help-0

[normal minnow]

its basically functions like finding range and domain of composites and skipping sets as well as sketching functions given information

and cuz our teacher really wants us to take precalc we have the difference quotient

[glass lichen]

channel's in use unless alvan's done

[normal minnow]

okay

sorry

[glass lichen]

in use

[alpine sable]

sorry

but is it correct ?

[pulsar lark]

6^2-4(k+3)(-1)=triangle sign?

[glass lichen]

Delta, but yes

[pulsar lark]

36+4k+12=delta
48+4k=delta

[slim spire]

I guess x_g > x_1?

[pulsar lark]

I stuck at here

[glass lichen]

-4*k is 4k?

didnt know

oh wait

nvm, forgot it was -1

[pulsar lark]

So i am right so far?

[glass lichen]

yes

[pulsar lark]

What should i do next?

[glass lichen]

wdym

you're done part a...

[pulsar lark]

Really?

[glass lichen]

...

Yes

A wants a function of k for the discriminant...

[pulsar lark]

I thought it want me to find k

[glass lichen]

??

that's part b

[pulsar lark]

Ok

Give me some time to do

Forget it,i am stuck

[slim spire]

First question just asks you to find Δ

[pulsar lark]

48+4k

[slim spire]

"in term of k" just means the answer will depend on k, so something like ...k+...

[slim spire]

Perfect!

[pulsar lark]

But how about part b

[wary stream]

Do you recall the 3 cases of the discriminant?

[slim spire]

Part b is the same as before!
The discriminant Δ of a polynomial is used to tell you if there is 0,1 or 2 real roots and how to compute them ok?
For instance if Δ<0, then there are no real roots, if Δ=1 there is only one real root and if Δ>0 there are 2 real roots

[glass lichen]

"D=1"

[pulsar lark]

I know but k can be negative

[glass lichen]

also there's not only 1 R root, it's 1 R root multiplicity 2

[glass lichen]

yeah and?

[spiral perch]

Hi. How many ways can you choose a pair of compositions from white and black squares on an 8x8 board?

[pulsar lark]

It means find k if there are 2 real root?

[glass lichen]

Yes

[pulsar lark]

48+4k>0

Right?

[glass lichen]

yes.

[slim spire]

Any square can be black or white? So if there was only one square, it would be 2 possibilities. If there are two, then there is 2 possibilities for the first one and 2 possibilities for the second one and so one ... What happens if there are 64 squares?

[normal minnow]

well its 8*8 = 64 squares and there are two possible balck or white so im pretty sure 64!/2!

I might be wrong

wait i am

[pulsar lark]

2^64?

[alpine sable]

is the channel claimed ?

[pulsar lark]

Yea

[normal minnow]

its always

claimed

sadness

[pulsar lark]

Always has been

[hasty hornet]

nvm just realized i missed a step

[nova raven]

Hey i have a question.

is there any methods to finding the equation of a polynomial function given a set of points

I am already using lagrange interpolation and just wondering if there are other methods

[slim spire]

@nova raven The polynomials are unique, so I don't think so

[nova raven]

ahh so just that kk thansk

[slim spire]

But there are other (smarter) ways to interpolate! Lagrange polynomial is not really stable (try changing a little some values and you will get another completely different polynomial)

[nova raven]

thats true i did see that

what are these smarter ways

@slim spire

[slim spire]

linear interpolation lol

[nova raven]

ok but would that work for a polynomial

[slim spire]

Check that: https://en.wikipedia.org/wiki/Interpolation

[pulsar lark]

Question 1a What should I do?

[nova raven]

the determinant (b^2 - 4ac) is equal to 0

you can use that and solve for k

[pulsar lark]

Ok

[nova raven]

thank you

[fallen plank]

channel taken

?

[pulsar lark]

Wait how do you know? Where to find?

[nova raven]

kind off but i dont mind

i was pretty much done

[slim spire]

When Δ=0, it means it has only one real root, i.e. the graph of the function intersect the x-axis only once

[thorn kindle]

Double root

[fallen plank]

A lattice point in a rectangular coordinate plane is a point both of whose coordinates are integers. How many lattice points are there on a circle that is the graph of the equation x2+y2=625?

[pulsar lark]

Ok, I understand

[slim spire]

just find the integer solutions of x^2+y^2≤625

[fallen plank]

how

wdym <=, it's just =

[thorn kindle]

Equal

[fallen plank]

yes

[thorn kindle]

Sqrt625?

[fallen plank]

25

[slim spire]

as y^2≥0 then x^2≤x^2+y^2≤625 hence x≤25 and similarly y≤25, so you "only" have to try for x,y smaller than 25 lol

[fallen plank]

it's just =

[thorn kindle]

True. But you wrote it weird

[slim spire]

Sorry I read inside the circle lol

[thorn kindle]

Consider the points upon the axes first

4 of them

[fallen plank]

i can think of a couple lattice points off the top of my head: (0,25), (25,0), (0,-25), (-25,0)

[slim spire]

Then x^2+y^2=625 you could proceed the same: write a list of square for n=0 to 25 and try to find any pair that sums to 625

[fallen plank]

there has to be an easier mehtod

[slim spire]

Surely haha

[fallen plank]

instead of guess and check

[thorn kindle]

There is only one pair

And you will multiply that by 8

You should have 12 solutions

Thats it lol

[fallen plank]

wdym there is only 1 pair

[thorn kindle]

That's all the question asks. Not for the actual values

[pulsar lark]

2x^2-8kx+3k is delta?

[fallen plank]

but how do you know there's a pair

i have to show my work btw

i can't just give an answer out of thin air

[slim spire]

No this is the polynomial of degree 2 which is of the form ax^2+bx+c, the associated Δ is just Δ=b^2-4ac

[thorn kindle]

One triple (a,b,r). Then consider (plus minus a, plus minus b, r) and (plus minus b, plus minus a, r)

[fallen plank]

(20,15) works i think

but how do you know that's it

how do you know there's nothing else

[thorn kindle]

Two solutions in each quadrant plus two on each axis

[pulsar lark]

How about the y?

[fallen plank]

so in the 1st quadrant it would be (20,15), (15,20)?

[slim spire]

Which y ???

[fallen plank]

2nd - (-20,15), (-15,20)?

3rd - (-20,-15), (-15,-20)

4th - (15,-20), (20,-15)

??

[pulsar lark]

it saids y=2x^2-8kx+3k

[thorn kindle]

Wait my bad. You also have to consider non primitive triples. 15 and 20, AND 7 and 24

[fallen plank]

oh so you're thinking about it as a right triangle?

pythagorean triplets - a multiple of 3-4-5 is 15-20-25

and 7-24-25 is also an answer

[pulsar lark]

Point Q x axis is 0. Then how can i find y axis?

[slim spire]

It must lie on the graph of the polynomial! So you know that y=ax^2+bx+c (this is the definition of the graph)

[fallen plank]

bc 8 solutions for 7-24-25, 8 solutions for 15-20-25, and 4 solutions for the axis points?

[pulsar lark]

@slim spire nothing now

[fallen plank]

bc 8 solutions for 7-24-25, 8 solutions for 15-20-25, and 4 solutions for the axis points?

[thorn kindle]

Yep

[fallen plank]

PHEW

TY

[pulsar lark]

@slim spire still don’t understand.

What should i find first?

😩😩😩😩

[slim spire]

Part a) find for which k we have that Δ=0
Part b) compute the x-coordinate of Q, this is the point (x,0) at which P(x)=0

[pulsar lark]

So part a, (-8)^2-4(2)(3k) is delta?

[slim spire]

Almost! Look closely what your b is! Spoil: ||you missed the k, b=-8k hence Δ=b^2-4ac=(-8k)^2-4(2)(3k)||

[pulsar lark]

Not yet

[pulsar lark]

So y is not matter, right?

[pulsar lark]

K=3/8

[slim spire]

The graph is just the set of points (x,y) for which this equality holds. This is just the graph of the right handside polynomial of degree 2 as you know it

[slim spire]

You missed a solution! In fact there is one more ... Solution: ||Δ=64k^24k=8k(8k-3)=0 hence k=0 or k=3/8||

[harsh belfry]

Could I jump in to ask a calc question?

Or is this channel still in use?

[pulsar lark]

You can

[harsh belfry]

Thanks

I tried to do this problem but I've been having some issues.

I thought I could start by finding the slope by calculating the derivative of the given equation.

I ended up getting

I input this into a y=mx+b equation where

Then I solved for b.

But I keep getting the wrong answer on all of my submissions.

Not too sure what to do or if I did the wrong thing in the first place.

This was the equation I used.

Would I insert 1/2 in for x?

[supple tundra]

Yes. But I don't know why you make it so hard on yourself

You need to two things

The gradient of the curve at the point x = 0.5

You've found the gradient function, so just sub x = 0.5 for the gradient/slope at that point

and you can use this equation for the line

$y-y_1 = m(x-x_1)$

[ocean seal]

azeem321

[supple tundra]

Where $(x_1,y_1)$ is a point on that line

[ocean seal]

azeem321

[harsh belfry]

I'm a little confused, so would I instead solve for

then take that value and input it into the equation above?

ah wait give me a monet I think I get it now

[supple tundra]

Do you get that the derivative gives you a gradient/slope function? It allows you to find the slope at any point on the original curve?

[harsh belfry]

Would I insert 0 as y

[harsh belfry]

Yes, the derivative is the slope function.

[supple tundra]

For the equation of a line $y = mx + c$ what does $m$ mean?

[ocean seal]

azeem321

[harsh belfry]

M is slope.

[supple tundra]

Right. And you have a slope function here $\frac{3}{\sqrt{1-x^2}}$

[ocean seal]

azeem321

[supple tundra]

Which means you can substitute any value of $x$ for which it is defined

[ocean seal]

azeem321

[supple tundra]

and get the slope at that point

Wait

[harsh belfry]

I'm sorry if I'm not following but in that case would this be true?

[supple tundra]

Yes

and that will give you the slope

at x = 0.5

[harsh belfry]

would be my equation then

solving for b

[supple tundra]

Yes, but it would be better to use the exact form instead of the decimal form

[harsh belfry]

gives me

−0.16125447

for my b

[supple tundra]

That's probably correct, but it's better to use the exact form because exam questions usually ask for exact form instead of as decimal

[harsh belfry]

Yes I was about to say that

I used my calculator for that.

I'll have to solve for it manually then.

Thanks for the help azeem

[supple tundra]

np, haven't done math in a while so sorry if my explanations were a bit confusing

[harsh belfry]

Hey

[strange raven]

Hi

[harsh belfry]

I'm sorry to bother you @supple tundra

But I did write this correctly right?

[strange raven]

123 which are natural numbers also come under the umbrella of real numbers right?

[harsh belfry]

It appears to be incorrect still.

[strange raven]

???

[flat ermine]

yes, natural numbers are real numbers

[strange raven]

@flat ermine thankyou

[harsh belfry]

Maybe I have the wrong B value

[supple tundra]

You must substitute x=0.5 into $\frac{3}{\sqrt{1-x^2}}$ and that will give you the m they want

[ocean seal]

azeem321

[harsh belfry]

ah they would want this then

[supple tundra]

correct

[harsh belfry]

very weird to me

thanks again

Ah i guess the B is incorrect if you change the value of X

I see

Nevermind.

[atomic lodge]

Can anyone help me understand what’s concave up and down

Like I know the shape of the graphs but I am confused

[supple tundra]

Never liked that concave up, concave down stuff. Basically, if a function's derivative is increasing over an interval, then it would be like a positive quadratic on that interval which is concave up or some call it convex. If a function's derivative is decreasing on an interval, then function would called concave down or just concave

[grim delta]

thats one of the many things i did in Calc 1 and then promptly forgot about

[supple tundra]

Note that, if a function's derivative is increasing, it doesn't necessarily mean that it's derivative is positive

It just means the slope of the function is increasing or becoming less negative

[atomic lodge]

Thank You for your help!! @supple tundra

[supple tundra]

Did you get it?

[pulsar lark]

Can i use the channel?

[supple tundra]

ya

[pulsar lark]

Thx

How to solve Question (a)?

[supple tundra]

Have you learned about complex numbers?

[robust geode]

You know that real and imaginary numbers can never be melted in order to make a single number, right?

[pulsar lark]

a+bi?

[lapis sluice]

that is cartesian yes

[wary stream]

Because it's an equation that means the LHS equals the RHS, so that means you can set the real terms equal to each other and the imaginary terms equal to each other

[pulsar lark]

So 2x wont be -yi?

[robust geode]

Just know that i is just here in order for you to k ow that the number by which it is multiplied has an other purpose than the other number

The imaginary part is real, as much as the real part

It's just that the imaginary part is always what's being multiplied by i

[wary stream]

Technically, this is false because if you use Pythagorean theorem, you can get a single magnitude with an angle

But that's with magnitude

[robust geode]

I'm not checking any single piece of rigourosity for his own understanding

[pulsar lark]

Ha?

Ok, so x=4, y=-5?

[robust geode]

Yup good job

You got it

[pulsar lark]

But how do i express it?

[wary stream]

Exactly like how you did

[robust geode]

Just use a factorisation

As you have normally done before

[pulsar lark]

Just like this?

[robust geode]

Could we talk in vc maybe?

It will be easier to explain if I talk lol

[pulsar lark]

I cant speak English…

But i can listen

[robust geode]

I will try my best in order to not have an accent and be as clear as possible

[wary stream]

That's a valid way to represent the answer

[crisp widget]

Can someone help me?

[quasi lodge]

anyone can help e

me

grade 8

[full marsh]

@quasi lodge not unless you send question

[brittle steeple]

heyy can someone help me rq

and tell me what this means

you can also just tell me the answer and I can make a pretty good guess how u got it

[azure jungle]

Derivation. Derivate it once. Number 3, task a) and f)

[wary stream]

No, we're not here to give you answers

[brittle steeple]

okay then can you give me a hint on what the heck the two means

[wary stream]

Use log properties

And that 2 is an exponent

[azure jungle]

need help on how to solve it

[brittle steeple]

so its log, base 3 1/3 squared?

[wary stream]

,rotate

[brittle steeple]

@stable basin thanks luv u <3

[wary stream]

Not the right person that you pinged but welcome

[azure jungle]

can u help me dldh06 ?

[wary stream]

What's the goal?

[azure jungle]

need help on number 3 task a and f, idk how to derivate it

[brittle steeple]

close enough right?

[wary stream]

Someone else got the ping so not really

[wary stream]

Power rule

Do you know power rule, chain rule, product rule?

Because you need the knowledge of all three to do those questions

[azure jungle]

we were not taught any power rules that i see on the net, we were only learned taught this f(x) = uv(x) + v(x) so it means f´(x) = u´(x) + v´(x)

[brittle steeple]

||@wary stream thanks luv u <3 ||

[azure jungle]

and idk how to use this rule in this task

[wary stream]

Do you know if given $f(x) = x^n$ then $f'(x) = nx^{n -1}$?

[azure jungle]

better said, idk what to do with the last number

[ocean seal]

dldh06

[wary stream]

That concept

[azure jungle]

yes

[azure jungle]

hence, why i dont know what to do with the last number that doesnt have an x

in a) its +3

[wary stream]

It's a constant

[azure jungle]

4x^2 will be 42x

[wary stream]

Derivative of constant is 0

[azure jungle]

so it just "dissapears" ?

[wary stream]

Yes

[azure jungle]

ahh

what about f) tho ? i never saw that task as an example

[wary stream]

It's just applying all the derivative concepts, like power rule, product, and chain rule

[worn prawn]

Hello can someone show me how to do these

[azure jungle]

1 more question.

in task a) at 8x, the derived version is 8 times 1 and thats it ? x dissapears ? or do i do 8 times 1 times x^0 or 8 times 1 times x^-1

[alpine sable]

tari for 117

use this

i dont rly know the name of it in english but im sure you know what this is

[worn prawn]

Asks for ac method:'(

[worn prawn]

Tyvm for the help ☺️

[azure jungle]

this is correct,yes ?

i still don't understand the brackets in derivation... do i have to solve the bracket before derivation ? like, what's the rule here

[wary stream]

Chain rule

[azure jungle]

but we didnt learn that

wth

[raw shard]

you don’t need to use it

you could just expand it

[wary stream]

That too

[raw shard]

which they did

[azure jungle]

how did they expand it ? i was sick that day so i could just write everything from a friend.. idk why is there suddenly -12x in the bracket and why is it +9 instead of -9

[wary stream]

Because $(2x - 3)^2 = (2x-3)(2x-3)$

[ocean seal]

dldh06

[wary stream]

Then you FOIL

[azure jungle]

we were only taught
Derivation rule for power function
Derivation rule for products
and
Derivation rule for sums

[raw shard]

do you know how to expand something like (x+y)^2

[azure jungle]

idk what do you mean by expanding, i didnt learn this math in english

[azure jungle]

ohhhh

[wary stream]

That's what quantum was referring to, too

[azure jungle]

okay, let me try to solve 3 d) and i will show you the results, could you tell me i got it correct, please ?

[raw shard]

yeah

[alpine sable]

can someone tell me why the first condition is impossible

[sand geode]

hi @alpine sable

[alpine sable]

hi

i need some help in proofs and logic

is there anyone active?

[sand geode]

@alpine sable em que quadrante encontramos o x-pi/3?

[alpine sable]

(p or q ) and r
if p=F
q=T
r=T

I did long division and synthetic division and it says this is incorrect

[azure jungle]

please tell me im correct

[raw shard]

i don’t know what the second to last line says

[azure jungle]

16x^2 + 12x * 12x + 9

[alpine sable]

se não sei a amplitude de x como haverei de saber?

[raw shard]

that’s wrong

it’s 16x^2 + 24x + 9

[sand geode]

a amplitude da função é 1 @alpine sable

[alpine sable]

ahhhh já percebi obrigado

[sand geode]

tem certeza?

[alpine sable]

quase certeza

[azure jungle]

24x ? but it
(4x + 3) * (4x + 3)
i have to multiply first number in the first bracket with both numbers in the second bracket
and then multiply the second number from the first bracket with the both numbers in the second bracket
so : 4x times 4x is 16x^2 + 4x times 3 which is 12x, so 16x^2 + 12x so far
then 3 times 4x which is again, 12x and 3 times 3, which is 9
so 12x + 9
all together it's : 16x^2 + 12x * 12x + 9
so derivation comes in play now:
32x + 12 * 12

how do you get 24x

[teal sun]

i need help

[alpine sable]

ficaria 0x = pi/3 +2kpi e nao ha nenhum numero para k que dê 0 certo?

[teal sun]

i need the area

[raw shard]

@azure jungle (a+b)^2 = a^2 + 2ab + b^2

[azure jungle]

omg im so dumb

tnx

[raw shard]

no problem

[sand geode]

https://tenor.com/view/the-promised-neverland-ray-yakusoku-gif-18347094

[alpine sable]

:) obrigado

[azure jungle]

sry 1 last question, how do you get 16x^2

[raw shard]

@azure jungle you didn’t do (4x)^2

you only did 4x^2

[azure jungle]

does every x number has to be in brackets ?

when expanding

[raw shard]

what do you mean

[alpine sable]

Not tryna be rude but i cant understand some of that hand writing

[nocturne gazelle]

F

[raw shard]

the only thing that looks weird to me is the 9

[azure jungle]

why does it have to be in brackets

[azure jungle]

wdym it looks weird

[alpine sable]

Anyone wanna help me multiply 3(4) i reallly dontntntntn know

[azure jungle]

yeah.. i get it a lot, its just how it is

[alpine sable]

It might be 405

Idk tho

Somebody said it was 12

They lying

[hasty hornet]

An astronomer suggests that on average 1.31 meteorites strike the earth per month. We assume that the number of meteorites that strike the earth per month follows a Poisson distribution. Find the probability of having no meteorite strikes in a month.
Is 1.0686 correct?

[flat ermine]

1.0686 is bigger than 1

[hasty hornet]

idk anything lol

[flat ermine]

so it cant be right since a probability cant be bigger than 1

[hasty hornet]

oh yea

[azure jungle]

you still there ?

[raw shard]

yes

[azure jungle]

why the brackets ? how do i know when do i have to use the brackets ?

[raw shard]

you have to square 4x

not just square x and multiply it by 4

wait this channel is in use

[azure jungle]

i got it now, thanks a lot man, really helped me out :))

[flat ermine]

the poisson distribution is $P(x;\lambda)=\lambda^{k} \cdot \frac{e^{-\lambda}}{k!}$

[ocean seal]

roobix

[flat ermine]

idk how you got 1.0686 but you should use that; (\lambda) is the number of average occurrences

[ocean seal]

roobix

[hasty hornet]

thanks

what is k?

i followed this before lol

[flat ermine]

basically same as x in that picture

[hasty hornet]

ok

[flat ermine]

its how many occurrences there really are so 0 in this problem

[hasty hornet]

$1.31^{0} \cdot \frac{e^{-0}}{0!}$

[flat ermine]

i think that should be (1.31^{0}\cdot \frac{e^{-1.31}}{0!})

[hasty hornet]

whoops

[ocean seal]

roobix

[lapis sluice]

can you end a task with $\blacksquare$ when you havent proved anything, but only answered the task?

[hasty hornet]

what is cdot

[ocean seal]

Danajax

[flat ermine]

"center dot"

[hasty hornet]

does it mean multiply

[lapis sluice]

means multiply

[hasty hornet]

ty

woo i did it

answer is 0.2698200564

[alpine sable]

question is there a math promblem that isnt solved

[flat ermine]

i don't really think you should because you haven't finished a proof

[flat ermine]

https://www.claymath.org/millennium-problems

[atomic dune]

i feel kind of stupid for asking this but I always sucked at factoring and I'm not sure how they factored 10(x-5) from this. I can see how the (x-5) would get pulled out but I'm beyond lost as to how they got that answer. Sorry if this is a dumb question but my brain is fried 😅

I'm also really not sure where the 10 before (x-5) came from

[civic jungle]

I think many steps were skipped

It was inviting you to do the algebraic computation yourself probably

Solutions that do that are promoting reader independence

[vale sapphire]

when you multiply the coefficients in the first parenthesis by 2, both of them are divisible by 10

and in the second term, the 10x-10 is divisible by 10 also, so you can factor a 10 there as well

then notice that in both terms you have an (x-5), so you can factor that

just like 4*2+4*9 = 4*(2+9) because there's a 4 multiplying both terms

[atomic dune]

oh holy shit yeah you're right, let me give it a shot from here. I can't believe I missed that

[rain mason]

can someone help with this?

i'm pretty sure that the curvatures are all the same and the tangent vectors can be one of two opposite vectors but i don't know where to start or how to prove that

[past sundial]

When they mean x is 5 times as many as y does it mean 5x=y

[vale sapphire]

yes

[muted kite]

"If log4 3 = x, then in terms find log8 72".

How do I solve this?

[raw shard]

@muted kite i can maybe help although i might be bad at explaining it

so you have log4(3) = x, this also means 1/log3(4) = x

[muted kite]

the inverse of the log flips the base and argument?

[raw shard]

we can do 1.5/1.5 * 1/log3(4) = x

yes

[muted kite]

I never knew that

[raw shard]

so that turns to 1.5 * 1/log3(8)

then that turns to 1.5 * log8(3) = log8(3^1.5)

now they have the same base

[muted kite]

reduce

I don't get it fully but I'll try to write it down on my paper and see if I can get a better understanding

I get the order

[raw shard]

you can test it with log3(9)

the base flip

now i’m actually not sure what to to from here, i just thought doing this would help

[muted kite]

it did help, thank you very much 😃

[raw shard]

no problem

[muted kite]

I just needed a little guidance like this to get me started

much appreciated

[cursive cobalt]

I'm not good with logs

🥴

[muted kite]

wait did you mean 2 instead of 1.5?

[raw shard]

no

[muted kite]

wait wait

no

[raw shard]

4^1.5 is 8

[muted kite]

I was thinking multiplication whoops

[raw shard]

i did that to get the same base

lol

@muted kite actually i think it would be better it the base was 64

because then it would be only integers

[muted kite]

oh I see

[muted kite]

if we use the inverse law to flip 3 and 8, wouldn't 1.5 become the denominator?

or am I thinking of something wrong

[raw shard]

remember if you have n*loga(b), that equals loga(b^n)

can you explain your question more?

[muted kite]

so 1.5 is the numerator currently, and the log is the denominator

[raw shard]

yeah

[muted kite]

I was wondering how the denominator become 1 instead of 1.5

[raw shard]

so we started with 1.5/1.5 * log4(3)

which is the same as 1.5/1.5 * 1/log3(4)

so multiply the two denominators

it turns to 1.5 * 1/log3(8), or 1.5 * log8(3)

[muted kite]

ooooooh

I was putting 1.5 and 1/log together

I forgot I could separate them and then reciprocate just 1/log

im so dumb lmao

[raw shard]

lol

[muted kite]

ty for clarifying that

[raw shard]

no problem

remember to change the base to 64

so it’s all integers

[muted kite]

ok, tysm for your help

I'll leave you alone and work on this

[raw shard]

ok, if you need help you can ask more questions of course

[rain mason]

can someone help with this?
i'm pretty sure that the curvatures are all the same and the tangent vectors can be one of two opposite vectors but i don't know where to start or how to prove that

[slim spire]

What is the definition of tangeant vectors and curvatures?

[rain mason]

the unit tangent vector is the unit vector tangent to the curve at that point and the curvature is |dT/ds|

where s is the arclength function and T is the unit tangent vector function

wait are you asking because you don't know or because you want to help lol

[slim spire]

Unit tangeant vectors doesn't depend on speed at which you go

[hollow cedar]

https://tenor.com/view/differentiation-steven-eshay-swimmin-gif-21167265

is it

18x^2 -9

?

[vale sapphire]

it is, but this has to be one of the strangest ways i've seen someone convey a question

[small bear]

No, is having 90% chance at 2 tries the same as 180% chance the first try?

What are you given? The probability that you can get something in 4 tries is 5%?

[rain mason]

take 1 minus the probability that you will fail every time

so 1 - (95/100)^4 i think

the possibility that it will happen at all (i.e. be triggered at least once) is about 0.1855

i don't think so i just thought it up

[small bear]

Complementary probability perhaps

Probability

[rain mason]

<@&286206848099549185> i've asked this question for like an hour and i haven't gotten any responses

[rich basin]

(b)

I tried multiplying point B by i because there is a 90 percent rotation anti clockwise, but it doesn't seem to work

[slim spire]

Because its 90° anti clockwise rotation but not centered at (0,0) !!!!

Try first to compute the vector AB as asked :p

[rich basin]

Oh right, this is not a 90 percent clockwise from the O origin

so it wouldn't work

@slim spire Is this right?

[slim spire]

Exactly!!

[rich basin]

@slim spire oh right I did it a different way and managed to get the answer

Okay thanks

[slim spire]

There is always multiple ways to find the answer ;p

[rich basin]

What is the fastest way?

[slim spire]

It's a fun exercise to try to find other ways of thinking haha

[rich basin]

yeah

[slim spire]

I dont see faster than computing AB to find the coordinates C or D 🤔

[rich basin]

wait how would you find D?

i think what i did was times i by B

and then added the vector B-A

Which doesn't seem to make sense given that Bi shouldn't be equal to C

[slim spire]

Compute vector AB -> -5+12i and rotate it 90° by multiplying by i -> -12-5i and add to A -> -3-4i

[rich basin]

why did you rotate AB?

[worthy adder]

how to find the x-intercept of x^4-8x^2+8=0

[slim spire]

To find the perpendicular vector of AB to the left, i.e. AD as drawn above

[green thicket]

this isn't really a question about a math problem

but I wanted to ask

how long would it take

to learn how to factor polynomials

I'm really bad at it and I have about 2 hours to study since I might take a retake for the quiz tomorrow

but I might take the retake on Wednesday if 2 hours to learn it isn't enough

[placid zinc]

Any polynomials? Or quadratics?

I mean start, imo. Get on YouTube and learn haha

[glass tree]

Help? Not needed for homework or anything, I'm just making something that requires a solution to this.

Or more specifically, define 3 of the 4 unknowns in terms of a, b, c, and the forth unknown.

[green thicket]

polynomials

[wanton spoke]

To help out a classmate in need, the students of 9-Strontium decided to send a cash aid of $2 000. The students shared the cost equally. At the last minute, 10 students from the SSG chipped in, lowering the contribution per person by $10 for each student. How many students are there in 9-Strontium?
I have two questions for this solution:

1. Why did he subtract 10 to c? c-10
2. Why are we subtracting the second from the first?

[glass tree]

also might be important to note that I want j, l, z, and t to end out as integers

[slim spire]

The cost by person is c, and it became c-10 this is why c-10 is appearing

[wanton spoke]

how did it became c-10

[slim spire]

You could also substract the first from the second, matter of taste
The point is that the c cancels anyway!! (It's just solving a linear system of equations)

[slim spire]

"Lowering the contribution per persom by 10$"
It's just what is given here

[wanton spoke]

oh i see

[glass tree]

Can someone help me with my probem? I have no idea how to do it

or even where to start

My guess is that it's a system of quadratics but idk how to solve those and I can't find anything that shows how when you have many variables

[slim spire]

Your problem seems so weird lol

Try factorizing using the identity (a+b)^2=a^2+b^2+2ab
Hint: you can generalize to (a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc

@glass tree

[glass tree]

Yeah the thing I'm making requires some really weird math

[wanton spoke]

Hello again. Sorry, I just didn't understand it well. So the equation c-10=2000/n+10 and c=2000/n are a linear system of equation. And, in order to solve it, we need to subtract the second from the first. Then we will solve for n to find the numbers of student, and hence, solve the problem, is that right?

[slim spire]

PERFECT
And why substract the 2nd from the 1st anyway? Because it will gives us a new equation where the variable "c" will disappear and we can easily solve it for "n" as you correctly guessed GG!!!

[wanton spoke]

alright, thank you!

[mossy kelp]

how would I go about solving this? not really sure where to start, im prolly overthinking it, but I'm not really sure

[slim spire]

As codf = Y then |codf|-2=3 you must choose a function whose range is less or equal to three images among the 5 of Y

For instance you could choose a range of only one image: a
This means I send 1->a, 2->a, 3->a and 4->a, then rng(f)={a} has size 1 where cod(f)=Y has size 5 and 1 is less or equal to 5-2=3
Hope you understand @mossy kelp

[mossy kelp]

yeah i think i understand

thanks

[primal hatch]

what’s 1+1

[charred pier]

nevermind I found out, sorry for the bother

[primal hatch]

okay

[toxic meadow]

i need assistance

[slim spire]

50(1.2)=60 and 60(1.2)=72 where 1.2=120% of the population

[toxic meadow]

i did that

that’s why i’m so confused

is it broken 🤣

[slim spire]

Broken

As hell lol

Sorry @toxic meadow

[toxic meadow]

it’s all good

[slate kayak]

In comparison to 1996 the expenses rised with 63.5% in 2002. In 2007 these expenses were 19.4% more than 2002.

with how many percentage are the expenses in 2007 higher than 2002?

Hi idk how to do this

I was given formulas like new = (1+ p/100) x old

But idk how to use that here

[slim spire]

Use it multiple times

[slate kayak]

What is the “old” the first time then?

2002 vs 1996
63.5% vs 0%
?

[slim spire]

First time: in 2002 we have 163.5% the expenses of 1996
In 2007 we have 119.4% the expenses of 2002
Hence in 2007 we have 119.4% * 163.5% the expenses of 1996

[slate kayak]

Oh like that

Thnx

[late parcel]

Is this channel open

[slate kayak]

Yes

[late parcel]

Can someone check this

[slate kayak]

That looks like a test

[late parcel]

It’s not look at the top, it says practice

[slate kayak]

srry

[slim spire]

,w plot int_1^x 100(t^2-3t+2)e^(-t^2)dt from x=(1,3)

[late parcel]

Wait what

[slim spire]

Lol nvm

[late parcel]

They are all true right?

Wait

[ocean seal]

Results provided by WolframAlpha

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

Requested by SkyTwX#9807

[slim spire]

🤔

Now think about why

[late parcel]

Wait is it actually E?

[slim spire]

e=2.718281828459045... is a nice EXPonentiation constant

[late parcel]

The letter choice E

1 2 and 3 are all true

[slim spire]

Lol sorry not it's II only

[slim spire]

Check the graph it decreases from 1 to 2 and g(3)<0

[late parcel]

Wait what

So it’s B?

[slim spire]

Yeppp

[late parcel]

Thx

[slim spire]

Np

Btw true way to answer is that integral of f is increasing iff f is increasing

[late parcel]

Thank you

[slim spire]

,w (d/dt t^2-3t+2)=0

[ocean seal]

Results provided by WolframAlpha

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

Requested by SkyTwX#9807

[devout summit]

But integral increasing doesn't mean function is increasing right?

Consider the function e^{-x}. It's integral is -e^{-x} which is increasing but the function is decreasing

[late parcel]

I have another question

57

Somehow the answer is A

This is what I have

[slim spire]

Exactly, think about the meaning of are under the curve: if f is increasing and positive then integral of f is also increasing, ty for the remark Im saying bs sometimes lol

[late parcel]

I have the second derivative

But am stuck from here

[slim spire]

@late parcel concave means f''(x)<=0

[late parcel]

Yep

I knew that

But how does that help for A

The A is confusing me

[slim spire]

Then 6ax+6<=0 solve for x

,w 6ax+6<=0 solve for x

[ocean seal]

Results provided by WolframAlpha

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

Requested by SkyTwX#9807

[late parcel]

How do you solve for x when there is an a

[slim spire]

Tadam

Think of a as a number like 5 or -5 depending on if it's positive or negative

Then proceed like usual

[late parcel]

What number do you use

[slim spire]

The letters represent just some numbers so think about them as numbers

[late parcel]

What number do you use

[devout summit]

Concave up means f''(x)>0

[slim spire]

Duuuuude english is weiiiird

Thank you lol

Im so choked it is not concave and convex but anyway

[late parcel]

Umm so what number would you use

Anything?

[devout summit]

,w 6ax+6>0, solve for x

[ocean seal]

Results provided by WolframAlpha

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

Requested by Euclid31415#9927

[shut parcel]

$399 is what percent more than $189?

[slim spire]

The best is just to use "a" but remember it represents a number

[slim spire]

399/199*100 simply

,w 399/189*100

[ocean seal]

Results provided by WolframAlpha

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

Requested by SkyTwX#9807

[devout summit]

Look at the first case. x<(-1/a) when a<0

[shut parcel]

I got an answer of 111.11%

[late parcel]

Occupied channel

[slim spire]

It is rather 211.11%

Im leaving

I need sleep

Bye friends

[late parcel]

Wait

What about my question

Almost done @slim spire

Can’t leave me hanging like this

[shut parcel]

Wouldn’t the original price be $189?

[devout summit]

.

[late parcel]

@devout summit I get a

How does that help

[devout summit]

What percent more means ((399-189)/189)*100

[devout summit]

$ax>-1\implies x<\frac{-1}{a}$

[ocean seal]

Euclid31415

[shut parcel]

More means add, right

[devout summit]

Sign flipped because a<0

[late parcel]

Can you elaborate on that

Why flipped sign

[shut parcel]

Anyone else got an answer of 111.11%?

[late parcel]

You flip sign whenever you divide by a negative

Is that how it works

[devout summit]

If you asked how much is 10 more than 5, you would do 10-5 wouldn't you?

[late parcel]

Is it divide or multiply by a negative? Or just divide @devout summit

[devout summit]

If you have x>y, ax<ay if you take a<0

[shut parcel]

You got 111.11%, right

Why did another person say 211.1%

[late parcel]

What

[shut parcel]

I got an answer of 111.11% but someone said the answer is 211.11% so I’m confused now

[late parcel]

Why is it A and not C

Couldn’t it also be C

[devout summit]

If you multiply a negative constant on both sides of an inequality, the inequality flips

[late parcel]

Ok

So I think it could be A or C

Look at this

[shut parcel]

Hey euclid can u help me

[late parcel]

@shut parcel this channel is occupied

[devout summit]

I multiplied by (1/a) on both sides here which is negative

[late parcel]

Ok I understand that

But why does C not work

It could go to positive infinity

[devout summit]

No it cannot!

[late parcel]

Why?

[devout summit]

x<-1/a

[late parcel]

But that’s just for a critical point

So X is bigger than that number

[devout summit]

No! for example, $x<3\implies x\in (-\infty,3)$

[ocean seal]

Euclid31415

[late parcel]

Ok correct

I follow that

Ohhhhhhhhhhhhhhh

I see now

I see

Thank you

[shut parcel]

So euclid lol

Can u help me with my hw lol

[devout summit]

They didn't subtract 100 from 211.11

[late parcel]

@shut parcel thanks for the patience, good luck with your problem

[shut parcel]

Thank u misty

Ok so i was right about it being 111.11%

[devout summit]

Yep

[shut parcel]

What sum of money decreased by 89% will amount to $235?

I got an answer of $2,136.36

[alpine sable]

x-.89x=235

[wary stream]

Why were you posting in multiple channels?

[shut parcel]

Bc this server was in used

[devout summit]

Decreased by 89% means 11% remains

[shut parcel]

Yes

But its asking the sum of money

[devout summit]

Let the sum of money be x.
Then, x(11/100)=235

[alpine sable]

.11x=235

[hard ether]

how do you do this

[shut parcel]

I’m confused now

[quiet forum]

euclid can u ans my calculas's question?

[shut parcel]

So the answer is $21.36

[queen mural]

can somen plz help

in descrete sturcuters

[glass lichen]

discrete structures

but yeah... on what question?

[queen mural]

the 2nd one

Let d be the set of finite functions

[glass lichen]

T(15)?

oh 2nd question

yeah what about it?

[queen mural]

idk how

i dont understand what its asking

[glass lichen]

it wants you to plug in some integers into T

and get the set from D

[queen mural]

can we meet in math vc?

[glass lichen]

no

[queen mural]

how would i write it?

[glass lichen]

for example, $T(p)={1,p}$ for any prime p

[ocean seal]

Mosh

[robust geode]

By {a, b, c,...}, you enumerate every integers for which T(x) can be equal to

[queen mural]

T(1)=(1)n?

[robust geode]

Be really careful about how the function is defined

You insert an integer

[glass lichen]

no

the output is a set

[robust geode]

And you get a result in D

And D is a set of sets

[glass lichen]

what are the positive divisors of 1?

[queen mural]

1

[cursive cobalt]

Which of the following is true? Select all that apply.
(A) If a number has only even powers in its prime factorisation, then it is a square.
(B) If an integer n has an odd number of factors, then n is a square number.
(C) If a number has only multiples of 3 in its prime factorisation, then it is a cube.
(D) If a number has n factors, and n is a multiple of three, then the number is a cube.

[glass lichen]

so what's the set that contains 1 and only 1?

[glass lichen]

in use

[robust geode]

Remember, just like {{0, 1}, {1,2,3},...}

A set of sets

[glass lichen]

positive integers

[cursive cobalt]

huh?

[queen mural]

1?

[glass lichen]

The channel is in use

1 is not a set

[queen mural]

im so sorry im a visual learner this is killing me

[glass lichen]

sets need proper notation

[robust geode]

I'm describing what a set of sets is from a previous session together, I know what I am saying lol

[slate kayak]

I tried forming an equation of a plane but it doesnt work

[robust geode]

Remember what a set is

In this case, a finite set

[queen mural]

ye

[devout summit]

Set of divisors of n\\=$\left{d\in \mathbb{Z}^+\mid n/d\in \mathbb{Z}^+\right}$

[robust geode]

Then since D (the set of things that the application T returns)

[ocean seal]

Euclid31415

[glass lichen]

I wouldn't worry about the explicit formula

@devout summit

[devout summit]

Ok yeah it can be written in elements...

[robust geode]

Since D is from the definition of the application T, a list of integers in which the number x in T(x) is divisible by

[glass lichen]

Nah, just the concept of it is sufficient

[robust geode]

Then the result of your application is simply a set

And in this case, regarding the results of T, a set of all the positive integers that your integer can be divided by

D is just a name used arbitrarly, it could be B or F or whatever

It's not an official name

Just to be clear

Maybe explaining it in vc might be better for you

[keen sandal]

Can someone please offer me some advice for this problem? I honestly have no idea where to start...

[cursive cobalt]

Which of the following is true? Select all that apply.
(A) If a number has only even powers in its prime factorisation, then it is a square.
(B) If an integer n has an odd number of factors, then n is a square number.
(C) If a number has only multiples of 3 in its prime factorisation, then it is a cube.
(D) If a number has n factors, and n is a multiple of three, then the number is a cube.

I am confused

nvm got it

[slate kayak]

The following points lie in one plane:
A (a,0,0)
B (0,2a,0)
C (0,0,a+1)
D (2,-1,2). Where (a ≠ 0)

What’s the value of a?

[civic jungle]

This sounds like a problem solving question

[devout summit]

You know vectors?

If you do then, $(\overrightarrow{AB}\times \overrightarrow{AC})\cdot \overrightarrow{AD}=0$ ensures the condition.

[slate kayak]

Yeah i know vectors

Oh

I didn’t know that formula

[ocean seal]

Euclid31415

[slate kayak]

I didnt know that formula existed so thanks

[civic jungle]

That's just a gimmick for the 3x3 determinant of the matrix formed by AB, AC, and AD

If you write the computation out

[slate kayak]

Ohh

[devout summit]

Exactly. Scalar triple product

[slate kayak]

Ok i’ll do that and see if it works

[amber frigate]

can someone help rq

pls

[slate kayak]

@devout summit Srry for ping but I get a = 0 v a = 2 but in my book it says the answer is a = -0.5 v a = 3

Should i send a pic of my work ?

[devout summit]

Ok…

[slate kayak]

@devout summit here ^

[devout summit]

That is supposed to be cross product inside parentheses

[slate kayak]

Oh

Okay

[harsh belfry]

Hey is this channel still being used?

[slate kayak]

No

[harsh belfry]

Thanks

I've been looking at this for while and I have a true statement
However upon adding +1 to the left side of the equation I'm not sure how to make the right side true

[slate kayak]

Np

[cursive cobalt]

How many factors of 2520 are even?

I got 36

[harsh belfry]

In this instance I was unsure how to make the statement true.

What happens to the one?

Would appreciate any insight.

[devout summit]

You would have to replace x^2 here by x^2+16

[harsh belfry]

I was wondering if the 1/4 is technically still being divided by 1 would the equation look like this

o

[cursive cobalt]

Sorry to interrupt, but
How many factors of 2520 are even?

[harsh belfry]

Is there any chance you could explain why

[harsh belfry]

should be correct btw

[cursive cobalt]

thx

[devout summit]

$\frac{\frac{1}{4}}{\frac{x^2}{16}+1}= \frac{\frac{1}{4}}{\frac{x^2+16}{16}}=\frac{1}{4}\cdot\frac{16}{x^2+16}$

[ocean seal]

Euclid31415

[cursive cobalt]

can I be a helper?

[harsh belfry]

oh so you added the one to make this simpler

I see

wow that explains alot

oh man this was so simple

[mellow tinsel]

I'm trying to find the determinant of an identity matrix subtracted by an n*n matrix.
Does this make sense?
|In-A|=|In|+|-A|

[harsh belfry]

Thanks a bunch euclid

[devout summit]

If you think you can answer the question, go for it!

[scarlet heath]

is the channel free rn?

[mellow tinsel]

I'm hoping someone can quickly respond to this

[devout summit]

I don't think this is true in general...

[cursive cobalt]

yes

[mellow tinsel]

I think you're right.

I'm trying to prove that In-A is invertible by getting it's determinant but I don't know where to start.

[devout summit]

In-A is invertible if A is invertible? (not true either)

[mellow tinsel]

I don't think A invertible in this case.

I'm given that A^21=0n.

[worn prawn]

X^2+bxy+cy^2 anyone know how to solve this problem with this equation >.<

[pearl solar]

there's no equation to solve there

[sick scaffold]

so, how would I use the log quotient property where loga-logb= log(a/b) when there are 3 values, so for example loga-logb-logc

[wary jungle]

can someone help me find dy/dx

<@&286206848099549185>

[wary stream]

Quotient rule

[wary jungle]

i dont get it

[wary stream]

You use the quotient rule to find the derivative

[wary jungle]

my answer isnt one of the options

[wary stream]

Then you probably did it wrong

[wary jungle]

-2x(x-3)/3(-2x+3)^2 is what i got

are you able to get one of the options

[worn prawn]

So what do I write?

[harsh belfry]

Should I post my question elsewhere? 😅

[wary jungle]

probably

[wary jungle]

i put it into a calculator and got the same thing

except positive

so i did something wrong still

[worn prawn]

Need help with this as well v.v

[wary jungle]

whats the question asking for here

[wary stream]

One, you did math wrong because I did get an answer that is an option, and 2, online calculators simplify so that's why it looks like that

[wary jungle]

what is the math i did wrong

can you explain the steps

other than saying do the quotient rule

like the process

[wary stream]

What do you get when you do quotient rule?

[wary jungle]

man idk

[wary stream]

What is quotient rule?

The formula

[wary jungle]

this

[wary stream]

So apply it

[wary jungle]

how

what is the process

[wary stream]

You have the formula, just apply it to the question you were given

[wary jungle]

how

[wary stream]

What's g(x) times f'(x)?

[worn prawn]

I'm lost rn was that for me

[wary stream]

No

[worn prawn]

Okie

[mortal mantle]

how do i know weather to integreate with respect to x or y

[clever folio]

You should be able to either iirc but typically one is easier than the other

Sometimes it doesn't matter and both are ez or hard.

[mortal mantle]

yeah i tried with both in the question but im only getting a single point that they intersect

i think you should find 2 points that intersect right?

and then make them your bounds

[clever folio]

I'm pretty sure they do intersect at two points.

Are you making an error while graphing?

[mortal mantle]

oh im supposed to do this without the graph

[clever folio]

Try y=7 and -7

[mortal mantle]

wait both factor into the same thign

x-7 and x+7

[clever folio]

My point is they intersect at (0,7),(0,-7)

[mortal mantle]

yeah i understand that

idk how i didnt think of that

[clever folio]

You can solve it algebraically for the intersection by noting 49-y^2 = x = y^2 - 49 I think.

[mortal mantle]

yeah i tried that but maybe i just did the math wrong

since it only gave one intersect

[clever folio]

Then solve for y so 2y^2 = 2(49) hence y^2 = 49 so y = 7 or -7.

Did you take both the positive and negative square root?

[mortal mantle]

no

but i got the answer

i was just being dumb

i got one more if you are able to help

[wanton spoke]

To help out a classmate in need, the students of 9 Strontium decided to send a cash aid of $2 000. The students shared the cost equally. At the last minute, 10 students from the SSG chipped in, lowering the contribution per person by $10 for each student. How many students are there in 9-Strontium?
In this solution, why are we subtracting the new cost equation from the original cost equation? Why should we not just solve for n in the new cost equation?

[clever folio]

I can't guarantee I'll know the answer but I don't mind looking

[mortal mantle]

its this one

i stuggled with this on my exam as well this same sort of concept

im just not sure how to approach it to begin with

so any guidance would be appreciated if you can

[clever folio]

Could it be integration by parts?

It's either that or u sub I bet.

This channel is occupied.

[mortal mantle]

none of those

its something about isolating the integral

but im not too sure

[sacred ledge]

hello

[clever folio]

Gimme a sec my calc is rusty as hell

[sacred ledge]

I need help to find the formula for this question

Over a short interval near time t = 0 the coordinate of an automobile in meters is given by x(t) = 27t − 4.0t3, where t is in seconds. At the end of 1.0 s the acceleration of the auto is -24 m/s2

just the formula please, thank you

[mortal mantle]

no worries, i already appreciate the help you gave 🙂

[clever folio]

Yeah I'm def still thinking it's ibp

Since you have g'(x) in ur integrand let dv=g'(x)dx and let u=x

Pretty sure when you work the ibp out you get the integral of xg'(x) on the lhs and on the rhs something you can evaluate using your given formulas

[mortal mantle]

so waht would our dv and u values be in this case

if we do ibp

[clever folio]

dv=g'(x)dx and u=x so v=g(x) and du=dx.

[mortal mantle]

hmm let me try it

[mortal mantle]

i treid it and i did not get it

i think i might leave it for todayt

and come back to it another day

[clever folio]

What expression do you get after ibp?

[mortal mantle]

whe n i did everything it was -5x^2+c

i think my brain is just done rn lolol

[clever folio]

Hmm so I get $xg(x)-\int g(x) \dd{x}$.

[ocean seal]

DootDooter

[thorn kindle]

Ok.

[clever folio]

There's a formula that lets you do the difference on that xg(x) bit and to use the definite integral.

It's just another version of ibp

So that seems like it gives you everything you need to get a constant on the rhs?

[mortal mantle]

rhs?

[clever folio]

Sorry my rhs was this formula lol

The left hand side was just the xg'(x) integral.

[mortal mantle]

ah kk

[clever folio]

Here is the version of ibp i'm talking about btw

https://qph.fs.quoracdn.net/main-qimg-da1d98c3e0dfddf851ff0e8fc0e0f9d4-lq

If you use the substitutions I mentioned you can compute the whole rhs from your given info.

[mortal mantle]

yeah taht makes sense

i got it from here

thank you for the help bro