help-27

[lilac portal]

12 white marbles

and 3x and y

so 12+3x+y=60 marbles

But we know that 3x=y so we substitute

12 +3x +3x =60

6x=60-12

6x=48

x=8

So there are 8 yellow marbles

Then let's substitute 8 with any of the equation

Any equation will do

so let's use 3x=y for obvious reasons

3(8) = y

24 = y

Oh, it only works on the first equation since there might be other marbles in the box

[lyric folio]

Ok

[lilac portal]

wait I think I did something wrong

[lyric folio]

Hmm

I think you did it right

What do u think u got it wrong though

[lilac portal]

Nah it doesn't add up
8 + 24 + 12 is just 24

[lilac portal]

I think it went wrong with here

[lyric folio]

Wait huh

Ok yeah this doesn’t make sense

[lilac portal]

K I already did it

It was right, I did something wrong there

[lilac portal]

It should be 60 = 3b + y +12

I should just used y and b

Instead of x and y

Too confusing

60 = 3b + b/3 + 12

Since b = 3y right?

Then when simplified

b = 36

b = 3y

36 = 3y

12 = y

12 + 36 + 12 =60

12(3) = 36

So that's the answer

I just got confused with the x and y thing, I think it might just be better to use variables that are first letter of the word itself

blue =36 and yellow = 12

[lyric folio]

Oh why

Will x and y still work though

[devout snow]

@lyric folio Has your question been resolved?

[polar wharf]

Yes variables are just names

I can give a number any name i like

We can call them x and y

b and y

Smiley face and frowning face

The symbol you use for the variable is only a name and it's up to you what name or symbol you like to use

(Unless the question specifically gave it a name already)

[devout snow]

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[restive river]

Kind of having a small misunderstanding with Stoke's theorem

[restive river]

Still trying to understand, but Stoke's theorem would just be that the circulation of a vector field around the boundary C of some oriented surface S in the direction counterclockwise with respect to the​ surface's unit, correct? But I am still confused on how to write it out

[supple knot]

Unsure of how to write out the math?

[restive river]

Yeah, more or less

Very new concept

[supple knot]

https://tutorial.math.lamar.edu/classes/calcIII/stokestheorem.aspx

I think you're supposed to compute the line integral instead

[restive river]

dont worry. just use this

[pseudo basin]

@restive river this is not the place for jokes.

[restive river]

srry

[novel coral]

good one @restive river lol

wrong place

but good one

[restive river]

Thank you, I will read up a bit more, I think my understanding is still lacking

[devout snow]

@restive river Has your question been resolved?

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[restive river]

can someone tell me what i did wrong in this question?
so i used cosine law to get the measure of the O angle (60 degrees) in the triangle then I just used this formula for area of segment

[restive river]

i got 3.26cm however which isnt in the answers

ik theres a simpler way to do this but im curious as to what i did wrong

[torn vessel]

so what did you plug into the formula?
and what does that formula give you? What is A?

[restive river]

i put 1/2 x (1.0471975512 - sin(1.0471975512)) x 6^2

[restive river]

A is area of segment

idk why i used cosine law

it says its a equilateral triangle

[devout snow]

@restive river Has your question been resolved?

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[small ingot]

the f(x) should be zero or maybe -12 (after subst the values into eq)?- Idk what should I do to find particular solution, yp at this point with this kind of ques. My working steps are just all about finding general solutions, yh (to check if it overlaps with yp

[small ingot]

if u are wondering what f(x) im talking about, this is the formula from my lecture slides

[devout snow]

@small ingot Has your question been resolved?

[small ingot]

<@&286206848099549185>

[devout snow]

@small ingot Has your question been resolved?

[devout snow]

@small ingot Has your question been resolved?

[devout snow]

@small ingot Has your question been resolved?

[small ingot]

<@&286206848099549185>

[small ingot]

🗿

is it my problem that I didnt explain clearly?

[small ingot]

nvm ig

.close

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[viscid mist]

.claim

is there a difference between [m\n] and [m\\n] ?
the definitions are from Knuth's Concrete Mathematics book

[restive river]

$2\mid 12$ but $2\not| 12$ and $4|12$

[woven radish]

Toby

[restive river]

exactly divides means that its the highest power of a number that divides n

[viscid mist]

thank you!

.close

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[finite inlet]

Let $a,b \in \mathbb{R}$ with $a \neq 0$ and let $f \colon \mathbb{R} \rightarrow \mathbb{R}, x \mapsto ax + b$

[woven radish]

madmike

[finite inlet]

Is this 1 function or is this actually an infinite number of functions depending on what we choose for a and b?

If I want to show that this is surjective, can I set a = 1 and b = 0, or is surjectivity then only proven for 1 of these functions?

[stone stump]

that would only show it for that specific choice

[finite inlet]

ahh that sounds difficult

[restive river]

you can use your other definition of surjectivity here, ie find an inverse (note that f is linear)

[finite inlet]

I think my script says there is only an inverse if f is bijective

Oh so if I find an inverse then I have proven that it's bijective?

[stone stump]

it is bijective but I would still just show surjectivity on its own

just to get practice showing it

working with the definition

[finite inlet]

ahh I see

I will try that

can I leave the channel open?

or is that bad

[stone stump]

yeah just leave it open

[finite inlet]

\textbf{$f$ injective:}

Let $g: \mathbb{R} \rightarrow \mathbb{R}, \ x \mapsto \dfrac{x - b}{a}$.

Then $g \circ f \colon \mathbb{R} \rightarrow \mathbb{R}, \ x \mapsto x$, thus $f$ is injective.

[woven radish]

madmike

[finite inlet]

f is defined here

Do you think this is correct?

$g \circ f \colon \mathbb{R} \rightarrow \mathbb{R}, \ x \mapsto x = Id_\mathbb{R}$

[woven radish]

madmike

[finite inlet]

Maybe I should explicitly write = Id_R like this?

not sure if that makes sense

[stone stump]

is that the definition you have for injective?

that there exists such a map g?

[finite inlet]

I have a definition for f: A -> B
"f is injective iff there is a map g : B -> A with g \circ f = Id_A

[stone stump]

ok yes

do you also have another definition?

[finite inlet]

I came up with that map g

[stone stump]

yes your solution is correct, don't worry about that

[finite inlet]

okay

Yes I do

[stone stump]

which one?

[finite inlet]

f(x1) = f(x2) => x1 = x2
and
f(x1) != f(x2) for all x1, x2 with x1 != x2

those two are also in my script

[stone stump]

good. for practice, can you show that f is injective using this definition?

often in practice it is hard to explicitly write down the function g

[finite inlet]

I can try but that seems a lot harder

[stone stump]

might seem hard. which is why it's good practice

it's not that bad

[finite inlet]

Let $x_1, x_2 \in \mathbb{R}$ with $f(x_1) = f(x_2)$.

Then $ax_1 + b = ax_2 + b \leftrightarrow ax_1 = ax_2 \leftrightarrow x_1 = x_2$.

[woven radish]

madmike

[finite inlet]

?

[stone stump]

yes

[finite inlet]

I thought that would be harder

math symbols are still intimidating yikes

surjectivity seems harder though

the regular definition is f : A->B is surjective if f(A) = B

[stone stump]

always depends on the function

[finite inlet]

Can you use that definition to prove surjectivity of the function?

I would not know how to start

I just did the same thing with f \circ g = Id_R now

[stone stump]

yes you can

f(A) is always a subset of B, so we need to show that B is a subset of f(A)

that means for every b in B there exists an a in A with f(a)=b

so we want to show that for some y in R there exists an x in R with f(x) =ax+b = y

can you solve this equation for x?

this should be how you got the function g with f circ g = Id

I assume anyway

[finite inlet]

x = (y - b)/a

that's the same fraction lol

and this is it?

if it was not surjective, what would happen here instead?

[stone stump]

yes. we see that f((y-b)/a) = y

we wouldn't be able to solve the equality

for example, x^2 is not surjective

because you can't solve the equality x^2=-1

(over R)

[finite inlet]

ah

[stone stump]

yes linear functions are pretty easy in that regard. for essentially all other functions this is not true

[finite inlet]

so we showed that for every y there is an x, namely (y-b)/a, right?

[stone stump]

yes

[finite inlet]

nice

thanks a lot for your help

why do we need the variable y?

can't we solve for x then we get x = -b/a

no that makes no sense

I don't understand what the y represents, in school I learned that f(x) = y

It represents any y in R, but doesn't f(x) also?

why do we have both in 1 equation

f(x) = ax+b <=> f(x)-b = ax <=> (f(x)-b)/a = x

[stone stump]

y represents any possible image

for example it might represent 4 and then we ask, is there an x with f(x)=4

or it might stand for -17 and then we ask if there is an x with f(x)=-17

and so on

but clearly we don't want to do this for every real number individually

[finite inlet]

ah I see

at the end of the day it doesn't change the fact that f(x) is y, or f(x) is -17, it's just a way of writing it down?

alrighty thanks again

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[astral mortar]

howw do i divide fractions

[lilac ferry]

example?

[astral mortar]

5/8 divided by 2/4

[hybrid snow]

Multiply by the divisor's reciprocal

[lilac ferry]

you multiply the outer numbers together and inner numbers together

or whatever they said

[astral mortar]

what is resciprocal

[lilac ferry]

essentially do what I said

5 gets multiplied by 4, 8 by 2 and the final fraction is 20/16

then 5/4, you get the idea

[astral mortar]

so the numerator is divided by the denominator of the second fracction

[lilac ferry]

yes

if i knew how to use the bot I would show you better

[restive river]

huh

[astral mortar]

but what if the fraction has an exponent

5^2/5 divided by 20/2

[lilac ferry]

then you multiply it anyway

[restive river]

i have a question too

[lilac ferry]

5^2 * 2 is the same as 25 * 2

[lilac ferry]

go into a help forum

[restive river]

its only a small question

[astral mortar]

so its 50/5

[lilac ferry]

it's 50/100

[astral mortar]

divded by 20/2

[lilac ferry]

you gotta multiply the 20 with 5 as well

[restive river]

umm

[astral mortar]

50 divided by 5 and 5 divided by 20 final result

i don know how exponents work sory

[lilac ferry]

5^2/5 / 20/2 = 5^2 * 2 / 5*20

[restive river]

what is 5^2

[astral mortar]

but i have 5^2 not 5^2*2

5^2/5 ÷ 20/2

whaat do i do first

[devout snow]

@astral mortar Has your question been resolved?

[rare mantle]

you can simplify both of those

5^2 / 5 = ?

basic math

unless of course you haven’t learned exponents

[astral mortar]

25 dvided by 5

[rare mantle]

yep

which is 5

and the right one is 20/2

[astral mortar]

that equaals 10

[rare mantle]

so you’re left with?

[astral mortar]

5 divided by 10

[rare mantle]

which can be simplfied

[astral mortar]

5/10

[rare mantle]

or you can make it a decimal, depends what the questions asks for

[rare mantle]

yeah that can be simplified

[astral mortar]

ohh so itts 0.5

thaank you kihei

[rare mantle]

yes or 1/2

no problem

[astral mortar]

.close

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[restive river]

seperate then find

[prime egret]

Turn them into geometric series

[proud perch]

Factor

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

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[restive river]

how do you simplify this

first i distributed the negation

so (p and q) or (p or not q)

(p or not q) can this simplify to T

[wooden veldt]

¬(A or B) is (¬A and ¬B)

[restive river]

yes?

in the second prt?

i distributed the negation

[wooden veldt]

(p or not q)

[restive river]

confused?

im sorry

[wooden veldt]

$\neg ( \neg p \vee q)$ is $p \wedge \neg q$

[patent marsh]

it's beautiful

[woven radish]

ΣAC

[wooden veldt]

lol

[restive river]

oh ueaj

sorry i didnt flip the signt

so how do i simplify from after that ig

waittt

i i ghink i know

no i do nt

wwait

p and not q

is false

[wooden veldt]

why?

[restive river]

actuallly

i lied

im sorry i suck at this

p and not p would be false

[wooden veldt]

you need to "expand", like in (a+b)*(c+d)

[restive river]

distributivity?

[wooden veldt]

"and" and "or" distribute over eachother yeah

[restive river]

uhh ive never distrubuted with this many terms

[patent marsh]

Hint: $(p \wedge q) \vee (p \wedge r) = p \wedge (q \vee r)$

[woven radish]

MellowDramaLlama

[restive river]

even with the negation?

[patent marsh]

yep! So the negation doesn't effect anything. For example

$(\neg p \wedge q) \vee (\neg p \wedge \neg r) = \neg p \wedge (q \vee \neg r)$

[woven radish]

MellowDramaLlama

[restive river]

if i simplified this properly the correct answer is p?

also for this statement

why isnt it y < 0 in the negation

why does the connectory only change for x+ y

[wooden veldt]

$\forall$ (something with property) $\exists$ (something else with property) s.t "statement", negated is
$\exists$ (something with property) $\forall$ (something else with property) s.t " negation of statement"

[woven radish]

ΣAC

[restive river]

sorry im a little confused as to why y<0 is not negated

[devout snow]

@restive river Has your question been resolved?

[restive river]

.close

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[verbal robin]

How do I do this?

The teacher only taught us about when the problem had a coefficient of one at the beginning :T

[devout snow]

@verbal robin Has your question been resolved?

[verbal robin]

<@&286206848099549185>

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[proud depot]

An entrepreneur borrowed $150,000 at 12% interest and paid $20,000 per year for the last 4 years. How much will be his final payment at the end of the fifth year?

[proud depot]

R = 12% , P = 150,000 n = 1
My solution is
0 ---> 150,000
1 ---> 168,000
2 ---> 168,160
3 ---> 168,339.20
4 ---> 168,539.90
5 ---> 168,764.69

Is this correct?

[lilac portal]

Just use the geometric sequence or the compound interest formula and see if the answers match

[devout snow]

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[proud depot]

Thanks!

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[boreal girder]

Hi, this is physic related but I need help understanding how to perform this on the calculator

[boreal girder]

equation on the bottom

[supple knot]

use google calc

[boreal girder]

on a physical calculator..

[supple knot]

27.3 * 24 * ...

[supple knot]

do it on google first

not everyone has your calc model

[boreal girder]

I just need to know what to input in order... for that equation

very useful

.close

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[supple knot]

its just numbers

[devout snow]

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[hushed pendant]

Could someone what they mean by factor out the 4x^2+13. I don't get how they got thier final answer

[hushed pendant]

Plz

This was the initial problem. To factory out completely

[stuck field]

Factor an x
Then factor like you usually would factor a quadratic. Except instead of x, there's x^2 everywhere.

[hushed pendant]

A ok I see now.

Thx!

.close

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[dusky adder]

$\int_{0}{2}\pi[\sqrt{4-y^2}]^2 dy$

[wooden wraith]

The bot's really having some trouble today

[dusky adder]

I think I can use trig substitution

[wooden wraith]

probably. But that's overkill

you have a square root, squared

[dusky adder]

uhm

I thought square roots didn't distribute

[wooden wraith]

I'm not talking about the y^2

I mean the square on the outside

[dusky adder]

oh, u sub?

😬

[wooden wraith]

[sqrt(a)]^2 = a

They cancel

[dusky adder]

oh sheit

u madman

ty

[wooden wraith]

Lol no problem

[dusky adder]

I think that's right

yeah

[restive river]

Also

Isn't that just the equation of a circle?

[wooden wraith]

without the outer square it would be

if it were just sqrt(4-y^2)

[restive river]

Oh I did not notice that. Fair enough

[wooden wraith]

well, half a circle anyway

[restive river]

Odd for a question to be presented with a squared square root

[restive river]

Yep. Always would notice that with those questions haha

[wooden wraith]

If all you have is something like sqrt(4-x^2), that's actually a nice way to do the integral. Just find the area of the semicircle rather than dealing with the trig sub

[restive river]

Oh yeah definitely. That's how we did it

[wooden wraith]

Yeah looks good, just need to plug in the bounds

[restive river]

My teacher really emphasised graphically solving the integrals for some of the harder questions if you can see some symmetry

This looks absolutely dreadful, but it is actually not that bad if you can figure out the graph

[dusky adder]

what in tarnation

[restive river]

Yeah here is a little spoiler, if you see integrals from -1 to 1 that usually is an indicator of some sort of symmetry

Helps a lot

[devout snow]

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[obsidian bear]

I dont know how to start this question

[supple knot]

Set the derivative to zero at x=3 in terms of a

Then solve for a

[obsidian bear]

So substitute all the x to 3?

<@&286206848099549185>

[devout snow]

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[alpine pier]

Hey I need some help, Where did the number 20 come from?

[alpine pier]

the +20t

where did that comefrom

As well as where did -5 come from??

[restive river]

It just did

[alpine pier]

Oh wait -5 is the direction the parabola goes

[hybrid snow]

It's just is

I mean it's the equation of the function

[alpine pier]

Oh I can just get vertex form first then go into standard

[hybrid snow]

Yes

[alpine pier]

y = a(x-2)+45

What would x and y be?

a point on the parabola?

Can't I use the vertex as x and y too?

[hybrid snow]

There's a y intercept

(0, 25)

[alpine pier]

Ohhh ok

[hybrid snow]

You can use that

To find a

[alpine pier]

Oh ok makes sense

thx

[hybrid snow]

Also don't forget the ^2

[alpine pier]

Yea

I gotta find the domain and range of this now oof

[restive river]

The vertex and the x intercept and other stuff could tell u how that equation is the way it is

[alpine pier]

Yea

[hybrid snow]

Domain is easy

[alpine pier]

{xER|x≤2)

correct?

[hybrid snow]

No

Well

Uhh

[alpine pier]

the answer key says x≥2

Idk how

[hybrid snow]

What is the function supposed to model

The trajectory?

[alpine pier]

A parabola

[hybrid snow]

Well yeah but all parabolas have a domain of all reals

What is it supposed to model specifically

[restive river]

The domain can be anything, but I have a sneaking suspension that your function isn't just a parabola

[hybrid snow]

A ball being thrown?

A missile being North Koreaed?

[alpine pier]

It just gives me the formula it's just asking for me to find the domain and range

[hybrid snow]

I mean the domain would legit be $x \in \bR$

[restive river]

The domain is all real numbers then

[woven radish]

Umbraleviathan

[hybrid snow]

If it's just giving you a random ass function and calling it a day

[alpine pier]

yea but the a value makes the parabola open down therefore the x value has to be less than something

[hybrid snow]

No

You're mixing domain and range

It's concavity has nothing to do with domain

[alpine pier]

Oh crap

That's y value then

That's the answer for it

[restive river]

The range is wrong on there too

[hybrid snow]

That's just wrong

Oh dude

[alpine pier]

What the

[hybrid snow]

That's the answer for b, not d

[alpine pier]

OHHHH

[restive river]

💀💀💀💀

[hybrid snow]

Man I'm dead

[hybrid snow]

Which is what I got

[alpine pier]

Yea

I get it now

Les gooo

[restive river]

Funky times eh

[alpine pier]

Im doing so bad in math rn 🤦‍♂️ I've never done so bad in my life

[restive river]

It do be what it do be innit

[alpine pier]

Idk I seem smart but when it comes to tests I'm legit dumb and I become paralyzed

I got a 39.8% on my recent test

[devout snow]

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[molten galleon]

probability of carelessness containing care or less?

[molten galleon]

would it be probability of anagrams containing care + probability of anagrams containing less - probability of anagrams containing care and less?

,tex $\binom{9}{2}$ $\binom{7}{2}$ $5!$ + $\binom{9}{4}$ $\binom{5}{2}$ 3! - $\binom{6}{2}$ 4!

[woven radish]

Praxis

[devout snow]

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[true wren]

Hello guys could you help me with the coshx question

I need to find the derative

This is what I done so far

Is this correct

Or should I take this app tech

Approach

Are they the same

?

[devout snow]

@true wren Has your question been resolved?

[true wren]

<@&286206848099549185>

[devout snow]

@true wren Has your question been resolved?

[devout snow]

@true wren Has your question been resolved?

[supple knot]

What even is the question

[supple knot]

You input the function wrong in the app

[true wren]

sorry i should have been more clear the question was cosh^-1 (Square roof of 1+u^2)

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[neon folio]

The equation ax²+ bx + c = 0 is given. Justify:
a) If b is replaced by the opposite number -b, the number of solutions does not change.
b) If a and c have different signs, then the equation has two solutions. Show with a counterexample that the converse of the theorem is false.

[lethal oxide]

Think about the discriminant formula: b^2 - 4ac

[neon folio]

yes

and b^2 and (-b)^2 are the same

so the number of solutions is the same

[lethal oxide]

Splendid

[neon folio]

what about b

[lethal oxide]

The same can also be used

[neon folio]

so at b) both a and c are -a and -c?

[lethal oxide]

For instance if a is negative and c is positive then -4ac will positive

[neon folio]

oh yeah

[lethal oxide]

It says that one of the two is negative

[neon folio]

yes

[neon folio]

yes

and if a is positive and c is negative -4ac will be positive

[lethal oxide]

Soo then this should work out, no?

[neon folio]

no

what does converse of the theorem mean

[pseudo basin]

the converse of A -> B is B -> A

so you need to disprove the statement "if the equation has two solutions then a and c have different signs"

[neon folio]

if the equation has 1 solution then a and c have the same signs

[pseudo basin]

no

disprove does not mean mangle

[neon folio]

if a and c have different signs then the equation has 2 solutions

and i need to disprove this statement with a counter example

am i correct?

[pseudo basin]

no

[neon folio]

then what

[pseudo basin]

so you need to disprove the statement "if the equation has two solutions then a and c have different signs"

[neon folio]

just tell me the answer

i tried, i got it wrong

now give me the answer

or at least a bigger hint

😐

[pseudo basin]

you need to find an equation that has two roots but in which a and c have the same sign

[neon folio]

ok

,w x^2-2x+16=0

[woven radish]

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Requested by Master Oogway#0599

[neon folio]

boom

2 roots

[pseudo basin]

presumably 2 real roots were meant

[neon folio]

ok

,w 5x^2+4x+1=0

[woven radish]

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[neon folio]

F

wait

,w 3x^2+ 4x + 2 = 0

[woven radish]

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[neon folio]

am i stupid or is this impossible?

[pseudo basin]

you are stupid

[neon folio]

ok

canyou tell me an example?

[pseudo basin]

x^2 - 10x + 16 = 0

[neon folio]

,w x^2 - 10x + 16 = 0

[woven radish]

Results provided by WolframAlpha

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[neon folio]

lol

ok

so i'm done?

i think so

thanks

.close

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[dark rampart]

can someone explain how y'= 8x^3(2x - 5)^3 + 3x^2(2x - 5)^4 went to y'= x^2 (2x - 5)^3 [8x + 3 (2x - 5)]?

[dark rampart]

the original question was x^3 (2x - 5)^4

[restive river]

Your factorise out x^2 and (2x-5)^3 I suppose

[dark rampart]

sorry but huh?

[pseudo basin]

factor out x^2, then factor out (2x-5)^3

[restive river]

You start off with $8x^{3}(2x-5)^{3}+ 3x^{2}(2x-5)^{4}$ then you factor out x^2 to get $x^{2}(8x(2x-5)^{3}+3(2x-5)^{4})$

[woven radish]

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

[restive river]

I'm so bad with latex 😭

[dark rampart]

ohh

ok thank you

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[young heron]

how am I supposed to do this?

[pseudo basin]

you have two similar triangles here

write down a similarity statement and solve for x. one possible way to do that here is (x+4)/9 = x/6

[young heron]

wait before that can I ask you how to do this

[pseudo basin]

same shit

similar triangles

[young heron]

so thats 12/10 = 6/x

alr thx man

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[gusty merlin]

Hi

[gusty merlin]

Should it be 0,3?

Pls @ me if u can help!

Thank you

[sonic smelt]

Is this a test you're taking rn?

[crimson plinth]

@gusty merlin its b

[gusty merlin]

Why?

[gusty merlin]

Nope

It’s a multiple choice thing that we do

@crimson plinth

[crimson plinth]

yeah

x int

0 =3x +3

-3 = 3x

-1=x

@gusty merlin

[gusty merlin]

Omg thank you so much

It makes sense now

I have another one could u tell me where I went wrong

[devout snow]

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[muted sierra]

https://cdn.discordapp.com/attachments/1018703193473024061/1040371947625791568/image.png

[muted sierra]

Did I do this right or would the correct answer for the second deriv at (1,1) be 2/9

[devout snow]

@muted sierra Has your question been resolved?

[muted sierra]

<@&286206848099549185>

I had done it this way but wasn’t sure which was correct

https://cdn.discordapp.com/attachments/1036714672545595394/1040371000644206662/image.png

[devout snow]

@muted sierra Has your question been resolved?

[muted sierra]

<@&286206848099549185> ?

[muted sierra]

?

[devout snow]

@muted sierra Has your question been resolved?

[restive river]

the first one is correct, this one should be -2(3y^2)+2x(6y)dy/dx

because quotient rule the second part is -

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[rare roost]

I want to make sure I understand this

[rare roost]

To reach the nth stair, I can only get there from either the (n-1)th stair or the (n-2)th stair. There are F(n-1) ways to get to the former, and F(n-2) ways to get to the latter

Therefore, to reach to nth stair, there are F(n-1) + F(n-2) ways to do it

[devout snow]

@rare roost Has your question been resolved?

[topaz axle]

right

it's about what kind of step you do last

then it's clear that there's two kinds of paths, and they don't intersect, and they don't leave unaccounted ways

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[naive sluice]

is this correct up until here?

because the integral on the left hand side looks pretty hard to compute

it's a differential equation

[left robin]

looks good

the integral is indeed hard

tip:
let v=e^u
and rewrite it accordingly
let w=v/(2v+3)
and rewrite accordingly

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[restive river]

hi

[restive river]

can we go over this answer

[supple knot]

• Ask your math question in a clear, concise manner.

[restive river]

i dont understand why its 1/2F(2x) + c

[supple knot]

Differentiate F(2x)/2

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[heady coral]

Is the succession convergent or divergent? If I do lim n --> infinity of sqrt(n) - lim n --> infinity of sqrt(n+23) I get 0, is correct?

[supple knot]

no

you tried to use the difference law here

but you didn't check that each converges first

and since neither converge, you can't apply the difference law

you have to manipulate the expression to get it into a single fraction. i.e. multiply by the conjugate in the numerator and denominator

[heady coral]

I don't understand why I have to manipulate the expression :c

[supple knot]

because you can't get the answer otherwise

[heady coral]

I see

Thank you

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[restive river]

here if try to get the y intercept of the lines on left and right, i get 24 and -24, but i dont get how the lines would even touch the y axis to begin with, they are going away from it

[restive river]

oh never mind i understood, they would touch if the line went it on but it doesnt because of the condition

.closes

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[reef pilot]

,,\sum_{i=1}^{n-3}\left(\sum_{j=i+3}^{n}\left(1\right)\right)

[reef pilot]

how would i write this as an expression without siga

sigma

,\sum_{i=1}^{n-3}\left(\sum_{j=i+3}^{n}\left(1\right)\right)

[woven radish]

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

[reef pilot]

$\sum_{i=1}^{n-3}\left(\sum_{j=i+3}^{n}\left(1\right)\right)$

[woven radish]

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

[restive river]

Latex moment

[reef pilot]

ugh

how do i rewrite this as an expression wit hjust n

its not loading isnt it

...

ugh

nvm.

.close

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[sand coral]

im having trouble finding the critical numbers

[sand coral]

looking at chegg im confused how he got the critical value for y

[coral knot]

ah no not chegg, big mistake

dont u have to pay for chegg

[dark dawn]

you can derive f(x) and set equal to 0

[coral knot]

yea

[dark dawn]

that will tell you the turning point of the function

its not asking for the nature so thats nice 🙂

oh its a quad

nvm

yeah should be able to get y with that

[devout snow]

@sand coral Has your question been resolved?

[sand coral]

So I set the derivate of f(x) equal to 0??

[sand coral]

thats how i got x though

@dark dawn

do you mean i set x equal to -5.5

yeah that worked

what did you mean derive f(x) and set equal to 0

???

@dark dawn

what worked was setting x equal to -5.5 in the original function

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[fossil moth]

can i get help explaining this answer

[fossil moth]

this is the question

i dont get the 4th step? v'=pih^2/4

[midnight dirge]

um

they literally just took out the 3 in the bracket

and like

3/12 = 1/4

@fossil moth

[fossil moth]

yea we get that

but im confused on the dh/dt

like how does it go from that to 12/pih^2

[midnight dirge]

oh nvm

i got confused cuz u said v'

[fossil moth]

my bad

[midnight dirge]

oh um

chain rule

[fossil moth]

https://tenor.com/view/brooklyn-nine-nine-terry-jeffords-why-b99-brooklyn99-gif-21715381

[midnight dirge]

well

[fossil moth]

like what happens between the steps because i dont understand the explanation given

[midnight dirge]

what u r diff is like

pi/12 is some constant

we can ignore it fr now

[fossil moth]

frfr

ong

[midnight dirge]

h^3 is like

[fossil moth]

3h^2

[midnight dirge]

f(g(t))
where f(t) = t^3
g(t) = h

so

derivative of that is like

f'(g(t)) g'(t)

[fossil moth]

so how does that apply in this example

[midnight dirge]

^

u literally

plug in the stuff that i pointed out how to

unless i made some mistake in which case ok but meh

[fossil moth]

how would you get f(t)=t^3 because when you put in g(t)=h then wouldnt it become f(h)?

sorry i dont understand

[midnight dirge]

f(g(t)) =f(h)

= h^3

function composition

[fossil moth]

alright, i'll look into it

.close

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[restive river]

The equation of this quadratic function is f(x)=k(x+m)(x+n)

[restive river]

How can I determine the value of M and N

[wooden zodiac]

wa

what are the zero values

[restive river]

What do u mean?

[wooden zodiac]

x values when y=0

(x-intercepts)

[restive river]

Oh

-4 and 2

[wooden zodiac]

yes

[restive river]

So I use this to find m and n?
f(x)=k(2+m)(2+n)
?

Oopps I gotta go... I'll ask bout this later. Thx for replying!

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[supple knot]

!15m

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

[supple knot]

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[lusty hearth]

Hello, I would like help with this question please : car we have lim inf An = empty set if An diferent than empty set ? Same question for lim sup

[lusty hearth]

with this definition for the lim sup and inf

[neon aspen]

Yes for liminf

If one of the A_n's is empty then liminf should also he empty

[magic thicket]

No ?

[neon aspen]

But also A_n = (0, 1/n), which is non empty, has liminf empty I think

[neon aspen]

Nvm this

[lusty hearth]

hmmm, and if we have A_n = (-1/n,0) ? lim inf steal empty ?

[neon aspen]

Yea ig

[lusty hearth]

thanks ! I don't really understand the logic for now

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[wooden veldt]

Is n>=1?

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[urban shadow]

How do I do all of question 3?

[violet wind]

,rotate

,rotatecw

[urban shadow]

Do I form a linear equation with the two coordinates given?

[violet wind]

you need equation of the perpendicular bisector

what do you know about it

[urban shadow]

What does bisector mean

[violet wind]

divides into 2 equal halves

[urban shadow]

Perpendicular means it like intersects at 90* angle

[violet wind]

yeah

bisector means it passes through the midpoint of the segment

[urban shadow]

I thought bisector could just mean it cuts through

Ty

Do I form that line equation

For a

[violet wind]

yeah

[urban shadow]

Basically y1-y2=m(x1-x2)

?

[violet wind]

yeah

[urban shadow]

For a

Then for b

[violet wind]

or well

[urban shadow]

Idk how to do be

[violet wind]

y - y1 = m(x - x1)

[urban shadow]

B*

[urban shadow]

Yea

[violet wind]

you have to find the center

(-1,3) here

and plug in x=-1, y=3 into the line equation

it lies on the line if it makes the equation true

[urban shadow]

Did you get that from the equation

[violet wind]

the circle equation yeah

[urban shadow]

Ohh

Ty

I got confused for a sec

Cheers

[violet wind]

np

[urban shadow]

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[topaz iron]

I have to find the intervals on which f increases and the
intervals on which f decreases.

[topaz iron]

am i on the right track

<@&286206848099549185>

[quaint citrus]

Uh

If u look closely, you’ll see that the radical does not extend to the x

It’s simply a sqrt3 coefficient

[topaz iron]

oh

oops

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[topaz iron]

.reopen

[devout snow]

✅

[topaz iron]

sorry so the interval would be pi/2 and pi right

wait no it would be [0, pi/2] [pi/2, pi] [pi, 2pi]

and so it increases from [0, pi/2] and decreases from [pi/2, pi] and increases from [pi, 2ip]

is this correct?

[late token]

no because the problem already has an interval from 0 <= x <= pi, so u cant have intervals greater than pi

[late token]

u have to set the equation equal to 0 and solve for x to get the critical points

[topaz iron]

oh right im keep missing these details lol my bad let me rewrite

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[warped snow]

how do I get arc NO and LM?

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[restive river]

i have no clue whatsoever on how to start this

[devout snow]

@restive river Has your question been resolved?

[restive river]

<@&286206848099549185>

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@restive river Has your question been resolved?

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@restive river Has your question been resolved?

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@restive river Has your question been resolved?

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[cerulean wagon]

How can you write the number 66 using five 3's?

[magic pine]

i can do it with 4

33 + 33

if you need 5, 33 + 33 + h(-3)

[stone locust]

exactly 5?

[cerulean wagon]

yes

[stone locust]

are other numbers allowed?

[cerulean wagon]

no

[magic pine]

i also like $\floor{\sqrt{3}}+ \floor{\sqrt{3}} + (3+\floor{\sqrt{3}})^3$

[woven radish]

maximo

[brazen parcel]

33 + 33 + d/dx(3)

[stone locust]

this is nice

[magic pine]

this is good

[cerulean wagon]

oh, I figured it out:
33*3-33

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[magic pine]

you’re saying this like our solutions weren’t stellar

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[surreal plinth]

I'm stuck on how to start and end 1. 3

[little escarp]

ok so you know how usually a quadratic has two roots?

[surreal plinth]

Yes

[little escarp]

the two roots here are given by using only the + in the equation and using only the - right?

as in, the first root is -5 + sqrt(3-12k^2) / 4 and the second root is -5 - sqrt(3-12k^2) / 4

[real grail]

roots will be equal if 3 - 12k² = 0

[surreal plinth]

Oh yes

[little escarp]

so the only way these two values are equal are if that square root thing is equal to 0, because then we get x = -5 + 0 / 4 and x = -5 - 0 / 4

which are obviously the same, equal to -5/4

so 3 - 12k^2 = 0

[surreal plinth]

I'm seeing it a bit now

I see

Thx

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[golden rose]

A mouse wheel is 16cm in diameter and the base of the wheel is 2cm off the ground. If the hamster spins the wheel 4 times each second, determine the cosine function that describes the movement of the wheel if it starts at lowest point

[restive river]

oops

soz

[golden rose]

All good

[golden rose]

Here’s my question^ if anyone can help that would be much appreciated

[restive river]

what grade is that

[golden rose]

12

[golden rose]

I know that d = 16, r = 8, and the period = 2pi/k so it would be 0.25 = 2pi/k

The max is 10 and min is 2

But how would I find the cosine function?

[lofty merlin]

hello

so udo u want me to find the equation of a cosine graph using the infrmation

the wave looking thing

[golden rose]

Yes please

[lofty merlin]

is the graph shifted left or right? the phase

because thats all i need to know to find it

i only know the basics of graphing trig functions :P

[golden rose]

It looks like this

[lofty merlin]

so it starts at 2?

y=-4 cos(kx) + 6, i think

wait, where did the 1/4 come from in the graph

[golden rose]

T = 1/4 sec I think

[lofty merlin]

the -4 in front of the cos is from the amplitude and the negative comes from the cos graph starting a 2 which basically means it is flipped (not correct reasoning but that is how i memorised it)

then the k infront of the x comes from the phase being 2pi/k

and the constant "+6" comes from the graph beign shifted upwards

but at the same time, i dont have too much practice on trig functions since im in year 9, so 90% i am wrong

[devout snow]

@golden rose Has your question been resolved?

[golden rose]

I appreciate it but I think that’s wrong

But that’s a step forward

Does anyone else know how to solve this?

It’s one of toughest questions Ive seen if no one know how to solve it it’s fine

[devout snow]

@golden rose Has your question been resolved?

[devout snow]

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[tender saddle]

Can someone explain what U substitution is and how it is used here?

idk if this is the right place for this