help-27

[wild creek]

the right side form

is a geometric series

with common ratio x^3

the left side is not

[median moat]

oh nice

I see

[wild creek]

so now we can apply what we just said

with a= x^3

so the equation becomes

[median moat]

5/1-x^3?

= 39?

[wild creek]

re read

[median moat]

x^3/1-x^3?

[wild creek]

yeah

the 1/1-a formula is for series that start at n=0

[median moat]

ok

so 5 *(x^3/1-x^3) = 39?

[wild creek]

yep

[median moat]

word

[wild creek]

so now you can solve it using algebra

[median moat]

that was right!

Thank you!

[devout snow]

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[devout snow]

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[tender roost]

how can i measure the “order” of a data set?

[tender roost]

so like

let me preface this

i made a little prng

you choose the function(s) (you only need one i just have two to compare them) and a depth value

it takes your function at an integer x, goes D_epth digits into the decimal expansion (multiplies the value by 10^(D_epth) takes the fractional part, multiplies the fractional part by 10, and returns the floor of that

which basically just

returns the (D_epth)th digit in the decimal expansion of the function at an integer x

and it does this 10000 times

producing a list of numbers

and i know how to measure the distribution of numbers with a table like this

but i realized that i don’t need this, i need a way to measure how much the list of data changes

like, how stable it is

because, despite the distribution, the data set could look very predictable

so is there a way to measure how unstably the data changes?

i hope i worded this decently

basically i just want to know if there’s a way to check how “unpredictably” the data values change

[devout snow]

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[devout snow]

@tender roost Has your question been resolved?

[devout snow]

@tender roost Has your question been resolved?

[devout snow]

@tender roost Has your question been resolved?

[tender roost]

So like um hi

[violet wind]

Desmos will not accurately calculate digits beyond the 15th or so digit

@tender roost

chi-squared test could tell you if they're about evenly distributed though

that's how you'd test if the distribution is unusual in this case

Pearson's chi squared test

[tender roost]

i don’t mind

[tender roost]

this is the right test?

i thought about it but didn’t think it would be right

[violet wind]

You could just look at things like standard deviation of the number of digits

If you want an easier way to quantify variation

But yes

test for goodness of fit

not the independence one

[devout snow]

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[tender roost]

@violet wind ty

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[mild lodge]

How do I do this problem?

I'm unsure if what I did is correct

[devout snow]

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[mild lodge]

<@&286206848099549185>

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[chrome swan]

I am reading our subject notes. How do I prove this function that I encircled?

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[neon folio]

How can i plot i on a graph

[pseudo basin]

what kind of graph

[neon folio]

Um

[pseudo basin]

if you just want a picture of the complex plane, then i is right here

[neon folio]

Normal

Oh ok

Thanks

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[hearty hound]

how do i solve this?

[tall knoll]

If the smallest is n, what is the 2nd smallest?

[hearty hound]

i dont know

thats the thing i dont know how to solve this

[tall knoll]

Do you know what "consecutive" means?

[hearty hound]

no

[tall knoll]

Things are consecutive if one comes right after the other

What's the number that comes after 6?

[hearty hound]

7

[tall knoll]

So 6 and 7 are consecutive

So what comes after n?

[hearty hound]

n+1??

[tall knoll]

Indeed

And after that?

[hearty hound]

n+2

[tall knoll]

Now compute the sum of those three

[hearty hound]

oh so n+3

[tall knoll]

No

n+n+1+n+2

[hearty hound]

ohh ok

that would be 3n+3 right

[tall knoll]

Yes

[hearty hound]

thanks i understand now

[tall knoll]

Np

[hearty hound]

idk how to solve this aswell if you mind helping me

[tall knoll]

What is the formula for a rectangle's perimeter?

[hearty hound]

2(l+w)

[tall knoll]

Good

So now it's just a matter of choosing l and w such that you match the given expression

There's no single right answer for this

[hearty hound]

so it could be 2(3x+2.5y)?

[tall knoll]

That's one possible arrangement

[hearty hound]

the question is asking for dimensions tho

[tall knoll]

Indeed

[hearty hound]

are you sure thats what im suppose to put?

[tall knoll]

Well no

l and w are your dimensions

[hearty hound]

im kinda confused on what to do tho

[tall knoll]

This expression tells you what l and h are

The dimensions of your rectangle are l × h cm

[hearty hound]

i still dont really get what to do tho

[tall knoll]

It asks for the dimensions

Pick dimensions that make sense

[hearty hound]

idk why i still dont get it

[tall knoll]

What don't you get

[hearty hound]

idk i've just never done those kind of questions

[tall knoll]

I've told you all I can gather

[hearty hound]

k ill ask someone else for help

.close

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[hearty hound]

.reopen

[devout snow]

✅

[hearty hound]

im not sure on how to solve this question can anybody help me?

<@&286206848099549185>

.close

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[winter hound]

Completely stuck in this

[winter hound]

Any hints on what’s my first step

[pseudo basin]

,rccw

[pseudo basin]

you want to find all k such that the equation f(x)=g(x) has no solutions.

[winter hound]

Right

genius, but why do we equate f(x) and g(x)?

[pseudo basin]

how else are you gonna find the intersection points of their graphs

[winter hound]

Oh right

anyways, I have more questions hold on

The few things I’ve known so far:

The y-coordinate of the turning point is 2.5.
When y = 1, the distance between two points on the graph is 1.8

I can try to use discriminant?

If I want to find the width at the base, then I’d need the roots of the quadratic equation

Then I have to know what are the values for a, b and c

I could imagine VA as the y-axis

So the width would be 2.3236m?

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[buoyant escarp]

How to solve number 2?

[pastel pasture]

Factor out -1 first if that helps

$-(x^2 - 6x + 5)$

Do you know how to factor a quadratic?

[buoyant escarp]

Err dont remember

[woven radish]

NEONPerseus

[buoyant escarp]

See 14?

[pastel pasture]

You need to split the x term into a sum such that the 2 new terms form the product of the x^2 and constant terms

[buoyant escarp]

I think thats factoring quadratic

[pastel pasture]

Yup thats a quadratic

[buoyant escarp]

? Uh

What u mean by that?

[pastel pasture]

We have with us $x^2 - 6x + 5$

[woven radish]

NEONPerseus

[pastel pasture]

Now you need to rewrite -6x as a sum of two other x terms such that if multiplied will give you the product of the constant and x^2 term

Like this

$x^2 - 1x - 5x + 5$

[woven radish]

NEONPerseus

[pastel pasture]

See how I split -6x?

If I multiply -1x and -5x I get 5x^2

Which is the product of the x^2 and constant terms

[buoyant escarp]

Hm

Sorry it tskes me a while

I see it now

[pastel pasture]

Yeah no problem

[buoyant escarp]

.close

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[forest geode]

!help

[devout snow]

Please don't occupy multiple help channels.

[forest geode]

Can someone run this question step by step with me please.

[rotund heron]

show what you have tried up till this point?

[forest geode]

k

5 + 1 + 2 +2 = 10
8640000/10 = 864000
5 x 864000 = 4320000
1 x 864000 = 864000
2 x 864000 = 1728000
4 x 864000 = 3456000
Answer = Cheryl's wage is £3456000
To Test It: 4320000+864000+1728000+3456000 = 10,368,000

But its wrong

So can you run step by step

[rotund heron]

your first step should be to

define appropriate variables

[forest geode]

Which is?

[torn vessel]

your first equality isn't correct. Cheryl's contract isn't double Louis' it's double Mel B's

[forest geode]

yeah.

4 x lewis wage

if mels is 2x lewis wage

then cherlys is 4x lewis wage?

[torn vessel]

yes

[forest geode]

i done that

Anyway keep going

[torn vessel]

youre first equality

[forest geode]

then why are you mentioning cheryl

[torn vessel]

where did your 5, 1, 2, 2 come from then?

[forest geode]

u mean 5 + 1 + 2 + 2

is it 5 + 1 + 2 + 4

[torn vessel]

yes

[forest geode]

Alright

let me change it up

5 + 1 + 2 +4 = 12
8640000/12 = 720,000
5 x 720000 = 3,600,000
1 x 720000 = 720000
2 x 720000 = 1,440,000
4 x 720000 = 2,880,000
Answer = Cheryl's wage is £2,880,000
To Test It: 720,000 + 3,600,000 + 1,440,000 + 2,880,000 = 8,640,000

That right

HEHEHEH

thank you so much u are legend

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[steel marlin]

Otto is now twice as old as Anna will be when Emma is as old as Otto is now. Which of the following is true if the children's ages are given by the initials of their names?

A<E<O
A<O<E
E<A<O
E<O<A
O<A<E

[steel marlin]

Its A<E<O right?

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[steel marlin]

.close

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[vocal grove]

This correct?

[vocal grove]

or is this correct?

[formal magnet]

A medium sized bowl is a hemisphere

[vocal grove]

ohh got it

ty

.close

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[neon wigeon]

could someone help me find the coordinates of the vertices of the tetragon, which I highlighted in the picture?

[devout snow]

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[normal phoenix]

hello

[normal phoenix]

i just did an exercise and would like someone to tell me if im right or wrong

here it is

,rotate

[supple knot]

where is the exercise

[normal phoenix]

its kinda on physics but il send it

What is the height above the surface of the earth where the intensity of gravity will be 4 times smaller than that on the surface of the earth (when the radius of the earth is R)?

basically the expressions i marked in squares are what i know

<@&286206848099549185>

[restive river]

Hmm @normal phoenix

I think u might find more help in the physics server

[normal phoenix]

like this is a normal math question i got all the info from the question and put it on the sqaures

[restive river]

But this is kind of what I do too so in will try it out later

Are u asking

If ur math is correct

[normal phoenix]

thats right

[restive river]

Or ur answer

[magic thicket]

For 2 given bodies, it's just in 1/r^2

So becomes /4 iff r doubles

[normal phoenix]

yea thats what i thought but the teacher told me to show my way and all this stuff

so if the ways correct im cool

i just gotta know that

[restive river]

Wait i just realised but do u write ur 4's as if they were u's?

[normal phoenix]

im not sure if im wrong or right....

[restive river]

I was confused for a second lmao

[normal phoenix]

its not u's its 4 lmao

[restive river]

But yeah what u did seems about right

[normal phoenix]

thx and sorry for my wierd hand writing

😂

[restive river]

It's okay 😂 I write my 4's like 9's

[normal phoenix]

hahaha glad im not the only one whos 4's are different

thx again for yalls time

.close

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[restive river]

Yepp goodluci with ur studies

[normal phoenix]

👍thx😊

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[sage smelt]

Hi, sorry to annoy you, but I have come across a problem that I solved correctly, but the given correct solution was different and I don't understand it. I include both images. I solved it just as computing (1+i)^2 and that equals 2i, and then I did 2i2i2i, which seems simpler to me, but still I would like to understand the solution given. Can you tell me what I should look up to learn the trigonometry here? Thanks

[gleaming socket]

You need to learn about the polar form of complex numbers

[sage smelt]

lovely, thanks

had no idea what to look up

[gleaming socket]

Learn to covert from polar to rectangular form and vice versa

[sage smelt]

thank you so much

.close

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[glass bison]

I need help with a problem

[glass bison]

how do I find the limit to infinity by this function:

[sand dove]

when dealing with a rational fraction (polynomial divided by polynomial) and taking limit to infinity, factor the numerator and the denominator by the "highest" term (here it's x^3 for both)

[glass bison]

like this?

[sand dove]

No, more like :
$\frac{x³(7-...)}{x³(...)}$

[woven radish]

rafilou2003

[glass bison]

what would the ... be?

[sand dove]

The rest of the polynomial at the numerator/denominator respectively

For example

I would write :

$x² + 5x + 3 = x²(1 + \frac{5}{x} + \frac{3}{x²})$

[woven radish]

rafilou2003

[glass bison]

oh I think I get it

[glass bison]

so it would be like this then:

[sand dove]

Yes

Now, you can simplify numerator and denominator by x³

And you're left with something that you can easily take the limit of as $x\to \infty$

[woven radish]

rafilou2003

[glass bison]

so cancel out the two x^3's?

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[spiral venture]

I just want to check my answer, can anyone check 1/2*4^2x=64^64

[atomic obsidian]

<@&286206848099549185>

[spiral venture]

goodnight!

[wooden wraith]

Are you trying to prove this?

[atomic obsidian]

Yeh

Should we ×4 both sides?

[wooden wraith]

That seems reasonable

[atomic obsidian]

Then put them all on one side =0 ?

Or we going work on each side alone

[wooden wraith]

My instinct is to gather the roots on one side and then square, but we'll get some extraneous solutions. Let me try it out real quick

[atomic obsidian]

This is what i was acctually trying

But wont work ...

[wooden wraith]

What do you mean?

It should, assuming the statement is actually true

[atomic obsidian]

Can u show me how?

[wooden wraith]

Hm, it doesn't really come out as nice as I thought actually

[atomic obsidian]

Its really complicated

And i got abt 10 more exercices ;-;

And its 1am

(:

[wooden wraith]

What is the topic you're studying for this chapter/section

[atomic obsidian]

Logic

10th grade

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[restive river]

I'm not too sure how to start doing this problem

[devout snow]

@restive river Has your question been resolved?

[restive river]

anyone?

[winter patrol]

consider intersecting chords theorem

[devout snow]

@restive river Has your question been resolved?

[restive river]

how do you solve it with the thereom

I tried it

nevermind

.close

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[worldly oar]

Hello, so I have 3 questions.
A triangle has a 90 degree angle, and I know 2 sides of it
Which means that I could use sohcahtoa, depending on the 2 sides I have. But for this triangle I can't use sohcahtoa.
Instead the book with the answers, refers to the sin- and cosin-rule.
Why is this while the triangle is right triangle?
Just annoys me.

Also in theorem, my book states that the sin- and cosin-rule are more exact to the answer is this also true?

When to use sohcahtoa and when to use sin- cosin-rule?

[winter patrol]

sohcahtoa is applicable when you have a right triangle
sine rule and cosine rule are applicable for all triangles (note that there is some ambiguity involved with the sine rule)
applying those to a right triangle is a bit of overkill

were you explicitly told that the triangle is a right triangle?

[worldly oar]

no the book, just lets me see a picture of a triangle, with a 90 degrees angle

may i then assume its a right triangle?

[winter patrol]

if the image clearly shows a 90° angle marking, then its definitely a right triangle,
its not an assumption

[main gull]

Does it have the perpendicular angle symbol on the triangle?

[winter patrol]

can you provide a pic of the question and exactly what the book is saying

[worldly oar]

uhm well i do know how to do that, but i don't have currently any camera or lens in my room

so thats no option for me, can provide text

[main gull]

Draw in paint, exactly what the triangle looks like?

Every detail that it has

[worldly oar]

good idea

[winter patrol]

Every detail that it has
as close as possible, (don't add in additional stuff not initially present either)

[worldly oar]

uhm whats a good program for fast drawing in linux?

XD

[worldly oar]

it does

[winter patrol]

could just use an online one like sketch.io

[worldly oar]

thats the triangle

[main gull]

Your answer lies here then

[worldly oar]

right

so too just clarify i can just, assume that an triangle is a right triangle. When it has a 90 degree angle?

therefore just applying socahtoa to it

ik i can 180-90-45

[main gull]

When it's clearly marked with the right angle sign, it's a right triangle

[worldly oar]

noice

just was freaking out, about why the hell does the book i have before me here, use cosin- sin-rule to calculate the side of 45 and 90 degrees,
instead of doing it just with sohcohtoa

[main gull]

sine rule and cosine rule are applicable for all triangles

applying those to a right triangle is a bit of overkill

[worldly oar]

nice to know that, now i know, i wasted a lot of time, but also learned much

XD

[main gull]

Your book just wanted to be overkill

[worldly oar]

sometimes needed for much confusion

well that was my question im closing this chat i guess.

.close

[devout snow]

Channel closed

Closed by @worldly oar

Use .reopen if this was a mistake.

[worldly oar]

.reopen

[devout snow]

✅

[winter patrol]

and there's something wrong with the tirangle

[worldly oar]

how so?

[winter patrol]

because such a triangle with those angles and lengths can't exist

[worldly oar]

oh yes the lenghts well, its not actually the lenthgs

lengths*

[winter patrol]

Every detail that it has
as close as possible, (don't add in additional stuff not initially present either)

[worldly oar]

i think the book want me to show to calculate with ratios sides of 1:1:sqrt(2)

because will the theorem above it also explains how to calculate with ratio's

[winter patrol]

you had 2 (not sqrt(2)) in your image

[worldly oar]

my mistake

sorry for not being exact.

late for me, yes i use time as excuse, to you to decide if its a good excuse

wait another question rises above, if i calculate with ratios, does sohcahtoa still work?

made a better sketch:

even better one

used ratio with sohcahtoa indicates i can use it.
also forgot to read what the actual value was of the side of 90 to |probably| 45 degrees.
think i have my answer, im closing it. if anyone is still intrested about teaching me this, they can dm me or whatever they want.

.close

[devout snow]

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[rare saffron]

need some help with partial dirivitives

[restive river]

whats the question

[rare saffron]

f(x,y)= 2x+3y +5x(y-2)^2 - 4

and were finding fx(x,y), fxx(x,y) and fxy(x,y)

[restive river]

well

[rare saffron]

this is what I have

[restive river]

when you take partial derivative you jsut treat other variable as a constant

[rare saffron]

I think I did it weong tho

yes I know

[restive river]

yeah thats right

for the f_x

[rare saffron]

all of it is correct?

[restive river]

f_xx doesnt look right

[rare saffron]

how so

[restive river]

well

if you take the derivative of a constant

[rare saffron]

would it just be (y-2)^2

[robust meteor]

hi everyone im Rishi from india can i get some help on how to work in this server?

im new here

[rare saffron]

Not this channel bro

[restive river]

...

[rare saffron]

go to your own help soction

read the rules man

[restive river]

okay so ur taking derivative of 5(y-2)^2+2

with respect to x

[robust meteor]

omg im soo sorry to disturb

[rare saffron]

It would just be (y-2)^2?

[restive river]

so theres no x in that

[rare saffron]

bc 5 is constant

ohhhhhh

would it just be zero?

[restive river]

yeah lol

[rare saffron]

ahhhhh

I see I see

[restive river]

fxy looks right

[rare saffron]

okay cool

I think I got it

thank you

[restive river]

np

[devout snow]

@rare saffron Has your question been resolved?

[devout snow]

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[devout snow]

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[random kiln]

Can someone help me with this integral? I don't know where to start

[restive river]

areccotan(x) is just inverse of cot(x) right?

[random kiln]

yess

[restive river]

hmmm

that sure is a thinker

i dont even know if u can have an antiderivative for that..

yeah thats some insane integral right there dont have a clue

wait until some of the most advanced peeps help out

[random kiln]

it does have an antiderivative but it's quite difficult to find it

[bright burrow]

I have two thoughts when i see this

This might need an ibp result

[random kiln]

ibp?

[bright burrow]

Or youd beed to take arc cot x = t as a substitution

[restive river]

oh wait

[bright burrow]

Integration by parts

[restive river]

i just realised

this is actually not that bad

u just need to split up that denominator

then it becomes semi nicer

[warm fulcrum]

LexQa's theorem. An integral becomes semi nicer if you just split up that denominator

[restive river]

Exactly!

works plenty of the time too

[random kiln]

and how would you split it up?

[warm fulcrum]

My intuition would say split it into product of 2x/(1 + x²)^(3/2) and e^arccotan(x)

2x/(1 + x²)^(3/2) looks like something that can be done with u-sub when doing ibp

[restive river]

oh i think i solved it actually

let me try writing it out though

[random kiln]

alright thank you really much guys!

[warm fulcrum]

Show off, smh my head

[restive river]

Jokes on you, the LexQa theorem turns out SUPREME!

[warm fulcrum]

[restive river]

just like my original completely new trigonometric identity

[random kiln]

i think i got it too

[restive river]

yea just a sec

[warm fulcrum]

Just do like that MacLaurin dude

Take something general and get famous for setting a = 0

[bright burrow]

How much did you get

[random kiln]

-exp(Pi/2)

[restive river]

i cba to do the definite integral

[bright burrow]

Its correct

[restive river]

oh nice then lmao

what was ur antiderivative

[bright burrow]

For me this worked, how did u do it @random kiln

[restive river]

i think i got more or less the same answer as u...albeit in a more roundabout way

[restive river]

same

[restive river]

oh i went another road haha

completely different

[random kiln]

can you show it? it’s always interesting to see how others do it

[restive river]

yep hjere

here\

[bright burrow]

Bruh

[restive river]

Don't mind the scribbles lmao

i kinda wrote the ibp on another page because why

but it is the same answer i think

[bright burrow]

The calculation was easier with the bounds in u

[restive river]

oop there should be a minus there next to the e

i forgot but yeah

[restive river]

yeah ik just thought it would be better to show it completely i guess

[random kiln]

alrighty

ty guys

it was fun

[restive river]

did u get the idea tho?

[random kiln]

yesss

[restive river]

just solve for x and do the boom boom trignometric identities and thats it really

[random kiln]

.close

[devout snow]

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[odd elbow]

So how do I solve it

I assume

That the answer is 4 but idk how

So I have two urn and I've to take two balls and transfer it to other

Then I believe its 3c2*11c2

I first take out 2 balls then I transfer it to the another urn so it becomes 9+2 = 11

[warm fulcrum]

Are you sure that's the correct order. Isn't it you take 2 from each and then transfer after?

[odd elbow]

Idk that's what I'm confused on

I think I take two from one urn then put it in other then take two from the urn and then put it back

[warm fulcrum]

3C2 • 11C2 doesn't give you any of the answers provided, so I think that's a wrong interpretation of the question

[odd elbow]

Hmm

So it would be 3c2*9c2

And it gives 208

*108

[warm fulcrum]

That's how I would do it

[odd elbow]

Ok

Thnakz

.close

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[clear night]

"where by an integer,
we mean 0, the sum of any number of 1s, and the additive inverses of these sums" what does 1s means?

[clear night]

it was mentioned in this paragraph: "The next theorem tells us that for every real number there is an integer (where by an integer,
we mean 0, the sum of any number of 1s, and the additive inverses of these sums) greater than this real number. This result is attributed to the Greek mathematician Archimedes. The result can be found in Book V of Euclid’s Elements."

[topaz axle]

ones

any number of ones, so a sum of 7 ones for example

[clear night]

thanks

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[odd elbow]

Helo

[odd elbow]

My answer to this question is D)

And my approach is

The question says there should be atleast 2 question from A and B, so that's 4 question now I've to take 2 question from either A or B, then another way is that I take 2 question from one of A or B then I take 4 question from other part

That should be

[woven radish]

Basudev

[odd elbow]

And

Yes that's it

Is it correct??

[topaz axle]

no

the answer is 200

i don't quite get what you did instead

[odd elbow]

Ok where did I go wrong

Well I've to atleast take 2 question from each part right

That's total 4 question right??

Then either I can take two more question from the same part or diff so it becomes

[topaz axle]

i'm completely lost

[woven radish]

Basudev

[odd elbow]

Well

[topaz axle]

can i just ignore it?

[odd elbow]

Ok

[topaz axle]

thank you

[odd elbow]

Just explain me how you got 200

[topaz axle]

either you pick 4 and 2, or 3 and 3, or 2 and 4

[odd elbow]

Oh ye

So

[topaz axle]

10×10 = 100: 3 and 3
5×10 = 50: 2 and 4

[odd elbow]

Oh ye

🇫

Thanks got it

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[wary fractal]

whats the difference between the thick double arrows and the thin double arrows

[wary fractal]

wasnt sure how to google this

[restive river]

Now that's weird. They're generally equivalent in logic.

Where is this from?

[wary fractal]

this is from my uni's reader that they gave us

should i just ignore it?

[restive river]

Just check if in that particular text different examples are given, such as a truth table for $p\rightarrow q$ and $p\Rightarrow q$.

[woven radish]

3317

[wary fractal]

they arent :/

well i guess ill just read on for now :P

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[spice kindle]

How many words in the alphabet {0,1} contain exactly five “1”s and five “0s” (such as the words “0101010101”, “1100110010”, . . . )? Justify.

[spice kindle]

For this question, which one of the following formulas would be the correct one to use if even

$\frac{n!}{(n-k)!}$

[woven radish]

DS

[spice kindle]

$C_n^k$

[woven radish]

DS

[spice kindle]

for n being 10 and k 5

[topaz axle]

what does the first one do, is it ever appropriate?

[spice kindle]

First one is to count the arrangements of a list

[topaz axle]

it doesn't look useful for anything

[spice kindle]

well, it doesnt have to be one of those two, those just came up

[topaz axle]

the second one solves it

[vocal lark]

10!/(5!×5!)

[spice kindle]

and n being 10 and k 5 is it also correct for the sec?

[topaz axle]

i don't know in which order, but it's 10 and 5 yes

10 choose 5

[vocal lark]

252 is the answer

[spice kindle]

alright thx both of u:)

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[signal sierra]

I have this math problem sent to me and the question on this is:

If the area of the orange region is 35, then what is the value of k?

[sonic smelt]

Notice that the area of the orange is k * (2k + 6) - k * 3

Set that equal to 35 and solve for k

[signal sierra]

So it's, (k+6) (k-3) = 35?

Is that also correct?

[sonic smelt]

Yes but I think it'd be easier if you expanded instead of factoring

2k + 6 tho*

Hmm actually that may work fine as well

Wait no no it's k(2k + 3) mb

So 2k^2 + 3k = 35

[signal sierra]

That gave me k = - 5, k = 3.5

But measurement cant be negative so k = 3.5 is the acceptable answer for this?

[sonic smelt]

Yeah

[signal sierra]

Okay thanks

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[hybrid snow]

Can you represent the number as a fraction whose numerator and denominator are integers?

If yes: it's rational

If not: it's irrational and stupid and I hate it

No

Well

pi is not rational

3.14 is

Not any number without square root

6 is rational

Doesn't have a square root

sqrt(6) is irrational

[manic sedge]

√5 had a non terminating decimal expansion

,w √5

[woven radish]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛#6985

[warm fulcrum]

π × 1/π is rational

Yeah?

[manic sedge]

The numbers which have non terminating decimal expansion and non repeating also then the number is irrational

[warm fulcrum]

Which is rational

[manic sedge]

2 is rational

• non repeating

Like

,w 2/3

[woven radish]

Results provided by WolframAlpha

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[warm fulcrum]

(1/2)/4 doesn't have an integer as its numerator, but it's still rational.

[manic sedge]

See it's non terminating but still it's rational

It should be non repeating also

[hybrid snow]

I mean simplify that

That's 1/8

[manic sedge]

Rational terminating

[warm fulcrum]

Yeah. It still can be represented as a fraction with a non-integer in the numerator, hence the claim "it's irrational because the numerator isn't an integer" doesn't hold

[manic sedge]

Then I don't know you didn't define the number

We can't answer that

You have to define the num first

[warm fulcrum]

How do you know you can't do something similar with sqrt(5)/2?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

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[scenic surge]

Oceanographers define layers of the ocean by patterns in the density. There are three layers to the Labrador Sea - the mixed layer (near the surface), pycnocline layer (below the mixed layer), and the deep layer (below the pycnocline layer).
The derivative dρ/dz is nearly zero (or small) in the mixed layer and also in the deep layer. Use your derivative graph to find the boundaries between the layers (approximate answers are enough). Draw horizontal dotted lines on Romina’s density plot at the approximate locations of the two boundaries. Then write a sentence or two describing the derivative dρ/dz in the pycnocline layer, and how the density changes in each of the three layers.

[scenic surge]

What do I do. I dont rlly understand the question

[devout snow]

@scenic surge Has your question been resolved?

[devout snow]

@scenic surge Has your question been resolved?

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[neon nebula]

Why divide by x³ here?

[neon nebula]

I thought you had to divide by the highest factor possible? In this case x^4?

[sonic smelt]

5x/x^4 = 5x/x^3*x = 5/x^3

[neon nebula]

Could you maybe enter that via the bot? Easier for me to see.

[sonic smelt]

$\frac{5x}{x^4} = \frac{5x}{x^3\cdot{x}} = \frac{5}{x^3}$

[woven radish]

A Lonely Bean

[neon nebula]

Ah I see!

Thank you so much!

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[gleaming socket]

30% off means it is 70% of the regular price

[long blaze]

ok

thx

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[stark coral]

hi

[stark coral]

can someone help with linear programming?

also, sorry for taking this one @azure mason

theres other channels tho

[azure mason]

i'll just paste it into another room

[stark coral]

"A boy has $28 dollars. He wants to buy x records at $35 each and y tapes at $4 each. He must buy more than one tape, but no more than four tapes. He must also buy at least three records."

Write three inequalities in x and y to represent the above information.

I dont even know where to start with this

<@&286206848099549185>

dude pleaase

just why

its been 15 minutes

[rose girder]

no

[stark coral]

why not :(

i just have to find the 3 inequalities

but im new to linear programming

[rose girder]

because the boy is poor

[stark coral]

dude

i dont really have a lot of time

[rose girder]

he can't even afford a record

is this a homework or exam?

[rose girder]

i mean, the solution is right there

[copper flower]

"it's trivial"

[rose girder]

1. He must buy more than one tape,
2. but no more than four tapes.
3. He must also buy at least three records.

[stark coral]

as i said

i was completely new to linear programming

had no idea

but its fine. i got the answer from the textbook

im starting to get the gist of it now

[rose girder]

forget the word "linear programming", just write down the three inequalities

[stark coral]

neither

im just practicing

[rose girder]

What's the answer, I'm curious. Because the boy can only afford 7 tapes.

[stark coral]

35x + 40y equal to or less than 280

[rose girder]

Oh, so the boy is not poor

I was confused by that

[stark coral]

1 < y _< 4

the underscore is the underline

which means like

not less than or equal to

idk how to do underlines on discord lol

even though ive been using it for 4 years

[rose girder]

$1< y\leq 4$

[stark coral]

um 💀 '

[woven radish]

᳄ᮐᮔᮁᮊᮨᮄᮔ᮪

[stark coral]

that command is kinda confusing

but ok

well, i just need to learn the command

then it wont be confusing anymore

anyways

the 3rd one

[rose girder]

Yeah, I know the answer now, it's good ol' linear programming

I was only confused by $28 instead of $280

[stark coral]

is x_>3

[stark coral]

mb

its 28

not 280

[rose girder]

You can continue if you want to

[stark coral]

wait

the other part of the answer

i thought it was just another thing

[rose girder]

Explaining it to others can make you understand it more

[stark coral]

is it really more than x_>3?

[rose girder]

[stark coral]

the complete thing is x_>3 max = $28 and (7,1)

but theres a big space

so i assumed its another inequality

is it the same inequality, or 2 different ones?

bro what

[rose girder]

At least 3 records, so $x\geq 3$

[woven radish]

᳄ᮐᮔᮁᮊᮨᮄᮔ᮪

[stark coral]

oh

so its just x_>3 then

cool

ok so

[stark coral]

this

is this just, y greater than 1 but less than or equal to 4?

or is it 1 less than y but less than y less than or equal to 4?

[stark coral]

i feel like its this

what do u think

[rose girder]

I don't understand your sentence here

[rose girder]

but this is fine

[stark coral]

you dont need to

[stark coral]

ok. this is way simpler for me

so basically

oh wait

i get it now lol

i thought we could just do y<4

but nh

nah

because it has to be greater than 1

i get it now

[rose girder]

[stark coral]

im gonna work on part ii of the question:
"Using a scale of 2cm to represent 1 unit on each axis, draw the graphs of the inequalities"

so basically, just draw a graph and draw the lines of the 3 inequalities?

[rose girder]

Yes

[stark coral]

oh

this isnt too bad then

[rose girder]

Yep

[stark coral]

thanks for the help, once again

[rose girder]

Np

[stark coral]

ive been going at it for like 3 hours so

im gonna eat, take a small break then do the questions

[rose girder]

Alr

[devout snow]

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[devout snow]

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[wooden bridge]

i’m a bit lost on my arithmetic

[wooden bridge]

what would i do with the absolute value of x/2?

would that just turn into a positive x/2?

[frail knot]

if think you can just keep it like this, or abs(x)/2

[wooden bridge]

hm

and from here greatest common factors?

[frail knot]

idk I can't help you sorry

[wooden bridge]

npnp

[devout snow]

@wooden bridge Has your question been resolved?

[restive river]

Keep it as is

You already found the derivative so anymore simplifications are unnecessary

[wooden bridge]

professor wants simplified tho

[restive river]

Ah simplifying derivatives what a pain

[restive river]

Well u can just write that 2 in the denominator and flip then fraction

Then you can subtract the fractions ? That's gonna look bad dor

Doe*

[devout snow]

@wooden bridge Has your question been resolved?

[devout snow]

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[ruby turret]

Got a solution for this, just wanted to check it

[ruby turret]

draw a horizontal line to make a rectangle and a right angled triangle

[woven radish]

The following error occured while calculating:
Error: Undefined function arctan

[ruby turret]

we know the rectangle-y bit of the angle is 90 degrees

[scarlet sequoia]

what did you get

[ruby turret]

the opposite side is 15

the adajacent side is 24

so with my limited knowledge of trigonometry

the tangent is the opposite / adjacent

so i need inverse tan (15/24)

[scarlet sequoia]

yes it's correct

90 + arctan(15/24) (in degrees)

[ruby turret]

what does arctan mean?

[scarlet sequoia]

inverse of tan

tan^(-1)

[hybrid snow]

the better way of writing it

[ruby turret]

when writing it into my calculator

should I write

90 + (tan⁻¹((15/24)))

[devout snow]

@ruby turret Has your question been resolved?

[ruby turret]

<@&286206848099549185>

[devout snow]

@ruby turret Has your question been resolved?

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[regal python]

does anyone know

what formula this is

i mean

what formula this is for

for some reason google isnt helping

[main gull]

What's the context?

[regal python]

i already got the right answer for (a)

i was confused on b) so i took a look at the answer and it used that formula

[formal haven]

volume of a cylinder

however h = 2r

[regal python]

i got that h=23

24

2r

shouldnjt b) be like that

also its asking for rate of change of the water level

shouldnt that be the height

<@&286206848099549185>

dude

🇱

[devout snow]

@regal python Has your question been resolved?

[regal python]

nah

[devout snow]

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[flat canopy]

Being 'a' and 'n' whole positive integers, 3a^-2n can be determined with:

1.- a^n = 16
2.- a * n = 8

a) 1 by itself
b) 2 by itself
c) 1 and 2 together
d) Each one stands by itself
e) additional info is required

[placid narwhal]

$$3a^{-2n}$$

[woven radish]

Pluton

[placid narwhal]

This?

[flat canopy]

yup

[placid narwhal]

Try both

[flat canopy]

oh

forgot to mention

did both already

both work

using a = 2 and n = 4

2^4 = 16

then, 2 * 4 = 8

[placid narwhal]

I meant try using only 1. Then try using only 2.

[flat canopy]

wdym by that

like uh

I already used only 1 and it worked fine

i also used only 2 and it also worked fine

a * n = 8 so that gives me p much 2 * 4 too

[placid narwhal]

Ok so you get $a * n = 8$ calculate $3a^{-2n}$ how would you do this?

[woven radish]

Pluton

[flat canopy]

well id say a * n would be like 4 * 2 bc it gives me 8

then i'd just 3(4)^-2(2)

[placid narwhal]

Ok that really is true
$an = 8$ is a diphantine equation with only 2 solutions

[woven radish]

Pluton

[placid narwhal]

But that is not enough info

You dont know if its (2 , 4) or (4 , 2)

[flat canopy]

OHH rightt

[placid narwhal]

So you dont really have enough info there

[flat canopy]

it could be both 3(2)^-2(4) or 3(4)^-2(2)

and they give different results

[placid narwhal]

Yes

[flat canopy]

ohh alr

thanks a lot i was scratching my head at that one

[placid narwhal]

I mean 1. Obv works

And if 1. Works then 1. And 2. Work too

[flat canopy]

wait. i just thought abt this

2 wouldnt work bc

2 x 4 isn't the only multiplication that gives you 8

it's also 1 x 8

or 8 x 1

and they would also offer different results

[placid narwhal]

Oh yeah it has 4 solutions

[flat canopy]

so that's why 2 wouldnt work

[placid narwhal]

Didnt see those 2

[flat canopy]

welp anyways it doesn't really change a lot i think

thanks for the help

.close

[devout snow]

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[crystal temple]

someone kindly help explain

[devout snow]

Please don't occupy multiple help channels.

[flat marlin]

@crystal temple Can you send me the problem

Well the problem here in this chat*

[crystal temple]

4

here

[flat marlin]

Ahh I see

[crystal temple]

how does the positive 2 change to -2?

[flat marlin]

It’s in vertex form

a(x-h)^2+k

So if h of the vertex is -2, in the equation it becomes (x-(-2))

So x+2

That’s why you go left two because h is a point on the vertex

At least that’s how I perceive it and it works

I am still taking precalc 1 so if there is a better explanation I’m curious to know what it is

Does that make sense @crystal temple?

[crystal temple]

yes i understand that

i will give you the problem

y=(x +2)^2 -1

the vertex is -2,-1

im wondering how does +2 turn into -2

[flat marlin]

Okay so

(x+2)^2 -1 is in the form a(x-h)^2+k

Have you learned vertex form yet?

[crystal temple]

yes

im just trying to fully undertand everything before i move on

[flat marlin]

So because we know the h of the vertex is -2, we can plug it into the vertex form to see how it reflects this

(x-(-2)) turns into (x+2)

[crystal temple]

ok im following

[flat marlin]

And if it were 2, it would be (x-2)

But if the h of the vertex is 2, x would have to be 2

I’m not sure I can explain it any deeper with my current level of understanding

But maybe this sort of breaks the bridge

[crystal temple]

so x- times -2 would make +2

[flat marlin]

Yes