help-38

[keen cedar]

in the question in says suff like y is 3 times smaller than r

and g is 2 times smaller

thats basically just an equation

with 3 unknowns

Yea

It's just a visual representation

An equations with 3 unknowns is the same as an equation of a plane in 3d

if you solve the equations you will get inf solutions

so if you get just 1 answer

it will be the top one

If it is a sheaf you will get an answer like this where a variable is equal to some other function

Instead of a specific answer

(THIS is just a random equation btw)

All you need to know

Is that the only way all those conditions are true in that question

Is if r=14

No other value of r will satisfy the conditions

Just write out the function you get when you solve it

So like x=z+3

So one thing is reliant on another

If something is reliant on an unknowns number

Then there will be inf solutions

As z could be any number

And x would just shift for z

Instead of converging onto one number

No it isnt

When you solve it they all converge to a number

Tell me an number other than r=14 that will satisfy the equations

So there you go

Do yk how to solve simultaneous equations?

So the point of the question

Is the create 3 equations following the terms of the q

And solve

Question

[keen cedar]

Yea

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[lunar galleon]

f

[frail heron]

!status

[trim jolt]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[lunar galleon]

I got 2/root7

and -2/root7

[frail heron]

How did you get root for the first question?

May I see your attempts?

[lunar galleon]

oh wait

opposite is meant to be 2

and adjacent is meant to be root3

I got it

. close

.close

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[severe narwhal]

Had this question for a finals today, no idea where to start: Suppose $A$ and $B$ are linear maps from $V$ to $V$ where $V$ has dimension 3. Also, given that $A$ and $B$ have eigenvalues $a$ and $b$ of multiplicity 2 respectively. Show that $A+B$ have eigenvalue $a+b$

[solid kiln]

Iusgnol

[severe narwhal]

I tried to manually expand the characteristic polynomial of their sum, but it was too messy and I'm not even sure if that would have given me anything

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[severe narwhal]

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[tiny pendant]

In this ques the function is many to one so there should be two cases from x = 0 to 1/2 and 1/2 to 1
for the transformation method

my ans is coming out to be double of this that way

[dapper swift]

They actually aren't doing the transformation method where you multiply by $\left|\frac{dg^{-1} (y)}{dy} \right|$

[solid kiln]

south

[dapper swift]

They're doing the CDF method

By integrating the PDF under the transformation $X \le y^{1/3}$

[solid kiln]

south

[dapper swift]

And then differentiating the CDF to get the PDF in the transformed variable

So it doesn't matter that 6x(1 - x) isn't monotonically increasing or decreasing in the entire interval

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[indigo socket]

anyone able to help

[whole coral]

Can you relate 3x^2 - 4x - 2 to 3x^2 - 2x - 1?

[indigo socket]

:D no (idk crap abt coordinate geometry)

[whole coral]

Awwww

[indigo socket]

thats why 😭

[whole coral]

The idea is that $3x^2 - 4x - 2 = 0$ represents the intersection of the curve $y = 3x^2 - 2x - 1$ and some stright line...

[solid kiln]

@whole coral

[indigo socket]

so

theres a straight

line passing through the each of the crap

[whole coral]

What can you notice about $3x^2 - 2x - 1$ and $3x^2 - 4x - 2$? If you tried to rearrange $3x^2 - 4x - 2 = 0$ to have one side having $3x^2 - 2x - 1$, what would be on the other side?

[solid kiln]

@whole coral

[indigo socket]

theres only one graph though 😭 im making another table?

[whole coral]

That's the point, you're meant to find the other equation

Then you plot the other equation on the same graph, and use that to see where they intersect

[indigo socket]

oh so i make another table

😭

[whole coral]

Well, how do you mean "table"?

Anyways, as per before, $3x^2 - 4x - 2 = 0$ is the same thing as $3x^2 - 2x - 1 =$ [something], what's that something?

[solid kiln]

@whole coral

[indigo socket]

ah uh

i mean by table

[whole coral]

Oh, well, you don't really need one honestly-

[indigo socket]

but how do we plot and know the x anyways-

[whole coral]

By finding that "something", you aren't meant to plot the new equation, you're supposed to find that "something" and then plot that on the grid you have

[indigo socket]

but how do we find the something

😭

without plotting it??

[whole coral]

Rearrange it

[indigo socket]

wdym by that?

[whole coral]

How do you turn -4x - 2 into -2x - 1?

[whole coral]

Or alternatively, notice that 3x^2 - 4x - 2 = 3x^2 - 2x - 1 + [another thing]

Do you know how to find said "other thing"?

[indigo socket]

divide by 2?

[indigo socket]

uh huh

[indigo socket]

no :D

[whole coral]

I'll take that...

So -4x - 2 = 2(-2x - 1)

Alternatively, notice that multiplying by 2 is the same as adding the thing to itself twice, so -4x - 2 = (-2x - 1) + (-2x - 1)

[whole coral]

So, in other words, 3x^2 - 4x - 2 = (3x^2 - 2x - 1) - (2x + 1)

Do you agree with that?

[indigo socket]

uh huh

[indigo socket]

yea

😭

[indigo socket]

so ur saying

its a double version of the graph i made?

[indigo socket]

i dont understand some of what u said

[whole coral]

Yep, you're meant to plot a line on the same graph you have

[whole coral]

Awww where don't you get?

[indigo socket]

uh huh

😭

but i dont get it

why not plot it

I HATE COORDINATE GEOMETRY

ALL I KNOW IS m = y2-y1/x2-x1

PERPEDICULLAR PARARELL

DIFFFRENTIATION

MID POINT

thats it 😭

[whole coral]

Why not plot what?

[indigo socket]

like

u said where the x intersects or meet between 2 graph

so why not plot again-

:]

[whole coral]

Yea, that's what I'm saying you should do, but you need to identify the other line

So, can you write 3x^2 - 2x - 1 - (2x + 1) = 0 so that you have 3x^2 - 2x - 1 by itself on one side?

[indigo socket]

uh huh

but i dont get it-

[whole coral]

Alright, let me make a new example for you-

[whole coral]

Let's say you wanna solve x^2 = 2x - 1

One way you can do that is to plot y = x^2 and y = 2x - 1 on the same graph, and see where they meet

Now, if I ask you afterwards to solve x^2 - 2x + 1 = 0, you can now notice that if you get x^2 on one side, that's the same as x^2 = 2x - 1

[whole coral]

So whatever solutions you found in the first part, here, are the same as for the question I asked last

[indigo socket]

uh huh

[indigo socket]

uh huh

[indigo socket]

why y = 2x - 1 again..

[indigo socket]

mhm :D

[whole coral]

Because one side is x^2, and one side is 2x - 1, so see where those are the same thing

[indigo socket]

sir or miss

do u have a yt video :)

i am abt to give up

because

the x^2 i kept thinking as x2

but im sorry 😭

i give up bro

I GOT a 54/70

IN PRACTICE

[whole coral]

https://youtu.be/_ks2K1FuB80?feature=shared here you go, these cover examples very similar to this one!

[indigo socket]

THAT GUY PLOTTED THE GRAPH

😭

wait lemme check

[whole coral]

Yea, exactly as you're to do here! They even say the same "by drawing an appropriate[/suitable] straight line"

[indigo socket]

YEA

THATS WHAT I MEAN B4

plotting a line graph

😭

[whole coral]

watch the whole video for me first and see whether it makes how to do this any clearer pleaseeeeeee

[indigo socket]

ah yes sir or miss :((

i am sad

😭

[whole coral]

Awww, how comes?

I'm sure the video will probably explain what I'm trying to get across better than I can in text

[indigo socket]

nah seeing coordinate geometry scares the hell out of me 😭

[whole coral]

Awwww well, there's one way to get over your fears

[indigo socket]

PRACTICE

ah u mind if i dm the answers to u-

[indigo socket]

im afraid others might go to this channel-

ightt

.close

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[whole coral]

You can always dm me if you want

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[sour tulip]

How to do this ques

[marsh forum]

,rotate

[marsh forum]

,rotate

[marsh forum]

,rotate

[astral ore]

[vernal warren]

u can use the reaction :p

[marsh forum]

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

[astral ore]

even better u can use the angle

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[obsidian hornet]

I cant think properly

my brain is shutting down

[wooden plover]

rip brain

[obsidian hornet]

um how is D(1)=0

[wooden plover]

you differentiate a constant

what should the result be ?

[obsidian hornet]

ohh

yes

ok

thank you!

oh my goodness

[wooden plover]

maybe you should watercool your brain, it's prolly overheating

or take a nap

[whole coral]

@trail ingot

[obsidian hornet]

cant afford to🥲

😭 Ive got an exam in, 5 hours💀

💀 its so over

[wooden plover]

it's gonna be more over if you don't sleep really

(assuming it's nighttime where you are)

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[whole coral]

Best of luck

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[livid dune]

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[mental aurora]

Can someone explain how u get the answer to part a?

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@mental aurora Has your question been resolved?

[mental aurora]

Yeah I just don't understand where the (1-k)c-a comes from

[shrewd vessel]

MC = MO + OC

and you worked out OM already

[mental aurora]

Okay thank you

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[flat wing]

is this question geometric

or binomial?

i cant really tell

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[digital girder]

this is worded weirdly. Is "Frequency" how many times they sprayed ? did they spray all 50 samples every time ? Is "number of dead flies" taken from the entire population of 250 flies ?

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[slate mortar]

i do not know how to start. if someone could just guide me on how to start I can finish from there

[burnt mulch]

For the first one, consider how you can factor the left hand side

Hint: ||perfect square||

[slate mortar]

thank you. is it (csc^2+1)(csc^2-1)?

[burnt mulch]

no

[slate mortar]

is it just (csc^2 - 1)^2

then (cot^2 )^2

which is cot^4

[slate mortar]

.

[burnt mulch]

[slate mortar]

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[signal drum]

Does anyone know how to do?

[burnt mulch]

You can find angle C by the law of sines

Thing is that there's two cases for angle C: the acute case and the obtuse case

so for each case, you need to check if choosing that will cause the angle sum to exceed 180 deg (since the angle sum of a triangle is 180 deg)

In this case, b/c B is obtuse, C can't also be obtuse

so you're limited to the acute case

[signal drum]

would it be

sin(100)/8=sinc/7

[burnt mulch]

[signal drum]

when i solve for that my answers is always a little off in my calculator

it would solve to

7sin(100)/sin(8)

right

i input it into the calculator and I would get 49.53

while the answer is 59.51

[burnt mulch]

,w (180/pi)arcsin(\frac{7sin(100 deg)}{8})

[solid kiln]

Results provided by WolframAlpha

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Requested by civil_service_pigeon

[burnt mulch]

are you sure you're in radian mode and not degree mode

[burnt mulch]

soooo

?

also why is the denominator sin(8)

[signal drum]

dont u multiply it with sinc

[burnt mulch]

??????

$\frac{\sin 100^{\circ}}{8}=\frac{\sin C}{7} \implies \sin C=\frac{7 \sin 100^{\circ}}{8}$

[solid kiln]

Civil Service Pigeon

[burnt mulch]

sin is a function, you can't just multiply/divide the "sin"

It's like saying $f(x)=2x \implies x=\frac{2x}{f}$

[solid kiln]

Civil Service Pigeon

[signal drum]

wait whattttttttt

ohh

If I get this

Um

[burnt mulch]

are you sure you're in radian mode and not degree mode

,w \frac{7sin(100 rad)}{8}

[signal drum]

i tried in both ways

[solid kiln]

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[burnt mulch]

b/c what you're getting rn matches with if you were in radians

,w \frac{7sin(100 deg)}{8}

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[burnt mulch]

whereas you should be getting this

[signal drum]

yea but what do you do with .8617

is that an angle?

[burnt mulch]

$\sin C=0.8617$

[solid kiln]

Civil Service Pigeon

[burnt mulch]

well, approximately

now take the inverse sine of both sides

[signal drum]

OHH

OK THANKS!!

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[lean prawn]

My coursebook, it states that: if a row does not consist entirely of zeroes, then the first nonzero number in the row is 1.
This sounds like the definition of reduced row echelon form

The unique solution part seems kinda sus because if k=0 then there is no unique solution

[supple copper]

Where did you say k = 2 or -2

If 1 row is inconsistent the entire system is inconsistent

So a is fine if you only check 1 row for inconsistency

Now you do have to make sure that there aren’t any more k’s that make other rows inconsistent

[lean prawn]

oh yeah sorry I misremembered the definition

[supple copper]

In part a row 2, if it said 0 k k | 1 then k = 0 would also be inconsistent~~ but you have that 2 there that makes it fine~~

Oh wait no if k = 0 then the last line says -4x₃ = 4, so x₃ = -1, but -2(-1) ≠ 1

So there’s another inconsistent k not just -2

Yea

Yeah because there are other rows with k’s

Like imagine if there was another row that said 0 0 0 | 5

Then no matter what k you consider it would be inconsistent

Then the list of all the k’s that make the system inconsistent would be all of them since k doesn’t even change the fact it’s inconsistent to begin with

Oh hold up

I looked at the wrong matrix

Row 3 says k² - 4 = k - 2

When k = 0 this says -4x₃ = -2 so x₃ = 1/2

And it’s true that 0 + 2(1/2) = 1 for row 2

Sorry about the mixup

Well you have to show that k = 0 doesn’t make it inconsistent

Similarly for part b you also need to check the 2nd row

Perhaps for some values of k, the 2nd and 3rd rows are multiples of each other

That would make the system have infinite solutions beyond just the last row being 0’s

There’s a way to make row 2 inconsistent if you end up at 0 0 0 | non zero

But you’d need row 3 to not say 0 = 0 or you can’t get rid of the 2 in row 2

But you also need k = 0 or row 2 will be stuck with a k which isn’t 0

So then you check if k = 0, are row 2 and 3 multiples of each other

If not then row 2 will be inconsistent for k = 0

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[untold folio]

i just wanna know if i did this right

[slender shard]

,w integral dx/sqrt(4x^2 + 16x+13)

[solid kiln]

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[untold folio]

i forgot to mention

i did plug it in on wolfram alpha

are they the same

[slender shard]

Well, you have a sqrt(3) in the denominator.

And WA doesn't.

[untold folio]

oh god

where did i go wrong then

[slender shard]

Looks like you used the wrong trig substitution.

For 1/sqrt(x^2 - a^2), use secant.

[untold folio]

another site shows this

i mean it is similar to my answer

do i still need to change the trig sub

wait

no its not

ty

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[delicate lance]

what does it mean for the curve to lie above or below the tangent line?

[tranquil widget]

all the points on the curve except at the point of tangency lie above

for example this

[strong zinc]

this is not always true

[tranquil widget]

oof

[strong zinc]

it depends on the concavity of the function

[tranquil widget]

if it was concave down wouldnt it then be the second case, i.e below the tangent line?

i was only referring to the first part of their question

[strong zinc]

yes, near the point of tangency

[tranquil widget]

oh

[delicate lance]

im confuse

why do they do this?

why 0?

[flint sluice]

if it's concave down, the curve lies under

if its concave up its lies above

[delicate lance]

oh ok

so if the second derivative is negative then its concave down

[flint sluice]

yuh

[delicate lance]

tyy

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[tacit rapids]

Question: Prove a number is divisible by 8 if and only if the last three digits form a number divisible by 8.

[tacit rapids]

Ive split it up into two sperate cases in order to prove the iff part

but when proving a number is divisible by 8 => the las 3 digits form a number divisible by 8 i get stuck

ive got 100a+10b+c=8p and i need to prove a+b+c =8q but its impossible

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[stoic jolt]

how did they get the angle value? i dont know what they subbed x = 9.7847 into

[raven loom]

Degree into radians

[stoic jolt]

so i sub it in tan^-1(image) with radian mode?

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[dim oyster]

my ap stats book shows the equation: SD of sampling distribution = sqrt(np(1-p))/n. My interpretation of this equation: standard deviation of sample distribution = (expected standard deviation of any sample of size n)/n. I don't understand why this equation makes sense

[edgy willow]

usually it's sqrt(p(1-p)), and sampling distribution shrinks the SD by 1/sqrt(n). turns out that's what this is, with a sqrt(n) on top and n on the bottom

[solid kiln]

MichaelJackson

[mental flame]

wait sorry

wrong chat

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[indigo socket]

do yall think this is correct??

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[indigo socket]

do u guys think its correct

[willow vessel]

sorry to say but its wrong

@indigo socket

[indigo socket]

ah anything i could do to fix it?

[willow vessel]

where you substituted the value of x in equation 2, you forgot the 4/5

[indigo socket]

but uh i found y already? 4/5 is just a 1/2 x -8/5 y

[willow vessel]

why are you making it complicated yourself?

lets solve it step by step

[indigo socket]

ah sure sure

[indigo socket]

let me erase it

[willow vessel]

shall i start?

[indigo socket]

ah sure sure

[willow vessel]

first get rid of all the fractions

do you see any?

[indigo socket]

😭

fractions?

[indigo socket]

1/2 ig

so we just multiply all of em with 1/2?

[willow vessel]

not all just equation 2

@indigo socket

[indigo socket]

?

[willow vessel]

yes

get rid of fractions from equation 2

[willow vessel]

no no you have to multiply

not divide

[indigo socket]

i did-

3 x 1/2

7 x 1/2

[willow vessel]

no not with 1/2

multiply with 2

[indigo socket]

hah :SPB

😭

OH YEAH

IT TURNS INTO 1

1/2 x 2

SORRY2

[willow vessel]

see think it in tems of LCM

[willow vessel]

no no dont apologise.

[indigo socket]

ofc ofc

[indigo socket]

my final exams r tomorrow :(

[willow vessel]

dont worry

[willow vessel]

yes this is correct

[indigo socket]

put it in 5 x + 8 y = 4?

[willow vessel]

now see here is the problem that you are making for yourself
The method you are using is substituting method.

that makes things complicated solve from this method only if you are struck

hold on let me use pen and paper to explain this

[indigo socket]

uh huh

[indigo socket]

o sure sure

[willow vessel]

we are here

now see

think of making coefficients of x or y any one variable equal

which coefficient would you think can become equal easily with just simple multiplication or division

@indigo socket

[indigo socket]

uh huh

[indigo socket]

the 5x + 8 y?

😭

[willow vessel]

and which operation mul or division??

[indigo socket]

the x?

[indigo socket]

im very confused as hell

:)

i only know elimination better

[willow vessel]

ight do by it

solve and if you have any doubt ping me

[indigo socket]

no no

but its asking me substitution

so i was questioning in the first place is it correct or wrong and why?

[willow vessel]

it was correct but you did a mistake

solve it again and ping me if you face any trouble

[indigo socket]

uh huh

😭

@willow vessel

i substitute it into the next equation

[willow vessel]

y=-3

rest is right

so x will also change

@indigo socket

i have to go make sure you correct it .

[indigo socket]

mhm

[indigo socket]

it is correct

tysmm

.close

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[tropic vapor]

Where did the i² come from?

[stark bison]

i = i(1+i)/(1+i) = (i + i^2)/(1 + i)

[tropic vapor]

How do you know that i is equal to i(1+I)/(1+i)

It says that w is equal to that

Is it just that, the one on the top is actually 1+i? So then you Just multiply the i outside of it to the top?

[frail heron]

i^2 =-1

[stark bison]

a = ab/b with b ≠ 0

[tropic vapor]

Yeah

[stark bison]

Review your algebra

[frozen sierra]

You want to combine + i into the fraction, so you multiple and divide with the same number. i = i * **(1 + i) / (1 + i) **. The bold fraction is equal to 1,so its like multiplication with 1, which doesn't change the number

[tropic vapor]

OHHH

Tyty

That makes more sense

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[tropic vapor]

.reopen

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✅

[tropic vapor]

Wait is it angle 45° at the end of it because of the first quadrant?

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[twilit oak]

how do i solve ii

the answers i got is different

my answer is 1<=f(x)<=11

[twilit oak]

answer is this.

[opaque dirge]

-3<=x<=3 right?

You can use this to get the range of 2x-5 then take its absolute value

Ok from your answer i believe you did these steps and found -11<=2x-5<=1

[twilit oak]

why is it 0

[opaque dirge]

The minimal value of an absloute value is 0

And 0 is in -11<=2x-5<=1

[twilit oak]

when do i know if i need to swap to 0?

[opaque dirge]

Check the ranges of the nonabsolute values

If the range includes 0 then thats the minimum value

In this case, -11<=2x-5<=1 [-11,1] includes 0

Well technically you can check if the end and start points are negative and positive, since if its both positive or both negative it wont include 0

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[twin shadow]

i can help

[slow owl]

hi

[twin shadow]

sweet so

it tells us that o is the middle

[slow owl]

yea

i tried using pytharus therom to find the radius

and then tried to find the angle qop with cos rule

but it gave me a neg angle

[twin shadow]

so

the chord is 24

meaning that when split in half its 12 12 right

[slow owl]

mhm

[twin shadow]

connect a line from o to q

that line has an unknown lenght x

so

[slow owl]

yeah thats what i did

i got x = 13

[twin shadow]

yup

[slow owl]

yeahh..?

[twin shadow]

now you want to find the the 2 angles

right

[slow owl]

which angles

[twin shadow]

so by finding angle of qoz

[slow owl]

z?

[twin shadow]

where z is the intersection of radius and chord

[slow owl]

yyea

[twin shadow]

to find the angle i highlighted

[slow owl]

that 67

degerees

[twin shadow]

it is sin(theta) = 12/13

[slow owl]

yea

[twin shadow]

times that by 2

[slow owl]

mhm

why didnt it work for the cos rule?

[twin shadow]

angle is 135

it would

so

[slow owl]

idk it didnt for me

[twin shadow]

a= 5

h=13

cos th = 5/13

inverse

[slow owl]

no

like

cos rule

[twin shadow]

ooh

[slow owl]

as in cos c = a^2+b^2-c^2/2ab

i used that

in order to try finding the angle

qop would make

[twin shadow]

it would work

idk why u would to it like that tho

[slow owl]

cuz its less steps 😭

[twin shadow]

not really

[slow owl]

i did 13^2+13^2-24^2/2 times 13 times 13

but it gave minus

did i do smth wrong

[twin shadow]

hol up

u did smth wrong

[slow owl]

o

[twin shadow]

i got 45.2

[slow owl]

for..?

[twin shadow]

well

i think the way u did it is js more confusing meaning that there is room for error

[slow owl]

oof

[twin shadow]

i mean the application of formula

i did

[slow owl]

wait uhh question

so i used like thr 134.7..... angle

to find the arc

but my answers wrong

[twin shadow]

nvm

[slow owl]

im getting 2.668 smth

[twin shadow]

i did it wrong too lmaoo

[slow owl]

oh lol

[twin shadow]

what grade are u in?

i think i might know why

[slow owl]

11

[twin shadow]

yh man

[slow owl]

???

[twin shadow]

the thing i was gonna tell u is calculus

but

[slow owl]

oh

[twin shadow]

even though u got a neg angle

its fine

once inversed

u still get 135

[slow owl]

oh

[twin shadow]

use cos rule

as

c^2 = a^2 + b^2 -2abcosC

less room gore error

[slow owl]

oop

[slow owl]

ic

anyways how do i get the arc length now

[twin shadow]

well

its a circle

but part of a circle

so it would be represented as 135/365 of a circle

so

[slow owl]

mmm

[twin shadow]

and the circumfrence is 2piR for a full circle right

[slow owl]

yea

[twin shadow]

so multiply 2piR by 135/365

and thats ur anser

you should get 30.2

[slow owl]

okk yeah

30.6

[twin shadow]

yh close enough

[slow owl]

thanks!

[twin shadow]

np bro

[slow owl]

.close

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[frozen sierra]

Trying to solve this differential equation: $y^{''}+xy=0$

[solid kiln]

Chlats

Chlats

Chlats

[runic dew]

You need to equate the coefficients based on the powers of x

[wraith hinge]

its because you really have (something positive) + (something positive) = 0

the a_2 can only ever satisfy that equation if it was 0 itself, then

[frozen sierra]

But we have (something positive) - (something positive)

[solid kiln]

Chlats

[frozen sierra]

The series is correct though

[frozen sierra]

So yeah, isn't it (something positive) - (something positive)?

[wraith hinge]

the coefficient of $x^n$ will need to be 0 for the recurrence relation to be satisfied on any interval. So [
2a_2 + \sum_{n=1}^\infty x^n(\dotsm) = 0
]
requires $a_2$ itself to be 0, since its akin to saying that [
2a_2 + 0 = 0
]

[frozen sierra]

I didn't understant why the coeffient of $x^n$ needs to be 0

[solid kiln]

Chlats

[wraith hinge]

the equality above needs to be satisifed for all x on some interval

you can only guarantee that when the coefficient of x^n itself is 0

u can find individual edge cases perhaps, but you cannot generalise that for all possible x^n's

[frozen sierra]

Okay, so we have $a + b = 0$, where
$a = 2a_2$ and $b = \sum{n=1}^\infty x^n(c) = 0$, c the coeffient of $x^n$
If a and b are both positive and a + b =0, then a and b must be 0. But how do we know
that a is zero? Meaning that how do we know that a_2 is non-negative?

[solid kiln]

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

[wraith hinge]

ok if it was a negative number what negative number would it be?

[frozen sierra]

Idk, inside $(-\infty,0)$

[solid kiln]

Chlats

[wraith hinge]

that just wont work out though, you have no idea what that sum will converge to

and you CANT know even, without some conditions on what a_n is supposed to be (like a_2 = 0)

[frozen sierra]

So when we declare $y(x) = \sum_{n=0}^\infty a_n x^n$ we assume that in converges?

[wraith hinge]

idk what u r trying to say here

[solid kiln]

Chlats

[frozen sierra]

At the start of the exercise, we say y(x) is a sum like above

[wraith hinge]

if it is a solution to a differential equation, the series needs to converge everywhere yes

[frozen sierra]

Okay, I think I got it, imma try and finish it and send my work

Just beacuse I tried to solve it by assuming a_2 = 0 and the results were weird

[frozen sierra]

I can't see the pattern

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[frozen sierra]

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[spare orchid]

How do I get better at logical reasoning?

[topaz pasture]

Practise using it?

[spare orchid]

That

[topaz pasture]

I mean, it's a pretty unclear question.

[marsh forum]

practice hard problems

spend hours on single problems

days even

[spare orchid]

Ah alright, I got confused for a sec cause I didn't know why I asked that question

Thanks

Wait, if I want to advance study lessons for grade 9, what are the lessons that I should study?

[topaz pasture]

Which lessons are you learning right now?

[spare orchid]

I'm turning grade 9 in the next few months

Our last lesson was probability

[marsh forum]

where are you from

that will determine which books you use

[spare orchid]

Philippines

[marsh forum]

hmm, so what are you doing rn

which chapters

[spare orchid]

Wdym?

[marsh forum]

I'm from India, so I can recommend some indian books with hard problems ( Free legal pdfs are avaible online)

[marsh forum]

which topics are you doing

like trignomerty

calculus

etc

[spare orchid]

None. I'm just having the motivation to advance study in math this summer

[marsh forum]

ok, so we have this set of books by the Government publisher called NCERT examplar here

really good

https://ncert.nic.in/exemplar-problems.php?ln=en

you can find them here

this is the offical site and is legal

[spare orchid]

oh okay

[marsh forum]

select your class and then chapter

[spare orchid]

alr thanks

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[wraith hinge]

how do i even do this??

like why is the column lopsided

[whole coral]

You should hopefully know some determinant properties, and how certain operations affect the determinant

[wraith hinge]

i know the 3 operations

row replacement does nothing to the determinant

interchange makes (-1)^r where r is number of interchanges

and scaling by k of one row does kdetA

if i do to 3 rows

k^3detA

oh

my

God

TRANSPOSE

detA^T = (detA)^T

[whole coral]

Well, det(A) is just a number, you can’t really transpose real numbers (well, I mean-)

[whole coral]

Did you like the hint

[wraith hinge]

yess

[whole coral]

But yeah, determinant of transpose is the same as the determinant of the original

So cooking time I’m sure you can cook up that second matrix from the first one with those in mind

[wraith hinge]

-15 !!!!

yay

thank youuu

.solved

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[wraith hinge]

i did something right

for this, am i allowed to row reduce

so i can get it into triangular matrix

ohh i read somewhere in the textbook that row reduction doesnt affect eigin values but it affects eigenVECTORS

[lilac flame]

no

it changes eigenvalues as well

for example

2 0
0 1

row reduces to identity matrix

[wraith hinge]

2,1 to 1,1

i see!

so how do i solve?

[lilac flame]

do u know whats an eigenvalue

[wraith hinge]

a scalar multiplied to an eigenvector x such that when matrix A is multiplied by x it produces the same result

Ax = lamba x

then x(A - lambaI) = 0

[lilac flame]

yeah

so A - λI has a non trivial kernel

[wraith hinge]

ohh

ill do that rq

[lilac flame]

so nullspace is non nontrivial

so det(A - λI) = 0

because it's not invertible

[wraith hinge]

sooo

[lilac flame]

do what

[lilac flame]

yes

find roots

[wraith hinge]

Thx you

Thx you

Thank* you

[lilac flame]

$p_A(x) = \text{det}(A - xI)$ is called the characteristic polynomial

[solid kiln]

xd

[lilac flame]

eigenvalues are it's roots

[wraith hinge]

you saved me

i did not learn this in class

.solved

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[lilac flame]

ur welcome

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[marsh forum]

Any way to do this that isn't painful?

[marsh forum]

so I was thinking

$\sqrt{\left(x-3\right)^2+y^2}+\sqrt{\left(x-9\right)^2+y^2}=12$

[solid kiln]

ƒ(Why am. I here)=misery

[marsh forum]

I mean I could square this and solve i

but that would be painful

[torpid depot]

you understand what curve this is?

[tall kernel]

This seems like a standard hyperbola or ellipse equation

Where the foci are the points given

[wraith hinge]

ellipse

[tall kernel]

Ye cuz sum

[marsh forum]

yeah

[tall kernel]

U know the equation for an ellipse?

[wraith hinge]

since both points on x'x axis you get:

[marsh forum]

yeah

[wraith hinge]

then js use that

[marsh forum]

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

[solid kiln]

ƒ(Why am. I here)=misery

[marsh forum]

oh

[wraith hinge]

that's for a ellipse yea

but

[marsh forum]

x^2/9 +y^2/144 =1

[wraith hinge]

that implies that the center is 0,0

which it isn't

[wraith hinge]

you can directly write equation of ellipse

the foci and length of semi major axis is given

distance between two focii of ellipse is 2Ae

where e is eccentricity of ellipse

you can find length of minor axis from e = sqrt 1 - b^2/a^2

hm

check centre

and write equation accordingly

note that centre is basically just midpoint of the focii of ellipse

[marsh forum]

hmm

[wraith hinge]

that's the easy part

[marsh forum]

just a min

[wraith hinge]

I'm confused as to how you get the a and b icl

[wraith hinge]

have you ever seen the derivation for the alternate definition of ellipse and for its eccentricity

if you have then you would know that distance between two focii of an ellipse is 2ae

where a is major axis length and e is eccentricity

oh

but you know neither a nor e

we know a

we can find distance between focii

as we have coordinates of focii

which is 12

using distance formula

in this case

[wraith hinge]

no 12 is 2a

so a = 6

I meant the distance is 12

definition of ellipse is PS1 + PS2 = 2A

[wraith hinge]

no distance is not 12 its 6

[marsh forum]

hmm

[wraith hinge]

coordinates are (3,0) and (9,0)

[marsh forum]

so the centre is (6,0)

=?

[wraith hinge]

distance between them is 6

[wraith hinge]

correct

man what

[marsh forum]

hmm

[wraith hinge]

I may be really confused but the center should be 3,0

[marsh forum]

and $e =\sqrt (1-9/81)?$

[wraith hinge]

no centre is midpoint of focii

[solid kiln]

ƒ(Why am. I here)=misery

[wraith hinge]

no

wrong

[wraith hinge]

which is 3,0

[wraith hinge]

its (6,0)

i saw -3

I may be going blind

my bas

bad

[marsh forum]

wait

ae is focus

right

hmm

[wraith hinge]

yes

and 2ae is distance between focus

so 2ae = 6

ae = 3

[marsh forum]

I feel I'm missing somethinng

[wraith hinge]

we know a is 6 as 12 = 2A from definition of ellipse

so a = 6

@marsh forum i suggest you to get familiar with all terminologies related to ellipse

[marsh forum]

Yeah, I will thanks

now how do I find b

[wraith hinge]

did you get how to find e

first

e = sqrt 1-b^2/a^2

so use this as you know e and a

[marsh forum]

wait, how do I know e

[wraith hinge]

distance between focus bro

its 2ae

and a is 6

[marsh forum]

sorry if this is a stupid question, I'm terrible at conics

[wraith hinge]

and distance between focus is also 6 in this case

so e is 1/2

[wraith hinge]

this is just use of the definition of ellipse

[marsh forum]

hmm

ok

[wraith hinge]

you can try more advanced problems once youre done with this

[marsh forum]

yeah, I find integral calculus easier, I really don't know what to do at this point

[wraith hinge]

it is easier

lol

[marsh forum]

so $1/2=1-b^2/36$

[solid kiln]

ƒ(Why am. I here)=misery

[marsh forum]

so $b^2=18$

[solid kiln]

ƒ(Why am. I here)=misery

[wraith hinge]

yes

no dude

e^2 = 1-b^2 / a^2

[marsh forum]

oh

right

[wraith hinge]

||it would be easier to solve the initial equation tbh||

you didn't square it before substituting

[wraith hinge]

trust me it may feel like it but once things get more advanced

[marsh forum]

so b^2=27

[wraith hinge]

we are more interested in finding specific things of an ellipse

[wraith hinge]

yea

so equation is (x-6)^2/36 + y^2/27 = 1

[marsh forum]

thanks!

.close

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Channel closed

Closed by @marsh forum

Use .reopen if this was a mistake.

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[wraith hinge]

Really need help with my HW, but its in a pdf form

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Please don't occupy multiple help channels.

[wraith hinge]

.close

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Channel closed

Closed by @dense gale

Use .reopen if this was a mistake.

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Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lean quiver]

How to do last part ii

[trim jolt]

Please don't occupy multiple help channels.

[half fjord]

Ahmed bro are you getting your hw done for free

😭

[lean quiver]

What

[lean quiver]

^^

<@&286206848099549185>

[tough iron]

Why you in a hurry

[lean quiver]

What

[final coyote]

!15min

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[lean quiver]

Why r u doing 80percenf of 60

Why 60

Also that’s wrong

This is the answer

How did they get 40 and 20

Why r u doing 60-40

So is 70

Why r u doing that

I’m confused

Why r u doing 60-40

Pls explain the theory of this

I’m rly not getting jt man

Simplify

The whole answer key

this is context specific

Stop