help-42

[dense fog]

How? You should find the pmf note the shape of the pmf (increasing reaching max then decreasing) to find most likely

[modern hemlock]

what is pmf

i tried some binomial stuff

[dense fog]

Probability mass function

[modern hemlock]

didn’t work though

[vernal crest]

nevermind i still ended up with 1

[vernal crest]

i have no idea what the pmf is

[dense fog]

To get 2 successes in x throws you need to have 1 success (and therefore x-2 failures) in the first x-1 trials then a success in the last throw

Write out the expression for this

[vernal crest]

this is what i did
there's a 1/36 chance he gets it, so suppose he does it first try, then the probabilty is 1/36, now suppose he doesn't get it and then gets it, that's 35/36 * 1/36, then suppose he doesn't get it twice and then gets it, that's 35/36 * 35/36 * 1/36, and that keeps going on until infinity

and then i took the infinite sum of that and still got 1 somehow

[dense fog]

Why would that give you the most likely?

you are just doing a sum over a pmf which sums to 1 by definition

[vernal crest]

well i'm essentially just discussing each probably outcome, and summing them up

[vernal crest]

well i have no idea what a pmf is

[dense fog]

Which has nothing to do with most likely value

[vernal crest]

oh yeah that's literally just giving the final probabilty of it happening

which is just 1

nvm then

[calm coral]

@modern hemlock Has your question been resolved?

[modern hemlock]

didn’t work

i probably did it wrong

never done pmf before

[dense fog]

Show your work. How can I help you if you don't?

<@&268886789983436800>

[calm coral]

@modern hemlock Has your question been resolved?

[calm coral]

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[fervent vortex]

any hints on this?

[fervent vortex]

One way I think I can approach this is to take for eg some number > 12 which might divide most of these nums like 14 and then check which number 14 is not dividing and remove it

But any other number which is > 14 might also do this same exact behavior

So I would have to check for all numbers from current_gcd to min(list)/2 and choose the maximum number which satisfies this behaviour

#helpers-info

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[night nimbus]

You can do trial and error method too

Or you could do prime factorisation

[night nimbus]

This is way better acc to me

[calm coral]

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[calm coral]

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[hollow frigate]

Why is negative reciprocal of the gradient

Used in part 15 b

[calm coral]

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[bitter wolf]

For finding slope of normal at a point we use negative reciprocal of derivative at that point

For tangent just the derivative

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[hollow frigate]

wait how dyu differntiate that

[remote mural]

take the derivative of both sides of the equation
remember that:
for f(x) = k, f'(x) = 0
for f(x) = x^n, f'(x) = nx^n
for f(x) = g(x)+h(x), f'(x) = g'(x)+h'(x)

[bitter wolf]

And use chain rule too. For example d/dx(y²) = 2y (dy/dx)

[hollow frigate]

ah damn my friend told me smthing about implict diff

i have not covered any of that

yet

chain rule as well

I only know basics of diff

thx tho

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[calm coral]

Please don't occupy multiple help channels.

[tiny robin]

Help is gladly appreciated

[supple mural]

have you learned L'hop?

[tiny robin]

Oh i just solved it i think its 3

Is it?

[covert lark]

should be 3 yes

[tiny robin]

Find the coordinates of point T, in which the tangent line to the function f(x)= x^2-7x+6 makes 135 degrees with the positive direction of the x axis. Find the equation of this tangent line

✅️✅️✅️BETTER TRANSLATION b) To find the coordinates of point 7, where the tangent to the graph of the function f(x) = 3x²-7x+6 concludes with the positive direction of the abscissa axis an angle of measure 135°. Find the equation of the tangent line at this point.

Please help me out brother

@supple mural @covert lark

[calm coral]

@tiny robin Has your question been resolved?

[tiny robin]

<@&286206848099549185>

[hybrid plover]

You could make a table or try to graph it

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[elder sand]

I’m not sure how to answer this if someone could explain how it would be great.

[amber bolt]

,rccw

[open hatch]

have you attempted the question ?

[elder sand]

Yeah, my answer is 23.1% but I’m 99% sure that’s wrong so that’s why I asked for help

231

I’m not quite sure I’m sorry 😭

yeah

[raw basin]

$$
E = mc^2 + \int{0}^{\infty} e^{-x^2} ,dx + \sum{n=1}^{\infty} \frac{n^2}{2^n} - \lim{x \to 0} \frac{\sin(x)}{x} + \left( \frac{d}{dx} e^x \right) \bigg|{x=1} + \left( \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} \right) - \frac{a + b + c}{a^2 + b^2 + c^2} + \left( \oint_{\partial \Sigma} \vec{F} \cdot d\vec{r} \right) + \sqrt[n]{x^n + y^n}
$$

[potent lotus]

leoleg2009

[elder sand]

Ohh right

[raw basin]

prepare you to see mega equation

[potent lotus]

faiyrose

[raw basin]

so easy

oh wait

[potent lotus]

faiyrose

[raw basin]

nice

you have 10s

xD

okay :)

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[calm coral]

@remote mural Has your question been resolved?

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@remote mural Has your question been resolved?

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[calm coral]

Please don't occupy multiple help channels.

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[hasty creek]

I'm supposed to find out whether -1 and 3 is a max, min or neither (was told to use the second derivative test) what am i doing wrong

[hasty creek]

I got when x=-1 its a minimum (but apperantly its a maximum) and I got when x=3 its neither (and its a minimum)

[gleaming vapor]

ohh

ok so you know wiht the second derivative test you plug in the critical point

to test its concavity

[hasty creek]

yes

thats what i was trying to do iwth the little chart and stuff

[gleaming vapor]

then f''(x) < 0 it is concave downwards

which makes it a maximum

when f''(x) > 0 it is concave up which makes it a minimum

think about it

when its concave downwards the extrema is at the top of the curve

making it a maximum

[hasty creek]

ohh i see

that makes sense

ok thank you

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[fleet zodiac]

$\int_{1}^{3} x^x , dx$

[potent lotus]

Alex

[fleet zodiac]

$\int_{1}^{3} e^{x \ln(x)}$

[potent lotus]

Alex

[fleet zodiac]

$\int_{1}^{3} \sum_{N=0}^{\infty} \frac{x \ln(x)}{N!}$

[potent lotus]

Alex

[fleet zodiac]

is this correct for now?

[grand glacier]

Well it should be x^n ln^n (x) shouldn‘t it? Cause of the expansion of e^x

x^n/n!

,w series e^(xlnx)

[potent lotus]

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[fleet zodiac]

$\int_{1}^{3} \sum_{N=0}^{\infty} \frac{(x \ln(x))^N}{N!}$

[potent lotus]

Alex

[fleet zodiac]

Ok, can i interchange now the sum and integral? Cause it looks illegal to me

[grand glacier]

Fubini‘s theorem iirc. You can swap them if everything converges absolutely or something like that

I don‘t know the specifics. However, for your information i‘m fairly certain this integral doesn‘t yield a nice closed form

[fleet zodiac]

i can then take N! Out

$\sum_{N=0}^{\infty} \frac{1}{N!} \int_{1}^{3} (x \ln(x))^N$

[potent lotus]

Alex

[fleet zodiac]

ok i solved, thx

.close

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[calm coral]

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[rough ferry]

is a) -0.3?

[rough ferry]

in my book its 286.1

[calm coral]

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

[rough ferry]

alr

so

$\frac{f(2.01)-f(2)}{0.01}$

[potent lotus]

rynite

[rustic osprey]

Oh you’re only approximating it?

[rough ferry]

yeah

this is a functions course, no calc

[rustic osprey]

,calc 15/49

[potent lotus]

Result:

0.30612244897959

[rustic osprey]

Yeah your approximation is pretty close then

[rough ferry]

oh ok, just wanted to make sure

thank you 👍

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[burnt robin]

what are you thinking

[ripe thorn]

i get the equation 5x +17 = 64

but its not an option

[burnt robin]

i dont think thats correct

[ripe thorn]

thats the problem 😭

[median marsh]

how’d you get this equation

[upper flare]

think about what the two smaller angles sum to

[ripe thorn]

so it would be 5x + 53 = 128

[upper flare]

yeah

the reason your other eqn didnt work

is cause u just assumed that the big angle was split in half

[ripe thorn]

yeah

i got x=15

ty

[upper flare]

nw

[ripe thorn]

the only guess i can make is that its x-2+x-2+x-2+x-2 = 180

well, with parentheses

[upper flare]

yeah

thats right

[ripe thorn]

ok

[upper flare]

since they're all the same angle

u couldve just said 4(x-2) = 180

but yeah

lmaoo

[ripe thorn]

😭

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[mossy wigeon]

im not too sure why theres one thats wrong

[subtle osprey]

,w radius of convergence of (-11x)^n/(√n+10)

[potent lotus]

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[subtle osprey]

only right endpoint is included

[calm coral]

@mossy wigeon Has your question been resolved?

[mossy wigeon]

ah ty

idk why two calc show differnet answers

[calm coral]

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[slow radish]

Hey! I was wondering if someone can point me on the right direction to get this one right. I am working on a school project, where I am basing my algorithm from this one. Originally, I solved it to the second image. But after experimenting, the second one (my solution) just explodes. The first one works though. I can just use it, but I want to understand why that is the solution. I can provide any more needed context. Thanks a lot!
(first image is original paper, second and third my solutions)

[slow radish]

My attempt for the solution

But as explained, in the practice that doesnt work, and in that paper the solution they tell is a different one

[calm coral]

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@slow radish Has your question been resolved?

[calm coral]

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[blazing coyote]

Find the line of intersection of x+y+z=1

[blazing coyote]

and 2x+y+z=3

so I first determined that x=2

or $x-2=0$

[potent lotus]

ƒ(Why am. I here)=I don't Know

[blazing coyote]

then $y+z=-1$

[potent lotus]

ƒ(Why am. I here)=I don't Know

[blazing coyote]

or $y+1=-z$

which is sort of the equation fo a line in $\mathbb{R}^3$

[potent lotus]

ƒ(Why am. I here)=I don't Know

[blazing coyote]

but I'm not able to relate $y+1=z$ to x

[potent lotus]

ƒ(Why am. I here)=I don't Know

[blazing coyote]

any hints?

maybe I solve for x

[potent lotus]

ƒ(Why am. I here)=I don't Know

[blazing coyote]

hmm

am I on the right track?

[untold drum]

you know x = 2 and y+z = -1

[blazing coyote]

yes

oh

[untold drum]

thats a line for me

[blazing coyote]

how to I express it in the cartesian form

*do

[untold drum]

what do you call a cartesian form?

[blazing coyote]

x-a/p=y-b/q=z-c/r

[blazing coyote]

even the vector form is fine with me

[untold drum]

line = (2,0,-1)+t(0,1,-1)

[blazing coyote]

how did you get the direction cosines

[untold drum]

line = P + t (Q-P), where P and Q are points on the line. For P take y = 0, for Q take y = 1

[blazing coyote]

ok

thanks

.close

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[rich nimbus]

think about the perfect squares which are around those

the values have to be in between

between 2 and 3 since 2^2=4 and 3^2=9

yes

[calm coral]

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[untold drum]

what is AB?

typically distances are without signs, but 0.85 is ok. now what is BC?

[calm coral]

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[left crown]

hello

[left crown]

i have to show that this is continuous

and that this isnt

but i struggle to find a way to start

[calm coral]

@left crown Has your question been resolved?

[granite ingot]

You want to use k-lipschitz I think

This is a typical way to show continuity in topology

And also because you work with metric space

[left crown]

ok i look into it

but it also works if i map the funktion to its derivitive yes?

the funktion goes from f to f'

[granite ingot]

Yes

[left crown]

ok ty

[granite ingot]

I said yes for that mb

I'm not fluent in English, may you explain me what mapping a function is please ?

[left crown]

if you map a to b you start with your function and get values in a value range

but im not fluent in english either so idk if that is a good formulation

[granite ingot]

May we speak the same language, where are you from ?

[left crown]

germany

you?

[granite ingot]

So we are not 😂 let's continue in English

I'm from France

[left crown]

XD

ah i see

[granite ingot]

So when you will use Lipschitz you will have to use this :

In this example the "g(y)" is for you D(f) whis is equal to f'

Which leads to something like
$$ |f' - g'| \leq K|f-g| $$

[potent lotus]

dragonrard

[left crown]

why g'?

and not f'(x) and f'(y)

[granite ingot]

I decided to take to vectors f and g froc C^1

[left crown]

ah ok

[granite ingot]

Be careful with what are your vectors in this example

Here, tour function D is from C1 to C0

The vectors are functions and not reals

[left crown]

ok

[granite ingot]

So your objective is to find a K whicj works

[left crown]

and K ist just a number right

[granite ingot]

Yes, it must not depends on vectors

For your exercise I don't understand what are $$ || \cdot ||{C^1} and || \cdot ||{I}$$

[potent lotus]

dragonrard

[left crown]

I is an interval and C1(I) represents the space of continuously differentiable functions

so II . II is the norm with C1

[granite ingot]

You have the definition of these please ?

Because in these exercise sometimes we prefer working with $$ || \cdot ||_\infty $$

[potent lotus]

dragonrard

[left crown]

C^n := {f : I → R | f n-times continuously dierenceable}
C^∞ := {f : I → R | f infinitely often continuously dierenceable}

stetig = continuous

[granite ingot]

I know the C^n but how do you define your norms ?

You must have definition of the both, don't you ?

[left crown]

and the other on is the supremum norm

[granite ingot]

I suppose that I is a compact ?

Because if not, the sup doesn't exist

[left crown]

I is just the interval [a,b]

[granite ingot]

So work with
$$ ||D(f) + D(g)|| $$
And see if you can do something with your norm definition

[potent lotus]

dragonrard

[granite ingot]

For the both, but as you know, when in math you want to say something does not exist, you want to suppose it exists and to show an absurdity

[left crown]

ok so for the first i try to show its not continuous until i get a contradiction and for the second i try to show that it is continuous until i get a contradiction right

[granite ingot]

For the first you work normally

For the second you work by the absurd

"by supposing D continuous we have "
"So we have "
.
.
.
"Impossible"

[left crown]

oh ok

and i can just do that with lipschitz

[calm coral]

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[calm coral]

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[proper spear]

does a column of 0's affect the column space of a matrix?

[proper spear]

nevermind

.close

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[proper spear]

The column space of matrices A and B is a plane in 3D. The column space of A + B is the whole R3 space

my textbook said that the column space of A + B is "usually" a plane in R3

"find matrices 𝐴 and𝐵 such that their corresponding column space is the plane of all vectors perpendicular to (1,1,1)"

for matrix A. I chose the above (2 independent columns and one dependent column)

for matrix B I did the same

[calm coral]

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[proper spear]

.close

[void frost]

Another Sage question: So something like this correctly shows me the roots. How do I do it with any constant a instead of 7?

[void frost]

I want it to show (-i*sqrt(a), 1), (i*sqrt(a), 1)

[glass heart]

I think f.roots(x) works

it thinks that a is the variable because it comes before x in the alphabet

you might need to make x a variable aswell

[void frost]

Ah, yep, seems to work. Thanks!

[glass heart]

go read through the documentation

its quite decent

[void frost]

Can you link me the one you mean, please? There are multiple ones

[glass heart]

https://doc.sagemath.org/html/en/reference/calculus/sage/symbolic/expression.html#sage.symbolic.expression.Expression.roots

[void frost]

Thanks

.close

[calm coral]

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[graceful dust]

this also works

var('a')
R.<x> = CC[]
f(x) = x^2 + a
f.roots(x)```

[void frost]

Thanks!

[graceful dust]

if you want to specify the ring

[calm coral]

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[brittle crow]

i have to find the real values

how do i do that

[jovial narwhal]

compare the real and imaginary parts

[brittle crow]

$a + b = 5 \ -2ab = -12i \ ab = 6 \ \ a + b = 5 \ ab = 6$

[quick karma]

real part = real part and imaginary = imaginary part

[potent lotus]

pixel

[brittle crow]

what now

[quick karma]

Yea

[jovial narwhal]

solve the system

[quick karma]

you have a+b = 5 , ab = 6

[brittle crow]

$a + b = 5 \ ab = 6 \ \ a = \frac{6}{b} \ \ \frac{6}{b} + b = 5$

[potent lotus]

pixel

[brittle crow]

like this?

[quick karma]

yep

[jovial narwhal]

like that or you could just look at the trivial solution

[quick karma]

2,3

[quick karma]

damn ur profile about

[brittle crow]

$\frac{6}{b} + b = 5 \ 6 + b^2 = 5b \ b^2 - 5b + 6 = 0 \ \ b = 2 \text{or} b = 3 \ a+2 = 5 \ a = 3 \ \ a+3 = 5 \ a=2$

[brittle crow]

whats trivial solution

[jovial narwhal]

3+2=5

[jovial narwhal]

i do a subtle amount of jumping

[quick karma]

what college/univ bro?

[potent lotus]

pixel

[quick karma]

yes

[brittle crow]

a = 2, 3
b = 2, 3

[quick karma]

a = 2,3
b = 3,2

[brittle crow]

yes yes right mb

[jovial narwhal]

not in college yet, i start in sept

[brittle crow]

when b = 3
a = 2

when b = 2, a =3

[quick karma]

Oh where will you be joining?

[quick karma]

yes

[jovial narwhal]

in dublin probably

[quick karma]

Cool

[jovial narwhal]

wbu?

[quick karma]

I will be giving Jee

[jovial narwhal]

next year?

[quick karma]

next to next

2026

[jovial narwhal]

oh thats far away

[quick karma]

Yes

@brittle crow

u didnt close it

[jovial narwhal]

lot of time to prep, gl

[quick karma]

Damn I wanna go abroad

giving SAT,AP etc

Lets see what destiny holds for me

[jovial narwhal]

it's a ratrace in US too, very low acceptance rates

[quick karma]

Yeah trying for several univ in and out of us

[jovial narwhal]

ic

[quick karma]

um could we discuss how you applied etc in dms?

[jovial narwhal]

yeah sure

[calm coral]

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[rough ferry]

is the answer, $310 per dollar, or $310 per thousand dollars?

[rough ferry]

I'm not sure how to get the right units

[amber wedge]

well

if the problem said

"where x is the amount spent on advertising in dollars"

what would the answer be

[rough ferry]

$310 per thousand dollars?

[amber wedge]

where did you get the thousand

wait]

[rough ferry]

the profit is in thousands too

i think it should be 310 thousand dollars

idk

[amber wedge]

it will be

310 thousand dollars per thousand dollars spent on advertising

assuming you calculated 310 correctly

[rough ferry]

wait why not per dollar?

[amber wedge]

cuz x is measured in thousands

[amber wedge]

if this were the problem

it would be per dollar

[rough ferry]

ok so for the original question, $310 per dollar spent is wrong? (units) bc that's how it is in my book

[rich nimbus]

that's also correct

so dollars profit per dollars spent?

[rough ferry]

yeah

do the thousands cancel out when divided maybe?

[amber wedge]

well if it's 310 thousand per thousand dollars, it's also 310 dollars per dollar

i guess

it seems wrong but idk

[rough ferry]

well it seems right to me, but im not sure either

.close

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[mossy wigeon]

how do i determine whether this serie converges

[bronze adder]

cant you just vibe guess it

numerator grows faster than denominator

[remote mural]

divergence test it

[mossy wigeon]

yeah btu i have to give a justification

ik its divergent

[remote mural]

use divergence test

[mossy wigeon]

im not too sure which one

i should use

[remote mural]

THE divergence test

[mossy wigeon]

oh so i put this whole thing to a limit

and i LH it?

[remote mural]

yeah that works

[mossy wigeon]

ah ok ty

.close

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[blissful carbon]

excuse me

[blissful carbon]

how would i do question ii

[remote mural]

6 pink, 3 navy, 1 red, 1 blue, 1 green, 1 orange

[blissful carbon]

yes

[remote mural]

just

putting that there so i don't have to open the image every time

so

if there were just 1 of each

it would be 3!

but

there are 8

but

6 are pink

so

i'm not sure

but i think

it's 8!/6!

,calc 8!/6!

[potent lotus]

Result:

56

[blissful carbon]

why

[remote mural]

because

6!

gets rid of the different arrangements of pinks

because they don't matter

[blissful carbon]

Why

?

@remote mural

[remote mural]

sorry

was doing something

and

[remote mural]

!15mins

[calm coral]

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.

[remote mural]

wdym why?

the 6! is the number of ways you could arrange it if you had 6 pink blocks

but we do not care about the different pink blocks

we have to remove them

[blissful carbon]

but the question has all the pink

[remote mural]

yea

6 pink

but we do not care about which pink is where

PPPPPPRO is the same as PPPPPPRO, even if the blocks are different

but the PPPPPP can be constructed 6! different ways

and all of them are the same to us

so we need to divide the 6!

[remote mural]

does that make sense?

[blissful carbon]

i think i will try again tomorrow

thank u though

uts kind of late

[remote mural]

you in asia?

[blissful carbon]

australia

[remote mural]

oh

yea

then

[remote mural]

really really late

[blissful carbon]

not really

,time

[potent lotus]

The current time for nutgun. is 12:39 AM (AWST) on Mon, 27/05/2024.

[remote mural]

oh

western

i assumed eastern

[blissful carbon]

.close

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[calm coral]

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[urban mica]

calculate the length of the diagonal of the regular body in the figure

[calm coral]

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[urban mica]

.close

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[gaunt pilot]

Is my approach correct

[rustic osprey]

yeah it seems fine

[gaunt pilot]

.close

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[tardy moon]

Can someone help me to do the integral of this function pls

[white ridge]

is the integral $\int_{2}^{4} \big(\frac{5x}{3x^2+6}\big)^2 dx$

[potent lotus]

tyler

[halcyon rock]

what about the π

[white ridge]

ok so there's an extra pi

that's largely irrelevant to the integral itself

but is the rest fine?

[halcyon rock]

looks fine to me

[tardy moon]

.close

[calm coral]

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[white ridge]

you have to use partial fractions

oh ok

[tardy moon]

.reopen

[calm coral]

✅

[tardy moon]

Sry I was testing, its my first time here

[tardy moon]

So I have to calculate the Volume of the functuon

And the formule is

V = pi . Integrale f(x)^2

But idk how to continue the calcule

@white ridge @halcyon rock if you can look at it quickly 🙏🏼

[white ridge]

you have to use partial fractions

first take 3 common (squared so 9) in the denominator and 25 out from numerator

so effectively you're integrating $\frac{x^2}{(x^2 + 2)^2}$

[potent lotus]

tyler

[white ridge]

then make numerator +2 and -2 so x^2+2 -2

split it to get $\frac{1}{x^2+2} - \frac{2}{(x^2+2)^2}$

[potent lotus]

tyler

[calm coral]

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[finite temple]

can someone help me solve this

[finite temple]

im like 90% sure i did it wrong so we can start from scratch

[upper sparrow]

The way you did it is fine (ignoring the crossing out, and the lack of function arguments)

[finite temple]

like the last 2-3 lines is where i messed up right?

[finite temple]

function arguements like theta?

[upper sparrow]

You didn't mess up at all and yea, theta (or whatever)

[finite temple]

yea i skip theta when im doing practice just to save time

ty tho

[finite temple]

can u help me finish then

[upper sparrow]

You could have done it a bit quicker though, though what you did was valid: write (cos(t)tan(t) + sin(t))/tan(t) = cos(t)tan(t)/tan(t) + sin(t)/tan(t) then work with that

[upper sparrow]

And you're done, you got to 2cos(t), which is what you wanted, wasn't it?

[finite temple]

wait this is correct?

ohh i thought fs it was wrong

the 2 is seperate from the sin?

[upper sparrow]

That's fine (of course with the assumption that sin(t) is nonzero, but that automatically comes from the fact that you divided by tan anyway)

[upper sparrow]

And it's multiplied by sin, it's not e.g. an argument of it, so you can like leave it outside and then turn what you had into 2cos(t)

[finite temple]

damn

okok i get it

tysm

.close

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[tough plover]

we substitute x+1 for x right?

[untold drum]

i would say x-1

[tough plover]

can you explain

[wet finch]

if h(x) is f(x) translated one unit to the right, h(1) should be f(0)

so h(x) = f(x - 1)

(and h(x + 1) = f(x))

[calm coral]

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[woven latch]

is this correct ?

[remote mural]

umm

yes

[woven latch]

thx

[calm coral]

@woven latch Has your question been resolved?

[woven latch]

this isnt correct is it
?

[calm coral]

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[woven latch]

.reopen

[calm coral]

✅

[delicate pumice]

sin2A = 2 sin A cos A.

=> 2sinx

thats your ans

[woven latch]

@delicate pumice for this

[delicate pumice]

yup

[woven latch]

appreciate it

'

[calm coral]

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[calm coral]

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[mossy wigeon]

how do i

know if this converge or not

[upper sparrow]

How do you
(do you have any ideas at all for it?)

[remote mural]

Where did u get this problem from

[mossy wigeon]

uh ik sin goes from -1 to 1

[upper sparrow]

Uh-huh, so sin^4 is at most 1 (and at least zero)

Any idea of a test you could use here?

[mossy wigeon]

ohh

then its

sin4n/n^5 < 1/n^5?

i think

[upper sparrow]

Yep, there you go

[mossy wigeon]

ahh tysm!

.close

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[trail wedge]

I need someone to explain to me how word problems work in systems of inequalities

[trail wedge]

yeah

np

[potent igloo]

okay inequalities... hm.

[trail wedge]

like im stuck on this one

Ethan makes $6 per hour mowing lawns and $7.50 per hour bagging groceries. Last week, he made a total of $129. The difference between the number of hours bagging groceries and the number of hours mowing lawns is 10. How many hours did Ethan spend mowing lawns

[potent igloo]

Do you have word problems given to you? Or what's going on exactly?

[trail wedge]

that one

[potent igloo]

Is this an inequality though?

[trail wedge]

it should be

tells me to set up a system of equations, then solve by substitution or elimination

[potent igloo]

None of this has to do with inequalities though...

[trail wedge]

ohh thats my fault, the whole title was system of equations and inequalities

[potent igloo]

oopsie

Okay, let x be the amount of hours spent mowing lawns, and y the amount of hours spent bagging groceries

In terms of x and y, how much money was earned?

[trail wedge]

so

129

but how do you change it to an equation

[potent igloo]

In terms of x and y, not just the final amount

[trail wedge]

x would be 6

and y would be 7.5

[potent igloo]

No, x and y the amount of hours worked, not the pay per hour

[trail wedge]

oh kk

idk that

all i know is that the difference is 10

[potent igloo]

Okay, if I make $6 per hour mowing lawns, and I mowed lawns for x hours, how much money did I make from mowing lawns?

[trail wedge]

6x

[potent igloo]

yup

and what do you think the money earned for bagging groceries would be?

[trail wedge]

7.5x

[potent igloo]

no. x is the amount of hours spent mowing lawns. Not bagging groceries. We're using y for that variable

[trail wedge]

oh true

so 7.5y

[potent igloo]

yes

So if we made 6x dollars mowing lawns and 7.5x dollars bagging groceries, how much money did we make in total?

[trail wedge]

6x + 7.5y = 129

[potent igloo]

exactly

That's one equation

Now we need one more

Any ideas?

[trail wedge]

lemme see

could you not solve it on its own ? cuz the questions in my work only provide one equation for each question

[potent igloo]

hint, you were given a difference of 10 between two things. Can you write that algebraically?

[trail wedge]

lemme think

x + y = 10 ?

no no

x + 10 = y ?

im lost

[potent igloo]

Correct

you have your system of equations

[trail wedge]

so do i just solve them like normal ?

[potent igloo]

yep

[trail wedge]

my main question is how do i know what is x and what is y and everything else for the questions ? is there a guide ?

[potent igloo]

That's a connection you just need to come to learn on your own

As you read a question, you must try to realize what quanities are given, which are unknown, and how do they all relate

I chose the names x and y arbitrarily as they are common. You can call them whatever you want

You're dealing with a trick now of turning english expressions into algebraic expressions

For example "It costs 5 dollars to enter the park, and 2 dollars per ride", model the total cost algebraically. I can choose x to represent the total number of rides ridden, and the total cost as y. Then the I can write it algebraically as y=2x+5

[trail wedge]

so for example Joe only has nickels and quarters in his piggybank, he has 94 coins total 8.85. how many of each coin do you have ? How do you do this ?

nickels and quarters are x and y

5x + 25y = 8.85 ?

and x + y = 95 ?

[reef nimbus]

they would equal 885 and 94

[trail wedge]

how so ?

oh i see

so .05x + .25 y = 8.85 ?

no no

now ?

[reef nimbus]

also valid

[trail wedge]

is there an easier way ?

[reef nimbus]

possibly, but I doubt it

[trail wedge]

and what of the second equation ?

[reef nimbus]

what of it?

[trail wedge]

you need 2 equations

[reef nimbus]

yes, you wrote 2 equations

[trail wedge]

and is the second correct ?

[reef nimbus]

no, as I stated above it should equal 94

[trail wedge]

oh thats true,

thats a typo

x + y = 94

is that corredct

?

[reef nimbus]

I just said yes...

[trail wedge]

alright

got it

thanks

.close

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[tranquil meteor]

is the correct way to do this to

1. find the gradient with (y2-y1)/(x2-x1)
2. use y - y1 = m(x-x1)

or is there a quicker way with only one formula??

[remote mural]

if u look all the lines given have different gradients

so u just have to work out the gradient in this question

[tranquil meteor]

are my methods correct though?

[remote mural]

yeah

[vernal crest]

not really

but i got it quicker by substituting

[tranquil meteor]

thanks

[remote mural]

line of best fit with 2 points is just the line connecting them

[tranquil meteor]

like trial and error?

[remote mural]

no

sticking y/x co-ordinates in

the equations

[tranquil meteor]

yes but if you're putting them into each equation isnt that just trial and error

i just realised, since every gradient is different i only have to find the gradient

im so dumb

my bad guys

.close

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[red lagoon]

abstract algebra course, what should Z_20 mean here? I know its a modulo group but i dont know if the operation is addition or multiplication

[red lagoon]

other two questions, if that makes it easier to guess

[alpine stone]

The operation in Z_n conventionally is addition modulo n

[red lagoon]

ok gotcha

tyty

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[thick sinew]

if a matrix has n jordan blocks for some eigenvalue lambda, then why does that imply the geometric multiplicity of lambda n?

[calm coral]

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[thick sinew]

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[onyx quiver]

does it matter wher i place the vertices

[glad grove]

It's convention to go clockwise or counterclockwise

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[wispy finch]

What is the irrational root theorum?

[finite iris]

https://letmegooglethat.com/?q=what+is+irrational+root+theorem%3F

[wispy finch]

💀

thx ig?

.close

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[frigid nimbus]

Im working on these questions and i have no idea how to set it up

if anybody could give me any pointers on formulas or anything of that sort

that would be much help

🙏

[old falcon]

optics

maybe the physics server

[frigid nimbus]

nah they deleted my question 😭

nvm

got it

.close

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[frigid nimbus]

physics server sucks balls btw

.close

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[tulip mulch]

Hi guys where did I go wrong ?

[tulip mulch]

original question

for some reason the answer is +1/4 and not -1/4

[remote mural]

,rotate

:/

[tulip mulch]

https://media.discordapp.net/attachments/948770026914213909/1244794920028344351/IMG_4731.jpg?ex=6656691c&is=6655179c&hm=378d30bb747a3e9d080d206e89e540f50f6c56c7aefc8e95465a843b48719a81&=&format=webp&width=526&height=701

,rotate

[reef garden]

Antiderivative of cos is just sin

[tulip mulch]

ohhh

lol silly mistake

thanks

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[split cypress]

how do you find the sum of the sequence : 3, 8, 15, 24, 35. Assume n starts at 1

[wispy finch]

so

to do this,

we have to first use the eq

[split cypress]

ik its like n^2 -1

[split cypress]

which eq

[wispy finch]

let me write it out

(n(a1+alast))/2

so the number of terms, times the first plus last, divided by 2

[split cypress]

thats arithmetic

[quaint sphinx]

are you asking for a proof, or for an answer

or rather, does the problem require a proof

[split cypress]

like the formula

[near crag]

One solution would be to use Wolfram Alpha to get the formula and then prove it by induction. But I know that's pretty lame.

[quaint sphinx]

index-shifts how fun

actually

[disregard]

[near crag]

The way that formula could be derived is by finding the formula for an n^2 sum, which has several different methods which honestly are pretty advanced/difficult

[split cypress]

ok so i just need summation notation right

[quaint sphinx]

to do what?

[split cypress]

for the equation

to get the sum

[near crag]

and then the final formula could be obtained by combining that with the -1 terms in the obvious way

[quaint sphinx]

you can express the sum using summation notation yes

[split cypress]

mhm

[quaint sphinx]

but extracting the closed form partial sum in terms of k requires more work as stipendi states

[split cypress]

ok ok

[split cypress]

what did you use here to get that

is that a site

[quaint sphinx]

https://www.wolframalpha.com/

the math calculator everyone uses

[split cypress]

oh alr thanks

[near crag]

I would like more context as to what "assume n starts at 1" means though, like what's n

[split cypress]

im pretty sure it just wants u to use an-1 or smth

[near crag]

I mean I wasn't really paying attention to the details here but the partial sum formula I gave is not for 3+8+15+24+35+... with k terms as Mqnic pointed out

[near crag]

That just shifts the question to what is an-1

[split cypress]

u start at n=1 and then an-1 to start at 0?

im pretty sure

[near crag]

Sometimes n is used to denote the index of the nth element of a sequence. Sometimes n is used to denote the length of the sequence. If n is an index, then "starting from n=1" doesn't really mean anything because there is an infinite sequence of terms and which term you decide to call the first one is a completely arbitrary choice

[split cypress]

oh ok

[near crag]

Under some generous assumptions we can of course assume that 3, 8, 15, 24, 35, ... defines the sequence a_n = n^2 - 1, but note that if we want 3 to be the n=1 term then in fact we must have a_n = (n+1)^2 - 1

So I suppose 3, 8, 15, 24, 35, ... doesn't define just one sequence, but rather an infinite amount of different sequences depending on which term you decide to call the first

And note, a_n = n^2 - 1 would be a completely reasonable sequenceification of the string "3, 8, 15, 24, 35, ..." because then the 3, arguably the "first" element, would have the index 0, which is how programmers count things

if we're just doing math for fun then we can leave the discussion at that but if it's super important that you get the right formula for your assignment then it would be very helpful to get the exact problem statement to try to figure out how they want the sequence to be defined

[near crag]

Of course something that resolves some ambiguity here is that in the a_n = n^2 - 1 sequence, the n=1 term is actually zero, so it doesn't affect the sum either way

So to me it seems that that formula given by Wolfram Alpha should be correct pretty much no matter how you interpret the assignment

hmm actually not quite because you'd be missing the last term

so... the right formula is probably either what I posted, or what I posted plus (k+1)^2 - 1

but either way to me that's a seriously unimportant detail and what's actually important is that you understand how many terms and which terms are included in a given partial sum formula

In fact I would argue that it's your duty to specify which sum your formula gives the answer to, given that it's not clearly defined in the assignment

[calm coral]

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[onyx quiver]

does it matter where i place the letters?

[manic timber]

no

[remote mural]

!status

[calm coral]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[onyx quiver]

1

i figured it out

too lazy to find the other angles tho

.close

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[static pumice]

is it true that on a frictionless ramp, an object being launched up the ramp will always reach the same height no matter how steep the ramp is?

[fathom shuttle]

yes, do you know how to justify why?

[static pumice]

no i just heard someone say it and wasnt sure if it was true or not

[fathom shuttle]

if youre familiar with the fact that potential energy is mg*h, since mg doesnt change and the amount of energy does not change, you know that height will not either

[static pumice]

but since the object is getting launched up the ramp

isnt kinetic energy what we should be looking at?

since the object is in motion

or am i midunderstanding

[fathom shuttle]

K initial = U final

so K initial = mgh

since three of those variables are constant, the fourth must also stay constant

[static pumice]

hmm i see i see

ty :)

[fathom shuttle]

yw :)

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[novel token]

!help

[calm coral]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[novel token]

how do i know which way

is it asking to go from left or right

cause if my starting point is the blue triangle i would shift it to the right

but if my starting point is the red triangle i would shift it to the left

so how am i suppose to know what my starting point is

[civic dirge]

A'B'C' is the image. The image refers to the triangle AFTER transformation

[clear delta]

so it goes from ABC to A'B'C'; it's shifting to the right

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@novel token Has your question been resolved?

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[warm turtle]

for a vector function to be solenoidal, is the divergence being zero the only condition? shouldn't the curl also be non zero?

[warm turtle]

.close

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[ripe wolf]

given integral:
$$
\int{\frac{1}{(x^2+16)^2}}dx
$$

[potent lotus]

Glorious Lynx

[ripe wolf]

need to find F(x)

$$
\int{\frac{1}{(x^2+16)^2}}dx = \int{(\frac{Ax+B}{(x^2+16)^2}+\frac{Cx+D}{x^2+16})}
$$

[potent lotus]

Glorious Lynx

[ripe wolf]

i got:
$$
Ax+B+(Cx+D)(x^2+16) = 1
$$

[potent lotus]

Glorious Lynx

[ripe wolf]

and when i solved it i got:
$$
\frac{B}{(x^2+16)^2} = \frac{1}{(x^2+16)^2}
$$

[potent lotus]

Glorious Lynx

[ripe wolf]

I got literally the same thing, is there mistake somewhere or i need to use something different?

[remote mural]

Put x=4costheta

[ripe wolf]

substitute?

[remote mural]

Ye

[ripe wolf]

So the method i used is useless?

[remote mural]

Wait

[remote mural]

Are u sure about the partial fraction formula

[ripe wolf]

i think yes

[modern peak]

i think you should recheck your PFD

[civic dirge]

The solution is:
A = 0
B = 1
C = 0
D = 0

Is your decomposition valid? Yes. Is it useful? No. The problem is that there's no factors to break up

[ripe wolf]

something seems off

[civic dirge]

Whoops! I meant B = 1, A = 0

[ripe wolf]

right then

I tried to substitute x^2+16 = t, but as i see it doesnt result in anything

so i have to use trigonometric substitution

[ripe wolf]

this one

[remote mural]

Yea partial fraction ain't helping

[ripe wolf]

.close

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[remote mural]

There are 10 students to be seated in desks arranged in 2 rows of 5 desks each

Alvin and Bobby should sit next to one another in the same row but Calvin and Delia are not to sit in the same row. Find the number of ways the children can be arranged

[amber bolt]

sounds compicated ngl

[pseudo wedge]

IEP

Inclusion-Exclusion principle

[amber bolt]

well yeah you could find (AB in row 1) − (ABCD in row 1) − (AB in row 1, CD in row 2)

and multiply by 2

[remote mural]

So here were my first thoughts

Let n be the number of ways the children can be seated

n = number of ways children can be seated with A and B together - number of ways children can be seated with (A and B) AND (C and D) together

This should be

$= 8*8!2! - 82!62!*6!$

[potent lotus]

Emploice Muswashans

[amber bolt]

that's alsmot right

almonts

[remote mural]

What the error there?

[amber bolt]

6 is where yo uput CD in the same row as AB