help-26

[thorny flame]

convergence

[thorny remnant]

this is equal to $4t^{1-4}(t+2)$

[thorny flame]

convergence

[violet sundial]

so t^-3 and will go to the denaminator to make it positive.

[thorny remnant]

yes

[violet sundial]

okay thank you, but can i have a favor. can i take notes first on our conversation before i leave?

[thorny remnant]

sure

after that close the channel by typing .close

[violet sundial]

a pleasure...

okay i got it

Thank you sir

[thorny remnant]

:)

[violet sundial]

last question sir. how common in numerator works?

[thorny remnant]

i see

you have that problem

[violet sundial]

yes

[thorny remnant]

see this equation a^2(b)+b^2(c+a)

[violet sundial]

yes im following

[thorny remnant]

now i can write this as
$a^2b+b\times b(c+a)$

am i right

[thorny flame]

convergence

[thorny remnant]

now i see there is a b common

in both a^2 b and b x b(c+a)

[violet sundial]

okay you expanded it. because b^2 is same as b x b

and now?

[thorny remnant]

now i take b common

[violet sundial]

only one?

b?

[thorny remnant]

if you remember a(b+c)=ab+ac

[violet sundial]

yes i do

[thorny remnant]

here in ab+ac a is common in both the terms right?

[violet sundial]

yes both has a

[thorny remnant]

and we know that ab+ac=a(b+c)

[violet sundial]

omg'

[thorny remnant]

so in this b is common

so i take b common

[violet sundial]

that makes so much sense.

[thorny remnant]

and i get $b(a^2+b(a+c))$

[violet sundial]

i got it

[thorny flame]

convergence

[thorny remnant]

now apply this concept to that

[violet sundial]

a^2 b + b x b (a + c)

byeee@thorny remnant A big help for me!!

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[thorny remnant]

bye

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[honest tartan]

is (A intersect B) intersect (B intersect C) equal to B intersect C

[verbal crater]

no

[honest tartan]

A intersect C

[verbal crater]

no

[honest tartan]

alr bett

it's not equal to anything cool right

[verbal crater]

its equal to A intersect B intersect C

[honest tartan]

yeah other then that lol

okay that's all

thank you

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[honest tartan]

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[honest tartan]

im tweaking rn

i’m trying to prove G being disconnected implies there is no internally disjoint u-v path

by contrapositive

[honest tartan]

does the fact that Pk intersect Pn being disjoint from P1 give me that there exist two dijoint paths or does that not follow

[verbal crater]

what is this topic

[honest tartan]

graph theory

[verbal crater]

what specific part of graph theory

[honest tartan]

this is just basic stuff

we're only doing simple graphs

[verbal crater]

sorry dont think i know enough to help you

[honest tartan]

its all good thank you for your time

[clever citrus]

ur handwriting is beautiful bro

[honest tartan]

im guessing that ironic lol

basically im saying that S is the set of all u v points

P1......Pn

that the intersection of the intersection of P1 and Pi for all i

im trying to show that removing any vertex from that set i called R disconnects the graph

<@&286206848099549185>

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@honest tartan Has your question been resolved?

[honest tartan]

<@&286206848099549185>

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@honest tartan Has your question been resolved?

[honest tartan]

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[neon iron]

How can I find this

[jade thunder]

try some big values of n

what happens

[neon iron]

How can I try it

The answer is convergent btw

But idk cos is always indeter.

[fallow heart]

Do the limit as n → +∞

[worthy storm]

find a bound for cos^2(n)

[neon iron]

Cos will be always indeterminant form and i cannot get rid of it

[fallow heart]

@neon iron

[neon iron]

is it true if I write this

[worthy storm]

where did the 1+ in the numerator come from?

[neon iron]

Cos^2(n)=1+cos(2n)/2

[worthy storm]

oh i see what you did

that's fine, or you could just say 0 <= cos^2(n) <= 1

[neon iron]

Oh thx for your help 🙂

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[urban raptor]

i know the formula is

where the center of the ellipse is (h,k) and a and b are the long and short sides respectively

[hazy pumice]

Foci eqn: c^2 = a^2 - b^2

[urban raptor]

yes

but first

we know the center is at (0,0)

meaning that h and k are 0

[urban raptor]

c is what?

[hazy pumice]

c is the distance from the center to a focus

[urban raptor]

ok

and theres 4 from center to vertex

[hazy pumice]

@urban raptor what is your question about this problem?

[urban raptor]

how i solve it

i am really bad at conic sections

[hazy pumice]

You were given enough info to immediately know a and c. Use that information to find b

[urban raptor]

so i know a is 4

so a^2 is 16

[hazy pumice]

a is 5

[urban raptor]

how

[hazy pumice]

Oh hang on

[urban raptor]

center at 0 and vertex at 4

[hazy pumice]

There are two questions here

Different ellipses

[urban raptor]

yeah

top one for now

so a=4 and c=2

[hazy pumice]

Uhuh

[urban raptor]

so 4=16-b^2

?

[hazy pumice]

Uhuh

[urban raptor]

b^2=12

b=2root3

[hazy pumice]

Good

2sqrt3

[urban raptor]

just to copy it down

[hazy pumice]

They gave you the center, so you have h and k too

You have everything you need now

[urban raptor]

this is the standard formula

[hazy pumice]

Uhuh

[urban raptor]

?

[hazy pumice]

Yeah

Done, done

[urban raptor]

yup it was correct

[hazy pumice]

Onto the next one

[urban raptor]

ok so the formula is

and

h is -2

and k is 4

[hazy pumice]

No

h is -2, k is 4

Don't get it twisted

[urban raptor]

yes that is what i wrote

[hazy pumice]

Oh

Damn, I should go to sleep

Let's hurry

[urban raptor]

a is 5

because center at 4 and vertex and -1

this means that we have a tall one correct?

[hazy pumice]

Yes

[urban raptor]

ok c^2=a^2-b^2

c=1

a=5

1=25-b^2

b^2=24

b=root24

[hazy pumice]

What I did was a = (|-1| + |9|)/2 = 5

[urban raptor]

2root6

[hazy pumice]

Good

[urban raptor]

but

[hazy pumice]

You got a typo

[urban raptor]

where

oooohhhh

wait what im just supposed to switch 25 and 24 because its a tall one right

[hazy pumice]

No, lol

You got two x's

[urban raptor]

wow

but i still flip them right

couldve sworn the guy in the video said so

[hazy pumice]

Maybe, I'm fading, didn't check

The a is always under the longest dimension

Remember that

[urban raptor]

YES

yes

jeez

so is it 24 and then 25 or 25 and then 24

[hazy pumice]

So the 25 should be under the y business

[hazy pumice]

Good

[urban raptor]

yup it was correct

thanks

now go sleep

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[violet pecan]

hi im quite new to linear algebra and im reading my first linear algebra book. I'm at the part about vector spaces and i need help understanding this part:

[violet pecan]

first, what does the first bullet mean in 1.24? (specifically, what does "...functions from S to F" mean?)
second, if i understand correctly, F^S have functions (instead of numbers) as its elements?

[thorny flame]

LucienF

[near steeple]

So since F is a set of numbers, your images are things in that number set F.

[violet pecan]

wait im still trynna understand this

ok makes sense, but can you give also an example function of R^[0,1] in the 2nd page of the screenshot

[chilly walrus]

f(x) = x^2, if you restrict the domain to [0,1]

[violet pecan]

so f(x) = x^2 is an element of F^S?

[storm hearth]

R^[0,1] yeah

[violet pecan]

oh right R^[0,1]

im just trying to see if elements in F^S are not numbers, cuz it's my first time hearing about elements of a set being functions

[storm hearth]

Actually, $\mathbb{R}^{[0,1]}$

[chilly walrus]

elements of a set can be literally anything

[violet pecan]

also, from what i understand a vector space sounds just like a set. Are they interchangeable?

[thorny flame]

Cyrenux

[chilly walrus]

it's a set with specific properties

[violet pecan]

like F^S was defined as a vector space, but also a set

[chilly walrus]

all vector spaces are sets but not all sets are vector spaces

[violet pecan]

oh ok it's kinda making sense now

and as for the properties, do u know what properties make a set a vector space

[chilly walrus]

these

V is the vector space, F is a field

[violet pecan]

is a "vector" interchangeable with "element"?

[chilly walrus]

in vector spaces - yes

[violet pecan]

so f(x) = x^2 is a vector in R^[0,1]?

[chilly walrus]

yes

[clever burrow]

what is the problem?

[chilly walrus]

that may sound weird but it is a vector technically

[violet pecan]

i'm just trying to understand terms

cuz my previous idea with vector is something like coordinates

so im guessing this book is more abstract

[chilly walrus]

you are learning about vector spaces now more abstractly

a vector is NOT a pointy arrow

albeit it can often be visualized as one

[storm hearth]

oriented line segment

[chilly walrus]

but in the case of a vector space of functions they are just elements of the vector space

[violet pecan]

i see so is it right to say, the previous knowledge I had with linear algebra (that vectors are points), is just one specific instance of like R^N

[chilly walrus]

precisely

[violet pecan]

i only know about R^2 before

and R^3

and that vectors should be like a list of real numbers, but actually it can be anything

[violet pecan]

as long as they satisfy these properties

[storm hearth]

Set of all ordered duos/triples whose components are real numbers

Not any ordinary number

[violet pecan]

oh ok

[chilly walrus]

"duos" lol

pair maybe?

[storm hearth]

Pairs yeah

My vocabularly died there lmao

[violet pecan]

ok i understand, i was just caught off guard from the vector space containing functions as its elements

[violet pecan]

so that's why the 2nd and 3rd bullet point here defined addition and scalar multiplication

ok thanks i think i got it 4 now

thanks for the help!11!1!11

ambatu close it

[chilly walrus]

no problem!

[violet pecan]

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[storm hearth]

I think i saw $$(f+g)(x) \neq f(x) + g(x)$$ (aka pointwise principle) in some space, dont remember which

[thorny flame]

Cyrenux

[storm hearth]

Its just saying that it satisfies pointwise principle, wikipedia has examples

[violet pecan]

is it =/= or =?

[storm hearth]

Also for better clarity, i recommend checking definitions of groups, abeliean groups as well as rings

[storm hearth]

No typo

So the former

[violet pecan]

oh ok

jus pointed it out cuz in my screenshot it's =

[storm hearth]

Otherwise no reason to tell but yeah every vector space satisfies pointwise principle

[storm hearth]

Thats odd

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[broken fulcrum]

how to solve this question

[brazen remnant]

first, let $\angle{ADE}=x.$

[thorny flame]

lpieleanu

[wintry rain]

find DBE

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[north steeple]

posted this a couple of times already but made progree

progress

im stumped for b tho

usualyl i can do absolute vales but im a bit confused with this one

i geuss i dont rlly know whats going on in the question, is the solution just x when they intersect

and i know in absolute value integrals i usually just times the part of the integral that is negative by -1 and i find where it is negative by using a graph

as in i split it up into two integrals , positive and (-1) times negative part

but this question has confused me for some reason

[shadow salmon]

When u split up, why are you going from 0 to pi in the right term?

[north steeple]

oh, sorry meant to put alpha

[shadow salmon]

Alright good! So using your sketch from a), in which of the intervals [0,alpha] and [alpha, pi] is sin(x) - kx positive resp. negative ?

[north steeple]

i think 0-alpha its positive

[shadow salmon]

Correct

[north steeple]

but then why is it negative in the other one?

its not crossing the x axis

well it is

but not before the interval

[shadow salmon]

Look at ur sketch, and comapre it to ur expression

[north steeple]

oh, so its wen sinx-kx is negative?

[shadow salmon]

Yeah!

[north steeple]

ahhh, ok so its after they cross each other

[shadow salmon]

Yup!

Since alpha is the unique root when sinx - kx = 0

[north steeple]

ahhhhhhh that makes more sense when u think of it like a root

[shadow salmon]

Neat!

So what does |sin x - kx| simplify to when sin x - kx is positive**?

i.e in the inteval [0, alpha] ?

[north steeple]

what do u mean simplify to?

oh

[shadow salmon]

sorry made a typo

[north steeple]

just sinx-kx ?

[shadow salmon]

Yup!

[north steeple]

cool

[shadow salmon]

and now consider how u can rewrite |sin x - kx| when the inside is negative, i.e in the interval [alpha, pi]

[north steeple]

since integral is area under a graph, if i were to think of it wihtout the absolute value it would be a negative number that would come out, but with absolute values in graphs u get the funny point where it just turns and becomes positive again where it would normally go straight through the x axis, so i would just do the normal sinx-kx integral times minus -1 wiht (alpha,pi) or, what i could do is switch the two around (pi,alpha)?

[shadow salmon]

Yeah, i mean you could also just think back to the def. of absolute value; |x| = x if x is non-negative

while |x| = -x if x is negative

since -x > 0 if x is negative

[north steeple]

wait, |x|=-x ?

[shadow salmon]

yeah if x is negative

[north steeple]

i didnt know abolute values could be negative

[shadow salmon]

Well it isnt

[north steeple]

oh -(x-)

[shadow salmon]

yup!

[north steeple]

ahhhh

[shadow salmon]

So in our case we're dealing with |sinx - kx| which is not any different

[north steeple]

yeah

so kx-sinx ?

[shadow salmon]

we've noticed that the inside is negative in the interval [alpha, pi]

yup!

[north steeple]

cool

ill try that now ]

got this far

and then simplify a bit more

but how do i now get the solution its asking for

[shadow salmon]

i cant help but notice that youre writing |x| = -(-x) if x < 0, why?

[north steeple]

that was just to remind me why |x|=-x sometimes

cos it confused me a bit

[shadow salmon]

i think it's important to realize that -x does not mean that x is negative

if x is negative, -x is positive

[north steeple]

but x would be negative if |x|=-x

[shadow salmon]

yeah

[north steeple]

ok i get what u r saying

[shadow salmon]

alright good! i think its an important step to learn when dealing with that kind of stuff

[north steeple]

yeah

[shadow salmon]

let me check ur work again

[north steeple]

have they maybe subbed in for kx

to get the sinx?

[shadow salmon]

yeah that might be what is happening, since alpha was the number such that k alpha = sin(alpha), they might of replaced any instances of k alpha with sin(alpha)

[north steeple]

yeah

o

ill give that a go

i hate how some of these questions are guessing games like im gonna be stressed in the exam enough lol

[shadow salmon]

Hey, dont worry; this sort of stuff stops feeling like a guess the more experience you get

so just keep at it!

[north steeple]

hm im not sure if this subbing is correct, im struggling with the sin(pi) bit

[shadow salmon]

well what is sin(pi) ?

[north steeple]

oh

ahahaha

[shadow salmon]

:P

[north steeple]

ok im struggling with how they get the pi^2sina/2a

[shadow salmon]

What do you have so far?

[north steeple]

oh wait nvm

ka=sina

so 2ka=2sina

[shadow salmon]

Yup!

[north steeple]

ok got it

ill finish it up

[clever burrow]

guys

just plot the graphs

doesn't that work?

[shadow salmon]

This is for b)

[clever burrow]

oh

[north steeple]

ahaha

got it

[shadow salmon]

Neat

[north steeple]

not too bad

was thrown at first by an absolue value graph but it wasnt one u had to think about crossing the x axis if that makes sense

but now thsnkfully know how to deal with them

[shadow salmon]

[north steeple]

thanks again

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[zenith dock]

doing another double integral question, its bounded like this:
https://itsmakiiuwu.s-ul.eu/B0MiDxVP
y=x
x=2
xy=1

would i set my equation up like this and just solve normally ?
https://itsmakiiuwu.s-ul.eu/cxSublqj

[zenith dock]

after setting it up this way, ive solved to get 1/2 - 3ln(2)

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[storm hearth]

I think you did a mistake while integrating

[zenith dock]

did i set up the bounds correctly though ?

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[violet sundial]

Hello sir this is differentiation

[raven sparrow]

What have you tried?

[violet sundial]

yes

[plush hollow]

have u heard of product rule

[violet sundial]

Yes sir

[violet sundial]

here is my solution

[plush hollow]

seems correct

[brave coral]

The last bit isn't

[violet sundial]

Yes

[brave coral]

You didn't simplify the fractions correctly

[violet sundial]

how can i simply it sir?

should i change the square root to (x+1)^1/2?

[brave coral]

That would help, yes

[brave coral]

Where is your addition sign going?

And you still haven't simplified correctly

[violet sundial]

I dont know how to simplify them sir

[brave coral]

$$ 5 + \frac{6}{7} = \frac{5 \times 7 + 6}{7} $$
I don't mind to be patronising but perhaps this will jog your memory

[thorny flame]

StrangeQuarkAL

[violet sundial]

Here is final answer, but i dont know how to turn it like this

[brave coral]

I'll just show you an example then

$$ (x + 1) + \frac{2x^2 + 1}{3x} = $$
$$ \frac{3x (x + 1) + 2x^2 + 1}{3x} $$
$$ \frac{3x^2 + 3x + 2x^2 + 1}{3x} $$
$$ \frac{5x^2 + 3x + 1}{3x} $$

[thorny flame]

StrangeQuarkAL

[violet sundial]

I multiplied 2x to x and 1

To the power of 1/2

[brave coral]

Multiply the 2x(x + 1)^(1/2) by the denominator

[violet sundial]

Is there a chain rule that will happen?

[brave coral]

You have already differentiated so no. You used the chain rule earlier on

[violet sundial]

Multiply like this?

The denominator to 2x(x+1)^1/2

I think i've got it

[violet sundial]

Sir

[violet sundial]

can i ask sir why do we multiply it to the denominator? what is it called?

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[violet sundial]

.reopen

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[violet sundial]

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[neon iron]

A student standing on a hill inclined at an angle q with respect to the horizontal and at a
height of 20 m, observes an object on the ground with an angle of depression a. Find the distance
from the object to the base of the hill

[neon iron]

What am I doing wrong?

[fresh sun]

angle of depression is this

[neon iron]

yes, I know

[wet sun]

Maybe fix it on your diagram and see

[neon iron]

theta angle of the hill

and alpha of depression

[neon iron]

oh

I see

[fresh sun]

(alpha is not the angle of depression)

[neon iron]

all my life I have thought the angle of the depression was the other even tho I learned it was this one

now I get 20(cot(alpha) - cot(theta))

[fresh sun]

I haven't ever done any problems with that lol

but i just know it for some reason

[neon iron]

me neither

I just got the concept wrong

and bc I didn't apply it I didn't realized it was wrong

[neon iron]

did u get this

?

[fresh sun]

I'm not sure I'll do it rn

[neon iron]

ok

[fresh sun]

is alpha = 90-theta

[neon iron]

no

[fresh sun]

ok

[fresh sun]

what's the distance we're looking for

I got 20/tana

[neon iron]

Find the distance from the object to the base of the hill

I got c

[neon iron]

same reasoning =, but with the angle theta below

[fresh sun]

mb

to the base of the hill

[neon iron]

what's mb

[fresh sun]

the studen'ts height doesn't matter right

[neon iron]

I also wondered that, but I guess not

[fresh sun]

ok yea it doesn't

the diagram threw me off mb

I got the same thing

[neon iron]

thanks for the help 👍

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[fresh sun]

np

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[quasi stratus]

can somebody help me with this physics c: mechanics problem? im not sure if 64 is the right answer, i found it from online, but idk how to get that answer, all the other answers ive gotten are different

[topaz sinew]

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[grave berry]

can someone explain how (s^3+27)/(s^2-9) got to ((s+3)(s^2-3s+3^2))/((s-3)(s+3))

[terse abyss]

It’s tricky but foil it out and you’ll see their factoring is correct

[grave berry]

where did they get -3s from the original equation?

[terse abyss]

I guess you just have to try to factor it? Idk how they expect you to see that

But if you multiply it out you get $s^3 - 3s^2 + 9s + 3s^2 - 9s + 27 = s^3 + 27$

[thorny flame]

Pixelius

[grave berry]

ohhh

okay

i think i understand now

wait

if multiplied like s(s^2-3s+3^2) 3(s^2-3s+3^2)?

how was it multiplied?

is 3 like a gcf of 27 and 9

is that why they used3?

but wouldn't it be negative?

[terse abyss]

It’s not a gcf it’s just the factor you can pull out of s^3 +27 that cancels with the denominator. You can find it in a few different ways

[grave berry]

k

[terse abyss]

Look up synthetic division and/or polynomial division

[grave berry]

ok

thanks

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[cobalt vector]

any other method than l'hopital

[neon iron]

Why not?

[rigid cloak]

Factorise it my bro

[neon iron]

it's just dx

[neon iron]

💀

[rigid cloak]

Lol

[neon iron]

But bro if u dk L'hospital it'll be very difficult to solve indeterminant forms of limits

[rigid cloak]

See

It's ez

By the fact

That there is a zero by zero form

[cinder sequoia]

your only options here are l'h or factorization

[neon iron]

thats just x^n by forn

[rigid cloak]

That is both the polynomials have a factor of (x-3)

[neon iron]

d/dx x^n = n.x^n-1

[rigid cloak]

We divide both the polynomials by (x-3)

[neon iron]

keep doing that

[rigid cloak]

And get the answer but by putting x=3

Na we ball

[neon iron]

for constants it'll be 0

You realise we cant factorise for every single question right??

[rigid cloak]

Sde

See

Both the polynomials

Have the factor (x-3)

So we can write them as

p(x)=(x-3)q(x)

Now you can see that

The polynomial in numerator has a degree 3

So we can express it in terms of a linear factor and quadratic

So we can take q(x)=(ax^2+bx+c)

Now by substituting different values you can get a,b and c

[neon iron]

2/9 is the limit

[rigid cloak]

Na we ball

[neon iron]

just dx it's much easier

BRO

[rigid cloak]

We do by factorisation

[neon iron]

what if its x^7

[rigid cloak]

Same case bro

[neon iron]

Dx is easier

[rigid cloak]

If it's x^7

[neon iron]

Bro

[rigid cloak]

Then imma try

Integer and rational root theorem

[neon iron]

😭

just use dx

[rigid cloak]

For finding more roots

[neon iron]

much easier

[rigid cloak]

And when I find 3

I will apply agaun

Fr

Na we ball

[neon iron]

Bro L'hospital is easy

[rigid cloak]

See imma show u

[neon iron]

if we know dx

[rigid cloak]

P(x)=(x-3)Q(x)

[neon iron]

just use dx formulaes

alright

[rigid cloak]

P(X)=(X-3)(ax^2+bx+c)

Putting x=0

We get

-9=-3.c

[neon iron]

i want x^8-5x^6+7x^3+2

[rigid cloak]

So c is 3

We ball

[neon iron]

factors

[rigid cloak]

Bro

I cannot factorise

Simply

[neon iron]

thats what im saying

just use dx

[rigid cloak]

It's the fact we have 3 as the root

[neon iron]

faster ,efficient

[rigid cloak]

See l' hospital is applicable

When 0/0 or infinity/infinity

Right

And x tends to 3

This means both the polynomials

[neon iron]

there are 6 more cases

[rigid cloak]

Must have (x-3) as a factor

For 0/0

[rigid cloak]

What

Bro

[neon iron]

ye

[rigid cloak]

Imma talking in general

Bro

[neon iron]

but bro

[rigid cloak]

U have polynomial/polynomial

And x tends to 3

U check limit becomes 0/0

This means

[neon iron]

but its indeterminant form bruhhhhhhhh

[rigid cloak]

Both have (x-3) as factor

Then we ball

[neon iron]

i understand

[rigid cloak]

We factorise

[neon iron]

u just wanna cancel them out

[cobalt vector]

(x-3)^2 cancels out

[rigid cloak]

Bro is not understanding the deepness

[cobalt vector]

any other simple method

[rigid cloak]

Aah

Na bruh

[neon iron]

but if no common factor then we have to use lhospital

[cobalt vector]

because both takes same time

[rigid cloak]

What can u more simple then dat

[rigid cloak]

It is not possible

[neon iron]

it took me 10seconds

[cobalt vector]

how show me

[rigid cloak]

For poly/poly to become 0/0 if they both don't have common factor

[neon iron]

I just did dx

[rigid cloak]

It's not possible

They will have common factor

[cobalt vector]

what how dx

[neon iron]

infinity/infinity

[cobalt vector]

l'hopital?

[neon iron]

or 1/0

[rigid cloak]

Bro

[neon iron]

Yes

[rigid cloak]

Bro is not understanding

[cobalt vector]

but i said than l'hopital

[rigid cloak]

Poly/poly can only become infinity if x tends to infinity

Bro is not understanding

Algebra

I knowing taking derivative till the form vanishes is ez

But what bout the og good methods

[cobalt vector]

,w x^4-5x^3+27x-27 farctorize

[thorny flame]

Results provided by WolframAlpha

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Requested by bill220220_58022

[rigid cloak]

U ain't learning l'hopital in first class

See

This I was telling

We have (x-3)

In both

We can find the factorised equations

,w factorise x^3-7x^2+15x-9

[thorny flame]

Results provided by WolframAlpha

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

Requested by oppailol.

[rigid cloak]

Both cancel

We ball

[cobalt vector]

okay bro

coool down

thanku

.close

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[rigid cloak]

So we have 9+3-3/9-1

That is 9/8

Yo

Na we have 8/9 it was the denominator

Okok

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[copper shard]

Can anyone help me with this really fasst

[copper shard]

anyone please?

sorry its urgent i only have 10 minutes left

<@&286206848099549185>

[topaz sinew]

@copper shard Has your question been resolved?

[copper shard]

.clsoe

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[neon iron]

Problem 4

[mellow arrow]

try finding the conjugate of 8-3sqrt(7)

[neon iron]

8 + 3sqrt(7)

[mellow arrow]

yeah

so effectively you have a hidden quadratic

[neon iron]

Idk how to combine terms

If that’s what I’m supposed to do

[mellow arrow]

multiple ways to go about it

let (8+3*sqrt(7))^(x^2-4x+20) be p

now you have a quadratic in p

[neon iron]

What about its conjugate

[mellow arrow]

$\left(8-3\sqrt{7}\right)=\frac{1}{\left(8+3\sqrt{7}\right)}$

[thorny flame]

B-eard

[neon iron]

I see

[brittle haven]

Hey

[neon iron]

Hi

[neon iron]

Then what I got stuck

Wait hold on

[neon iron]

$p + 1/p = 16$

[thorny flame]

Yuki

[neon iron]

And then solve is that how you do it

Ok I see Ty

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[gleaming coral]

can i say im not sure where to start at all

[verbal crater]

whats the period of tan

[gleaming coral]

pi?

[verbal crater]

yes

now can you find A and C?

their coords

[gleaming coral]

a wld be h-pi and c wld be h+pi?

[verbal crater]

indeed

[gleaming coral]

ohhh

lemme try part 2

ohhh i get it now

i might have more qns

ok for this ik the eqn here which is y=3cosx+2

i only got 3 and 2 from guessing

like comparing the amplitude

but im not sure if there is a actual method to find the amplitude and shift in y coordinate here

also for writing trigo eqns graph for example if i have y=sin3(pi)x

1 period would be 360/3(180)=2/3?

[verbal crater]

yeah

[gleaming coral]

hmm how about this?

[verbal crater]

yeah its correct

[gleaming coral]

but like im not sure how to find a and c

like here

i cant just guess the eqn

im not sure what are the steps to do it

[verbal crater]

well one way is since the max and min is not equal distance, you first move the axes up or down until they are equal distance

that will give you your amplitude

then the amount that you moved up or down will be the vertical shift

[gleaming coral]

how do i move the axes up and down?

[verbal crater]

or another way is you find the distance of the max and min point

so here, the distance between 3 and -1 is 4

so the amplitude should be 2

makes sense?

[gleaming coral]

yes i get that

[verbal crater]

then the max point should have y = 2 and min y = -2

to get 3 and -1, you just add 1

so the vertical shift is +1

[gleaming coral]

ohh

so it wld be y=2sinbx+1

im not sure how to find the period tho 360/2pi?

[verbal crater]

wait the amplitude should be -2

[gleaming coral]

oh

[verbal crater]

because its flipped from the positive graph

[gleaming coral]

ohhh alright

[verbal crater]

then the period is 2pi / b

[gleaming coral]

what would b be here in this case?

[verbal crater]

thats what you're trying to find

[gleaming coral]

oh

[verbal crater]

you read from the graph whats the period

[gleaming coral]

one period here is 2pi right

[verbal crater]

yes

2pi / b = 2pi

so b = 1

[gleaming coral]

ohh

wait but the ans here is

y=-2sin(pi/2)x+1

[verbal crater]

why pi/2?

[gleaming coral]

im not sure thats the ans key here

no wait b is =1 but eh

oh wait it is 1 here

but if we had a graph like y=-2sin(pi/2)x+1

is it posible to conver pi/2 to degree

oh wait js use the actual value of pi nvm idk what i was thinking

tks a lot !

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[stiff apex]

5b I’m not sure how to work it out

I was thinking bc the radii r 10

U can assume the straight lines parallel to 60 are 40

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[chrome arrow]

I find setting up constrained optimization problems quite intuitively difficult. I have an example question and would appreciate a demonstration of what my thought process should look like when setting up the objective and constraint equations

[rigid cloak]

Yo

@chrome arrow

[chrome arrow]

Yeah?

[unborn jewel]

Umm, I don't remember these things cuz I am out of practice for long tims

But I think basic logic should go like

[rigid cloak]

See

U can form basic equations

[unborn jewel]

Flat roof is costliest, so we gotta use it's dimensions in less amount

[rigid cloak]

U have to treat cost as a function of dimensions

[unborn jewel]

Yeah

seems like you know this thing, go on, I go

[chrome arrow]

Do you mean multivariable?

[rigid cloak]

No

See

U want to have a rectangular building

[unreal crow]

whats the square root of 144

HELP

[rigid cloak]

12

[chrome arrow]

<@&286206848099549185>

[chrome arrow]

Can you show me how the set up should look like?

[rigid cloak]

Your front is square

So all sides should be equal

If u want a rectangular building

.

And the top is rectangle

@chrome arrow send me a white page

Yo draw the structure

@chrome arrow

[chrome arrow]

Alright gimma a sec

This is what i understood from the description

[unborn jewel]

waow

ig he knows how a rectangle gonna look like

[rigid cloak]

Yes

It's correct

[chrome arrow]

Objective and constraint functions?

[unborn jewel]

There will be use of lbh = 64000 at some point ig

[rigid cloak]

See take the side of squares as x

And the length of roof and sides

Which extend till the back as y

So u will have a cuboidal shape

[unborn jewel]

Hmm, makes sense

[tired turret]

ew dont know if the back is also a square

[unborn jewel]

If front is square, then back will be square too obv

[tired turret]

no, it could be a trapezoid too

[unborn jewel]

Rectangular building is mentioned

So ig, rectangular building means cuboid

[tired turret]

hm okay

[unborn jewel]

Now we have 2, variables and 2 equationns

[unborn jewel]

First equation will be of volume

Yeah this one

And next will be of total cost

[chrome arrow]

So our constraint is v(x,y) = x^2y

[rigid cloak]

Yes

but given x^2y=64000 something

Whatever is given

[unborn jewel]

The cost equation will be ig 9x^2 + 16xy + 18xy

[rigid cloak]

Yes

[chrome arrow]

C(x,y) = 18xy + 2*16xy + 16x^2 + 9x^2
V(x,y) = x^2y = 64,000

Now…

∇C = λ∇V

The rest should be easy.

[unborn jewel]

9x^2 + 34xy

Where you got that 16x^2 from

[chrome arrow]

The back

[unborn jewel]

And why 2*16m

[chrome arrow]

It says 16 for the sides and back

[unborn jewel]

Oh yes, mb

[rigid cloak]

I just told what u have to add

[chrome arrow]

Cuz, all other things considered, there are 2 sides

[unborn jewel]

Got it

mb

[unborn jewel]

So now we put value of x^2 or y from first equation

y = 64000/x^2

We put this is the second equation

Of cost

[rigid cloak]

Yes

He is correct

[chrome arrow]

C(x,y) = 18xy + 2*16xy + 16x^2 + 9x^2
V(x,y) = x^2y = 64,000

Now…

∇C = λ∇V

The rest should be easy.

[rigid cloak]

No no

Write y=64000/x^2

And then it becomes C(x)

[chrome arrow]

Ohhh so it becomes a single variable question

Takes less time

Gotcha

Thanks!! At first what I attempted with the set up was setting roof, sides, back/front as variables🤦‍♂️.

[unborn jewel]

Is the answer 48000

[rigid cloak]

Yes

[unborn jewel]

Got it

[rigid cloak]

Welcome

[unborn jewel]

x = 40

[rigid cloak]

Bro is man of graphene

Fr

Bro can withstand 1ton pressure by one single layer of himself

[unborn jewel]

lmfao

[chrome arrow]

.close

[topaz sinew]

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[unborn jewel]

Hey wait...

Y is also 40

It ain't rectangular or cuboid

It's a cube!

Cubes are a subset of cuboids tho, like a special case of cuboids

[rigid cloak]

Lol

Na bruh

We should have though bout it

4x4x4 is 64

Shit

[unborn jewel]

Ye

Cube is literally cuboid with same sides

So maybe, it's correct

Or did we mistakenly eliminated any roots xd

[rigid cloak]

Lol na bruh

Wait imma do it

[unborn jewel]

Hmm I will recheck too

It's x=y=40

And same 48000

Bad question making

Anyways, the guy who asked seems cool with this

Oh he already closed, nvm

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[lunar blaze]

I'm working on some practice questions for my Probability/Statistics course: For this question, I tried graphing this and then tracing to see the value once I reached 50 but I'm seeing a negative value and even chatgpt seems to come up with the same thing. Is there something I am misinterpreting?

[lunar blaze]

Using the TI-Nspire CX (Non-CAS) calculator btw

[rigid cloak]

See y is age

And x is total sales

So u need x for 50 as age

Do it now

@lunar blaze

Fr

[unborn jewel]

This gives the age in negative 💀

[rigid cloak]

O

No*

[unborn jewel]

uncle is -28 years old

[rigid cloak]

no

We need to find sales

Y is age

We put y=50

So we get 50=-3x+122

[unborn jewel]

Oh, this makes sense

[rigid cloak]

We get -72=-3x

X=24

Now as sales is in 1000

[unborn jewel]

Nice

[rigid cloak]

We get 24 thousand total sales

C.

[unborn jewel]

ez

[rigid cloak]

Bro but we told the answer

💀

!noans

[topaz sinew]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[lunar blaze]

what a problem

[rigid cloak]

!status

[topaz sinew]

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

[unborn jewel]

It be good if you choose 6. XD

[rigid cloak]

Lol

[lunar blaze]

I guess 6 since i can just* ask chatgpt now

[rigid cloak]

What

Answer is C bro

I explained also above

[fallow igloo]

Plz no

[unborn jewel]

Brah, then us sending answers should not be an issue if you ask ai

[rigid cloak]

[lunar blaze]

I'm talking about the response

[fallow igloo]

It will spit nonsense

[lunar blaze]

For my question I will still need a bit more handhonlding to get ot the answer on my own

[rigid cloak]

U need to understand bout the variables

[lunar blaze]

Not really its been pretty great, I do have the paid version tho

[rigid cloak]

Like here y was the age

And x was the total sales

[fallow igloo]

Damn, good for you

[topaz sinew]

@lunar blaze Has your question been resolved?

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[lunar blaze]

Thanks I had to take some time to read over it a bit more

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[hot sky]

how do i do question 7 eii?

answers supposidly are ^

i did 0.043767 = 2.5783 * sqrt((p(1-p))/600)

giving me 0.222917

not 0.778

wait 1 - 0.222917 = 0.778

but why

interesting when u do it by hand you get 2 solution which a those 2 we speak about

but which 1 choose

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[hot sky]

k

:(,

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[cunning kayak]

I tried to think like to solve it with functional equations but that doesn't seems to work

[fiery badge]

I'm having a deja vu over here

[cunning kayak]

[fiery badge]

Like, I solved this 2 months ago or something