help-13

[subtle raven]

Since you just had the partial fractions organised in a different order

It's still okay because it has the same meaning

[wary anchor]

but i got it wrong for question B

[subtle raven]

You only got it wrong because you had B and C in the wrong fractions. Part A should be correct with your ordering

Just follow through with it in part B

Instead of using the form you were given in the question

[wary anchor]

im pretty sure i did follow through with my answer

[subtle raven]

Ok, that's good

Then it's probably just a small mistake somewhere down the line

[wary anchor]

im gonna try again

[subtle raven]

Not sure how you got from line 5 to line 6 in your second image

[wary anchor]

i did 3(-1/3) -2 which is -3

2/3 ln(-3) = ln(-3^2/3)

but ln(-3) gives me undefined

[subtle raven]

BTW you have ln |-3|

Those vertical bars indicate the absolute value

[wary anchor]

so its just 3?

[subtle raven]

So you should be computing ln (3)

Yeah

[wary anchor]

right okay

thats prob where i went wrong

yep that was it

thanks!! :)))))

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[subtle raven]

No worries

[cedar kiln]

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[untold locust]

how do i solve this

[untold locust]

this is all new to me i only know how to solve right triangles

[dusk finch]

do you know cosine law?

[untold locust]

nope

[dusk finch]

https://www.khanacademy.org/math/trigonometry/trig-with-general-triangles

this is whole about non-right triangles and applications of sin, cos etc

[untold locust]

nice

[dusk finch]

You are particularly interested in law of cosines now, but I also recommend law of sines

[untold locust]

is there also a law of tan

nvm anyways thanks

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[dusk finch]

with law of sine and cosine, you can solve for all sides and angles in all the side-side-side, angle-side-angle etc. triangles

I dont think there is law of tan

oh, there is

this one

[cedar kiln]

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[crimson sedge]

Hello, so I'm facing another problem now :
A regular pentagon with apothem length 3.24m and the radius of its circle is 4m.

I know that A=1/2(nsa)
N being number of sides
s being side length
a being apothem
and I also know that perimeter is p=ns, how does one solve this exactly?

[crimson sedge]

I know I have to use pythagoreas theorem to get the side length

but how will I get the number of sides?

[dusk finch]

didnt you say it's pentagon?

sorry if I misunderstood, but since it's pentagon it should have 5 sides

[crimson sedge]

Sorry I meant polygon

[tropic oxide]

radius of its circle...? which circle

circumscribed or inscribed?

ah, wait. no.

it can only be the former.

[crimson sedge]

Doesn't say it anywhere

[opaque root]

Apothem = radius * cos(a); where a=360º/n; where n = number of sides.

apothem = radius * cos(π/n)
3.24m = 4m * cos(π/n)

now solve for n, and you will get the number of sides

if the number you get is not integer, you always raise the number up

so if you get x,0001 it will be x+1

number of side

[crimson sedge]

Ah alright

thank you!

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[thorny granite]

how to show that a sequence is cyclic? and know its period T?
(in my case i have the relation between two consecutives terms U(k+1) = (U(k)+STEP)%MOD and U(0) = some integer (can be anything) )

• well, i knw that bcz it has % MOD in it then it must be cyclic but is there a way in general to show that a sequence is cyclic (or not).
• also another question : the period T can't possibly exceed MOD value right?

*STEP and MOD are const parameters

[thorny granite]

this is the whole problem : (it's cp) :

[cedar kiln]

@thorny granite Has your question been resolved?

[thorny granite]

<@&286206848099549185>

[cedar kiln]

@thorny granite Has your question been resolved?

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[queen sonnet]

-9+6 is -3.

This is because when you add to a negative number, its like subtracting from it as you move up in the numberline.

Try using the same principle.

If adding makes the negative closer to 0, subtracting should do the opposite.

[cold briar]

?

[queen sonnet]

You can make a ticket anytime, but I won't be available any time.

[cold briar]

random question, how old are you?

if you don't mind me asking

<@&268886789983436800>

you can't be below 13 to use discord bro

oh he's gone

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[jagged parrot]

Hi, I’m having problem with this improper integral. How do we use the comparison test for this? Appreciate any help!

[west gazelle]

maybe try factoring e^4x in the denominator

then you’ll get an integral of a sum

the term are positive and the sum converges so you can switch the integral and the sum

then you calculate the integral and you sum the result

@jagged parrot

[jagged parrot]

I’m currently using the same integral, but wth in 3e^x

It’s troubling

Factoring of e^4x gives the correct answer which is divergent, but my school website does not accept that

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[wary anchor]

where did i do wrong?

[west gazelle]

what’s the question

[wary anchor]

second pic

[crimson sedge]

so, what's tripping you up?

imagine the graph

[wary anchor]

the answer is 8/3 and they used a different method

[crimson sedge]

,w graph x(4-x^2)^(1/2)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Renegade#4545

[crimson sedge]

how can we find the area from 0 to 2 of f(x)

[cinder urchin]

they might have used integration

[wary anchor]

thats what i did

[wild spear]

i believe the integral of -1/2 u^1/2 is not -3u^3/2

[wary anchor]

its all integration

[fringe nest]

is there even a different way to do it instead of integration?

[fringe nest]

put limits from 0 to 2

[wary anchor]

oh yeah its 1/3

[wild spear]

-1/3

[crimson sedge]

I was asking the OP

[cinder urchin]

if we know the exact geometry then maybe

[crimson sedge]

but yes, that's correct

[wary anchor]

yh that was it

i just did integration wrong

[fringe nest]

i thought you were the op lol

[wary anchor]

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[south remnant]

what is e^2?

[south remnant]

is it just e*e?

[ancient lodge]

Yes, $e^2=e \cdot e$.

[wraith dagger]

Civil Service Pigeon

[ancient lodge]

@south remnant

[south remnant]

ok

i thought i remember that e^x was something else

[crimson sedge]

$e^x = e \cdot e \cdot \hdots \cdot e$, $x$ times.

[south remnant]

i thought i heard something about exp(x) related to e^x in the past

[wraith dagger]

null

[ancient lodge]

They're the same thing

[south remnant]

ye but exp(x) is a infinite series or something

[crimson sedge]

no

exp(x) is equal to the exponential function

[south remnant]

oh really?

[crimson sedge]

yeah, it's just a matter of notation

[south remnant]

i thought it was 1/1!+...

[crimson sedge]

well, $e^x = 1 + x + \frac{x^2}{2} + \frac{x^3}{3!} + \hdots$, yes.

[wraith dagger]

null

[crimson sedge]

this is just the Maclaurin series for e^x

it approximates the behavior of e^x near zero

[south remnant]

ye this

oh thats all?

[crimson sedge]

yes

[south remnant]

damn

its like the taylor series

[crimson sedge]

that's how e^x is defined as a polynomial

well, Taylor series is a generalized version of the Maclaurin series

the Maclaurin series is centered at x = 0

[south remnant]

ok

[crimson sedge]

The Taylor series, say for $e^x$, is $\sum_{n=0}^\infty \frac{(x-a)^n}{n!}$

[wraith dagger]

null

[south remnant]

ok

thanks for the explanation, have a nice day

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[crimson sedge]

Hello, I have another question, so I know that bN=2, BL=2.5,NL=1.5,KL=3, but in this triangle, how does one get MT, MN, and TC?

[supple forge]

where is MT?

can't see T point

[crimson sedge]

Oop

T is the intersection point

the red dot in the middle

[supple forge]

the one in the middle?

alright

[crimson sedge]

Yep

[crimson sedge]

I'm stuck in getting MT, MN and TC

[supple forge]

No any ideas how to start?

[crimson sedge]

None

[supple forge]

are you sure KL is 3?

[crimson sedge]

Yes

I used the pythagoreas theorem

[crimson sedge]

the two parts are 1.5 so I added them to make the whole thing 3 (MN is the perpindicular bisectors)

[supple forge]

is there more info to this task

[crimson sedge]

Nope

[crimson sedge]

Not anything else

only everything I've said

[supple forge]

hmm, I will let you know if I will know how to

[supple forge]

Is LC equal to KL?

[crimson sedge]

Doesn't specify it.

[supple forge]

on LM line there is sign

by pencil

[crimson sedge]

Oh yeah, that was to show LC=CM

[supple forge]

do you have answers, by any chance?

[crimson sedge]

No idea where to start

[supple forge]

NT is 1:3 of MN

We should work with NL and LC

because it's the only triangle who has known 2 lengths

if we will get NT we could multiply it by 2 and we will get MT

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

Ah alright

thank you

[cedar kiln]

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[spark kiln]

help

[spark kiln]

.close

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[spark kiln]

.reopen

[cedar kiln]

✅

[spark kiln]

$[
f(x) = \sum_{n=0}^{\infty} c_n x^n = \sum_{n=0}^{\infty} (1^{(1-n\mod 2)}\cdot9^{n\mod 2}) x^n
]$

[wraith dagger]

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

[spark kiln]

simply my question is how to define alternation of 9 and 1 into the geometric series representation of the function ?

[modern compass]

5 - 4(-1)^n

when n is even, it's 5 - 4 = 1
when n is odd is 5 - (-4) = 9

[spark kiln]

you're saving my a** tonight man thank you so much have a good night

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[crystal raptor]

test

[crystal raptor]

.close

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[crystal raptor]

.reopen

[cedar kiln]

✅

[crystal raptor]

multiple channel message bypass

.close

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[south tundra]

test

.coose

[cedar kiln]

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[frigid sierra]

im blank

k^2 = 64

Square root

isnt it

±k = ±8

so k = 8 because ± the ' - ' will cancel out ( the " + " cannot ? )

[bright bridge]

no?

[royal loom]

No

[upper garnet]

No

[royal loom]

The square root of 64 is strictly positive 8

yet the square root of k^2 is |k|

[south tundra]

Just one plus or minus

[cedar kiln]

@frigid sierra Has your question been resolved?

[frigid sierra]

So ± does not go to both sides of the equation?

Oh i see

thanks everyone

[cedar kiln]

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[spark kiln]

Help

[spark kiln]

in which step I am making mistake

<@&286206848099549185>

[crude chasm]

@spark kiln

[spark kiln]

☠️

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[warm vector]

With this question

Is this fine?

[cosmic steppe]

Identify the type of curve it is

Sure

But be aware of the t-bounds

Is it parametrized clockwise or anticlockwise

[warm vector]

How do i determine that?

Its a circle right

[cosmic steppe]

x = a cos(t), y = b sin(t) -> anticlockwise
x = a sin(t), y = b cos(t) -> clockwise

[cosmic steppe]

No

[warm vector]

Oh

[cosmic steppe]

It's an ellipse

[warm vector]

I see

[warm vector]

But how will this help in the question?

Like what’s the point of it

[cosmic steppe]

It tells you that the t-bounds simply just follows the direction of the unit circle

Starts on the positive x axis

[warm vector]

Oh

[cosmic steppe]

And because t goes from 0 to pi, it'll end on the negative x axis

[warm vector]

True

Ok makes sense

Thanks

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[night finch]

I have to graph f(x) = 4 times 2 to the power of x, How do I do that?

[upper garnet]

https://www.youtube.com/watch?v=DASfP8KAyvs

[cosmic steppe]

Just choose random points

Random x values

Plot them

Connect the dots

Yield to the horizontal asymptote

[night finch]

Ive watched this but it doesnt rlly help

[night finch]

what about the times four?

[cosmic steppe]

You consider that

Like

Here

What would f(1) be

f(0)

f(2)

And what's the horizontal asymptote

[night finch]

0

[cosmic steppe]

I would get the y-intercept, 2 other points , and the asymptote

[night finch]

oh ok thank you so much

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[gilded rain]

have a question to share.... A transporter company has THREE 30-passenger busses and NINE 15-passenger buses. The company contracts to transport more than 120 passengers a day to national parks. it costs 3000 dollars per day to run each 15 passenger bus ( for example) and the company must spend less than 12000 dollars per day in order to meet costs. If x and y are respectively the number of 30-passenger and 15-passenger buses used each day i. show that 2x+y>8 ii. write down three other inequalities involving x and y iii. illustrate the solution set of the four inequalities on a graph paper and shade the unwanted region

[bright bridge]

!status

[cedar kiln]

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

[gilded rain]

6

[cedar kiln]

@gilded rain Has your question been resolved?

[gilded rain]

nop

[cedar kiln]

@gilded rain Has your question been resolved?

[cedar kiln]

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[sweet moss]

I didn’t get the same answer for x and y… anyone know what I did wrong?

[cedar kiln]

Please don't occupy multiple help channels.

@sweet moss Has your question been resolved?

[carmine bronze]

For "with x", you did not change the bounds for x. You have two different variables, x and u at the end.

[sweet moss]

oh right thank you!

[cedar kiln]

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[stark lily]

https://i.imgur.com/cwyezfA.png

[stark lily]

is this $9 * 10^4 - 9^5$?

[wraith dagger]

Suro

[stark lily]

I just realized

that's a negative number

🤦‍♂️

oh wait

no its not

[mental trail]

Yeah it isn't the correct answer

[mental trail]

What is your reasoning behind this?

[stark lily]

the first digit can't be 0, so 9 choices

then rest of the 4 digits can be 0-9 so 10 choices each

that's how we get 9 * 10^4 total possible 5 digit numbers

then if we want numbers that don't have any 0s

we pick 1 of 9 numbers 5 times

so 9^5

[mental trail]

Yes, correct!

[stark lily]

then the question just wants the difference no?

[mental trail]

Oh I thought the question was asking for all numbers below 100000, instead of 5 digit numbers

Mb

[stark lily]

oh so its correct?

[mental trail]

It is xd

[stark lily]

ok thanks lol had me worried

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[jade stag]

how would you find a's formula using p_o e ^-tk ?

[halcyon marlin]

what is a's formula

you just want it in expontial form with e as base?

[leaden snow]

what the heck is "a"

[lethal jackal]

part a I think

[jade stag]

a_0 is original amount invested

[halcyon marlin]

so p_0?

[jade stag]

teah

yeah

[halcyon marlin]

just use one point of V(t)

to solve for k

or put e^(ln(0.7^t))

[jade stag]

mkay well i found k but what about the -.70 in the e function

8400e^-0.99021 ?

[halcyon marlin]

i dont think -0.99021 is correct

also its a function of t

but you put no t?

first, how did you find -0.99021

[jade stag]

ln(2) / .7

[halcyon marlin]

ok but where did that come from

[jade stag]

ln2/.7

= k

then plugged it into formula

[halcyon marlin]

what steps did you take to get there 💀

im not asking you for a calculation

[jade stag]

i read the problem

and plugged shit in man

not that hard

[halcyon marlin]

is there a formula for k i dont know about?

that is ln(2)/0.7?

[jade stag]

the formula

for doubling time

at decrease

is ln2/0.7

which you agree with correct

? @halcyon marlin

[halcyon marlin]

that would be the halving time if 0.7=k

[jade stag]

-0.99021

[halcyon marlin]

you are trying to find k

you are mixing things up i think

you found the halving time using the variable you are trying to find

and then put the halving time equal to it

just do one of the things two things i suggested

$T_{1/2}=\frac{ln(2)}{k}$

[wraith dagger]

Køter

[halcyon marlin]

i mean you can see here that its not very useful to use this no?

when you dont know T or k yet

[jade stag]

i know what r is

.70

ln2/.7

=t

halfing time

so put nagative

infront

bang

[halcyon marlin]

k is what youre trying to find

if you knew it was 0.7

your answer would just be 8400e^(-0.7t)

you wouldnt need to do anything

and the 2nd problem is thinking k is somehow equal to T_1/2

just do one of the 2 things i suggested 💀

[jade stag]

one of two things u suggested...? where

[halcyon marlin]

like the 1st thing i said

[jade stag]

8400(.70) ^ 9

8400e^-.70(9) ?

or 8400e^(ln2/.7)(9)

? @halcyon marlin

[halcyon marlin]

yes and what is this equal?

[halcyon marlin]

no.

[jade stag]

338

[halcyon marlin]

ok, so you have

338=p_0e^(-kt)

we know the value of 2 of the variables

p_0=?

t=?

[jade stag]

8400

t= (ln (4200/8400)) / -.9902

[halcyon marlin]

jesus

how did you even get the value 338?

8400(.70) ^ 9

[jade stag]

oops im going far ahead

myb

i was solving for c

i told u

how i got 338 man

just plugged it in

[halcyon marlin]

but your answer for t

[jade stag]

using the other doubling formula

[halcyon marlin]

shows me you dont understand

[jade stag]

8400(0.8)^t t=9

[halcyon marlin]

what does the 9 represent

8400(.70) ^ 9

YES

so t=9

[jade stag]

bro im trying to be a good mood today. legit my neck doctor fucked me up real good

like 3-4 months ago

now i gota hump on my neck

i look like a lama

[halcyon marlin]

338=8400e^(-9k)

we knew t and p_0

now you just solve for k

[jade stag]

0.342192472

[halcyon marlin]

sure its a bit inaccurate i think cause 338 is rounded

using 5880 at t=1 would be 100% accurate

[jade stag]

i plugged in more digits

i got .34191

[jade stag]

5880???

t=1?

[halcyon marlin]

8400*0.7^1=5880

[jade stag]

why 1

[halcyon marlin]

you can use any point you want

1 just gives a simple whole number

[jade stag]

o.o

[halcyon marlin]

,w 5880=8400e^(-k)

[wraith dagger]

Results provided by WolframAlpha

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Requested by Køter#5504

[halcyon marlin]

,w ln(10/7)

[wraith dagger]

Results provided by WolframAlpha

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Requested by Køter#5504

[halcyon marlin]

did you do it by hand or just put it into calc?

the easier way for me is just

[jade stag]

c

[halcyon marlin]

$8400e^{ln(0.7^t)}=8400e^{ln(0.7)t}$

[wraith dagger]

Køter

[halcyon marlin]

do you need to do it by hand and can you?

is just algebra

i think we did it once before

[jade stag]

im in bed rn dawg

pain is so bad

got like 6 sections

to do

by thursday

[halcyon marlin]

ok, well you have your answer here

[jade stag]

idk how ima pull it off

[halcyon marlin]

for furture just do e^(ln()) method its so much easier imo

than solving an equation

[jade stag]

answer is here?

[jade stag]

why is ln up there

[halcyon marlin]

no that was the alternative way of doing it

[jade stag]

and t as exponent on the left

[halcyon marlin]

we literally solved for k right before that tho

which is what you wanted to find

[cedar kiln]

@jade stag Has your question been resolved?

[neat forum]

hey can someone help me with my math

[cedar kiln]

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[brittle field]

chain rule?

i cant just say -sin(2theta) ?

[royal loom]

that you can not

yes use the chain rule

[cedar kiln]

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[brittle field]

.close

[coral surge]

help

[coral surge]

this would be -ve 4 or +ve 4?

what should I take?

[subtle raven]

Well you've done one case, namely x <= -4

And your working seems okay

You gotta do the other case now

Namely x > 4

You haven't done anything wrong so far

[coral surge]

i am asking on what basis i am taking -ve 4?

@subtle raven

[subtle raven]

You're taking -ve 4 since that will make the expression x + 4 zero or negative

The absolute value function is defined in cases

Or in a piecewise manner

If x + 4 is negative

Then the only way to make it positive again using the absolute value is to take - (x+4)

[coral surge]

then why again I will take positive 4?

it won't make the expression zero this time

[subtle raven]

It will make the expression positive

I.e: x + 4 is now positive

This is not the same as taking -(x + 4)

In other words, |x + 4| = x + 4

If x > -4

On the other hand, if x <= -4 we have |x + 4| = -(x + 4)

[cedar kiln]

@coral surge Has your question been resolved?

[cedar kiln]

@coral surge Has your question been resolved?

[cedar kiln]

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[inland creek]

help

[wet bay]

ok

[inland creek]

i dont get

it

[royal loom]

Which question?

[wet bay]

lets do an easy one first, $x/2+x/3$

[wraith dagger]

Helen Granda Musa

[wet bay]

do you know how to solve it

[royal loom]

you can input fractions like this btw helen $\frac{x}{2}$

[wraith dagger]

AustinU

[wet bay]

oh ty

but / is much more easier so lol

[wet bay]

$\frac{x}{2}$+$\frac{x}{3}$

[wraith dagger]

Helen Granda Musa

[inland creek]

what

[inland creek]

uhh

[wet bay]

try solve for the question i provide

[inland creek]

5x/6

right

[royal loom]

yes, and what process did you use to figure that out

if you could write them out step by step

[inland creek]

uhh

i made the denominators

the same

like

2x3 and 3x2

and the the numerators would be liek

[royal loom]

Yes, I get what you are saying

[inland creek]

3 x x and 2 x x

oh

[royal loom]

What is stopping you from doing the same for the questions above?

[inland creek]

uh

oh

[wraith dagger]

AustinU

[inland creek]

bc

the asnwer

says its like

39a / 70

[royal loom]

then you are looking at the wrong question

this doesn't involve any "a"s

[inland creek]

oh

oh

okay also

i dont get part. c

@cedar kiln

[cedar kiln]

@inland creek Has your question been resolved?

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[final lily]

How do I find a and b

[wet bay]

where is k?

plug x value into the function

[final lily]

Beside the function in the question

When x cannot be k

I plugged it

[wet bay]

what you get

[final lily]

Is it like this?

[wet bay]

yuup

and for x=2

[final lily]

How do I find a n b

Oh wait

[wet bay]

do the same things

you will get 2 functions contain a and b

i think you are able to solve it when i saying that

[final lily]

Let me try

@wet bay is a = 1?

[wet bay]

show me your work

[final lily]

Looks correct?

[wet bay]

looks decent, anything else that has question?

[final lily]

Only this question for now

Tysm

.closed

.close

[cedar kiln]

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[exotic verge]

Quick rref question

[lethal jackal]

that is the rref

[exotic verge]

Why is that like

allowed tho?

[lethal jackal]

wdym what is allowed

that is literally the rref

[exotic verge]

Well

When u have a row of all zeros

I only have 1 pivot

which is in column 1

so like.. now i'm done?

why?

[lethal jackal]

if you compute the rref of the original matrix, you get that matrix

[exotic verge]

yes

[lethal jackal]

not sure what you're asking

[exotic verge]

lol

nvm

.close

[cedar kiln]

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[long swan]

so what is the significance of the trace of a matrix? like i get that it's the sum of diagonal elements (or sum of eigenvalues) but i don't see the significance

[royal loom]

the significance is all in its connections to other topics

like you said that it is the sum of the eigenvalues

It's properties are what are important

[long swan]

so?

[royal loom]

So?

[buoyant latch]

i mean that's like asking what's the significance of the determinant of a matrix

[royal loom]

^

[buoyant latch]

it relates a bunch of the properties of said matrix together

[royal loom]

All that matters are the properties and the things that it tells you

[buoyant latch]

that's what's important about it

[long swan]

yeah and i have a pretty good answer for that. it's the signed volume of transformation

but what does the trace tell you

[buoyant latch]

matrices dont have to be from R3 to R3 though

[long swan]

just using the word 'volume' generally speaking

[royal loom]

https://en.wikipedia.org/wiki/Trace_(linear_algebra)

This tells you a ton of properties about the trace of a matrix

[tropic oxide]

trace doesn't have a geometric meaning does it

[buoyant latch]

i mean if u rref it it relates to the det which does have a geometric meaning

[royal loom]

the trace is the infinitesimal version of the determinant.

[solid juniper]

it's used in a formula for characteristic polynomials

[long swan]

i'm not seeing it

[cedar kiln]

@long swan Has your question been resolved?

[clear berry]

Trace has some interesting invariant properties

for example, trace(AB) = trace(BA)

it doesn't change during transpose, conjugation etc.

[long swan]

yeah but like why does it matter

i think ann was onto something mentioning the geometric interpretation (if there is any?)

[cedar kiln]

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[cosmic steppe]

Wondering why they let 0 <= t <= 2

[cosmic steppe]

Btw their log is basically ln

Oh wait I'm dumb

.close

[cedar kiln]

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[cosmic steppe]

Real genius moemnt

[mighty drift]

Umbra > Feynman

[cedar kiln]

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[plush tartan]

So, I'm working on a math paper about how derivatives can be used to maximize the surface area to volume ratio of a cell to optimize the efficiency in which substances can travel across the cell membrane. The scope of my paper only covers a perfect sphere so I'm using derivatives to find a radius that gets me the largest surface area to volume ratio possible of that sphere. My constraint is 100 micrometers since that's the largest a cell can get (an ovum).
So far, I've taken the formula for the surface area of a sphere (4πr^2) and divided it by the formula for the volume of a sphere (4/3*πr^3). From there, I got my new formula (A/V) and that was 3/r. Then, I found the first derivative and found it to be -3/r^-2. After, I set that equal to 100, which is my constraint, and now my radius is going to end up being the square root of a negative number.
Now, I'm not sure how to fix that and where I am to go from there.

[cedar kiln]

@plush tartan Has your question been resolved?

[crimson sedge]

I'm using derivatives to find a radius that gets me the largest surface area to volume ratio possible of that sphere.
Why use derivatives to find that? The theoretical largest surface area to volume ratio in a sphere would be just when radius approaches 0. It's equal to 3/r as you said. Essentially, the smaller your sphere is, the higher the A/V ratio. So A/V will be largest at the smallest possible cell radius i guess

[plush tartan]

That's what I've been noticing but my paper requires me to use some sort of calculus. And this topic was suggested to me by my teacher and now it's too late to go back. But I get what you're saying. Is there anyone to fix this? Do you suggest something else other than derivatives?

Sorry if my questions are vague I just really don't know what to do

[crimson sedge]

I don't understand where your teacher wanted you to use calculus in this case. I think he was referring to a different problem entirely?

[plush tartan]

Well for these papers we need to choose a topic. Each class we have has like a big paper and we choose a topic. But since this paper is for my math class, I need to do math that is included in the curriculum of our class, not something easier. She thought it would be good to optimize a cell's surface area to volume ratio using derivatives since that's what we are currently learning.

[crimson sedge]

https://www.khanacademy.org/science/ap-biology/cell-structure-and-function/cell-size/v/surface-area-to-volume-ratio-of-cells
I found this. I hope this helps.

[plush tartan]

Let me check it right now

[crimson sedge]

I think your teacher rather wanted you to prove that a sphere has the highest S/V ratio, compared to other symmetric 3d shapes with equal volume and no holes.

[plush tartan]

tbh i think she just didnt check that this wouldnt rlly work out in the end

the video you sent kind of just confirmed that i did 3/r right but

[crimson sedge]

yeah

[plush tartan]

like you said before i dont think there's much i can do other than show what happens when the radius increases and decreases

i saw smthn that said i could make estimates with the newton-raphson method or the bisection method but that doesn't seem like it'll work since a smaller radius is just better all the time

[crimson sedge]

yeah smaller is always better in this case

the smallest cell radius possible, is the solution

[plush tartan]

So to make sure my paper at least looks good should I just show how the derivative doesn't do much and show some kind of graph or?

i just need to finish the paper and ive basically run out of time

[crimson sedge]

I think you should try showing this if you want to

[crimson sedge]

yeah

[plush tartan]

is there anyway to use calculus to do that?

[crimson sedge]

https://math.stackexchange.com/questions/1797554/proving-that-a-sphere-has-a-minimal-surface-to-volume-ratio-using-calculus-of-va

check this out

[plush tartan]

alr

sorry bro i think this is a bit ahead of my class 😭

[crimson sedge]

you can just do this instead

goodluck with your paper

[plush tartan]

yeah i might just make do with what i have

thanks anyways man

[cedar kiln]

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[coral surge]

help

[coral surge]

is this correct so far?

[frosty ocean]

Yes

[coral surge]

what should I do with the denominator?

[dull oxide]

Cross multiply

[coral surge]

no

i mean i don't know if the denominator is positive or negative so how can I cross multiply

@dull oxide

[dull oxide]

Consider |x|>2, then 2-|x|<0

Which means it cannot be greater than 1

[coral surge]

yeah...

[cedar kiln]

@coral surge Has your question been resolved?

[cedar kiln]

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[sick flame]

how do I start?

[sick flame]

I know that I have to split up the polynomial but I don't know how

[radiant topaz]

What have you tried

[sick flame]

I don't know

[crimson delta]

Try polynomial division

[radiant topaz]

Yeah

[sick flame]

how

[radiant topaz]

Divide x²-8x+3 by x+2

[sick flame]

I don't know how to do that

[radiant topaz]

Search how to do that

[sick flame]

ok

my test is in an hour💀

[radiant topaz]

That's unfortunate saehi

I hope you do better the next time 🙂

[gritty galleon]

can u factorize the numerator

oh shit its not possible

[radiant topaz]

Polynomial division does it

[cedar kiln]

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[sick flame]

,close

.close

[cedar kiln]

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[last prairie]

bruh

[last prairie]

do i just make q & p the subject of the equation

<@&286206848099549185>

[tropic oxide]

that won't help you much

!15m

[cedar kiln]

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.

[last prairie]

oh mb

[tropic oxide]

you know the 3 roots of your cubic

and you know its leading coefficient (4)

this means you can just write down the equation of the cubic and read the values of p and q from it (after expansion)

[last prairie]

.close

[cedar kiln]

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[wanton summit]

how do i make a new polynomial with roots alpha squared beta squared and gamma squared

[wanton summit]

<@&286206848099549185>

like what algebra manipulations do i use

[last prairie]

do u have an example

my brain is kinda fried

i need to look at an equation

[wanton summit]

these roots

its a cubic question

[livid hound]

can you show the full question

[wanton summit]

thats the polynmial

we are struggling

[last prairie]

so wdym make a new polynomial

[wanton summit]

the question asks to resconstruct a polynomial with roots alpha squared beta squared and gamma squared

we already did the -b/a part

the addition

but struggling with the addition of two roots

[last prairie]

wait is alpha, beta, and gamma the coefficients

soz im australian i just use a b and c

[wanton summit]

so are we

[last prairie]

bruh

[wanton summit]

alpa beta nd gamma are the roots

a b and c are the coefficients

of the polynomial

[livid hound]

get expressions for sum of roots,
sums of products
product of roots
for your original polynomial

[wanton summit]

yes but struggling iwth sum of products

[livid hound]

you'll get a few equations from those

[wanton summit]

like how d you get (ab)^2+(ac)^2+(bc)^2

into terms of abc a+b+c and ab+bc+ac

[wanton summit]

please give more detailed help

[livid hound]

can you show ALL the work you've done so far?

[wanton summit]

none

for this part

we worked out that b of the polynomial is -62

which is the x square term

[livid hound]

ALL the work you've done for the entirety of this question,
ALL parts

[wanton summit]

can i just tell you the idea

of what i did

i rubbed out my work

[livid hound]

redo,show

why does everyone rub out their work

[wanton summit]

because i like whiteboard

okay

[livid hound]

are you saying that you erased the stuff concerning
$$\alpha + \beta + \gamma = , ?$$
$$\alpha\beta + \alpha\gamma + \beta\gamma = , ?$$
$$\alpha \beta\gamma = , ?$$

[wraith dagger]

ℝamonov

[wanton summit]

i erased my working for a^2+b^2+c^2

with a b and c being alpha bet nad gamma

[livid hound]

ALL the work you've done for the entirety of this question,
ALL parts
from the very beginning

or everything that you currently still have on your whiteboard

[wanton summit]

ok

this is for the addition of roots

the concept

thats the full working

!!

[livid hound]

...

why ping helpers when I'm already here

[last prairie]

lol

[livid hound]

rude

similar idea,
start with
(ab + ac + bc)
and square it

[wanton summit]

and then subtract the difference

okay

thank you!

thank you

🙏

.close

[cedar kiln]

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[real crag]

Hey

[real crag]

I need help with trigonometry

I’ve been struggling for a few days

[tropic oxide]

http://dontasktoask.com/

[real crag]

I’m not sure what to do

[tropic oxide]

do you have a problem you're struggling with?

post that, for a start.

[real crag]

Let me take a picture of it

Hold on

[stone flame]

first whats $sinx$ geometrically

[wraith dagger]

Tangerine

[upper garnet]

u know the pythagorean identity?

[real crag]

Yes but

[tropic oxide]

technically insufficient info here.

unless we know for a fact that x lies between 0 and 90°.

[real crag]

I always get the wrong answer

[livid hound]

show your attempt

[tropic oxide]

do you have some work to show?

[real crag]

Wait let me get my pen out

[tropic oxide]

if we see your work we can try to diagnose what goes wrong

[real crag]

Because I do online school this was from Friday

Give me a sec to write it

Wait

[latent bloom]

@real crag hey are you there?

Did you write out your problem?

[real crag]

I’m back. So this is my work

I don’t understand how

The answer is 9/23

[stone flame]

just keep doing this part?

[real crag]

I did

And

I ended up with 53/3

[stone flame]

the power 2 should be outside the bracket btw

because everything in the bracket is squared

[latent bloom]

Wait

[livid hound]

you're not respecting the order of operations

[latent bloom]

Wait

[real crag]

And I’m nervous because I still have 5 more questions left

[livid hound]

and also vanishing expressions

[real crag]

Of the same

[stone flame]

$1 - (\frac{8\sqrt{7}}{23})^{2} = \sin^2{x}$

[latent bloom]

Wait though

[livid hound]

firstly as mentioned

the power 2 should be outside the bracket btw
you want the square the hold thing, not just the last component of the numerator

also the original denominator is 23, not 3

[latent bloom]

Do you really need pythagoras here?

[real crag]

That’s what it said

[livid hound]

you apply pythag in some form

[stone flame]

$\frac{81}{529} = sin^2x$

[livid hound]

also the original denominator is 23, not 3

[stone flame]

tbh I think you shouldnt be doing it like this

oh yeah its 23

[latent bloom]

You have two ways to do this problem

[wraith dagger]

Tangerine

[latent bloom]

One easy way

And one using pythagoras

[real crag]

Ok so let me try again

[wraith dagger]

Tangerine

[stone flame]

$sinx = \frac{9}{23}$

[wraith dagger]

Tangerine

[stone flame]

$1 - (\frac{8\sqrt{7}}{23})^{2} = \sin^2{x}$\
$\frac{81}{529} = sin^2x$\
$sinx = \frac{9}{23}$

[wraith dagger]

Tangerine

[livid hound]

!nosols

[cedar kiln]

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

[real crag]

This still comes out as 56

[latent bloom]

Hmm

[stone flame]

he already did half of it

[latent bloom]

@real crag are you aware of this property

[stone flame]

@real crag just keep going from here

[latent bloom]

$(a\sqrt b)^2 = a^2 b$

[wraith dagger]

VulcanOne

[latent bloom]

?

@real crag are you aware of this property?

[real crag]

448/529

Is where I’m at

[stone flame]

look at the picture above you

[latent bloom]

Great

That's the cosine squared

[livid hound]

show the full equation you have

[stone flame]

yes

now just solve it like a normal equation

but treating (sinx) as the unknown

[latent bloom]

Yep

[stone flame]

next time be more careful while writing things like exponents

[livid hound]

remember parentheses around that $\red{(}\sin (x)\red{)}^2$ or write it as $\sin^2(x)$

[wraith dagger]

ℝamonov

[livid hound]

and don't forget the x for the cos in that first line as well

cos is not a number

[real crag]

Ok now I’m at 81/529

I have to simplify?

[livid hound]

show the full equation you have

[stone flame]

What does that equal to

[livid hound]

an expression by itself is meaningless

[stone flame]

In your equation

[real crag]

9/23 ?

[livid hound]

show the full equation you have

where's 81/529 in your equation
what's that supposed to be equal to

.
where's 9/23 in your equation
what's that supposed to be equal to

[real crag]

hold on

Let me write it better

[livid hound]

if i just say the number 420,
what does that tell you

[stone flame]

[livid hound]

can you please address those issues with notation that i've been mentioning

and no, that equation is invalid

[stone flame]

Please solve equations with clear steps

[livid hound]

you should've made a new line of work

[stone flame]

Dont just write whatever you think

[livid hound]

where upon subtracting 448/529 from both sides, you'll no longer have 448/529 on the left side

[real crag]

😓

Srry guys I’m very slow

i got to do to do something with my mom right now

But thank u so much

I’ll be telling her how much y’all helped

[cedar kiln]

@real crag Has your question been resolved?

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[fresh loom]

.close

[cedar kiln]

Channel closed

Closed by @fresh loom

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Available help channel!

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

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

[slate pasture]

i need to find SA of a regular triangular pyramid when base sides are a and the length of pyramid is H

[slate pasture]

i thought i did it right but apparently i didnt

[livid hound]

and the length of pyramid is H
which length?
was a diagram provided to you?
can you show the work you did

[slate pasture]

length of pyramid. not apothem and not the length of base

1sec ill take a picture of my work rq

well its bad quality but basically i can get what the length of base is and from that i can get area of base

or rather, from that i can get what apothem is, not base length

base length is (a/2)^2 + h^2 = a^2

and h^2 is 3a^2/4, so h is a* sqrt(3)/2

[livid hound]

length of pyramid. not apothem and not the length of base
still doesn't answer my question

[slate pasture]

this

[livid hound]

proper term would be altitude

[slate pasture]

ye i dont know the english terms

but i know the base area, so now i just need area of side right? and then triple that

SA is base area plus area of sides right

<@&286206848099549185>

[livid hound]

consider properties of medians of a triangle

[slate pasture]

which triangle ?

[slate pasture]

yeah

[livid hound]

did you get an expression for the length of that (in terms of side length a)

[slate pasture]

length of base?