help-17

[undone aurora]

I dont get what Im missing

[wraith venture]

converges

[burnt totem]

https://www.youtube.com/watch?v=FPK6LO1iiXc&t=519s

[wraith venture]

Not converged absolutely

[undone aurora]

oh

ty

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[weak dome]

Hi! How do I find the area of a scalene triangle? I know the side lengths, not the height

[urban edge]

sorry for the low quality

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[wooden sable]

Hey so why doesn’t 1/2AB sinC work for 14, but it does for 15? I got a incorrect answer when applying that rule for 14, but 15 worked?

[wooden sable]

1/2 times 8.5 times 12 times Sin125 gave me -31.418, why didnt this work?

<@&286206848099549185>

[rose raft]

you did sin 125 in radians

[wooden sable]

can you explain what that means?

i just put Sin125 and thats what it told me?

[rose raft]

,calc sin(125)

see

[twin meteor]

Result:

-0.61604045918866

[rose raft]

uh

[wooden sable]

Okay so let me calculate with that number now 1 sec

[rose raft]

thats wrong

[wooden sable]

okay so you see why im confused right?

[wooden sable]

Oh'

[rose raft]

ye

[wooden sable]

Okay well whats the difference between radians and degrees?

[rose raft]

360 degrees = 2 pi radians

[wooden sable]

Oh okay

I appreciate the help you saved a lot of stress

[rose raft]

ok

[wooden sable]

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[gray yarrow]

right side

third row

you have 2/3

you forgot the 9

i think so

which should be 2/5+6=32/5 or 6.4

nice

[eager walrus]

is this no calculator

you sub

[acoustic monolith]

what's the derivative of sin(x^36)/36

Simple as

The shortcut is probably what they taught you in class lol

Yea

u=x³⁶ du=36x³⁵dx
Change the boundaries
If x is 0 u is 0
If x is ³⁶√π u is π
Integrate

Yes, basically, in these examples the complicated part or the part that it's easier nested inside another is u

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[red crystal]

i just have two quick questions
https://youtu.be/3d6DsjIBzJ4?t=71

[red crystal]

why does he sub in theta squared over 2 instead of 1 - theta squared over 2

wait nvm

lmao

i just realizied

anyway

where can i use or find math animation softwares to help with tutoring friends online

i think his is harder to use for the purpose of tutoring which i think is manim right?

[trim walrus]

Well there's a software that 3blue1brown has made but you've know coding for that

[red crystal]

yeah ik how to code but nothing crazy but pretty good knowledge

[trim walrus]

Yes

[red crystal]

its python right

[trim walrus]

Ye

[red crystal]

i think its harder to use for like making quick animations i think it really takes time and dedication to shell out what he does

i truly admire him

i was looking for anything that would be fairly easy to write math in so that i dont have to draw it in microsoft paint or something and then it would look awful

do they use latex when they make those animations too? i wonder how they actually write out the math

[trim walrus]

Manim is based on latex I guess

[red crystal]

i think after learning it it could make things easier but im not sure

alr i'll look into it

thx!

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[chrome blade]

how?

[chrome blade]

how is it -x+5

[spare girder]

I dont think they finished the question

[spare girder]

-x+5 is the expansion of (x-5)(0-1)

[exotic arrow]

can someone help?

[vast shale]

#❓how-to-get-help

[chrome blade]

looks like he first did 0-1

and then started multiplying

[vast shale]

yep

what exactly are you confused on?

[chrome blade]

when you do the 0-1 it = (-1) right? or is it without brackets

[vast shale]

doesn't really matter

(-1)=-1

[chrome blade]

gotcha

makes sense, thanks

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[cinder aurora]

how do I solve for angle 1, and angle 2 in this problem?

[vast shale]

What is 150° and 84°

[cinder aurora]

they're arcs on the circle

[vast shale]

Length of those arcs?

[cinder aurora]

yeah the lengths of them

[vast shale]

Length of arcs

[cinder aurora]

wait would angle 2 be 117

if I use the bowtie method

150+84 / 2

[vast shale]

,, X/360 × 2(22/7)r²

[twin meteor]

Hakken

[vast shale]

Right?

X be theta

And 22/7 be pie

[cinder aurora]

I don't know that one to be honest

this is just geometry

[vast shale]

We dont have radius?

[cinder aurora]

nah not really

OMG

OMG

I FIGURED IT OUT

THX

LET SGO

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[civic drift]

I'm having trouble finding the sum for the G.P for $cos{\frac{\pi}{3} + \frac{\pi}{3^2}.....}$ I found out it was in the form of $\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + ..... \frac{1}{3^n}$ and the sum came out to be $\frac{1}{3} \times \frac{1 - \frac{1}{3^n}}{1 - \frac{1}{3}}$ which is not as shown in the book.

[twin meteor]

ColdTee

[civic drift]

Nvm

I missed pi

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[inner lodge]

can i get help with 16b pls thanks

[noble lily]

in problem a, both the numerator and denominator are in AP, and in problem b both the numerator and denominator are in GP.

use the nth term formulas for both and then you'll get your answer

[inner lodge]

do i separate the numerator and denominator

and dviide them both in terms of n?

also for a what would the difference be?

[noble lily]

all you have to do is use the formula $a_n = a_0 + d(n-1)$ for problem a and $T_n = a * r^{n-1}$ for the second part

[inner lodge]

is the difference 2 for 16a?

[twin meteor]

skadoosh

[noble lily]

yes, for both the numerator and denominator

[inner lodge]

wait why is it two because for the nuimerator if u expand it ( or just add it) it ouwld be 2, 6, 12

[noble lily]

well think about it in terms of the arithmetic series and geometric series... the new terms in each series will still be 4 in the second one and 6 in the third one even though the sums will be 2, 6, 12 respectively ... for context, if you know the formula for the sum of an AP which is $S_n = \frac{n}{2}(2a + d(n-1))$, you should be able to solve this... looking at the first three terms alone which is n = 3, taking the sum of the arithmetic series you should have $\frac{3}{2}(2 * 2 + (3-1) * 2)$ which comes out to be 12... now instead of n = 3, replace it with just n, and cancel out the numerators and denomiators if need-be.

[twin meteor]

skadoosh

[inner lodge]

woiuld you do this for the first question?

[noble lily]

looks okay, yes

[inner lodge]

wait im a bit confused how come we use the sum formula

?

instead of Tn=a+(n-1)d

[noble lily]

because the nth term is the sum of all terms right from the first term onwards...

look at term 3 for example

2,4,6 are in arithmetic progression but the answer is simply 12, which is the sum of the arithmetic progression

now do the same thing with part b, except use the formulas for geometric progression instead

[inner lodge]

would thius be right??

[noble lily]

should be fine

yes

[inner lodge]

the answer says 3/(2^n) +1

are they equivalent

[noble lily]

yes

the denominator $4^{n}-1$ can be expressed of $2^{2n} - 1$, and then you can simply express it in terms of $(a+b)(a-b)$ as it will be in the form of $a^{2} + b^{2}$ and then cancel terms in the numerator and denominator appropriately

[twin meteor]

skadoosh

[inner lodge]

wow

thanks so much

skadoosh

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[unborn vale]

i undersand writing the formula for the terms i dont get what you put above and below the sigma

[granite flicker]

below the sigma is the integer you should plug in to get 47 and above the sigma is the integer your should plug in to get -83 (using the first example)

[unborn vale]

im not following sorry, this is what my teacher had written as an answer but i just dont get how she got 11 and n=1

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[fleet vessel]

What did I do wrong?

[rose raft]

,rotate

[rose raft]

now how do i do the other one

[fleet vessel]

I can send it again

[rose raft]

,rotate

[fleet vessel]

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[tall ore]

I'm trying to solve the part c to this question, parts a and b are correct

These are my workings, I used the planes that are parallel to l1 and contain l2 to work out the shortest distance from any point on the line to the plane using the planes normal vector. Is this the correct approach or is there a better way

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@tall ore Has your question been resolved?

[tall ore]

<@&286206848099549185>

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@tall ore Has your question been resolved?

[wet cedar]

well there is a procedure to do that

basically what you have to do is

So yk what points l1 and l2 pass through

First just find the vector joining those 2 points

And yk the vector perpendicular to those 2 vectors

[wet cedar]

let us call this vector m

[wet cedar]

and this as vector n

now the shortest distance will be the component of vector m on vector n

[tall ore]

To find the vector joining them just subtract them right?

[wet cedar]

yup

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[earnest whale]

<@&286206848099549185>

[rose raft]

!15m

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[rose raft]

which

[earnest whale]

7

[half imp]

what's the function?

[earnest whale]

y = e^3x^2

@rose raft

@half imp

<@&286206848099549185>

[half imp]

!status

[vocal sleet]

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

[earnest whale]

1

1. I don't know where to begin

[half imp]

first step is to set up the integral

[earnest whale]

Can u show me your work for this

I am really lost and have like 10 more problems like this. Just need an example from this problem.

[half imp]

it's area under a curve

practically the definition of integral

$\int_0^1e^{3x^2}~dx$

[twin meteor]

RedstonePlayz09

[earnest whale]

Now how do you get the first five terms of the maclaurin series

<@&286206848099549185>

Yea thanks for the help d bag

[strange crater]

being rude ensures you won't get the help you ask for

[earnest whale]

I wasnt getting help anyway but its good that your lookout out for you team

You guys appear to be a lower level of math help group

Im looking for the more elite group

[strange crater]

k

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@earnest whale Has your question been resolved?

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[twin meteor]

AustinU

[worthy citrus]

presumably in this case the generalized derivative is just the normal derivative

also presumably they're using "generalized" for things like the "derivative" of the step function being a dirac delta

[thin vale]

That does seem to be the case

because I went to check my work, and I saw this in the solution and I wasn't really able to follow

Why is f(t) actually f(t)u(t) ?

[worthy citrus]

because you're doing laplace transforms you only care about the value of the function for t > 0

so may aswell cut off everything before that

thats what u(t) does

[thin vale]

right

Okay

Why is the information about f(0+)=1 important?

[worthy citrus]

and then is not a derivative in the usual sense because dirac delta isnt a function

hm

im not sure

probably some weird condition required

like the function not blowing up close to 0

but its been ages since ive done this so i wouldnt really know

[thin vale]

because if $f(t)=e^{-t}cos(3t)$ or even if you include u(t) I feel like shouldn't we just be able to say f(0)=1

[twin meteor]

AustinU

[thin vale]

with or without including unit step function

[worthy citrus]

oh, no you cant do that

bc u(t) isnt defined at 0

[thin vale]

okay

Got it

[worthy citrus]

hm well

maybe it is, depends who you ask

[thin vale]

right

XD

I have one last question

Here is from the table of formulas the "t'th derivative" rule I am to be verifying with this question

I remember something happens about like initial conditions or what not that I don't see in this formula

is it really just tacking on an "s" to F(s)?

[worthy citrus]

ohhh

thats why they included it lol

yeah the full formula is sF(s) - f(0)

take f(0+) is fine i would imagine

[thin vale]

so and then since we know f(0+)=1 we just subtract 1 off

[worthy citrus]

yee

[thin vale]

Okay nice

I kinda knew it was all connected but I couldn't piece together how lol

thanks for your help

[worthy citrus]

haha yeah you just gotta lay it all out

no probs

[thin vale]

.close

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[thin vale]

Actually I end up getting the wrong thing still :|

[thin vale]

Previous channel right above ^

I find $f'(t)= \delta (t) -u(t) e^{-t}(cos(3t)+3sin(3t))$

[twin meteor]

AustinU

[thin vale]

taking the laplace transform of that gives me

$1-\frac{(s+1)}{(s+1)^{2}+9}-\frac{9}{(s+1)^{2}+9}-f(0)$

[twin meteor]

AustinU

[thin vale]

and since f(0+)=1 I get that the laplace transfrom is

$-(\frac{(s+1)}{(s+1)^2+9}+\frac{9}{(s+1)^2+9)})$

[twin meteor]

AustinU

[thin vale]

which is $\frac{-(s+10)}{s^2+2s+10}$

[twin meteor]

AustinU

[worthy citrus]

you shouldnt be taking off f(0) here

[thin vale]

oh

where should I

[worthy citrus]

L{f'(t)} = sF(s) - f(0)

compute the left and right separately

[thin vale]

Okay

so forget that I subtracted 1 then

and I am just going for L{f'(t)}

I'll see if that makes this better

one sec

[thin vale]

so I am still up to here, except not -f(0)

so I want to show that $1-\frac{s+10}{s^2+2s+10}=s \cdot \frac{s+1}{s^2+2s+10} -1$

unless I've made a mistake

[worthy citrus]

-1 on the rhs

[twin meteor]

AustinU

[thin vale]

right

[worthy citrus]

oo weird somethings off you dont need the -1 on the right

[hybrid flicker]

I'd suggest put everything on the same side and on the same denominator

[hybrid flicker]

I think so too

[thin vale]

yeah because when I simplify that LHS

I get the desired result

except no -1

[worthy citrus]

checks out in desmos without the -1 on the RHS, dont think i know enough about the derivative rule for laplace to know why you shouldn't take off f(0)

[thin vale]

is this helpful

[worthy citrus]

ahhh neat

bottom formula is for the usual derivative

top is for generalized

with generalised you dont need to take off f(0+)

[thin vale]

and we did generalized because we included u(t)

?

[worthy citrus]

yeah

[thin vale]

and we could've done it the other way

if we didn't

[worthy citrus]

yeah it should come out the same

[thin vale]

I think it looks like it would've worked out both ways

Okay nice

phew

tricky

[worthy citrus]

a pretty good thing to know imo

interesting to me atleast

[thin vale]

Yeah, I wonder when that would be handy

well thank you again

.close

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[late sky]

Why is the characteristic polynomial of C the same as the characteristic polynomial of T?

[worthy citrus]

well whats your definition of characteristic polynomial of a linear map?

[late sky]

Det([T]_c-xI_n)=0

[worthy citrus]

and how are you defining Det of a linear map

[late sky]

Det([T]_c-xI_n)= Det(P^-1CP-xI_n)=det(C-xIn)

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@late sky Has your question been resolved?

[worthy citrus]

that should answer your question then

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[woven thicket]

would anyone know how to do part iii? Im struggling to see the resemblence between the prior equations and that graph

[woven thicket]

<@&286206848099549185>

[flat whale]

show your work for i) and ii)

[woven thicket]

for some reason its upside down, I dont know how to rotate it

[strange crater]

,rotate

[woven thicket]

ahh awesome thank you

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@woven thicket Has your question been resolved?

[woven thicket]

<@&286206848099549185>

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@woven thicket Has your question been resolved?

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[vast shale]

<@&268886789983436800>

[vocal sleet]

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[cobalt fiber]

where do i start

im thinking maybe multiply everything by 2

[paper depot]

not necessary

and probably won't do much good

[cobalt fiber]

so what should i do first

[paper depot]

instead you can write this equation in the form (cos(x)+a)(sin(x)+b)=c

find a, b and c to make that work

@royal garden #chill is that way ⬇️

[cobalt fiber]

i dont understand how to get to that equation

[paper depot]

you don't "get to" it

you recognize that the lhs of yours could have resulted from the expansion of (cos(x)+something)(sin(x)+something)

[cobalt fiber]

okay let me try to manipulate it, dont leave please lol

[paper depot]

give or take a constant

[cobalt fiber]

is it the expansion of sin(u + v)

that's the closest thing i can think of

@paper depot

[paper depot]

no

you're overthinking or not actually following my instructions

[cobalt fiber]

must be overthinking but im still confused

[paper depot]

you recognize that the lhs of yours could have resulted from the expansion of (cos(x)+something)(sin(x)+something)

i am asking you to find those somethings

not by any formal process but just pattern matching

and knowledge of the distributive law...

[cobalt fiber]

i figured it out, had to factor out the common terms

thanks for the help

.close

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[molten rain]

how do I start question ii)

[sharp lynx]

Plug in t=7 and evaluate, rounding to the nearest 100

[molten rain]

i need to find k

u r not helping, u r just restating what the question is telling me

[sharp lynx]

Then you should've started by saying "I need to find k"

[molten rain]

okay

[sharp lynx]

What about that is giving you issue?

[molten rain]

i dont know how to find k

im not sure how to start

[sharp lynx]

You need to use the additional information provided

Everything after "where k is a positive constant"

[molten rain]

let me tru

try

i didnt get the answer

[sharp lynx]

Show your work

[molten rain]

i ln bothside at the equation u see on the right

and I divide them

and

divide by -5

[sharp lynx]

You need to divide both sides by 142800 before you use ln

[molten rain]

why

[sharp lynx]

Because using log laws, ln(142800e^[-5k]) = ln(142800) + ln(e^-5k)

[molten rain]

yes

i see

i got the answer

[sharp lynx]

[molten rain]

.close

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[molten rain]

i think I did something wrong

im stuck

[sudden compass]

When u obtain (log base 5 x + log base 5 10)/2 = 1/2, it means log base 5 x + log base 5 10 = 1

[molten rain]

ye

no?

[sudden compass]

Instead of writing RHS as log base 5 5

[molten rain]

[sudden compass]

Yes i mean

[molten rain]

do i just

compare

without cross multiply

[sudden compass]

Yeah

[molten rain]

ouh

[sudden compass]

Then by log a + log b = log(ab)

[molten rain]

ye

wha

[sudden compass]

It becomes log base 5 10x = 1

[molten rain]

can i just start compare?

since all log 5

[sudden compass]

What..?

[molten rain]

x+10=5

1=log 55

[sudden compass]

U could, it isn't wrong

[molten rain]

i only get -5

but the answer have 2 answer

[sudden compass]

Huh

[molten rain]

ye

the answer rejected -5

and accepted 10

i see answer sheet

but i dont know why

[sudden compass]

Welp that's just weird

[molten rain]

a

[worthy citrus]

You have to reject -5 as you can't input a negative number into a log

[molten rain]

but

i know

i didnt get 10

which is weird

i only got -5 as the answer

[worthy citrus]

Log(x+10) is not log(x) + log(10)

[molten rain]

oh

uh

help

i stuck again

[cursive turret]

no, you didnt get -5 as answer as you mixed up notation. you have a x in the given equation and you used x then as log_5(x)

[molten rain]

hm

[worthy citrus]

You need to use log(a)-log(b)= log(a/b)

[molten rain]

oh

I GOT IT

[vocal sleet]

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[half willow]

yo

for the H1 hypothesis how do we know that it is p>0.2

@ancient panther

pls help 😦

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@half willow Has your question been resolved?

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[twin rampart]

Guys, how to solve an example like this?

I need to solve inequality using graphs

[vocal sleet]

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[twin rampart]

.close

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[wanton hound]

.close

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[coarse compass]

I need help with this, I have never been taught this and this website doesn't explain how to do do this. Can someone please help.

[vocal sleet]

@coarse compass Has your question been resolved?

[coarse compass]

<@&286206848099549185>

can you @ me when you get around to this, thanks

[torpid warren]

is there any previous information i need to know

also does this website happen to be called seneca?

[coarse compass]

yes

[coarse compass]

im not sure, it didnt give me any equasions

[torpid warren]

lol shittest website ever

[coarse compass]

yeah its terrible

[torpid warren]

is it a level physics lmao

[coarse compass]

im in year 9

[torpid warren]

bruh

[coarse compass]

yeah

not even at gcses yet lmao

[torpid warren]

Lol

send what it had before this

[coarse compass]

yeah it was all easy before

one sec

yeah this is what there was on the assignement

[torpid warren]

ok so

use E_el = fx to find the elastic energy

since it is transferred into kinetic

find kinetic using 1/2 mv^2

useful / total energy

= 23%

[coarse compass]

ok

thanks

[coarse compass]

what does this bit mean?

[torpid warren]

gradient is 100Nm^-1

use that to find F

and find the triangular area

[coarse compass]

ok

.close

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[mystic swift]

5 one

[dapper meteor]

Translate plz

[mystic swift]

Calculate sin if sin x=3/5 dharp angle and yis pi/2

[echo badger]

If $\sin(x) = \frac{3}{5}$, $x = \arcsin(\frac{3}{5})$

[twin meteor]

Rub05

[vocal sleet]

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[acoustic lance]

i was trying to solve this question, generating functions. i'm stuck here now

[acoustic lance]

how can i proceed

[fluid obsidian]

Get all the sums in n>=3 form

Write down the remaining terms

have you been provided with a1,a2,a3?

[acoustic lance]

yea

a_0 = 1

a_1 = -2 and a_2 = 4

[acoustic lance]

first one is in that form, first equation i mean

[fluid obsidian]

Wdym

[acoustic lance]

like first one i wrote is, in n >= 3 form isnt it

[fluid obsidian]

You can write $\sum_{n\geq 2} a_n x^n = a_2 x^2 + \sum_{n\geq 3} a_n x^n$

[twin meteor]

fäf

[fluid obsidian]

Similarly do others

[acoustic lance]

i meant this part:

$2\sum_{n\geq 3}^{\infty} a_n x^n = -3\sum_{n\geq3}^{\infty} a_{n-1} x^n + 3\sum_{n\geq3}^{\infty} a_{n-2} x^n + 2\sum_{n\geq3}^{\infty} a_{n-3} x^n$

[twin meteor]

fromliberty

[fluid obsidian]

What about it?

[acoustic lance]

isnt it form you said ?

[fluid obsidian]

Nope

We want an to be coefficient on x^n

[fluid obsidian]

So whatever you did till last line is right

[fluid obsidian]

Now you just need to write like this

[acoustic lance]

ah this one:

$2\sum_{n\geq 3}^{\infty} a_n x^n = -3x\sum_{n\geq 2}^{\infty} a_{n} x^{n} + 3x^2\sum_{n\geq1}^{\infty} a_{n} x^{n} + 2x^3\sum_{n\geq0}^{\infty} a_{n} x^{n}$

[twin meteor]

fromliberty

[acoustic lance]

shouldnt i get to $\sum_{n\geq 0} a_n x^n$

[twin meteor]

fromliberty

[acoustic lance]

since thats definition of GF

[fluid obsidian]

GF?

[acoustic lance]

generating function

like $a_0 + a_1x_1 + ...$

[fluid obsidian]

Yeah I think both ways work

[twin meteor]

fromliberty

[acoustic lance]

hmm

if you go to n >= 3, then can you still call it A(z) and solve that way

[fluid obsidian]

Yes

[acoustic lance]

In slides there is another way to solve

but i didnt understand

[fluid obsidian]

Do it to 0

[acoustic lance]

i will post it

[acoustic lance]

how ?

[fluid obsidian]

Why don't you try this first?

[acoustic lance]

which one

[fluid obsidian]

Well by $\sum_{n\geq 3} a_n x^n = \sum_{n\geq 0} a_n x^n - a_0 - a_1 x - a_2 x²$

[twin meteor]

fäf

[acoustic lance]

the oher one

[fluid obsidian]

We are getting those deltas

It's the same method

[acoustic lance]

hmm

[fluid obsidian]

Can you first try solving by this

Maybe you get to some point

It's the same method, you will realise that, but first you have to try it

[acoustic lance]

hmm okay i'm trying now

although writing latex is hard :p

[fluid obsidian]

Then try it by hand first

[acoustic lance]

https://i.imgur.com/w5aI2X3.png

[acoustic lance]

i did now

[fluid obsidian]

Now substitute a0 ,a1 , a2

Write the sum as A now

Cuz all sums are equivalent

Then isolate A

[acoustic lance]

https://i.imgur.com/L65UdBR.png

hmm right

[fluid obsidian]

.

[acoustic lance]

oh right

[acoustic lance]

https://i.imgur.com/xiydo3g.png

lol this doesnt look trivial, cubic equation

[fluid obsidian]

Isolate A

Get all terms with A on one side and rest on the other

Factor out A and isolate it

Please

[acoustic lance]

yeah im doing that now

[fluid obsidian]

Do that for me

[acoustic lance]

yeah did it

[fluid obsidian]

For me?

[acoustic lance]

huh ?

[fluid obsidian]

Given that you did everything right in the way factorize the denominator

[acoustic lance]

hmm thats cubic equation

partial fraction sum maybe ?

[fluid obsidian]

Yeah so

[acoustic lance]

(x+1)*(2x^2 - x - 2)

[acoustic lance]

it gives strange equation

like tihs

[fluid obsidian]

That's strange

[acoustic lance]

maybe i did some mistake on math

lol yeah i have one mistake

[fluid obsidian]

Don't disappoint me please

[acoustic lance]

https://i.imgur.com/Tbzg61d.png

lol corrected one

but output is still strange

[fluid obsidian]

Don't be like me

Don't disappoint

Don't make any mistakes

[acoustic lance]

it gives this

it seems

[fluid obsidian]

Don't make any mistakes

You have the potential to be better

x²-x+2 = (x+1)(x-2)

Don't be like me

[acoustic lance]

lol i spotted my another mistake

[fluid obsidian]

Oh my god

[acoustic lance]

but i fgured out now i believe

[fluid obsidian]

You won't have a stable relationship if you make two mistakes

[acoustic lance]

https://i.imgur.com/46IxaXs.png

[fluid obsidian]

One is acceptable but two is over

[acoustic lance]

lol okay 😄 i need help though

[fluid obsidian]

And you do something right but it's too late now, cuz she's gone already

That's how it is

[acoustic lance]

hmmm

oh actually we can write in form of

1 - (-2x)

and thats GF for c^n * z^n

[vocal sleet]

@acoustic lance Has your question been resolved?

[fluid obsidian]

Yea

[vocal sleet]

@acoustic lance Has your question been resolved?

[vocal sleet]

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[nova stump]

Hello. How are you? I was wondering if this is the correct explanation to the solution of this problem.

[river minnow]

Wait how do you get y = 1/2 though?

The rest is perfectly fine btw

[nova stump]

It is the radius of the larger circle

Since the square is of length 1

The radius of the larger circle must be 1/2 I think

[river minnow]

Yeah but that doesn't make y equal to the radius, unless you get that beta is 60 degrees

That line segment over there is just a chord

[nova stump]

I see.

[river minnow]

What I think you can do is write that r = (x + y + y - 1)/2

Because generally a circle inscribed in a right rectangle has the radius (a + b - c)/2 iirc

c being the hypotenuse and a and b being the legs

[nova stump]

So a circle inscribed in a right triangle has radius (a + b - c)/2

[river minnow]

Yup

[nova stump]

I did not know that

I am curious why that is

[river minnow]

I accidentally proved it once

I will show you after this question is solved

[nova stump]

Sure! 🙂

[river minnow]

Anyways this should get you r = r + y - 1/2

Oh and y = 1/2

Okay yeah your answer is correct

One moment let me find my old notebook

[nova stump]

https://cdn.discordapp.com/attachments/903463353417072641/1096844193810350211/IMG_2626.jpg
(to make it closer)

I actually didn't make this answer

So I was just curious on how to understand it

[river minnow]

After y = 1/2 it's just applying the Pythagorean theorem

[nova stump]

Ohh so the Phthagorean theorem is used

py

[river minnow]

Here comes the proof

Oh wait

,rotate

[river minnow]

Alright so this is the diagram

You basically draw those radii from the center of the circle onto the sides of a right triangle

here c is getting divided into c1 and c2

[nova stump]

Are those kites? :0

[river minnow]

Hm? Those things on the lines you mean?

[nova stump]

The little shapes made by the radius of the circle and the points of intersection of the circle with the right triangle

[river minnow]

No those are right triangles

[nova stump]

Oh

Ah

[river minnow]

Anyways, notice that there is a symmetry

[nova stump]

So you made right triangles

Yes

[river minnow]

a = r + c1 and b = r + c2, right?

Because those parts are equal

[nova stump]

I can see that

Yeaa

[river minnow]

Right

Let's add a and b up

We get a + b = 2r + c1 + c2

[river minnow]

But c1 + c2 is simply c

So we have a + b = 2r + c

[nova stump]

Hold on he might be right

[river minnow]

Solving for r you will get r = (a + b - c)/2

[river minnow]

He is a troll, ignore him

[nova stump]

Still here

Just takes some time for me

[river minnow]

<@&268886789983436800>

[nova stump]

I hope you have a good day DOC

[river minnow]

Alright, anyways, do you see now?

[nova stump]

Yes, very impressive honestly

I understand the geometry now

https://cdn.discordapp.com/attachments/903463353417072641/1096844193810350211/IMG_2626.jpg
(closer)

OHHHHHHH

[nova stump]

Thank you so much for your time helping me lonely bean :) I appreciate it

[vocal sleet]

@nova stump Has your question been resolved?

[nova stump]

Yes but more to it

I'm just thinking rn

still

Okay.

Okay friends

I also found this solution

[river minnow]

There is a more general family of integrals btw

Wait I will link the video

[nova stump]

to keep up with the style

[river minnow]

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

What's on the thumbnail may seem irrelevant, but it's not

[nova stump]

Flammable maths

I used to watch that person a lot

I'm still processing some stuff

This is a lot more complicated

geez

[river minnow]

But it's the same

[nova stump]

It is?

[river minnow]

Yeah it goes in line with what's in the video

[nova stump]

haha don't judge guys I-

Oh okay

I'll watch

It appears that there are different approaches to understanding this problem

[vocal sleet]

@nova stump Has your question been resolved?

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[gritty onyx]

An exponential function is given by f(x)=20∙1.15xa) Sketch the graph in the range −5≤𝑥≤10 How do I sketch this?

[gritty onyx]

An exponential function is given by f(x)=20∙1.15^x) Sketch the graph in the range −5≤𝑥≤10 How do I sketch this?

[vocal sleet]

@gritty onyx Has your question been resolved?

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

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[rain shuttle]

How to do 10

[rain shuttle]

The function is (1-x^2)^1/4 btw

[vocal sleet]

@rain shuttle Has your question been resolved?

[rain shuttle]

Anyone 🙏🏽

[vocal sleet]

@rain shuttle Has your question been resolved?

[lone niche]

where are the x boundaries of the shape

then you find area of the cross section at every point and integrate from one side to the other

[rain shuttle]

X boundaries are 0 to 1

But idk how there’s pu

Pi

It’s squared right so why bring in pu

Pi

[lone niche]

pi just appears sometimes

something you kinda have to deal with

in this one it's not surprising

because ((1-x^2)^0.25)^2 is (1-x^2)^0.5, which graphs out ...

[random wave]

Pi appears in circles

It's been defined with circles at the first place

And a point M=(x,y) which is on a circle of radius R means that x²+y²=R²

There is squares in the equation of a circle, based on the Pythagoras's theorem

Although here it's x²+y^4=1

[rain shuttle]

I see ok

Thanks

.close

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[winter hawk]

.close

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[brave ruin]

Could someone explain why the limit is - infinity

[desert hornet]

Whenever you get (negative number)/0, it goes to -infinity

If it were a positive number in the numerator it would be +infinity

[brave ruin]

Why wouldn't it be undefined ?

That does answer my question though thank you!

[stiff sandal]

close the channel if you are done

[brave ruin]

I'm still waiting on why it wouldn't be undef

[desert hornet]

Well

It's a limit

The limit is -infinity means that if you graph the function, it will keep on decreasing without an asymptote

[brave ruin]

I'm not sure how to express this. So, should I have figured that out before I directly subbed in pi/2 + ?

Cause when I subbed in that, I got -1 / 0

[desert hornet]

Yeah

[brave ruin]

So to me it's like, there is no limit here

[desert hornet]

The fact that you got (negative number)/0 tells you the limit is -infinity

[brave ruin]

darn

okay

I guess I'll just need to look that up

cause idk why that is true

oh

so like

If I wrote 1 / x

hmm

[desert hornet]

That's the simplest case

[lone niche]

specifically if it's 0+

[desert hornet]

True

[brave ruin]

it's approaching from the right

so

hmm

will looking at a graph help me?

okie

I think I see that now

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[limpid vale]

Which of the following topics

Comes under data interpretation Or data sufficiency

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@limpid vale Has your question been resolved?

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[molten rain]

how do I continue this question

i cant find the answer

[half imp]

ln(4y)-ln(3y) is not ln(y)

Nor can you do whatever the step before that is

[molten rain]

okay

so what do i do

[half imp]

3rd line from the bottom you have a quadratic equation

it's just hard to recognize

because it's a quadratic equation of e^y, not of y

So substitute u = e^y and then solve

also its hard to tell but you might have dropped a negative sign

from the line before that, unless it's the really faint dash

[molten rain]

okay

i see now

thanks

[half imp]

you're welcome

[molten rain]

i didnt get both answers right

something is wrong

[half imp]

u = -2 not 2

[molten rain]

i cannot ln a negative number

[half imp]

So

[molten rain]

uh

the answer sheet says

oh

oh

im suppose to find x

also

thank you

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[half imp]

np

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[vast shale]

Hey I was trying to prove this but I seem to have reached the negative of this somehow

[vast shale]

$\chi_2(z)$ is the Legendre Chi function of order 2 btw

[twin meteor]

whatevermanjustcallmeanything

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[rough barn]

determine the minimum value of

[rough barn]

for -1 < x, y, z < 1

how could I approach this one?

[vague wadi]

I would conjecture it's 13.5, but I am not so sure

you could try proving ... >= 13.5 but that would be a mess probably

it's definite that's you shouldn't use negative values so 0 <= x, y, z < 1

[rough barn]

how did you arrive to that guess?

[vague wadi]

minimum of 3(5 - 3x)/sqrt(1 - x^2)

just said x = y = z

[rough barn]

because it's symmetrical?

[vague wadi]

quite

maybe you could use rearrangement inequality to simplify

[rough barn]

I see

[vague wadi]

say x =< y =< z. then 5 - 3x >= 5 - 3y >= 5 - 3z and 1/sqrt(1 - x^2) <= 1/sqrt(1 - y^2) <= ...

so maybe you could try doing (5 - 3x)/sqrt(1 - z^2) + (5 - 3y)/sqrt(1 - y^2) + (5 - 3z)/sqrt(1 - x^2)

which simplifies the inequality into two: min of the second term and the first and third

you just have to show that the minimum is achievable by our big inequality

[rough barn]

Alright, I'll give it a shot

[vague wadi]

(5 - 3y)/sqrt(1 - y^2) can be resolved by calculus lol
or maybe your typical power inequalities, I didn't check

it's just 100% resolvable

[vague wadi]

ye try. ping me when you're done

[rough barn]

yes, but this is a simulation for an olympiad which syllabus does not include calculus

[vague wadi]

well AM-GM-HM to your rescue

[rough barn]

im familiar with that one

[vague wadi]

no HM needed here prob

[rough barn]

alright

[vague wadi]

nvm, it's 12

I didn't see the minimum right

[vocal sleet]

@rough barn Has your question been resolved?

[rough barn]

yeah, no, I didn't get it, sorry @vague wadi

[vague wadi]

ok it happens

it's just my ideas

I am quite bad at ineqs anyway. you could try asking this on the math olympiad server I think

[rough barn]

ah alright

[vague wadi]

it's in the #old-network

somewhere

[rough barn]

alright

thanks!

[vague wadi]

np

[rough barn]

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[vague parcel]

the uniform charge density of an insulator-filled sphere with radius a is p and the total positive charge Q is. Using the Gaussian structure, calculate the electric field and electric potential at a point outside the sphere.

[vague parcel]

the uniform charge density of an insulator-filled sphere with radius a is p and the total positive charge Q is. Using the Gaussian structure, calculate the electric field and electric potential at a point outside the sphere.

[fluid obsidian]

Do you know the formula for electric field?

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[cloud quiver]

this is just f(4) right?

it seems too straightforward...

[river minnow]

Are you sure? Cuz F(4) is negative

And some of the options are nonnegative

[cloud quiver]

f(4) isn't an abs max?

i'm looking at it wrong

t(4)

i meant

it asks about the antiderivative