help-13

[maiden osprey]

ive been only practicing with rectangular prism and getting a bit confused

[livid hound]

what exactly are you confused about

the same principles/definitions for surface area and volume can be applied

[maiden osprey]

the side lengths

what would i have to do abt the side lengths?

the 10ft and 8ft

volume for triangle is 1/2 Bj

Bh

so would i do

[leaden snow]

volume of triangle wot

[ember python]

Why are you worried about random side lengths

And yes triangles don’t have volume

They have area

[maiden osprey]

area

my bad*

[ember python]

If you can find the area of the triangle, do it

Then find the volume

[maiden osprey]

ok

one sec

[ember python]

It doesn’t matter if you haven’t used some of the information

[maiden osprey]

thanks

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[clear grail]

how do i solve this?

[lament sonnet]

For the partial fractions, write $\dfrac{7}{k(k+8)}=\dfrac{A}{k}+\dfrac{B}{k+8}$ for some $A,B$. Then solve for $A,B$.

[wraith dagger]

1345631

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[crimson sedge]

why is the x sin and not cos?

[leaden snow]

@crimson sedge You can actually parametrize it both ways. It only changes where you start "walking along the curve". For example, if you set x = a cos(t) and y = b sin(t), then for t=0, the first point you get is (a, 0) while for x = a sin(t) and y = b cos(t) you start at (0, b)

[crimson sedge]

im afraid I don't follow

isn't[0, 2pi) just your standard thing?

in the polar coordinat

@leaden snowhello?

oh

so my solution starts from the x axis while this solutino starts from the y

how do I know for sure this ends at 2pi and not pi?

[leaden snow]

Yes that doesn't make either one wrong

[crimson sedge]

ok thanks

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[crimson sedge]

Hi could someone help me with this question I attempted it but I’m not sure if it’s right at all

[crimson sedge]

That’s the question

Here’s my answer

[upper abyss]

Looks good

[cedar kiln]

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[crimson sedge]

Thanks

[cedar kiln]

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[crimson sedge]

ofc I wouldn't have done all of this in a normal situation, but I wanted to show the whole thing so that I know the procedure is ok

[lament sonnet]

It isn't. This is an abuse of notation and is wrong. You should do it the way you are taught, rather than trying to use something you do not fully understand.

[crimson sedge]

except I'm not taught but I'm self-learning .-.

[lament sonnet]

Then you should learn it properly

It is a mess of notation. Please try to learn the correct way to solve and write it. Note that the integral in your question does not actually converge

[crimson sedge]

Ok, but please calm down, I'm sorry. I'm just trying to learn this stuff by myself, I know I used improper notation but I didn't know how to show what I did without abusing of notation. And for the fact that the integral doesn't converge, yeah you're right, I just remembered. Thank you, but try to be less intimidating when you help someone 😅

[lament sonnet]

Okay. Didn't know it was intimidating

[crimson sedge]

Sorry, didn't mean you were intimidating. I just felt stupid for a moment haha.

Anyway, is this how I should've solved it?

[crimson sedge]

last time I completely forgot to check the domain of the function that's why I did all of that mess

<@&286206848099549185>

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[vocal halo]

Hi, my math book is in norwegian. The topic is vectors, and how to find the distance from a point to the line. I'm just wondering how they went from -15-45+90k to k = 2/3, that's where I'm stuck. I'm not sure what happend between those lines

[cedar kiln]

@vocal halo Has your question been resolved?

[cedar kiln]

@vocal halo Has your question been resolved?

[vocal halo]

<@&286206848099549185>

[normal wraith]

\begin{align*}
0&=-15-45+90k\
0&= -60+90k\
0&= 30(-2+3k)\
0&= -2+3k\
2&=3k\
\frac{2}{3}&=k\
\end{align*}

[wraith dagger]

Brun。

[normal wraith]

are all of these steps clear?

[vocal halo]

yes

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[thick stone]

ok I saw this problem on a youtube shorts and im confused on how the awnser is 9 the problem is 6 ÷ 2(1 + 2). I got 1 by using PEMDAS by adding the 1 and 2 in parentheses and then multiplying it by the 2 next to it and dividing 6 by 6

[cedar kiln]

@thick stone Has your question been resolved?

[pure leaf]

Tell me, what does PEMDAS mean to you

[thick stone]

Parentheses, exponents, multiplication, division, addition and subtraction and it should be done in that order

[pure leaf]

Almost, but here's what it actually is:

1. Parentheses
2. Exponents
3. Multiplication/Division
4. Addition/Subtraction

As you see, multiplication and division have the same importance.

If two operators have the same importance, they must be applied from left to right

[thick stone]

Ah so what I should do is solve parentheses and then divide the 6 by 2 and then multiply by three?

[pure leaf]

Yes.

So you get 3(3), which is 9

[thick stone]

Thank you very much

[pure leaf]

You're welcome

[thick stone]

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[little spruce]

So I got this question wrong and don't understand it

The first pic is for context

I need help on 3b

so far what im doing is taking the equation and plugging in 1 and 2 into the time

then i am subtracting to get the decimal

i then multiply by 100 to get the percent

but its wrong

[pure leaf]

2.94 is the difference, in milligrams, between the amount of drug left in the body after 1 hour and after 2 hours. But you submitted that value as a percentage, which is wrong.

[little spruce]

right i saw that mistake

what i dont get is what to do after getting the difference

[pure leaf]

To get the difference as a percentage, you need to divide it by 19.55

before multiplying it by 100

[little spruce]

so divide 16.61 by 19.55?

[pure leaf]

no

2.94

[little spruce]

ohh i got it now

thank you soo much

[pure leaf]

np

[little spruce]

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[little spruce]

.reopen

[cedar kiln]

✅

[little spruce]

so i got 15.03 as the final answer

would that be right?

@pure leaf

[pure leaf]

15 actually, because you have rounded off your values

[little spruce]

right

ok i get it now

thank you soooo much agian

[pure leaf]

No problem

[little spruce]

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[random oyster]

no idea how to do this

also not calculus class so I can't use derivatives haha

[flint plinth]

how are you defining "tangent" without the concept of derivative?

[random oyster]

i am on

average rate of change

and instantaneous rate of change unit

AROC IROC

difference quotient

etc

[cedar kiln]

@random oyster Has your question been resolved?

[cedar kiln]

@random oyster Has your question been resolved?

[hot bison]

need help?

[random oyster]

not this anymore

[hot bison]

alright

[random oyster]

Determine the values of a and b so that the function f(x) = x^2 + ax + b has a minimum at (3,9)
i

no calculus allowed

[hot bison]

a no calculus?

hm

what your definition of minimum in function

[random oyster]

i am on AROC and IROC unit

average rat eof change

instant rate of change

[random oyster]

where IROC is slightly negative to the left slightlgy positive to the right

[cedar kiln]

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[dark iris]

probably a very simple question but I'm struggling. I have values that are between 0 and 1, and I want to amplify them so that they skew closer to the extreme ends of the scale if that makes sense

[dark iris]

not sure how to do it in a way that keeps it in between 0 and 1

[cedar kiln]

@dark iris Has your question been resolved?

[obtuse gyro]

Could you multiply them by something >1 and <2 ?

@dark iris

[dark iris]

mm probably not bc multiplying some of my values by anything greater than one would take it outside of the 0-1 bound

[obtuse gyro]

Not if it is smaller than two

Try multiplying by 1.999999

Wait

What am i thinking L0L

Dont mind me im sleep deprived

[dark iris]

lol it’s ok

[obtuse gyro]

If ur number is n you could try multiplying it with 2-n

[cedar kiln]

@dark iris Has your question been resolved?

[dire geode]

Apply a density function to it that has more mass where you want

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@dark iris Has your question been resolved?

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[dense abyss]

hi everyone, i hope you're having a great day. i'm an igcse maths student and my exams are in around 2-ish months, i'm doing past papers for practice and i don't understand this particular question about vectors, kindly take a look and tell me what you think

[dense abyss]

i've included screenshots

i was able to do it until part (d)

[sleek condor]

i'm reading

[dense abyss]

yay someone's here

[sleek condor]

did you do d?

[dense abyss]

thanks benjamin

no i'm afraid i have no idea what to do

[sleek condor]

lets check what you got for a b and c then

to be sure

[dense abyss]

okay yeah

b) a+2b/u = OP

c) b - a/lamda = AP

[sleek condor]

to be sure

what is divided?

like is it a + (2b/µ)?

[dense abyss]

nah it's like uh

[sleek condor]

or (a+2b)/µ

[dense abyss]

(a + 2b)

yeah the second one

[sleek condor]

ok

right

[dense abyss]

i have the mark scheme and i checked

so we chillin

but i don't understand scalar comparisons :/

[sleek condor]

i think it has to dowith pythagoreas

since there are right angles

[dense abyss]

uhm

nah i think it's more w like scalar comparisons

and equating vector components

[sleek condor]

oh yeah

but since your vector base is a and b

with a and b being perpendicular

[dense abyss]

hmmm

[sleek condor]

its just pythagoreas

its the same

[dense abyss]

look i get pythago thingy

but like it's like i have to find the value of scalar quantities

[sleek condor]

ok maybe you could explain me what you mean by "scalar comparison" then because ive never heard it (i'm coming from france and we have different names for most things)

[dense abyss]

hmmmm

alright

uh

scalar and vector quantities?

[sleek condor]

i know what a scalar and a vector is

[dense abyss]

okay

[sleek condor]

but you seemed to talk about a method

[dense abyss]

yeah

[sleek condor]

or something

[dense abyss]

yeah yeah yeah

so essentially we have column vectors and we have a constant represented by a variable multiplied to it

now you understand the method of substitution

i think it's somthing to do w that

[sleek condor]

what i guess from what youve said is that if we can have µ*X = Y we can derive µ from X and Y?

[dense abyss]

bc derivative kyu len ge?

sorry

why would we take derivative?

ohhhh derive

probably

[sleek condor]

derive as deduce

im sorry if that wasnt clear

ok so i think i got it

or at least a good starting point

try to link OP and AP together

through an equality between vectors

@dense abyss

then express everything in terms of a and b

[cedar kiln]

@dense abyss Has your question been resolved?

[cedar kiln]

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[worldly atlas]

It is given that 371n+25 is a four digit perfect square (n is positive)

[tropic oxide]

what's the question?

[worldly atlas]

Whats n

[tropic oxide]

okay

and have you made any progress so far?

[worldly atlas]

I have no ideas wha to do

I turned it into 371n+25=xsqaure

[sleek condor]

try to determine for what values of n you would get a result thats 4 digits

and then determine perfect squares of 4 digits

that would be a good starting point i think

[worldly atlas]

1500 possibilities

Can’t

[sleek condor]

i'm not telling you to check them one by one

just starting to have intervals for the values of n and a (with 371n+25=a²)

[tropic oxide]

1500 possibilities for what?

[sleek condor]

for n i guess

but there are much less for a

ok so i guess i may give some better advice: consider the equation a² = 25 mod(371) , you are trying to find the square root of 25 mod 371

hint: 371 prime decomposition is 7 and 53

use the chinese remainder theorem

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[fallen prawn]

some place don’t understand

if c=6

then a b undefined?

im too bad at math

[green hornet]

they are the two roots of the quadratic right?

[fallen prawn]

yes

[green hornet]

a,b

since you know the whole quadratic, find the roots

[fallen prawn]

but no real root

[green hornet]

c is -6 btw

[fallen prawn]

bruh

can u teach me when it become -

[green hornet]

there is no rule as such

just when x=0 y=6

[fallen prawn]

ok

thank you

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[crimson sedge]

What's the skater's displacement from A-D.

[heady grotto]

140m

basically you look at the absolute distance between the initial position and the final position

[heady grotto]

which is displacement.. it basically means like how far out he is from the original position

[cedar kiln]

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[crimson sedge]

Thanks so much

[cedar kiln]

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[austere hollow]

Hi, I don’t know from where to start in this question

[gray condor]

2013
8x+7x+5x = S
7y+5y+4y = S

right?

20x = S

16y = S

20x =16 y

5x = 4y

[austere hollow]

But Amanda received €240 more in 2014

[gray condor]

wait bro, I’m talking

[austere hollow]

👍🏽

[gray condor]

7y = 8x +240

solve simultaneous eqns

and voila

[austere hollow]

Yes thank you so much 😊

[gray condor]

no worries my guy

Don’t forget to close the channel

[austere hollow]

How?

[gray condor]

.close

[austere hollow]

.close

[cedar kiln]

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[gray condor]

also, if you don’t mind

what did the channel name say

Ruben Toss was a good CB?

[austere hollow]

Ruben toss?

[gray condor]

@austere hollow you there bro?

I prolly didn’t use google translate right

anyways

[austere hollow]

Oh that’s Ruben Dias

[cedar kiln]

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[austere hollow]

Man City’s Portuguese defender

[austere hollow]

.close

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[grand condor]

If the distance between (a, 2) and (1, -3) is ✓29 . Find the value of a.

[grand condor]

helpp

[lost bough]

lemme look

[solid quarry]

use distance formula and solve for a

[lost bough]

@grand condor

sry

i'll do it withıt formula

[bitter reef]

without formula you get a right triangle

[grand condor]

ohh

[lost bough]

@grand condor close the channel if you done

[grand condor]

oohh how

.close

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[grand condor]

thanks

[cedar kiln]

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[smoky stump]

How do you do the second last one at the bottom of the page

[solid quarry]

do u know cross product

[smoky stump]

Yeah

[solid quarry]

use that to find a normal to the plane and then plug into dot(p-c,n)=0

[smoky stump]

What is p c n

[solid quarry]

where p is a point in space, c is the center point (any point in the plane works), n is the normal

[smoky stump]

What cross product do I take

[solid quarry]

you know that the cross product of 2 vectors is perpendicular to both?

[smoky stump]

Yeah

So anyone right

[solid quarry]

in order to get a normal to the plane, you must choose 2 vectors which are tangent to it

[smoky stump]

This is what I got

[solid quarry]

cant read that

what vectors r u crossing

[smoky stump]

The first and second vector

It’s wrong and I pass in each of the vectors

[solid quarry]

u misunderstood

try again

[smoky stump]

I’m confused

[solid quarry]

your vectors look like this

they dont exactly look tangent to the plane do they

rather the plane sits on their tips

[smoky stump]

Yeah

And in order to find the equation to the plane done we need to find the normal

So do we do the p - c and the cross product to d-c

Assuming p,c,d are any of the vectors

[solid quarry]

yeah thats better

unfortunate labelling tho

i already used p and c in the plane equation

[smoky stump]

Let me try to do the working a lot neater to see if I was right

No I’m lost

.close

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[smoky stump]

Thanks

[cedar kiln]

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[vale atlas]

I would greatly appreciate if someone can check my answer for problem 1 & 2, the quarterly part messed me up quite a bit

It looks like I followed the formula in this picture to the tee, but I have a gut feeling I did something wrong

[cedar kiln]

@vale atlas Has your question been resolved?

[vale atlas]

<@&286206848099549185>

[cedar kiln]

@vale atlas Has your question been resolved?

[vale atlas]

No

[heady grotto]

@vale atlas do you happen to have the actual solution to it?

Q1 should be 16,827.32 if im not mistaken

[cedar kiln]

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[vale atlas]

.reopen

[cedar kiln]

✅

[vale atlas]

I do not have the actual solution for it, nor do I have any examples using quarterly

@hot dock is there anyway you could show me how you solved it?I know I have # 2&3 correct

[heady grotto]

okay so basically the way i like to think of it

isnt with the formula but with what it exactly is

so you have your deposit

which is $640 dollars

and it gets compounded by 5.6% every quarter

for 15 years

basically you're getting 1.056 of your initial amount every quarter

rather than thinking of it in quarters of a year

i just thought of it as 60 years

since you're gonna be getting it compounded 60 times

thus you should end up with 640(1.056)^60

[vale atlas]

Okay thank you!

[heady grotto]

no worries

[cedar kiln]

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[glad moth]

This more involves science than math

but in case you could help

[cedar kiln]

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[glad moth]

<@&286206848099549185>

[cedar kiln]

@glad moth Has your question been resolved?

[cedar kiln]

@glad moth Has your question been resolved?

[cedar kiln]

@glad moth Has your question been resolved?

[dire geode]

.close

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[crimson sedge]

Im confused

[crimson sedge]

Why is it 434?

I got a = 7

r = 2

k = 5

used the geometric series equation

[dire geode]

Use a calculator

[crimson sedge]

and i got 217

but that answer is double

my answer

why?

[dire geode]

Show your formula

[dire geode]

This only works if your sum starts at 0

[crimson sedge]

Oh? Then what formula do i use?

do i have to add it all up?

do k = 1,2,3,4,5

[rustic siren]

if you got 217 why did u say NaN?

[dire geode]

You manipulate your sum so that the index starts at zero. Factor something out of the sum

[crimson sedge]

because none of my options had 217

[glad kestrel]

NaN is not a number lol

[crimson sedge]

Lol, i did the long way

and i got 434

here's what i did

Has to be a faster way than this

[dire geode]

.

[rustic siren]

u need 7*2 there

cuz its the place of the first element

[crimson sedge]

yeah

7* 2^1 is the same as 7* 2

[rustic siren]

so 14(1-2^5)/-1

[crimson sedge]

14?

what

where?

how?

[glad kestrel]

?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

What's the name of this topic?

Is it convergence of geometric series?

[crimson sedge]

.close

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[crimson sedge]

Is it to be expected that the standardized coefficients increase in magnitude when variable are removed from a regression model?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

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[crimson sedge]

.close

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[crimson sedge]

How do I calculate this ? Pls help

[crimson sedge]

I’m also having issues with this problem too if anyone understand this

<@&286206848099549185>

Sorry for pinging 5 mins early I only have 10 mins left to solve these two questions and im super clueless 🥺

[cedar kiln]

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[crimson sedge]

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[loud anchor]

can u first write the transition matrix?

[cedar kiln]

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[versed arch]

can this be rearranged for x?

(x^2)*ln(0.5-x)=y```

[glad kestrel]

definitely not in an elementary way

i don't even know if you can in a nonelementary way

[cedar kiln]

@versed arch Has your question been resolved?

[glad kestrel]

,w solve for x, y=x^2ln(.5-x)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by a disappointing son#0540

[glad kestrel]

you're outta luck friend

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[crimson sedge]

i need help

[crimson sedge]

😭

[glad kestrel]

it's about 3 and a half

[crimson sedge]

huh

nvm

[glad kestrel]

sorry i'm still working on my telekinesis :(

[crimson sedge]

its alr

[cedar kiln]

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[crimson sedge]

ooops

[cedar kiln]

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[glad kestrel]

what have you tried

[warm condor]

so

i did 15/2^2 and -2^2

but i only know how to do it when the center is the origin so im confused

[glad kestrel]

the equation for a circle is (x-h)^2+(y-k)^2=r^2, where (h, k) is the origin and r is the radius

[warm condor]

yup

(x-9)^2+y^2=r^2

[glad kestrel]

and how could you go about finding the radius?

[warm condor]

doing pythagorean theoram from the center

[glad kestrel]

right

so do that and see what you get

[warm condor]

but idk how to do it from a point that isnt the center

i mean the origin

@glad kestrel

[glad kestrel]

well how do you get the distance between two points?

[warm condor]

OH

distance theoram

formula*

[glad kestrel]

mhm

[warm condor]

alr

i got 5/2

and i have to square that right

(x-9)^2+y^2=25/4

@glad kestrel this is my final answer, would this be correct

.close

[cedar kiln]

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[glad kestrel]

looks good, and remember you can always graph it to make sure

[warm condor]

mhm ty

[cedar kiln]

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[frail edge]

b is making me scratch my head

how do I find the basis?

[flint plinth]

you don't necessarily have to find it explicitly if you use the first part and the fact that any square matrix can be expressed as a triangular matrix with respect to some basis, and the diagonal elements of that triangular matrix are precisely the eigenvalues of the original matrix

[frail edge]

I see. How can any square matrix be represented as upper triangular?

Like with basis (0, 1) (0, t)?

[flint plinth]

it's a standard proof that you should be able to find in textbooks. for example, I know that Axler's "Linear Algebra Done Right" has a proof

this channel is in use, you should open one of your own

[frail edge]

Thanks, I'll look for it and see if it makes sense. I might be back.

.close

[cedar kiln]

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[crimson sedge]

Hello

Can I ask a physics question here?

[glad kestrel]

#❓how-to-get-help you can get an open channel and ask it there

[cedar kiln]

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[fast ledge]

let a,b in Z not both 0 and let d = gcd(a,b). suppose that: there exists (s,t) in Z: as+bt = c
prove that d|c.
How would you prove this?

[flint plinth]

well d is a common divisor of a and s, so it divides as and bt, right?

[fast ledge]

yess

[flint plinth]

and therefore it divides as + bt

[fast ledge]

how would i write this as a formal proof?

[flint plinth]

honestly if I were writing the proof I'd write what I wrote above, I'm not sure how much more formal you can make it without pointlessly obfuscating it

but only you know what sort of formality is required in your situation

[fast ledge]

ok thank you

[cedar kiln]

@fast ledge Has your question been resolved?

[cedar kiln]

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[lucid maple]

ADB = 45deg
ACB = 15deg
BD = DC
BAC = ?

[fleet breach]

Idrk but I would create a point S on the line BD perpindicular to A
Then see what you can do with the right angle triangles

[rugged palm]

Is BAD 90deg?

[lucid maple]

i don't know

it's the median

BD = DC

[fallen heath]

wow I'm curious how you concluded that from the given construction
"BAD is 90°"

[fleet breach]

no I am wrong

i think

[fleet breach]

How far are you?

[lucid maple]

wdym?

[fallen heath]

if you're allowed to use trigonometry, you can write BD and DC in terms of AB and AC and equate them

[fleet breach]

LIke do you need help?

[lucid maple]

yeah i need to make an auxiliary construction and i can't figure out which one

[lucid maple]

sure lemme try

ok now i have this

[fallen heath]

perfect, solve it

[lucid maple]

how?

[fallen heath]

2 sin(A) sin(B) = cos(A - B) - cos(A + B)

[cedar kiln]

@lucid maple Has your question been resolved?

[lucid maple]

yeah, 2sin45 = sqrt2 but then what?

any ideas for an auxiliary construction?

[cedar kiln]

@lucid maple Has your question been resolved?

[lucid maple]

nobody?

[fallen heath]

ofcourse you won't get anywhere with it cause your equation's faulty in the first place

AB/AC = [sin 15] / [sin 45 + x]
AB/AC = [BD (sin 45) / (sin x)] / [DC (sin 45) / (sin 30)] = 2/(sin x)

[lucid maple]

and x is?

which angle?

so i came at a much simpler equation:
sin(135 - x) = 2 * sin15 * sinx

no idea what identity to use

the solution is supposed to be 135

so x is supposed to be 105

[cedar kiln]

@lucid maple Has your question been resolved?

[lucid maple]

how do i solve sin(135 - x) = 2 * sin15 * sinx

[rustic siren]

use sin(alfa-beta) rule

[lucid maple]

sin45 * (sinx + cosx) = 2 * sin15 * sinx

now what?

[rustic siren]

/cos

[lucid maple]

sin45 * ((sinx/cosx) + 1) = 2 * sin15 * (sinx/cosx)

now?

[rustic siren]

now solve it

[lucid maple]

wdym solve it?

how?

[rustic siren]

what is the unknown here?

[lucid maple]

well what exactly are the steps to solve this?

isnt there more manipulation?

[rustic siren]

answer pls

[lucid maple]

the unknown is x

[rustic siren]

here?

[lucid maple]

yes

[rustic siren]

okay

so whats sinx/cosx

[lucid maple]

tanx

[rustic siren]

yup

tanx=y => number * (y+1) = number * y

[rustic siren]

.

[lucid maple]

now i have tanx = sin45 / (2sin15 + sin45)

@rustic siren

[rustic siren]

tanx = sin45 / (2sin15 minus sin45)

by me

but yeah

whats the question from here?

[lucid maple]

well don't i need to transform the nominator into cos?

[rustic siren]

?

no

just write in the numbers

[lucid maple]

wdym?

[rustic siren]

???

why do you need cos?

[lucid maple]

well i need to get x

oh

how do i get x?

[rustic siren]

whats the right side equal to?

[lucid maple]

sin45 / (2sin15 + sin45)

[rustic siren]

what does it equal to?

[lucid maple]

tanx

[rustic siren]

no

give me the number

like 1.5 or something

[lucid maple]

oh you're right it's minus

it's -3.732

sin45 / (2sin15 - sin45)

[rustic siren]

yeah

and use arctan now

[lucid maple]

-75 deg

but im not allowed with a calculator

[rustic siren]

wow

then u need to know the values of all these?

eww

well, i dont know how i could help with that

try to learn 15 30 45 60 degrees of sin and cos

[lucid maple]

yeah and once i have the value then what?

i have to learn that arctan(-3.732) = -75?

[rustic siren]

its just -2-root(3)

which is kinda similar to sin75 and cos 75

but if you didnt see a lot of these before its hard to notice, maybe ask your teacher then, why cant you use a calc in these cases

[lucid maple]

well i can't use a calculator in the olympiad

[rustic siren]

😮

what olympiad?

[lucid maple]

the maths olympiad?

[rustic siren]

well, gl firstly

and maybe this isnt the easiest way to solve it

maybe some sin rule would have been enough from the start

[lucid maple]

well the problem would be solved by some auxiliary construction or trigonometry

[rustic siren]

oh, that too, i always liked the "and notice, that..." parts

[lucid maple]

.close

[cedar kiln]

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[night orchid]

Hey

[night orchid]

Question states: "Considering the differential triangle, find the relationship between (ds)^2 and the other coordinates (r, theta)"

I Used pythag to find this eqn:

$ds = \sqrt{(1+(\frac{rd\theta}{dr})^2)} dr$

[wraith dagger]

Xyz.

[night orchid]

the logarithmic spiral has equation $r=r_0 e^{\theta \cot(\phi)}$

[wraith dagger]

Xyz.

[night orchid]

however my problem here is how exactly do I "find the relationship between (ds)^2 and the other coordinates (r, theta)".

[winged sonnet]

Someone do this

[night orchid]

bro what

[night orchid]

thats just pythag bro

[cedar kiln]

@night orchid Has your question been resolved?

[cedar kiln]

@night orchid Has your question been resolved?

[night orchid]

<@&286206848099549185>

[gray condor]

not your page

$(ds)^2 = (1+(\frac{rd\theta}{dr})^2) (dr)^2$

[wraith dagger]

Rylo

[gray condor]

Am I missing something?

isn’t this just a modified version of what you sent

[night orchid]

yh its just this squared

[gray condor]

I’ve defo seen dr/dtheta before

but not ds

so I’m kinda trying this with you

[night orchid]

ds here is the arc length of the spiral

[gray condor]

please bare with me

[night orchid]

no worries

I've been going at this problem all day, this is the first part but luckily none of the other parts relied on it

[gray condor]

ds? not even s, just ds??

[night orchid]

yup

i found the eqn for s(theta) in a later part of the q

if u think its helpful

[gray condor]

ds^2 = dr^2 + dtheta ^2 right ?

[gray condor]

if it’s a later part, we might not need it for this

[night orchid]

(rdtheta)^2

from the eqn for arc length L= r*theta

[gray condor]

considering you already found this and (ds)^2 is what pythagorus would have given you anyways, why sqrt it ?

[night orchid]

why not lol

i tried inserting it as the answer but it says its wrong

[gray condor]

because you want to find ds^2

that ds^2 ?

[night orchid]

yh

I think it has to do with them wanting

[gray condor]

wanting… .

[night orchid]

"relationship between (ds)^2 and the other coordinates (r, theta)"

[gray condor]

?

ahh

[night orchid]

and since dr and dtheta are differentials maybe they don't want it in that form

[gray condor]

cot(phi)r = dr/dtheta

just to make sure, are phi and theta independent?

[night orchid]

yes

[night orchid]

i got that too dk where it comes into play tho

[gray condor]

r is a constant

[night orchid]

r_0 is

[gray condor]

well yeah

r(dr/dtheta)

= r(rcot(phi))

and then that squared

but what about dr^2

[night orchid]

here I factored it out

[gray condor]

can we just keep that ?

OH WAIT

[night orchid]

in hopes that finding ds/dr would help

[gray condor]

it’s r(dtheta/dr)

[night orchid]

yh

[gray condor]

so that’s (tan(phi)dr)^2

right ?

i’m stupid

[night orchid]

hmmmmmm

hold on would $\theta = \ln{\frac{r}{r_{0}}}-\cot\phi$

[gray condor]

wait, why?

[night orchid]

no ry

sry

i subbed wrong equation

from my book

hold on

thats theta

[wraith dagger]

Xyz.

[night orchid]

then differentiate wrt r,

[gray condor]

hold on would $\frac{d\theta}{dr} = 1/ \frac{dr}{d\theta}$

[wraith dagger]

Rylo

[night orchid]

bro i dont trust that shit

it doesnt work in my head so i never do it

[gray condor]

wdym 😂

[night orchid]

i just go the long way

i heard ppl do that

[gray condor]

bro,

[night orchid]

i was like nahhhhh

[gray condor]

that works

please

trust me

[night orchid]

bro but?

[gray condor]

just look at dr/dtheta

what’s dr/dtheta

[night orchid]

ur telling me reciprocating a differntial works

[gray condor]

yes

first differentials

[night orchid]

and u trust that?

yh ofc

[gray condor]

I’ve been doing this since high school

defo doesn’t work for second differentials or higher

[night orchid]

ok prove it

[gray condor]

prove what ?

idk how to except it just does

[night orchid]

$r=r_0 e^{\theta \cot(\phi)}$

[wraith dagger]

Xyz.

[gray condor]

mhmm

what’s dr/dtheta

we can do it both ways right, but for now,

[night orchid]

1/(r_0 * r)

hol on i need to go eat

imma be back in a bit

[night orchid]

nvm im braindead

its 1/(r_0 * r cot phi)

[dire geode]

.close

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

can anyone tell me the approach to this question

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[glacial steppe]

This question

[glacial steppe]

I am given no context on what it is I just need help determining what strategy or formula to use

.close

[cedar kiln]

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[indigo badge]

This is all this question is asking, what am I doing wrong here? I thought the first vector would just be the unit vector of x, no? Ignore the rest of the vectors, I'm just confused on how to do the process

[indigo badge]

And no, it's not itself

This is what I was going by

[obsidian coral]

The first vector is itself, then for the others, you use that equation

[indigo badge]

but it's not

I already tried submitting it like that

oh I messed up the unit vector calculation didn't I

it wants a unit vector in the end

[obsidian coral]

You might have did math wrong

[cedar kiln]

@indigo badge Has your question been resolved?

[indigo badge]

I did, thank you anyways :)

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[cedar kiln]

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[vital anvil]

<@&286206848099549185>

[cedar kiln]

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[reef venture]

what do you need to do? simplify?

[craggy anchor]

yep

[reef venture]

what have you tried

[craggy anchor]

uh i just dont know how to start

i probably have to remove the -1/2 from the right side but im not sure how i do that

[lucid maple]

well the second parantheses is the inverse of the first one

so you can rewrite the second term as (x^2 / y^4) ^ (1/2 - 1/m)

[craggy anchor]

so you can just reverse both?

[lucid maple]

the point of this is to get the 2 powers on the same base

i guess you can reverse the first one instead of the second

but you have to reverse just one

[craggy anchor]

okay yea that helps a lot

tysm for your time

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[cedar kiln]

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[arctic bluff]

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[ocean viper]

#❓how-to-get-help
• When asking for help, do not insist on getting just the answer; we are here to help you learn, not do the work for you. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.

[warped ingot]

I’m not good with these big questions

[heady grotto]

add up the quarters in each year, seperately and then divide them by 4 to get the mean

then you should be able to know what to do to find the % increase

[warped ingot]

So i do 1+2+3+4?

[heady grotto]

no

the value of the profits in each quarter

add those up

[warped ingot]

So the middle box?

[elfin hemlock]

Sounds like you don’t even understand what it is asking of you

Step 1 is understanding the question

Anything you don’t understand in the question?

[warped ingot]

Yh I don’t understand the question

[elfin hemlock]

Why is that not how you ask for help then?

And say what you don’t understand

Surely you understand some of the words

[warped ingot]

It’s asking me to find the mean right?

Of the table?

[elfin hemlock]

You will need the mean

But that is not the answer it is asking for

[cedar kiln]

@warped ingot Has your question been resolved?

[cedar kiln]

@warped ingot Has your question been resolved?

[crimson sedge]

200 people stand in a circle in order to 1 to 200 . number 1 has a sword he kills the next person (i.e. No. 2) and gives the sword to the next living person (i.e. No. 3). all people do the same until only 1 survives. wich number surivives to the end?

[cedar kiln]

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[quaint cove]

helloo can I ask for help?

[vagrant breach]

yeah that's what the channel is for

just post the question

someone will come by and help

[quaint cove]

in calculus

[crimson sedge]

so easy

[quaint cove]

really?

[crimson sedge]

nah

im ass at math

[quaint cove]

oh I think Ive found the right person

[crimson sedge]

ok

[quaint cove]

that's from Techniques of Integration

Im stuck I dont know how to solve it

[livid hound]

try u-sub

[quaint cove]

Okay, thank u so much

is it possible that we can use both u-sub and intergration by parts?

[bitter reef]

you don't need integration by parts here I think

[livid hound]

u-sub should be sufficient here

sometimes ibp won't get you anywhere

(and may even get you further from the result)

[quaint cove]

Okay, thank you so much guys!

[quaint cove]

btw, how to derive x^2 so I can get the same x^3 here

[cosmic steppe]

Use IBP

I don't think you can use u sub

[livid hound]

sub works

[cosmic steppe]

I mean I guess you can

But then you'll get x = sqrt(u - 8)

and then that's just going in circles

[livid hound]

there's no need to explicitly isolate x

[cosmic steppe]

actually

I guess you can u sub

But wouldn't that just be (u-8)sqrt(u)

And then that's just an IBP problem from there

So you might as well do IBP from the get go

[livid hound]

why do you insist on ibp

[cosmic steppe]

Square root and the u-8

[livid hound]

when you can just distribute

[cosmic steppe]

Distribute the u-8 into the square root?

Then you just get a quadratic under the square root

[livid hound]

you're overthinking this

and overcomplicating it

consider basic distributive property

[cosmic steppe]

Do I have to get up from bed and write this down on paper

Hold on

You know what

I didn't even need paper I'm just being a dumb dumb

@quaint cove use u sub, then use your integral laws to break it up

If you need to break it up, that is

[quaint cove]

i envy you guya

guys

I already got that part

is this right?

?

[cosmic steppe]

@quaint cove come here lemme Latex it

[cosmic steppe]

$\frac{1}{2}\int x^{2}\sqrt{u}du$

[wraith dagger]

Umbraleviathan

[cosmic steppe]

So you're on the right track

But now you have that stupid x^2

You know that u = x^2 + 8

So what is x^2 in terms of u?

@quaint cove

[quaint cove]

idk either

we plus 1 plus 1?

[cosmic steppe]

You have $u = x^2 + 8$, correct?

[wraith dagger]

Umbraleviathan

[quaint cove]

yes

[cosmic steppe]

So you wanna get rid of the x^2 in the integral

[cosmic steppe]

So what is x^2 in terms of u?

[cosmic steppe]

Simply manipulate the equation here so x^2 =

So if $u = x^2 + 8$

[wraith dagger]

Umbraleviathan

[cosmic steppe]

Then $x^2 = ?$

[wraith dagger]

Umbraleviathan

[quaint cove]

1?

[cosmic steppe]

in terms of u

Know what I mean by "in terms of u" right

[quaint cove]

what do u mean in terms of u

nope

[cosmic steppe]

the variable "u"

$x^2 = u - 8$

[wraith dagger]

Umbraleviathan

[cosmic steppe]

You understand ?

[quaint cove]

oh so thats what u meant

[quaint cove]

yea2 now ik

[cosmic steppe]

Yeah

So now replace x^2 with u-8

$\frac{1}{2}\int (u-8)\sqrt{u}du$

Distribute the sqrt(u)

[wraith dagger]

Umbraleviathan