help-23

[fickle trail]

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[fickle trail]

these composite functions f(g(x)) and g(f(x)) both have the same domain, yeah?

also, would there be a calculator online to check for myself? trying to find one that handles composite functions

[quasi bison]

how many more dozens of problems like this are you planning to do?

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[dreamy finch]

i need help with 42

[dreamy finch]

this is what ive done so far

<@&286206848099549185>

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[patent vault]

where do i starT?

[quasi bison]

8 + 16 + 24 + 32 + ... + 2021*8 is a sum you can compute explicitly-ish

[hallow egret]

I mean, tha 8 + ... is an arithmetic series

since 1 + (2021 (summation notation) n = 1) 8n

don't really know how to do this in latex

since we have the n here, this equation.

[patent vault]

oh

[dense prism]

The catch here is to realise that no matter upto how many terms you sum the series in the right bracket, adding 1 to it will always give a perfect square.
So let's assume the sum in the bracket is upto some n terms where n is an integer (in this case it's 2021). After you apply the summation formula for an arithmetic series, you'll arrive at an expression which can be easily factorised into a perfect square. Try doing this and tell me if you need more help

Instead of using the series sum formula for 2021 terms, use it for a general integer n since it will be easy to factorize it into a perfect square that way

[patent vault]

ah thanks that helps a lot

[hallow egret]

ey I got the equation for the whole formula

Its (2n+1)^2

[dense prism]

Yes it's that

[hallow egret]

So it is really a perfect square

[elfin raven]

it's the square of 4043

[patent vault]

thansk!

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[patent vault]

.reopen

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✅

[patent vault]

i get this @dense prism 4n+4n^2

is this always a square?

[dense prism]

Yes good, now you add the 1 to it

[patent vault]

oh right

[dense prism]

And now 4n+4n²+1 can be written as (2n+1)², you know how to factorise right?

[patent vault]

yes ofc

[dense prism]

Cool then you're done

[patent vault]

yay!

thanks so much

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[narrow vault]

What happens to ^1/2 when you cube it?

[foggy harbor]

it becomes 3/2

[narrow vault]

So just multiplying

[foggy harbor]

yip

[narrow vault]

Oké thx

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[fickle abyss]

cant i use logs here?

$K^{20} = 20$

[flat frigate]

yomiko

[fickle abyss]

$log_{20}(20) = K$

but K would = to 1

[ornate acorn]

_ instead of ^ for the LaTeX

[flat frigate]

yomiko

[ornate acorn]

I think that’s wrong

[fickle abyss]

would it be $log_{k}(20) = 20$ ?

[flat frigate]

yomiko

[ornate acorn]

I think it would be $log_K(20)=20$

[flat frigate]

clip

[ornate acorn]

Yes

[fickle abyss]

ah okay yh

[ornate acorn]

It would be easiest to just take both sides to the power of 1/20

[fickle abyss]

yh then you'd get the amswer straight away

thanks

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[royal gyro]

,rotate

[royal gyro]

i need help with c

i dont even know where to start

ive triedd the discriminatnt

but didnt work

[plucky elk]

show this

[royal gyro]

,rotate

[royal gyro]

wait

i think i know

i factorise

[plucky elk]

you calculated the discriminant on the wrong polynomial

[royal gyro]

the 2x^3...

and then

in the triple bracket form

there should be one

that is positive

hence

the one real root

lemme try it one second

[icy lance]

you need to do the discriminant of the ax^2+bx+c found in part b

[royal gyro]

yeah

for the number

i got -39

so

that means 1 right?

or is it when its equal to 0 its one

[icy lance]

<0 means no real roots, >0 means two, =0 means 1

[royal gyro]

ah

so

ive done goof

[icy lance]

no, thats what you wanted to show

that means x=-3 is the only real root of the cubic since the quadratic has no real roots

[royal gyro]

is that why

i couldnt factorise it??

oh

[icy lance]

yeah

[royal gyro]

omg

hahaha

i was here

thinking im stupid

for not being able to factorise it

but

what about part d?

f(x-5)

is it that

i just substitue

5 into the original equation??

[icy lance]

you would replace (x) with (x-5)

[royal gyro]

let me do that

one sec

okay

i got

x^3 -13x^2 - 47x -70

and now what

do i now divide that

by x-5?

[icy lance]

you didnt really need to do that. replacing x with x-5 is just translating f(x) to the right by 5 - so the root moves right by 5

[royal gyro]

so? what changes?

[icy lance]

(x+3)-> (x-5+3)->(x-2) so the root goes from x=-3 to x=2

[silent roost]

How do you solve a continuous exponential thing like
5^5^5^5^5

[icy lance]

#❓how-to-get-help

[silent roost]

whoops I thought this was an open channel

Didn't load

[icy lance]

nw

[royal gyro]

okay

wait

where are you getting x+3 -> (x-5+3) -> (x-2)

is that the root?

you men

mean*?

[icy lance]

you replace x with x-5. and the (x+3) is from the factorised form of f(x)

[royal gyro]

ahhhh

okay

thanks man

[icy lance]

np

[royal gyro]

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[wheat cave]

What is the approach to calculating tasks like\
$18x=12\mod{25}$, x being a whole number between 0 and 25 ?

[flat frigate]

Jigglyproff

[wheat cave]

does the advanced Euclidean algorithm help me here?
gg(18,25) is 1, so I would just have to multiply the left factor by 12 afterwards, but is that the quickest way?

[peak estuary]

yes

[wheat cave]

mhm...

those tasks are so time consuming then for the amount of points they give

thanks anyway

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[peak estuary]

the numbers are pretty small

not that bad

you could also just try to guess the inverse of 18

not sure what it is tho

[wheat cave]

that was just an example, its usually with higher numbers

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[agile stag]

I need help doing these 2 problems, I don’t know how to them, can yall please help? Thanks

[safe radish]

@agile stag Has your question been resolved?

[agile stag]

<@&286206848099549185> yo can I get some help pls 💀

Please?

[plucky elk]

use the definition of covariance

[agile stag]

Ok so its C as well?

[plucky elk]

!show

[safe radish]

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

[agile stag]

I couldnt show work for this problem since its formula based and I don’t understand what I’m missing

All I know is that covariance is true

Cov = 0

Sorry

[plucky elk]

covariance is a formula where you do calculations

show how you got cov = 0

[agile stag]

That was part of the homework excercise as the professor derived it

I don’t have my notes on me

But the property

Is that if X and Y are independent cov = 0

[plucky elk]

Where are you given U and X are independent?

[agile stag]

And in this scenario I assumed independence

[plucky elk]

why would you assume that

[agile stag]

I’m don’t remember… there was something in the notes

But

I think I figured that one out

It’s A

Since

Rowe sub XU = Cov (X, U) / sigmaX*sigmaU

That’s a formula that exists

So when isolating the covariance

A is true

But the other one for the Order Statistics I’m not sure what to do

Here is the problem

I have no idea where I’m going with this one

I understand the other one

@plucky elk I get the other one… can you help with this one? Thanks

[agile stag]

<@&286206848099549185> I need help with this problem… I just don’t understand how to do it. Thanks

[agile stag]

…

<@&286206848099549185> ?

<@&286206848099549185> 😭

[agile stag]

<@&286206848099549185> please man I been waiting for a while

It’s been an hour and a half almost

And its due in 45 mins

YO SOMEONE IS TYPING

I’m completely lost man

[primal granite]

I wish I could help but I would suggest putting it in the appropriate channel as well

[agile stag]

Shoot

Ok

[primal granite]

Sry lol

[agile stag]

Posting again hoping for response, I don’t know what I’m doing <@&286206848099549185>

[patent vault]

try closing and reopening

it puts the channel back at the top

[agile stag]

.close

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[fickle trail]

is this why cos^2(x) we see exponents before arguments for trig functions?

otherwise it becomes cos(x^4)

which do you prefer? top or bottom line

[drowsy moss]

yes, it's just for clarity

[agile stag]

Bottom honestly. With the brackets. However, the top is good too if you dislike brackets

[fickle trail]

yeah, I think I prefer bottom too

it's just crystal clear

if you are tired might accidentally square the argument twice or something with the top line

[drowsy moss]

top line, all day

[fickle trail]

hmmmm

less writing is good

I should get used to them both

it's weird, for someone new, they may look at this and say "oh, we have 2 factors here.. cosine squared is being multiplied by x squared"

[agile stag]

Yes. Will come in clutch in calculus to understand both

[fickle trail]

but i guess you gotta understand trig functions, cos doesn't mean anything on it's own without an argument ()

same with log without an argument ()

[drowsy moss]

that's true for virtually all new notation in math.

[fickle trail]

i have always said, maybe math would be easier if arguments used different notation? a different style of brackets, only for arguments

or would that be impossible to do, pointless to do, and actually a bad idea

I suppose I could do this?

arguments use (()) double brackets

sin((x))

f((x))

log((x))

[drowsy moss]

gross. more brackets

[fickle trail]

but not to be confused with multiplication

[drowsy moss]

$\sin (((x+2)^2))$

[flat frigate]

Zybikron

[fickle trail]

do you prefer writing sin(x) as sinx?

technically i guess everything is an argument with brackets... everything is a composite function!

[drowsy moss]

depends

[fickle trail]

yeah the whole idea of different bracket style for argument is pointless. I forgot about this

you can write x^2 as a composite, f(g(x)), or f(g(h(k(l(m(n(x)))))))) depending on how far you wanna take it

f((g((h((k((l((m((n((x))))))))))))))))

https://tenor.com/view/incredible-double-glasses-gif-5410995

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[lean otter]

Any1 know the formula to the bottom 2?

[safe radish]

@lean otter Has your question been resolved?

[misty bay]

uh yeah there's actually a neat way to get all of them

but

I'll just give you the results from Google

basically you can prove that all of these can be calculated by polynomials with degree 1 greater than the exponent

and then just solve a system of linear equations for it

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[shell wren]

Could some one help explain how to solve this

[hardy lion]

,rotate

[hardy lion]

!status

[safe radish]

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

[shell wren]

I don't know what other equations other than x+y<=10 to do

so i dont know where to begin

[hardy lion]

i would you cant have negative meat nor vegetables

[hardy lion]

this is good, but whats the line that is on the paper

[shell wren]

that's a failed attempt and it's in pen so there's no getting rid of it

[hardy lion]

oh

so i would have 3 inequalities

you got the first one

[hardy lion]

the other two are based on this statement

[shell wren]

and what would that look like?

[hardy lion]

if you cant have negative meat what do you think it means

[shell wren]

so x>0 and y>0 but x+y<=10

[hardy lion]

you can have 0 meat

[shell wren]

so would it be 2 inequalities

x+y>=0

and x+y<=10

[hardy lion]

no, because that still allows the possibility of negative meat, postive vegatables

[shell wren]

oh

ok i get it

thank you

[hardy lion]

anytime

[shell wren]

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[safe radish]

Please don't occupy multiple help channels.

[midnight patio]

what would be an efficient way to solve this]

[safe radish]

@midnight patio Has your question been resolved?

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[stuck falcon]

here, is softmax applied row wise, column wise, or matrix wise?

[misty bay]

attention is all you need

but it's where you pack all of the vectors into the rows of K, V, Q

[indigo magnet]

I've been trying this question for a few days but I didn't have success in the result, can someone help me?
[Number Theory - Natural Numbers - Order - p-adic Valuation]

Let a, x, k, p be natural numbers with a>11, x, k≥1, and p a prime number.

Show that if k is the largest natural exponent such that a raised to x ≡ 1 (mod p raised to k), then there exists an integer b such that p does not divide b and a raised to x ≡ bp raised to k with this result +1 (mod p raised to k+1).

[stuck falcon]

🤔how do you mean

[misty bay]

let's say you have query vectors q1, q2, ... qn, key vectors k1, k2, ..., kn, and value vectors v1, ..., vn

you pack them as rows into matrices called Q, K, V

and then compute this to find the attention

[safe radish]

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[safe radish]

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[jagged snow]

Does a scalene triangle have 3 sides with the same length?

[primal granite]

no

a scalene triangle has 3 sides all different length and 3 angles all different degrees

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[fickle trail]

in regards to the quotient rule

I'm gonna say yes, just wanna make sure...

numerator = term
denominator = term

therefor, brackets are a must?

we are treating each term like a function, right?

so each term behaves like an argument, the brackets need to be there?

[safe radish]

@fickle trail Has your question been resolved?

[empty gyro]

yes

brackets required

g(x) is 5x+4

We'll simplify d/dx[2x-3] to just 2

2*5x+4 and 2*[5x+4] are two very different things

The first one, you are not multiplying 2 by 5x+4, you're only multiplying it by 5x then you're adding 4 out of nowehere

Very different situation

[safe radish]

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[broken ginkgo]

am i supposed to use distance upon time on this question?

[broken ginkgo]

or plot the points on the graph?

[wild copper]

That would be the answer to the question, so, no hints

[broken ginkgo]

wait i can just use the points given directly right

like (1,1) (5.58,1.5) and (20,0.3)

and make a piecewise defined function from that

[wild copper]

Here's a hint, you should define what f and g take and what they will output. Decide what unit they will take

[broken ginkgo]

f and g are distance of hare n tortoise

[wild copper]

in?

[pseudo scroll]

Yeah pretty much

You got it

[broken ginkgo]

in time x

that way f(x) = 20x

[wild copper]

No, I mean what unit

[broken ginkgo]

0 <= x <= 1?

u mean that?

[wild copper]

No, I mean mile or km

[broken ginkgo]

miles

[wild copper]

Okay, then, so what is the input?

[broken ginkgo]

assuming race starts at 0

and the final point is 1.5 miles

hares runs at 20mph

[wild copper]

No, what is the unit of x in f(x)?

[broken ginkgo]

mph

i think

[wild copper]

So, the function takes in a velocity and returns distance?

[broken ginkgo]

yea

[wild copper]

Why?

[broken ginkgo]

cuz of 5:58pm

i have to go by hour

[wild copper]

That doesn't make any sense.

For the ease of understanding, let's look at g, the tortoise.

Your scheme means that the tortoise has varying velocity, and the distance won't change if you keep the distance equal.

[broken ginkgo]

so like 0.3x? for tortoise

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[gray rose]

What’s the difference between when an equation that says y = x+1 and when you have an equation that says f(x) = x+1

[gray rose]

Like what’s the difference between y and f(x)

Like when do you know if one variable is a function of the other and when are they just two independent variables

I feel like this is something I should have learned way a long time ago but I just don’t understand the difference

Especially in regards to topics like calculus when you take partial derivatives and stuff

[arctic condor]

The f(x) notation is more general although both are interchangeably used for most purposes

In partial derivatives though it might not be true always as in general f(x) means a function in x only

@gray rose

[gray rose]

Thanks although is there a term when variables are not functions of each other?

[arctic condor]

Independent variables

[gray rose]

Ahh okay thank you so much

[safe radish]

@gray rose Has your question been resolved?

[safe radish]

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[fickle trail]

the first two rules I remember very well, it's the third one I have a hard time with

anybody else have this issue too?

should I be thinking about this as a composite inverse function somehow?

to make things easier

[trim swan]

what third one?

You mean $a^{\log_a(b)} = b$?

[flat frigate]

tatpoj

[quasi bison]

you mean the last line??

bc log_10(100) is 2, not 10 as you write.

[fickle trail]

10^(log_10(100))

oh i see

thanks

[fickle trail]

ya

[trim swan]

Yes, exponentials and logarithms are inverses

[trim swan]

this is exactly how you should think about them

[fickle trail]

OK

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[little reef]

Hi, I am not sure how to solve the last question.

[pseudo scroll]

Set $\dv[2]{H}{t} = 0$ and solve for t

[flat frigate]

NEONPerseus

[little reef]

the second derivative?

but it says for the first derivative

[pseudo scroll]

yeah since you need the max value of dH/dt and not H

So $\dv[2]{H}{t} = 0$ and $\dv[3]{H}{t} < 0$

[flat frigate]

NEONPerseus

[pseudo scroll]

Although I think you're gonna run into some issues since its an exponential

[little reef]

on this, they took the derivative initial value and made it positive which is what i based my first answer off of

[pseudo scroll]

That would make the value of H maximum not dH/dt

[little reef]

do I plug 72 in the derivative function?

[pseudo scroll]

Oh they want t >= 0 so you don't even need to differentiate

you just need to utilize the fact that the function is always decreasing

[little reef]

but its asking for magnitude of the derivative

[pseudo scroll]

yup 72 is right

should be then

[little reef]

I did 72 but says its not correct

[pseudo scroll]

they asked for the time

[pseudo scroll]

not the magnitude

so at t = 0

at t = 0, the max magnitude is 72

[little reef]

so I plug 0 into the derivative function?

[pseudo scroll]

no no

the answer is 0

you're right about the max magnitude being 72

the question asks at what time is the magnitude maximum

[little reef]

yeah sorry, we didn't go over this in class so I was a little lost on what magnitude was

[pseudo scroll]

which is at t = 0

just the absolute value

[little reef]

ahh ok, so when time is 0, magnitude is 72, and 72 is the largest, but I just needed to give the time which 72 was at

[pseudo scroll]

yes

precisely

[little reef]

Thank you so much for the help, have a good rest of your day/night

.close

[safe radish]

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[blazing roost]

HOW TO APPROACH

[lean otter]

what have you tried

[dusk iron]

Turn into product maybe

[blazing roost]

nothing

[dusk iron]

Stuff inside bracket

[lean otter]

then come back once you've tried something

[pseudo scroll]

!status

[safe radish]

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

[blazing roost]

i literally asked how to approch

1

[pseudo scroll]

Fair

Get rid of that log

asap

its there to make your life hard

[blazing roost]

which

[lean otter]

^

,tex log rules

[pseudo scroll]

the one on the left

in any case both will vanish

[blazing roost]

ok

[pseudo scroll]

$\log_b a = c \implies b^c = a$

[flat frigate]

NEONPerseus

[pseudo scroll]

Use this

[blazing roost]

ok

so its 5^rhs=5^1/x + 5^3

now what

[pseudo scroll]

now substitute 5^(1/2x) for a new variable

you have a quadratic

[blazing roost]

ok

lets say it a

'a'

[pseudo scroll]

sure

[blazing roost]

why 1/2x why not 1/x

[pseudo scroll]

because you'll get a square root if you substitute 1/x

and it isn't easily visible as a quadratic

[blazing roost]

oh

[pseudo scroll]

¯_(ツ)_/¯

[blazing roost]

i seeee

[pseudo scroll]

although you can if you want

i think its better to sub 5^(1/2x)

[blazing roost]

ok got it

bro

thanks

now i can solve

.close

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[versed sand]

Hi guys

[peak smelt]

hello!

[versed sand]

If selling price is doubled, the profit triples. Find the profit percent

[versed sand]

Can u help me with the question shavet

[peak smelt]

hmm

lemme think

[versed sand]

shavet this is the solution pls

explain me 3(y-x) = (2y - x)

[peak smelt]

ok so

this is what i would have set up too i think

normally

lets say u sell something for 100$

[versed sand]

ohk

[peak smelt]

and it cost 20$ to make

profit is 80$

[versed sand]

hmm

[peak smelt]

here

[versed sand]

yes

[peak smelt]

the sale price is 100$

[versed sand]

yes

[peak smelt]

lets say that the value for sale price is y

and cost price is x

y-x = p (profit)

right?

and if ur tripling profits

aka 3p

[versed sand]

yes

[peak smelt]

u need to triple what profit is equal to

aka, 3(y-x)

right?

[versed sand]

yes

[peak smelt]

so

3(y-x) = 3p

now

[versed sand]

yes

[peak smelt]

what is y?

[versed sand]

sale price

[peak smelt]

ok so

if we are doubling the selling price

what is our new sale price?

[versed sand]

2y

[peak smelt]

has the cost price changed?

[versed sand]

no

[peak smelt]

so whats our new equation for profit?

with double the sale price

[versed sand]

how 3(y-x) is equal to new selling price

?

[peak smelt]

so y-x = p

[versed sand]

yes

[peak smelt]

and they told us that when we double the sale price

we triple the profit

so

2y - x = 3p

but p = (y-x)

so

[versed sand]

ohk I understood it now

[peak smelt]

3p = 3(y-x)

and u sub in

2y - x = 3(y-x)

[versed sand]

Thanks shavet I've math exam tmrw I as solving practice paper and I found the sum

*was

[peak smelt]

its no problem

gl!

[versed sand]

thanks

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[lean otter]

I've simplified it down to -2(x^2+1) +x^4, Have I done it right and if I have did I factor it completely?

[supple shore]

+x⁴ ?

Where did it come from

[uneven jacinth]

you factored it incorrectly

x^4 shouldnt be there

you are close though

[supple shore]

Show your work, calculation

Maybe we can see the mistake

[uneven jacinth]

i think you factored out -2 from -2x^2 and -2

which is the first step to solving this

[lean otter]

combining x + x^3

Oh wait

then it is -2(x^2 + 1) + x(x^2 + 1) right?

[supple shore]

Yes

[lean otter]

oh I see

thanks

[wise shell]

You can take it further

[supple shore]

X+X³ is not equal to x⁴

[wise shell]

Now factor a common term out again

[supple shore]

And yes you can factorize it

[lean otter]

?

[wise shell]

You can factor (x^2 + 1) out to get (x^2+1)(-2+x)

[lean otter]

oh ye

thx

[uneven jacinth]

W

[lean otter]

how to close this

[wise shell]

.close

[lean otter]

oh

.close

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[winged willow]

equation is x^2 - 2ax + 3 = 0

[drowsy trench]

in order for there to be 1 real solution the discriminant must equal to 0

[winged willow]

how so ?

if we set discriminant = 0. we get 1

@drowsy trench

[drowsy trench]

ok so when you set discriminant equal to 0 right

you're not suppose to solve for x

you're suppose to solve for a

[winged willow]

how do i do that ?

[drowsy trench]

so basically B^2 - 4AC = 0 then solve for a after plugging in A, B, C values

[winged willow]

ok

a = 1, b = -2, c = 3 right?

[drowsy trench]

B = -2a

[winged willow]

got it thanks.

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[drowsy trench]

no problem

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[orchid wave]

how do I do these questions ?

[orchid wave]

<@&286206848099549185>

.close

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[dull sundial]

Need help solving the DE

[white roost]

Is that D^2 ?

[dull sundial]

Yes

D meaning differentiation

D^2 is double diff

I need help solving the differential equation

[white roost]

Bruh I forgot how to do this

Srry for wasting ur time

[dull sundial]

<@&286206848099549185>

[dull sundial]

No probs

[safe radish]

@dull sundial Has your question been resolved?

[safe radish]

@dull sundial Has your question been resolved?

[dull sundial]

No

[safe radish]

@dull sundial Has your question been resolved?

[dull sundial]

No

[safe radish]

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[leaden sorrel]

can someone explain how to find the last one

everything else i've done seems correct and all

question b

ping me back pls

[solid timber]

did u convert the speed to miles per minute?

cuz its given in miles per hour

[leaden sorrel]

yeah so how do i do tha

and how do i calculate the speed in mph in the first place

[solid timber]

the speed is given as 200 miles/hour

= 200miles/60 minutes

= (200/60) miles/minute

=3.333 miles per minute

[leaden sorrel]

es

yes

[solid timber]

according to ur answer, Baker is closer

[leaden sorrel]

ok so how do i figure out how long it'll take

[solid timber]

speed = distance/time

[leaden sorrel]

9514.98/60

?

so 158 minutes?

[solid timber]

the denominator is wrong...

[leaden sorrel]

yeah i corrected in the second

[solid timber]

ah cool

I haven't calculated the answer

but that must b right then

[leaden sorrel]

ok

lets see

[leaden sorrel]

its wrong

159 minutes is wrong

so i redid some math

set up a ratio

[solid timber]

dude 158.583/3.333

is 47.57

so its 48

[leaden sorrel]

158.583 200
-------- = ----------
x 1

yeah thats what i got with this ratio-

[leaden sorrel]

it was 41

[solid timber]

200/60*

[leaden sorrel]

no

i did it in miles

then i would convert the final answer to minutes

[solid timber]

per minute

oh okay

[leaden sorrel]

the distance is given in miles too

[solid timber]

Im sorry then idk what's wrong here

[leaden sorrel]

hm ok

[safe radish]

@leaden sorrel Has your question been resolved?

[leaden sorrel]

@meager igloo

[safe radish]

@leaden sorrel Has your question been resolved?

[safe radish]

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[midnight isle]

How to solve?

[midnight isle]

App says to substitute but I don't know how

[split ether]

You can consider substituting for (x + 4)/(x - 4) (or its multiplicative inverse)

[midnight isle]

what next?

got it

.close

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[wide acorn]

how to do thi

[buoyant trellis]

calculate the smaller cylinder's volume

with that, you can make an equation for the 2nd cylinder where the height is 5, the volume is that of the smaller cylinder and the radius is what you want to find out

[wide acorn]

ah ok thanks

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[severe lance]

i need help with this - calculus

A rectangular playing field is to have an area of 600 square meters. Fencing is required to enclose the field
and divide it into two equal halves. Find the minimum amount of fencing needed to do this.

[severe lance]

Here’s my work:

<@&286206848099549185>

[lethal lance]

it should be xy=600

so then y=600/x

[severe lance]

so
1st equation in xy = 600
and whats the second

[lethal lance]

so since y=600/x

you want to find the total amount of fencing

[severe lance]

yea but to start off i need 2 equations and then i minuplate the second one and plug into the first

[lethal lance]

yeah

so what is the equation for amount of fencing

[severe lance]

which is?

[lethal lance]

?

i am asking u to find it

[severe lance]

idk how to find it

[lethal lance]

use the diagram u have but substitue y=600/x

[severe lance]

wait im confused

are any of the equations i have correct

or i need to make 2 new ones

[lethal lance]

your initial ones aren’t

because in yourr equations the total amount of fencing is 600

while it should be the area is 600

[severe lance]

so would it be:

1. 600 = xy
2. 2x+3y = ___

[lethal lance]

yep

but u should substitute 600/x for y in the second one

[severe lance]

okjay what goes in the ___

[lethal lance]

a variable

since that is the unknown

and it is the quantity u want to minimize

[severe lance]

so there would be 3 variabkes

x, y and z

[lethal lance]

no

u can eliminate x

i mean y

and then you would have an equation in x for the fencing

[severe lance]

can u write out the 2 equations for mw

[lethal lance]

so xy=600 right

[severe lance]

yes

[lethal lance]

this means that y=600/x

so you have the right equation before

[lethal lance]

here

but then u should use 600/x for y in number 2

because then once you get this then you can take the derivative

[severe lance]

yea but that has to equal something, no

[lethal lance]

it’s just a variable

[severe lance]

you cant have it not equal something

[lethal lance]

whatever it is on the other side it doesn’t have an x term

so like u can use F for fencing or smth

i think

and then once you take the derivative you would have something=0

[severe lance]

okay ur saying later on it doesent even mqtter bc we are gonna chnage it to 0 for critical values

[lethal lance]

yeah

it’s similar to what u did with A in ur origninal work

u had like A’ = something then next line was 0=same thing

[severe lance]

okay let me do iit and send it wait

is thios the answer

@lethal lance

[lethal lance]

ya ur x and y are right

now u just gotta find the total amount of fencing

[severe lance]

120?

[lethal lance]

👍

nice job

[severe lance]

ok ty

[lethal lance]

np

[severe lance]

wait can we work thru another

[lethal lance]

uh idk i have to go soon

someone else should be able to help tho

[severe lance]

okay alright cause the last guy dident know how to do it

so i dont want that to happen again

[shrewd island]

whats the next one

i can have a look and see

[severe lance]

okay ty

A rectangular container with an open top is required to have a volume of 16 cubic meters/ Also, one side of
the rectangular base is required to be 4 meters long. If the material for the base costs $8/square meter and the
material for the sides costs $2/square meter, find the dimensions of the container so that the cost of material to
make the container will be a minimum.

[shrewd island]

ill draw out a diagram give me a minute

[severe lance]

thanjs

[shrewd island]

so we’re here i think?

am i missing anything at all?

sorry its sideways ;-;

[severe lance]

thats okay lemme try to make the equations and then can u chcek them

[shrewd island]

alright

wait this is a weird one

if one base has to be 4 then the one above it is also 4

…oh MAN

[severe lance]

yea this is werid

should i send u the one we did in class

[shrewd island]

yeah go on

that might be useful

[shrewd island]

oh wait no

its not

[shrewd island]

im silly

the problem is thats a 2D shape

it gets more complicated wth 3D

[severe lance]

oh

[shrewd island]

its similar

dont get me wrong

bht theres extra dimensions and such which make jt slightly more annoying

but this is just algebra in a real life scenario correct?

[severe lance]

this is calc

highschool calc :((

[shrewd island]

calculus has ä different name here but idk what it is

but itndoes just seem like forming equations

with algebra

[severe lance]

oh where r u from

[shrewd island]

uk

[severe lance]

ahhh

10opm?

[shrewd island]

9

[severe lance]

oof

[shrewd island]

you coukd also do this with trial and error

bc yiuve got one value already

[severe lance]

what would the 2 equatuons be

thats what i dont get

[shrewd island]

theres only two sets of values that could make 16m3

[severe lance]

everuthign after i knpow

[shrewd island]

with this you dont reeeeally need to use equations

youve been told that one of the measurements is 4m

the volume must be 16m3

the ither two measurements must either be 1 and 4 or 2 and 2

if you use the amounts of money with both sets of measurements and compare them

you coukd do it that way

[severe lance]

its okay ill just do the other one

ill ask the teacher help for this

[shrewd island]

do you have to do it with equations?

[severe lance]

yea

[shrewd island]

ahhh okay that makes more sense now

thats really annoying even tho theres literally an easier method

[severe lance]

yea

im working on this one

A rectangular box with open top is the constructed from a rectangular piece of cardboard 80 cm by 30 cm by
cutting out equal squares from each corner of the sheet and folding up the sides. Find the dimensions of
maximum volume.

last one

[shrewd island]

hmmm

[severe lance]

i know how to do it but small question

is the 30 and 80 includin the grey shaded boxes

or excludimng

[shrewd island]

including

i would imagine

[severe lance]

okay

[shrewd island]

it says that the cardboard is 80x30 before jt says ab the squares so

[severe lance]

ok im working on it - u do it to and then we can sahre answer

if u got timw

[shrewd island]

could you give me like 5 mins and then ill come back? im very thirsty and hungry lol

[severe lance]

yea take ut time

i finished

[shrewd island]

i got really confused in it

[severe lance]

does that seem right

thats exactly how the class example was

[shrewd island]

hiw is 31 min 5 max

or am i misreading

[severe lance]

huh

[shrewd island]

have i msiread

[severe lance]

idk lmaoo

[shrewd island]

youve got max under 5 min under 31

wouldn’t it be the other way round

[severe lance]

oh so thats the first derivitive test

[shrewd island]

the

what?

[severe lance]

you have to check weather that the number you got is actually the maximumn

my teacher said u gotta do it

its called the first derivitive test

[shrewd island]

i havent learnt that yet

new research task here i come

[severe lance]

its okay im pretty confident on this one

LOL

[shrewd island]

from what i see tho it looks good!

[severe lance]

okay thats all i had then

tysm for ur time and effort

[shrewd island]

not a problem and sorry i cpuldnt be of more help!

[severe lance]

nah its all good

c ya

[shrewd island]

bye!

[severe lance]

.close

[safe radish]

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[subtle kernel]

Questions on this

[subtle kernel]

I’m pretty sure the second is just 5.196

[lethal lance]

well u want to write it in exponential form

do you know the laws of exponents

[subtle kernel]

Yeah got a brief of it

A^n x a^m

Something of that sort

Anyone could pick up from him?

[lethal lance]

well so for fractional exponents

$n^{\frac{a}{b}} = \sqrt[b]{n^a}$

[flat frigate]

RetroTurtle

[lethal lance]

so u can use these properties

and also

$a^{-1}=\frac{1}{a}$

[flat frigate]

RetroTurtle

[lethal lance]

i think u can solve all the boxes with these

[subtle kernel]

Um I think the trouble I’m getting is

There’s no a b on 27 square root

Just 27

Usually that would be like in a fraction

[lethal lance]

for just square root

the exponent on the fraction would be 1

so like

$2^{\frac{1}{2}} = \sqrt{2}$

[flat frigate]

RetroTurtle

[lethal lance]

because it is $\sqrt{2^1}$

[flat frigate]

RetroTurtle

[lethal lance]

which is just sqrt2

[subtle kernel]

So this would be

Yeah uh one sec

[subtle kernel]

Are you able to do the second one for me? I think visually seeing it helps a lot more

[lethal lance]

it’s similar to what i did above

so like it is $\sqrt{27^1}$

[flat frigate]

RetroTurtle

[subtle kernel]

Wouldn’t it have to be like

27^1/5?

Something like that to show the power of 27

[lethal lance]

yeah so i’m saying that’s the radical

and u want to make that into exponential

so how would you do that then

[subtle kernel]

Wouldn’t this be it

As the exponential?

[lethal lance]

not quite

so the square root without a number on the left

is just 2nd root

[subtle kernel]

Like this?

[lethal lance]

ur talking about $\sqrt{27}$ right?

[flat frigate]

RetroTurtle

[lethal lance]

so it would be 2nd root of 27^1

sorry if my explaining doesn’t make sense

i want u to try and figure it out on ur own instead of giving the answer right away

but i’m not sure how else to explain this concept

[subtle kernel]

Yeah it’s just I’m better with getting the answer and finding out why from certain parts

It just comes together easier for me

But 2nd root of 27^1 is 5.196

Which is what I said earlier

@lethal lance ?

[hasty wagon]

mind if i pick up from here? @subtle kernel

https://media.discordapp.net/attachments/903481106819612714/1080603515099037727/IMG_0778.png

[safe radish]

@subtle kernel Has your question been resolved?

[hasty wagon]

seems yes ...

[safe radish]

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[thorny bone]

I don’t know where to go with this

[ebon oriole]

find the gradient of AB using change in y/ change in x

[thorny bone]

Alr

[ebon oriole]

then make the gradient perpendicular by doing the reciprocal and multiplying by -1

then form an equation using y - y1 = m(x-x1), where m is the perp. gradient and y1 and x1 can be A or B

[thorny bone]

Alr Ty

[ebon oriole]

i'm not entirely sure how to show that (2,0) is the normal, i guess you could sub in the the x value(0) and then get 2 for y proving that it crossed

[thorny bone]

Alr

[ebon oriole]

alevel?

[thorny bone]

Yeah

[ebon oriole]

yr 12 or yr13

[thorny bone]

12 I’m horrible at it but enjoy it

[ebon oriole]

alr topic isn't too hard get better with more practise

[thorny bone]

Yeah well Ty for the help

.close