4a_0} \cos\theta))^2 \sin\theta dr} d\theta d\phi=1$

[wraith dagger]

Trenton

[tough osprey]

But my lecture notes solve the outer part first

And I am not quite follow what is happening in the fourth line

Can anyone tell me what happens?

And why can we do that ?

[cedar kiln]

@tough osprey Has your question been resolved?

[cedar kiln]

@tough osprey Has your question been resolved?

[cedar kiln]

@tough osprey Has your question been resolved?

[cedar kiln]

@tough osprey Has your question been resolved?

[vocal fulcrum]

from the 4th line to 5th line ?

if so

the outer integral is dr therefore everything that doesn't have a r is a constant to this integral

so he takes out all those terms that don't have a r which is that cos^2 * sin

[tough osprey]

Ok thank you

[tough osprey]

Can I do similar thing for this?

[tough osprey]

I mean this, can I do this?

[foggy merlin]

yes

[tough osprey]

Ok thank you, I will continue

[tough osprey]

So I continue and get this

Am I correct?

[tough osprey]

Umm can anyone help me to have a look please

[dire geode]

You can check by plugging C into your original integral

[cedar kiln]

@tough osprey Has your question been resolved?

[tough osprey]

Ok I found the problem thank you

.close

[cedar kiln]

Channel closed

Closed by @tough osprey

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.

[tough osprey]

I am not sure about F and G

I guess A,B,C,D,E are all correct

[cedar kiln]

@tough osprey Has your question been resolved?

[cedar kiln]

@tough osprey Has your question been resolved?

[cedar kiln]

@tough osprey Has your question been resolved?

[bold hinge]

Does continuity imply differentiability?

[cedar kiln]

@tough osprey Has your question been resolved?

[tough osprey]

I guess same for single variable case?

[flint plinth]

you can rule out several of these by the fact that they are not even true for n=1

[tough osprey]

ok but is it true that ABCDEG all correct? At least I cant find any counter examples

.close

[cedar kiln]

Channel closed

Closed by @tough osprey

Use .reopen if this was a mistake.

[tough osprey]

.reopen

[cedar kiln]

✅

[tough osprey]

Can anyone tell me what is wrong here

[hasty pelican]

Nothing, it says "the answer above is NOT correct" 🤣

Sorry

[tough osprey]

So I am asking about what is wrong lol

[hasty pelican]

answer above

[tough osprey]

………

Alright

[hasty pelican]

I don't think above means below lol

Sorry for wasting your time

[tough osprey]

That is typo for the web page I think

[obsidian coral]

It's not a typo, because if I remember correctly, that site displays your answer above as well

[tough osprey]

Oic ok

[tough osprey]

But can you tell me what is wrong in my choice of answers?

[obsidian coral]

No

[tough osprey]

My partial derivative is really suck

[tough osprey]

.close

[cedar kiln]

Channel closed

Closed by @tough osprey

Use .reopen if this was a mistake.

[tough osprey]

.reopen

[cedar kiln]

✅

[tough osprey]

If all first partial derivatives of $f$ exist on $D\subset R^n$ and are continuous at $\vec{x_0}$, then does it imply that $f$ is differentiable at $\vec{x_0}$?

[wraith dagger]

Trenton

[tough osprey]

.close

[cedar kiln]

Channel closed

Closed by @tough osprey

Use .reopen if this was a mistake.

[tough osprey]

.reopen

[cedar kiln]

✅

[tough osprey]

If $f$ is differentiable at $\vec{x_0}$, does that implies all first partial derivatives of $f$ at $\vec{x_0}$ exist?

[wraith dagger]

Trenton

[tough osprey]

Ok problem solved, thank you.

.close

[cedar kiln]

Channel closed

Closed by @tough osprey

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.

[warm vector]

V =ah
But I don’t know what face area are they referring to.

[dusty hazel]

All of them.

Together.

@warm vector

[warm vector]

Oh

So I use the area of the curved cylinder right?

[dusty hazel]

Yes, and there are three such cylinders.

If that helps.

[warm vector]

And do I times that by the perpendicular height which is 6+6+6

[warm vector]

Ye ok

[tropic oxide]

your cake is composed of 3 cylindrical pieces

find the volume of each and add them up

just as you would find the volume of any other 'composite' shape

[warm vector]

Instead of using the volume formula?

[dusty hazel]

Wdym? You will require the volume formula to calculate the volume of each cylinder.

[warm vector]

Yes but I mean v=ah

[dusty hazel]

Yes.

[warm vector]

Instead I could just find the volume of each cake and add that up

Would that work

[dusty hazel]

That's what Ann said too.

That would work perfectly.

[warm vector]

Yh that’s also what I meant ok

[dusty hazel]

Alright great then.

[warm vector]

Thanks for help

.close

[cedar kiln]

Channel closed

Closed by @warm vector

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.

[warm vector]

I don’t understand how to do this question

[warm vector]

I subtracted 5 from all sides and then calculated the volume but I’m still getting it incorrect so maybe my technique is wrong

[dusty hazel]

That is incorrect.

You don't have to subtract from all the sides.

[warm vector]

Then what should I do?

[dusty hazel]

Water is filled 5cm below the top
No change with the other two dimensions.

[warm vector]

Oh

[dusty hazel]

Imagine a tank, which is not fully filled.

[wispy talon]

If you're filling a bottle till 3cm below it's limit, do you have empty gaps in the sides or the base of the bottle?

[warm vector]

Only the height then

[warm vector]

No

That means the change is the height

[wispy talon]

✅

[warm vector]

Ok I got it thanks

.close

[cedar kiln]

Channel closed

Closed by @warm vector

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.

[azure magnet]

@leaden snow

[azure magnet]

R u free rn man?

[leaden snow]

sup

[azure magnet]

I'll post question

Do u mind if i @ u for help sometimes. I really liked ur explanation

But here is the tant from yesterday

[leaden snow]

cos^2(x)?

[azure magnet]

does tant not just go to sec^2?

[leaden snow]

post the full problem

[leaden snow]

Oh this one

I remember

[azure magnet]

yeah

So I got a thanks to u

but tan is a bit different cause my first is 0 and my 2nd is 1 and my 3rd is 0

[leaden snow]

Yeah so you need more terms

until you get 3 non-zero terms

[azure magnet]

KK

I'll do it and then I'll check with u if that's alright

[leaden snow]

@azure magnet You could also find the first few terms using the Maclaurin series for sin and cos

If the derivatives get too nasty for tan

[cedar kiln]

@azure magnet Has your question been resolved?

[azure magnet]

Wait a min

amn't I meant to divide by n! here

on each term

@leaden snow

I just used a differential calculator

But I gotta divide by N! on each term then????????

[leaden snow]

@azure magnet
$$\tan(x) = \sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!} x^n$$

So yes, you have to

[azure magnet]

Oh shit

[wraith dagger]

Navix

[azure magnet]

so if I divide by n!

I'll get the right answer then

pog

[leaden snow]

You should have calculated
$$f^{(0)}(0)$$
$$f^{(3)}(0)$$
$$f^{(5)}(0)$$

[wraith dagger]

Navix

[leaden snow]

So one is for n=0, one is for n=3 and one for n=5

[azure magnet]

thanks

and for

I use the first 3 terms only

right that should work out nicelt

I got one more question for u man

this

so I use I hopital I diff the top and bottem (2nd fraction)

and end up with picospix/1

if I sub in 0 I get the answer to be 1

It seems a bit too easy for 4 marks each roughly (both fractions)

[upper abyss]

Have you been taught L'h?

You can do these by expanding e^(2x) and sin(πx)

[azure magnet]

Yeah

L hopital

pi sin pix /1

and u sub in 0

but Idk if the answer is 1 or pi

I wish I could write in latex

[cedar kiln]

@azure magnet Has your question been resolved?

[cedar kiln]

@azure magnet Has your question been resolved?

Channel closed

Closed by @azure magnet

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.

[gaunt lake]

can anyone help me with this physics qn?

[leaden snow]

@gaunt lake So work is Force * Distance right.

Essentially you want to estimate the area under the curve

[cedar kiln]

@gaunt lake 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.

[gaunt lake]

uh yes but how do I estimate it

[gaunt lake]

do I use a triangle?

it also asked me to explain how I made my estimate

so how do I explain why I used a triangle as a formula

@leaden snow

[cedar kiln]

@gaunt lake Has your question been resolved?

[leaden snow]

@gaunt lake You could use a bunch of trapezoids

or a bunch of rectangles

or a triangle, even

[gaunt lake]

...

aight

so what would my explaination be

[gaunt lake]

sounds super long 💀

[leaden snow]

Explain how you decomposed the area under the curve into triangles

For example you could give the coordinates of the points of the triangle

Decompose it into a right triangle and a rectangle below it

[cedar kiln]

@gaunt lake Has your question been resolved?

[cedar kiln]

Channel closed

Closed by @deft venture

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]

can anyoni confirm if my proof is correct?

STATEMENTS
1. AC bisects ∠A and ∠C
2. ∠ABC ≅ ∠ADC
3. ∠AC ≅ ∠AC
4. ⊿ABC ≅ ⊿ADC

REASONS
1. Given
2. Definition of Bisector
3. Reflexive Property
4. By SSS

[livid hound]

is incorrect

[crimson sedge]

🗿

how do i correct it

[livid hound]

apply definition of bisector properly

where is

∠ABC ≅ ∠ADC
coming form

[crimson sedge]

∠ACB ≅ ∠ACD
is it

[livid hound]

that would be more appropriate

[crimson sedge]

ohh why is it

[livid hound]

∠AC ≅ ∠AC
using two letters to denote an angle is also nonsense

[crimson sedge]

oh fuck uh

that's a line right

so there must be a macron on top

ĀC ≅ ĀC

something similae

[livid hound]

$\overline{AC} \cong \overline{AC}$

[wraith dagger]

ℝamonov

[crimson sedge]

so i got only two stuff incorrect?

[livid hound]

rewrite your new attempt

from what you initially wrote, only 1. was correct

[crimson sedge]

STATEMENTS
1. AC bisects ∠A and ∠C
2. ∠ACB ≅ ∠ACD
3. A͡C ≅ A͡C
4. ⊿ABC ≅ ⊿ADC

REASONS
1. Given
2. Definition of Bisector
3. Reflexive Property
4. By SSS

pretend the thing on top is an overline

[livid hound]

is still wrong

where's SSS coming from?

[crimson sedge]

i don't understand the side angle side thing so i just guessed

would it be ASA