help-0

[ruby elbow]

h(x)

[lethal belfry]

yeah, pretty much

[ruby elbow]

so x = 4

cause its y = 2

[lethal belfry]

yup

[ruby elbow]

and that as he only answer?

not x = 6

cause x = 6 is y = 4

and its not asking for y = 4

its asking for y = 2

[lethal belfry]

the only input which ouputs 2 as far as I can see is x=4

[ruby elbow]

yeah

👍

.close thanks I was understanding till the part about the "= 2"

[lone heart]

Channel closed

Closed by @ruby elbow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[cold pumice]

How can I find the value of alpha?

[cold pumice]

I got a partial work, in order to complete it I need to find BD/CK but idk how, or maybe there is much simpler way

[somber eagle]

i would say the sin rule if you know it

[cold pumice]

Where specifically?

[somber eagle]

actually i dont think its even necessaru

since the triangle is isosceles

the one with side length 8

[tall talon]

Did you notice this triangle? You can work out alpha from there

[cold pumice]

I don't see how can it help

[somber eagle]

wait what im stupid

[cold pumice]

How? Notice that the 82 degree angle is ABE, not ABC

[tall talon]

Since the sum of angles is 180

[somber eagle]

you know 2 angles in the triangle

[cold pumice]

I don't

[somber eagle]

idk how i didnt see that

82 and 90

you know them both

[cold pumice]

Bruh

Look

[tall talon]

There is 82 and 90 (the right angle)

[cold pumice]

At the picture

the 82 degree

Is

ABD

NOT

ABC

The angle inside the triangle is 82 minus something

[somber eagle]

oh my mistake

[tall talon]

Do you mean ABD = 82 deg ?

[cold pumice]

Yes

[tall talon]

my bad

[cold pumice]

Maybe it wasn't clear as I thought

[somber eagle]

ok once again i suggest the sin rule

[tall talon]

Good recommendation

[somber eagle]

with the entire triangle

[cold pumice]

What triangle

[somber eagle]

the big one

thats split up into small ones

[cold pumice]

Which

[tall talon]

He/ she/ it meant ABE

[cold pumice]

ABC?

BCE?

[somber eagle]

yeah ABE

aka the "big" one

[cold pumice]

You could just use "they"

[somber eagle]

oh yeah i forgot i set that

[tall talon]

I'm not into the "pronouns" thing

[cold pumice]

So if I use the sine rule

[somber eagle]

honestly speedran the enter to the server

[cold pumice]

It's not about pronouns, if you don't know someones gender you can call them as "they" and it will be grammatically valid

That's just how English works

[somber eagle]

sorry i'll actually set them, i thought they were mandatory so i just picked at random

[cold pumice]

Yea I can find angle BEA

And then the other angle

I can't believe I didn't see that

I am so stupid

[tall talon]

And when you find AEB , what do you do? (just to see if you need further assistance)

Azu?

[cold pumice]

180-the two angles I know

Yea

[tall talon]

Yup

[cold pumice]

Can't believe I didn't see that

Thanks

.close

[lone heart]

Channel closed

Closed by @cold pumice

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.

[viscid dock]

3^x=2
2^[(x-1)/x]=?

[tacit arch]

,rotate

[tardy tapir]

!status

[lone heart]

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

[viscid dock]

2

[tardy tapir]

what have you tried?

[viscid dock]

logging and getting x

but im not supposed to log i think

[tardy tapir]

you are

[viscid dock]

can you show the steps

[tardy tapir]

sub the value of x

[tardy tapir]

!nosols

[lone heart]

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.

[viscid dock]

ik but i dont know how to solce this

i may be missing a rule on log

[tardy tapir]

you need to use loga - logb = loga/b

and base change property

[viscid dock]

did that then?

[tardy tapir]

show me

[viscid dock]

bad writing but

[tardy tapir]

no worries

[viscid dock]

the base is 2

i didnt write the two

[tardy tapir]

what is log32?

what is base

[viscid dock]

2 is the base

[tardy tapir]

why is 2 in the air

[viscid dock]

bad pencil

no sorry

3 is the base

[tardy tapir]

you got x as?

[viscid dock]

log3(2)

[tardy tapir]

now use loga-logb = log(a/b)

[viscid dock]

yea i got stuck on log3(3/2)/log3(2)

what can i write this as

[tardy tapir]

aha

careful

[viscid dock]

hmm

[tardy tapir]

its log3(2/3)

not 3/2

[viscid dock]

ohh yea

my bad handwriting caused the problem

[tardy tapir]

now again use base change property

[viscid dock]

so write it as a-b?

[tardy tapir]

nah

[viscid dock]

what is base change proprty

[tardy tapir]

whats logc(a)/logc(b)

[viscid dock]

hmm

im not very good with properties

as no one taught me

[viscid dock]

oh

[tardy tapir]

use this

[viscid dock]

so its logb(a)

[tardy tapir]

yes

[viscid dock]

i got this

its 3/2 right

thanks for the help

[tardy tapir]

2/3

[viscid dock]

how

[tardy tapir]

.

[tardy tapir]

.

[viscid dock]

oh lol thanks

[low glen]

3/2 or 2/3?

[viscid dock]

its supposed to be 3/2

[low glen]

im confused a lil bit

[viscid dock]

i also am

2/3

[low glen]

i think its 3/2

[tardy tapir]

it is 2/3

[viscid dock]

is the right answer i made the mistakes

[viscid dock]

no i wrote it wrongly

[low glen]

how how

[viscid dock]

look up

[tardy tapir]

try to solve it again, with a nice pencil

[viscid dock]

yeah thanks for the help i need to write better

[low glen]

this got a identity

i forgot

[viscid dock]

.close

[lone heart]

Channel closed

Closed by @viscid dock

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.

[ruby elbow]

simplify it to 30 * -3f * -7g

[ruby elbow]

?

[worn fox]

f(-3) means the value of the function f at the point x=-3

[ruby elbow]

yeah

that would be y = -3

if f(-3) then y = -3

[worn fox]

So you can replace f(-3) with -3

[ruby elbow]

and if g(-7) then 7

[ruby elbow]

ok

so

it would be

-6 * -3 * -5 * 7

?

[worn fox]

It's not everything being multiplied

Its -6f(-3) take away 5g(-7)

[ruby elbow]

oh

oops

sso

-6(-3) @worn fox

and 5(7)

if replacing them

[worn fox]

What is g(-7)?

[ruby elbow]

its y = 7

[ruby elbow]

look

[worn fox]

Are you sure

[ruby elbow]

nope

its 6

im blind

lol

so y= 6

[ruby elbow]

so -6(-3) * 5(6)

18 * 30

[worn fox]

Again^

[ruby elbow]

uh

[worn fox]

Youre conjuring a multiplication out of thin air :p

[ruby elbow]

are we just forgetting about 5g(-7)?

[worn fox]

You have $(-6f(-3)) - (5g(-7))$

[ocean seal]

ΣΑC

[worn fox]

Precisely this

[ruby elbow]

this is all we are doing?

but then why would we need the entire graph

[worn fox]

To find the values of f(-3) and g(-7)

[ruby elbow]

we did tha

and it came out as y = -3 and y = 6

so where do we put the -3 and the 6

[worn fox]

Right so you plug those into here

[ruby elbow]

into the f and g??

[worn fox]

You have found that f(-3) = -3 and g(-7) = 6

[ruby elbow]

yes

[worn fox]

So that is what you replace in here

[ruby elbow]

so

(-6(-3)(-3))-(5(6)(-7))

that doesnt make sense

[ruby elbow]

we ae replacing f with -3

and g with 6?

is what your saying

[worn fox]

You replace f(-3) with -3

f(-3) is not f times (-3)

It's the value of f at the point x=-3

[ruby elbow]

so (-6(-3)) - (5(6))

[worn fox]

Yes

[ruby elbow]

i thought thats what i said though

replace the f(-3) with -3

and replace g(-7) with 6

[ruby elbow]

then it would just be 18-30

-12

[worn fox]

Yes but then you multiplied instead of taking away and then asked why we needed the whole graph

-12 is correct

[ruby elbow]

oh

[ruby elbow]

why did we take it away though

how do I see next time that I'm suppose to take it away instead of doing other things with it

[worn fox]

Because this is what the question says

They are using a dot when there is multiplication

[ruby elbow]

i thought that was negative 5

it was but I didn't know

I was suppose to combine

5 with g

[worn fox]

You thought it was $(-6\cdot f(-3))\cdot (-5\cdot g(-7))$

[ocean seal]

ΣΑC

[ruby elbow]

yeah

[worn fox]

But see i had to add brackets and another mult symbol to make it that

[ruby elbow]

i see

[ruby elbow]

so thats wht you meant by "summoning an equation out of nothing"

[worn fox]

Right you added a multiplication that didn't exist

[ruby elbow]

oh

[worn fox]

Remember your orders of operations too

Do the multiplications first and then addition or subtraction

[ruby elbow]

yeah I know that but I just got confused with the -5 lol

[worn fox]

It's okay now hopefully you won't be

[ruby elbow]

yeah

thanks alot

😄

.close

[lone heart]

Channel closed

Closed by @ruby elbow

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.

[weak ridge]

How to integrate this by substitution the eight part is what i am not getting

Should i do 8u

[minor needle]

what have you tried

[weak ridge]

Sending bpictrue

[minor needle]

wdym by "8u"

8u equals what

[weak ridge]

This is what i mean

[minor needle]

u = x - 2 is good

so

[weak ridge]

there is to be an 8x

[minor needle]

it looks correct, now just come back to the original variable x

[weak ridge]

how do i get tha

t

yes but no 8x

[weak ridge]

but i need the 8x

[minor needle]

why 8x

[weak ridge]

This is ans

[minor needle]

answer might be different due to constant

according to this

8(x-2) = 8x - 16

we can "remove" -16 (derivative of a constant = 0)

so it becomes 8x

[weak ridge]

im integrating

[minor needle]

and?

look at simple example

[weak ridge]

Why derivative

[minor needle]

int of 2x = x^2 + C, yes?

we can say answer is x^2 + 1, x^2 + 2, x^2 + 3, x^2 - 1000 etc.

and we're still right

[weak ridge]

ok

got it

.close

[lone heart]

Channel closed

Closed by @weak ridge

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.

[warped topaz]

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

[warped topaz]

I remember how to solve this but I dont really understand the logic

I just replace a with y'(t), b with x'(t) and replace x with x(t) and y with y(t)

I dont really remember why I replace a with y'(t) or b with x'(t)

[marsh rapids]

dy/dx = dy/dt * 1/ (dx/dt)

[warped topaz]

What does this come from sry

[marsh rapids]

derivative rules

we already went over this something like 2 or 3 weeks ago I think

if y = ax+b, then you can rewrite this as y - ax = b

so it's enough to find the slope

oh wait

in this case

nice little linalg trick

[marsh rapids]

oh well you already know

but there's a similar proof to the one for the normal vector and the plane equation

because it's basically the same thing

[near apex]

I don't think OP is there yet. Maybe keep it simple.

[warped topaz]

Ye im dumb 😂

[near apex]

Lol. No. Not that.

[marsh rapids]

because if a line has directing vector (a, b) then (-b, a) (90° rotation) is orthogonal to the line.
So all vectors of the line are described as being orthogonal to (-b, a), which means (-b, a) . (x, y) = 0, i.e. -bx + ay = 0
which gives back y = b/a x, with b/a = dy/dx

so you can take b = y'(t), a = x'(t)

(and it turns out there's a very similar proof to why a plane with normal vector (a, b, c) can be described by ax+by+cz = d)

[warped topaz]

But what has this got to do with orthogonal lines sry

[marsh rapids]

just using the dot product as a way of describing lines

like you can say "the x-axis is the line of all points orthogonal to (0, 1)"

every line, as such, has a set of orthogonal vectors

[warped topaz]

OHHHH WAIT

[marsh rapids]

if (a, b) is a directing vector, then every point is of the form L(t) = (at + a0, bt + b0)
Then (-b, a) . L(t) = -bat -ba0 + bat + ab0 = ba0 + ab0 is constant

[warped topaz]

I just got it

So all vectors of the line are described as being orthogonal to (-b, a), which means (-b, a) . (x, y) = 0, i.e. -bx + ay = 0
This makes sense

[marsh rapids]

that one is a result you'd only really see when studying linalg an euclidian spaces

[warped topaz]

I had to reread all your messages like 10 times hahahaha but I finally got it

[marsh rapids]

because then you prove it for any dimension

so it's fair that it's hard to understand for you

[warped topaz]

Hopefully I never have to do that 😓

[marsh rapids]

depends on how much math you come to do

[warped topaz]

This is hard enough hahaha

[marsh rapids]

but don't worry, you'll be a lot more mature when you get there

[warped topaz]

I wouldnt count on it hahaha

But thank you

You explained it well

[marsh rapids]

math is about understanding and visualizing sometimes

[warped topaz]

I am just a square brain

[warped topaz]

Yeye makes so much more sense now

[marsh rapids]

high school is crunching numbers, undergrad is having intuition to carry you

[warped topaz]

I miss when all I had to do was crunching numbers 😅

[marsh rapids]

the great students are the ones that manage to get that intuition in high school

[warped topaz]

True tbh

[marsh rapids]

and there aren't exactly many

at least not in your standard school with your standard teacher

where the objective is just to know the few techniques needed to pass the exam

(this is not india btw)

[warped topaz]

I dont need to just pass my exam I need 70% minimum to get accepted 💀

[marsh rapids]

US ?

[warped topaz]

Nah NL

Netherlands

[marsh rapids]

I forgor

[marsh rapids]

that's "passing" if you define it conveniently

[warped topaz]

I guess haha

[marsh rapids]

who cares if the bar for success is 50% or 70%, it's a bar

[warped topaz]

Yeye true, a high bar tho lol

[marsh rapids]

didn't say it was easy

[warped topaz]

And its a hard test (for me anyway)

[marsh rapids]

if you got an translated version I might enjoy taking a look at it

unless it's transparent enough

[warped topaz]

I actually do 1 moment

I think youre on my friends list so I will just dm it

.close

[lone heart]

Channel closed

Closed by @warped topaz

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.

[lean wraith]

I have a question about about a Fourier Transform

[lament forge]

well nobody will be able to answer the question if you don't ask it

[lean wraith]

Technology being difficult one sec

I am stuck at the end part here

The provided answer looks like this

And I have gotten it to here

Did I go wrong somewhere or are these actually equal

[ancient saddle]

Mmm there's probably a mistake 🤔

cos(w) = ( e^(-jw) + e^(jw) )/ 2

[lone heart]

@lean wraith Has your question been resolved?

[lean wraith]

.close

[lone heart]

Channel closed

Closed by @lean wraith

Use .reopen if this was a mistake.

[lone heart]

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.

[violet bear]

I need help with this question

[violet bear]

was thinking of deriving the cosine using triangles and the pythagorean theorem but i don't know

[lone heart]

@violet bear Has your question been resolved?

[lone heart]

@violet bear Has your question been resolved?

[violet bear]

forget it

.close

[lone heart]

Channel closed

Closed by @violet bear

Use .reopen if this was a mistake.

[lone heart]

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.

[median oar]

ok, given $B^TB=n, B, X \in \mathbb{R}^n\$
show $\frac{1}{n}||X-\frac{1}{n}(B\cdot X)B||^2=\frac{1}{n}||X||^2-\left(\frac{1}{n}(B\cdot X)\right)^2$

[tardy stag]

you should probably have an equals sign or something

[median oar]

it's coming

where • is the dot product

B is a column of 1's if that helps

[ocean seal]

Frosst

[tacit arch]

do you just open up the parentheses with dot product

[median oar]

now if we ignore the 1/n and expand the norm on the left $\left(X^T-\frac{1}{n}(B\cdot X)B^T\right)\left(X-\frac{1}{n}(B\cdot X)B\right)$

[ocean seal]

Frosst

[median oar]

that gives $X^TX - \frac{1}{n}(B\cdot X)X^TB - \frac{1}{n}(B\cdot X)B^TX + \frac{1}{n^2}(B\cdot X)^2B^TB$

[ocean seal]

Frosst

[median oar]

now since both X and B are R^n vectors, X^TB is X • B and B^TX is B • X and we know those are the same

$||X||^2 - \frac{2}{n}(B\cdot X)^2 + \frac{1}{n^2}(B\cdot X)^2 B^TB$

[ocean seal]

Frosst

[median oar]

then we use the identity of B^TB = n to simplify it to

$||X||^2 - \frac{1}{n}(B\cdot X)^2$

[ocean seal]

Frosst

[median oar]

WAIT

ISN'T THIS IT

[median oar]

i get the 1/n i left in this step

$\frac{1}{n}\left(||X||^2 - \frac{1}{n}(B\cdot X)^2\right)$

[ocean seal]

Frosst

[median oar]

ok i just needed to use latex to figure this out i think this is right

@mellow grail if u wanted to see

(except i need to go the other direction but that should be trivial)

ok thank you for the help channel and latex bot

.close

[lone heart]

Channel closed

Closed by @median oar

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.

[crystal lotus]

IM trying to solve this question.

[crystal lotus]

That is my work in order to get values of T.

[near apex]

Do you know what's slope of a tangent?

[crystal lotus]

I know you can obtain the equation of a tan line by using Y - y1 = m(x-x1) when given a value, thats what I was doing up until now. But this is a bit different which is why I thought to ask. My work here is based off the tutorial the webassign gave me... Unfortunatley its not very helpful though.

OH, wait.

NVM. i was just writing my answer wrong.

.close

[lone heart]

Channel closed

Closed by @crystal lotus

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.

[chilly idol]

A. n represents the term

a_n is the number accsiatoed with the term?

[upbeat gorge]

Be more specific

[chilly idol]

ok

so for example, n=1 is the first term

a_n is the number of quilts

quilt squares

[thorny patio]

There's a more explicit pattern emerging i think

Take a look at n = 3 in particular

[chilly idol]

ok

[thorny patio]

What does 5 mean in that photo

[chilly idol]

oh

it could be

the center and edge squares

[thorny patio]

Number of blue squares for sure

[chilly idol]

yup

[thorny patio]

If i had to describe it in words

[chilly idol]

n is the term number, while a_n is the number of blue squares in the quilt

[thorny patio]

How to tell if a square would be blue or not is tougher to describe

[chilly idol]

ok

i think it could be blue squares

a_n represents the blue squares

[thorny patio]

I definitely think so too but i really am not sure what pattern the blue squares follow

[chilly idol]

wait

doesnt it give you the equation in C

the rule

[upbeat gorge]

I mean, the upper-rightmost and the lower-leftmost square are always blue so you can set either one as a baseline and say the rest follows a checkerboard pattern

[chilly idol]

yeah, we could also say that

what if the pattern is

the n term value divided by the total squares

for example

4 (the total squares in the quilt) divided by 2 (the term number)

4/2

which gets you 2

[upbeat gorge]

Well that fails with n=3

[chilly idol]

yes

thats true

[upbeat gorge]

I think you have to state what n represents in terms of the quilt

We already have a_n as the number of blue squares in the design

[chilly idol]

yup

[upbeat gorge]

But we may have to be more specific than stating n as the index number

[chilly idol]

so n cannot just be the number of squares in teh quilt

o

[upbeat gorge]

Well, in n=2, are there 2 squares in the quilt?

[chilly idol]

nope

maybe the n value represents the side of the quilt

for n=2, their are two squares at the side of the quilt

and for n=3 there are 3 squares at the side of the quilt

[upbeat gorge]

Yep, this works!

[chilly idol]

yay

[upbeat gorge]

Ok, so we’re done with a

Now we move on to b

[chilly idol]

yup

we need to know the pattern

to find the other n values

[upbeat gorge]

You theoretically can just bash it

[chilly idol]

bash it?

how do you do that

[upbeat gorge]

Draw figures like 1 to 4

for 5 to 8

[chilly idol]

oh

alr i shall do that

so i got a_n = 13

for n=5

im trying to figure out a pattern

[upbeat gorge]

Yeah sounds right

[chilly idol]

alr i finished

im on C now

@upbeat gorge you their?

[upbeat gorge]

Yeah, what part of the question do you need help for now

[chilly idol]

im on C

i think i could do these on my own

ill ping you if i need help

[upbeat gorge]

Yeah just plug in n

[chilly idol]

yup

@upbeat gorge alr i gotta go, this looks pretty simple enough so i think i can finish this on my own

thanks for your help!

[upbeat gorge]

Ok, no problem

[chilly idol]

.close

[lone heart]

Channel closed

Closed by @chilly idol

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.

[vagrant agate]

for b is it just 3000(1+0.005)^2

[solemn juniper]

Yes

Assuming that's how you've been taught to change rates

[vagrant agate]

ok thank you

.close

[lone heart]

Channel closed

Closed by @vagrant agate

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[alpine sable]

AD is parallel to BC not not equivalent?

at least i think that’s what the arrows mean

fuck

geometry exam tomorrow lol, i’m doing last minute studying

i don’t think that that necessarily proves it but i just want someone to check me

[royal socket]

It does prove it since AD = BC as well

[alpine sable]

explain?

[royal socket]

Construct AC

[alpine sable]

?

[royal socket]

Draw AC

[alpine sable]

ok?

[royal socket]

AD=BC
angle DAC = angle ACB
AC is common

hence ADC is congruent to CBA

[alpine sable]

ok

thanks

i get it now

.close

[lone heart]

Channel closed

Closed by @upbeat dome

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[tardy stag]

differential geometry -

Is there some metric space where all geodesics (in any direction) converge to a point, or at least converge together?

I'm thinking of a black hole and how "all paths lead to the singularity" but I don't think that's an accurate statement

[tardy stag]

this started because someone said all roads lead to rome and my mind got a little distracted

[carmine reef]

I don't suppose spherical counts

[tardy stag]

I would also settle for all geodesics getting arbitrarily close to a target point an infinite number of times

[carmine reef]

All geodesics through one point converge to another but

Not all geodesics

[tardy stag]

yeah I want all of them

[carmine reef]

something involving projective geometry and infinity maybe?

[tardy stag]

one basic issue here is that going "backwards" on a geodesic would, in theory, take you away from whatever point

double sided Gabriel's horn seems neat but has some issues

[alpine sable]

i am very much enjoying following along on this conversation

[carmine reef]

I'm imagining starting with a euclidean disc and using a metric where distances are larger the further from the center you are

I feel like that would have a tendency to suck in geodesics towards the center but I don't really know how any of this stuff works

[tardy stag]

I think you could easily construct orbits or something on that, and if you go directly away from center you're not coming back

but that's a good start! this problem seems fun

[carmine reef]

One note with orbits is that there's no inherent notion of velocity

So I don't know that a periapsis and an apoapsis should really behave differently

And it feels like a circular orbit is only stable for a very specific metric

or well, perhaps there's a lot of metrics where a circular orbit is stable for one specific r but it feels like by making the metric extreme enough we can fix that

Maybe we could base it on elliptical geometry instead of euclidean to get rid of the problem of a line leading directly away from the hole

Or well, just spherical

[tardy stag]

elliptical seems like a start

sphere seems easier

[carmine reef]

Is it allowed to start with a Euclidean disc and identify antipodal boundary points with each other

[tardy stag]

yes that's fine I think

hmm

[lone heart]

@tardy stag Has your question been resolved?

[tardy stag]

i guess if we start with the euclidean disk and tie all the edges together it technically works but that absolutely feels like cheating so hmm

[tardy stag]

okay if we just want a space where every geodesic crosses over a certain point we have that it's called a circle

ugh i don't feel like i'm qualified to answer this question anymore

[bold pollen]

Them this question lol

Damm*

[lone heart]

@tardy stag Has your question been resolved?

[tardy stag]

not going to leave this open for too long because it's both specific and ill-defined and i really need to re-learn differential geometry before i can get an answer to it, but essentially:

I'm looking for a metric space such that all geodesics, starting at any location except perhaps the point P, have the same limit of P

this may be impossible

[summer dirge]

just a suggestion, but maybe the folks at MathStackExchange or MathOverflow can help you with your question

[tardy stag]

yeah that's probably the next step

that, or actually figuring out what i'm asking lol

.close

[lone heart]

Channel closed

Closed by @tardy stag

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[vapid steppe]

Approximate $\sqrt{\pi}$ using the local linearization of $f(x)=\sqrt{x}$ at the point where $x=3$.

[ocean seal]

Jash

[echo socket]

!status

[lone heart]

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

[remote heron]

hmm whered you get stuck?

[vapid steppe]

1

what does it mean to use the local linearization

[remote heron]

this means to assume that, near to some point, the function is just a line

[vapid steppe]

oh

[remote heron]

mechanically it means constructing the tangent line

[vapid steppe]

so i find the tangent line of f at x=pi?

[remote heron]

not quite

[vapid steppe]

x=3

[remote heron]

yea, construct the linearization at x=3

then you just assume that for values near 3, like say pi, the approximation will be OK

[vapid steppe]

so like f(3)=sqrt(3) and f'(3)=1/(2sqrt(3))

so y=(1/(2sqrt(3))) (x-3)+sqrt(3)

so do i just plug in pi?

[remote heron]

yea, into your line

[vapid steppe]

can i just use this to approximate any value of f

[echo socket]

No, not any

[remote heron]

well it doesnt make sense for every value

the domains dont match up

but otherwise yea, the approximation just gets poorer and poorer

its pretty good here

[vapid steppe]

oh ok

uh so the next part is Determine if your approximation is an underestimate or overestimate of the actual value of sqrt(pi). Justify your answer.

[remote heron]

there are a few ways you could go about this, whats your thought

[vapid steppe]

can i use a calculater to just like compare this value to the actual value

[remote heron]

i guess

thats pretty uhh

not in the spirit of the question

i think

[vapid steppe]

how would i do it otherwise

[remote heron]

you have a few ways

one would be to take a number ||a little smaller than your estimate, square it, and show that this squared is still xyz||

alternatively, you can look at derivatives

you know your approximation is equal to the function at x=3

[vapid steppe]

my teacher was talking about like using the concavity of the function

[remote heron]

whats happening from there

yea

you can show that sqrt is pulling away from this line

[vapid steppe]

so i find d^2(sqrtx)/dx^2

at x=pi?

[remote heron]

,w second derivative sqrt(x)

[ocean seal]

Results provided by WolframAlpha

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

Requested by janniku

[remote heron]

clearly the second derivative of the line is 0

[vapid steppe]

ye

[vapid steppe]

would i evaluate at pi or 3?

[remote heron]

just make an argument for an x in the area

[vapid steppe]

i mean ik it doesnt matter in this case

[remote heron]

the rate of change of our line isnt changing

but for the sqrt line, its decreasing

that seems sufficient to me is anybody watching

[vapid steppe]

oh so like the line is always increasing at a constant rate but the sqrt graph increases at a decreasing rate

[remote heron]

right

so theyre equal at x=3

but in the area to the right

[vapid steppe]

implying that the line is above the sqrt near x=3

[remote heron]

sqrt increases less than your line

because its derivative will have decreased when you moved rightwards of x=3

[vapid steppe]

ohh

ok ty

[remote heron]

this is always negative if its not clear that part of the argument

[vapid steppe]

yea

for part c it would be an overestimate right

[remote heron]

can you argue it?

[vapid steppe]

since S is concave down, the approximation will be an overestimate

[remote heron]

that seems fair to me

[vapid steppe]

ok ty

.close

[lone heart]

Channel closed

Closed by @vapid steppe

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[simple saddle]

how to do this?

[vale wigeon]

you have 101 numbers, one of them is 10,000,000 and the rest are 2, their average is?

[lone heart]

@simple saddle Has your question been resolved?

[simple saddle]

but how can i do without calculator?

[vale wigeon]

do you know how to divide numbers without a calculator?

long division, etc?

you have here an eight digit long number but dividing by 101 is not even that much time consuming or painful.

[simple saddle]

ya but won't it be still time consuming

can we estimate using the data

[vale wigeon]

well maybe if you have 5 seconds to solve this question

then yeah it will be time consuming

are you at least able to write down the exact value of the average as a fraction Y/N

[simple saddle]

yeah

[vale wigeon]

ok

what is it

[simple saddle]

10,000,200/ 101

[vale wigeon]

ok great

do you know how to do long division

i promise you this is not any harder than any other long division problem

[simple saddle]

okk

[vale wigeon]

trying to do some big brain estimation gymnastics will be harder

[simple saddle]

okay ann

thanks

.close

[lone heart]

Channel closed

Closed by @simple saddle

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.

[fallow solar]

'

[fallow solar]

Where will the friction force go ?

[vapid shuttle]

please don't close and reopen a new channel just to ask the same question

[fallow solar]

ok sry

[summer dirge]

is the applied force just 8N?

[naive valley]

what is going on in this photo

[fallow solar]

yes

[summer dirge]

then my intuition says friction force points up

[fallow solar]

and also the weight

[fallow solar]

but how

[summer dirge]

is the box at rest?

[fallow solar]

it's about to move

[summer dirge]

??

[fallow solar]

sry I edited

[summer dirge]

i mean it doesn't matter tbh

friction points up here I'm 95% sure

the gravitational force exerts 10N on the block downwards

while the applied force exerts only 8sin30 N on the block upwards

so friction should point up

to help the applied force counter gravity

[fallow solar]

You're right but how? doesn't friciton work in the opposite direction of the estimated direction of motion?

[summer dirge]

what do you mean?

friction opposes movement

[fallow solar]

yes

[summer dirge]

so then, what's the issue?

[fallow solar]

when the object moves it will move upwards right?

[summer dirge]

how would it move upwards?

[fallow solar]

the force F points in that way

[summer dirge]

yeah but you can't ignore gravity

who is stronger than the y component of the applied force here

so w/o friction, the expected result is that the block falls

[summer dirge]

the 10N is Fg, yes?

[fallow solar]

aha now I get it

[summer dirge]

or am i wrong

[fallow solar]

What's Fg

[summer dirge]

gravitational force

[fallow solar]

yup

[summer dirge]

so yeah, 10N > 8sin30 N (4N)

so block should fall

[fallow solar]

yes yes I got it

thank you

[summer dirge]

👍

[fallow solar]

,close

.close

[lone heart]

Channel closed

Closed by @fallow solar

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.

[naive gale]

hello every1

[naive gale]

how to part ii and iii of this q

<@&286206848099549185>

[lone heart]

@naive gale Has your question been resolved?

[lone heart]

@naive gale Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[naive gale]

.reopen

[lone heart]

✅

[lone heart]

@naive gale Has your question been resolved?

Show your work, and if possible, explain where you are stuck.

[lone heart]

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.

[jolly pilot]

Hi could someone help me with this problem

[jolly pilot]

We have to find the percentage of shaded area for the shape

It seems basic ik, but I have no clue what to do without assuming anything

[echo socket]

Are you familiar with the formula for the radius of the circle inscribed in a right triangle?

[echo socket]

Wrong channel

[jolly pilot]

No i'm not

never heard of it

[echo socket]

It's equal to (a + b - c)/2 where a and b are the legs and c is the hypotenuse of the right triangle

Want to see how this formula is proven?

[jolly pilot]

Yeah that would be great

[echo socket]

Okay, let me draw a diagram

[jolly pilot]

Wait so we simply have to substitute a value for the legs, calculate the hypotenuse and then divide by two to get the radius

[jolly pilot]

alright thanks

[echo socket]

I drew some radii here, so ED = DI = DJ = r, right?

[jolly pilot]

Yep

[echo socket]

Let's call the horizontal leg a and vertical leg b for convenience

[jolly pilot]

Alright

[echo socket]

You may notice that EDIB is a square

So BI = BE = r

[jolly pilot]

oh yh thats true

[echo socket]

So we have IH = a - r and EF = b - r

[jolly pilot]

yep

[echo socket]

Now, thanks to the symmetry, we can say that FJ = FE and HI = HJ

But FJ and HJ add up to the hypotenuse, c

[jolly pilot]

wait so we can just assume that

[echo socket]

So c = FJ + HJ = FE + HI = a - r + b - r

[echo socket]

The symmetry can be proven, you would just need to show that the right triangles are the same

[jolly pilot]

oh alright

[echo socket]

So here you isolate r and get r = (a + b - c)/2

[jolly pilot]

alright yeah i follow

[echo socket]

E.g. the right triangles JDH and DIH have the same hypotenuse and legs (DJ and DI) are equal, meaning the other legs (HI and HJ) are also equal

Similar argument for the other ones

[echo socket]

Okay, so, using Pythagorean theorem, you can show that the hypotenuse here is x * sqrt(2)

And simply apply the formula

That's it

[jolly pilot]

alright wait

so (1+1+sqrt(2))/2 = r

then r^2 x pi equals the area

and then u just divide that by 1/2 to get the percentage

[echo socket]

Yeah, x shouldn't have disappeared though

[jolly pilot]

what do u mean by that

[echo socket]

Should be $r = \frac{x + x - x\sqrt{2}}2$

[ocean seal]

A Lonely Bean

[echo socket]

Oh and the minus sign too yeah

[jolly pilot]

oh ok mb

yh i screwed that up

but you can still substitute 1 right

or any number and u would get the right answer

[echo socket]

Not really, you can't assume the answer is a constant no matter the value of x yet

Unless you realize that when you divide, the x^2 terms cancel out

Then sure

[echo socket]

Anyway, this means that $r = x\frac{2 - \sqrt2}2$ and $\pi r^2 = x^2 \frac{3 - 2\sqrt{2}}2$

[ocean seal]

A Lonely Bean

[jolly pilot]

alright so ((2x - x * sqrt(2)/2)^2 x pi) / 0.5 would get me the percentage

[echo socket]

Yeah, 0.5x^2 though

And you get 3 - 2sqrt(2)

[jolly pilot]

oh i see

so is the answer 53.9%

or did i screw sumthing up

[echo socket]

Oh I forgot about pi here my bad

[echo socket]

Yeah

[jolly pilot]

dam

thank u so much

i've been stuck on that for half and hour

ur actually a life saver

.close

[lone heart]

Channel closed

Closed by @jolly pilot

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.

[steel olive]

I didn't get the bottom right part

[vale wigeon]

it's a sleight of hand

[steel olive]

If inifinity/infinity is indeterminate

Shouldn't this be too

[vale wigeon]

yeah, exactly. they're doing black magic.

i mean here you can substitute t := 2^(1/x) and acknowledge t -> +∞

then you have (t-1)/(t+1) = (1 - 1/t)/(1 + 1/t) -> 1

[steel olive]

Ook

Thnx

. Close

.close

[lone heart]

Channel closed

Closed by @steel olive

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.

[safe tartan]

how do i draw y^2=x^2-1

[buoyant storm]

it is a hyperbola right

do you know how to graph hyperbolas

[safe tartan]

yes , how is this a hyperbola thouhg

[buoyant storm]

this is literally the prototypical example of a hyperbola...

x^2-y^2=1

[safe tartan]

wait actual,

i thought it was like y=1/x or xy=1

ok guessim dumb

[buoyant storm]

thats a rotated hyperbola

it is indeed a hyperbola but uh

[vale wigeon]

it's a hyperbola aligned differently wrt the axes

[buoyant storm]

x^2-y^2=1 is easier to understand

[safe tartan]

is it the same as y=+-sqrt(x^2-1)

by graphing both of those

no it is not

lmao

oh wait it is

[lone heart]

@safe tartan Has your question been resolved?

[safe tartan]

.close

[lone heart]

Channel closed

Closed by @safe tartan

Use .reopen if this was a mistake.

[lone heart]

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.

[flint inlet]

how tf am i supposed to makje this a fraction

[echo socket]

By doing it without a graphing calculator? Consider integrating

[flint inlet]

i have to integrate

stupid teacher wants a fraction answer with a decimal like that

[echo socket]

What exactly is the teacher asking for? The same as what's asked for here?

[flint inlet]

yeah

a fraction

an exact fraction answer

[echo socket]

Well some of the coefficients will be fractions

[flint inlet]

something like this

with 0,2 being a postivive integral subtracted from 2,3

positive

[echo socket]

Yeah for part d you don't need to have bounds of integrations, just integrate indefinitely and choose the value of +C correctly so that s(0) = 1

[flint inlet]

i did d already

just c mb

but my brain hurts trying to turn that into a fraction

like how

i only need to integrate 0, .55 - .55,5 right?

[echo socket]

Oh, you wanted c

Can you show what's given before part c?

[flint inlet]

i did all except c

[echo socket]

This is really weird, they give v(t) only at the end?

Anyway, to get the distance travelled you need to integrate the absolute value of v(t) rather than v(t) itself

So $\int_0^5(2t^2 - 12t + 6)\dd{t} = \frac{2\cdot5^3}3 - 6\cdot5^2 + 6\cdot5$

Wait no

[ocean seal]

A Lonely Bean

[echo socket]

The antiderivative is 2t^3/3 - 6t^2 + 6t and when you plug in t = 0, it's 0, so just plug in t = 5

[echo socket]

So this is just 250/3 - 120, can you make the denominators common here?

Damn I made the very mistake I warned you from doing lol

[flint inlet]

i mean i already got 110/3

for b

but c is the only one im confused on

[echo socket]

Yeah but that's gonna be irrelevant as we have to integrate |v(t)| here

So integrate $\int_0^5\abs{2t^2 - 12t + 6}\dd{t}$

[ocean seal]

A Lonely Bean

[flint inlet]

pos 110/3

?

wait

[echo socket]

No

[flint inlet]

im stupid

[echo socket]

You are gonna have to break up the interval depends on the roots

Alternatively you could take your answer from b and just add $2\int_{t_1}^{t_2}(-2t^2 + 12t - 6)\dd{t}$

[flint inlet]

hm

[echo socket]

Where t_1 and t_2 are the roots

[ocean seal]

A Lonely Bean

[echo socket]

I think this is easier yeah

[flint inlet]

roots of what though?

[echo socket]

v(t) = 0

Solutions to this

[flint inlet]

so like 0 and -110/3

[echo socket]

0 is not a root of v(t)

[winter light]

Do you know how to solve that quadratic equation? v(t) = 0

[echo socket]

Solve 2t^2 - 12t + 6 = 0 using quadratic formula or whatever method you want

[flint inlet]

yeah

.5505

and 5.449

when i get the decimals i get stumped

as she wants a pure fraction answer

[echo socket]

So you just don't approximate, leave the roots as $3+\sqrt6$ and $3-\sqrt6$

[ocean seal]

A Lonely Bean

[flint inlet]

OHHHHHHHHHHHH

[echo socket]

So we can now calculate $2\int_{3-\sqrt6}^{3+\sqrt6}(-2t^2 + 12t - 6)\dd{t}$

[ocean seal]

A Lonely Bean

[echo socket]

Eh, which gets really messy unless we complete the square

So -2t^2 + 12t - 6 is the same as -2(t - 3)^2 + 12, meaning that's symmetrical around t = 3

And we can rewrite that integral as $4\int_3^{3+\sqrt6}(-(t - 3)^2 + 6)\dd{t}$

[ocean seal]

A Lonely Bean

[flint inlet]

I see it

[echo socket]

Can you integrate this or do I continue?

[flint inlet]

yeah

i think i can

thank you sm

[echo socket]

Okay, don't forget that you have to add this to -110/3

[flint inlet]

thank you sm

[echo socket]

You are welcome

[flint inlet]

@echo socket i was just looking back

and the interval ends at 5 doesnt it

[echo socket]

The entire interval, yeah

[flint inlet]

so it means i dont need the 3+sqrt6

[echo socket]

No we took a different approach here

I will explain

[echo socket]

So, when are take the absolute value of this function, everything that is below the x-axis gets flipped around the x-axis and becomes positive

[flint inlet]

kk

[echo socket]

In terms of the area, it stays the same except we add twice the geometric area of the part of the graph that used to be below the x-axis

That's basically what we did here

[flint inlet]

okay i got it

thank you again

[lone heart]

@flint inlet Has your question been resolved?

Channel closed

Closed by @flint inlet

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.

[warped topaz]

https://i.imgur.com/rc5KI4d.png

[warped topaz]

Not really sure what im doing wrong

Sorry if my work is hard to read

[near apex]

Why are you even doing that ?

[warped topaz]

Doing which sry?

[near apex]

Never mind. You can do that however you have made a big blunder.

Firstly, do you think that you can simply take 1/9 out from ((u-8)/9)^5 ?

[warped topaz]

Ah yes true

[near apex]

Ah. Gosh. Wait

No. That's correct.

[warped topaz]

oh haha

[near apex]

What's wrong with me? 🤦‍♂️

[upbeat gorge]

Why did you remove your integral sign tho

Where’s your du lol

[warped topaz]

Sry I was just lazy, I hate writing in paint

Du is just 1 right? So I left it out

[near apex]

No.

Firstly, du can never just be a number. 😐

du will always be of form (some expression)dx.

[warped topaz]

OHHHHH

I see what I did wrong

forgot to multiply by 1/9

[near apex]

Why don't you try doing du business more systematically?

Always write u = (whatever expression you assume as u)
differentiate w.r.t. x(or whichever variable you have).

you'll get, du/dx = (some expression)
So, you have du = (some expression * dx)

[warped topaz]

Yep my lazyness is a problem