help-19

[shy smelt]

1 - g(x) doesnt work in general, try some small values of x though. Then prove 1 - x is the only solution with induction

[odd edge]

@rigid bramble Has your question been resolved?

[rigid bramble]

I know how induction works (for inequalities, equations etc.), but from my knowledge, I don't see how you could use induction to prove that f(x) = 1 - x is the ONLY solution. How would you start that up?

[odd edge]

@rigid bramble Has your question been resolved?

[odd edge]

@rigid bramble Has your question been resolved?

[odd edge]

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[candid turret]

how do i solve this?

im assuming by the bushes in the rows that the number of bushes is

a1 = 11 and d = -2 and an = 36

and im solving for n?

the rows

[tepid acorn]

yeah

[candid turret]

an = a1 + d(n-1)

[tepid acorn]

the total sum would be average * n

[candid turret]

oh so im looking for the sum?

[tepid acorn]

no, you are given that the sum is 36

d = -2

[candid turret]

ohhhhhh

[tepid acorn]

and that a_1 = 11

[candid turret]

the sum is 36

wait which equation do i use to find n

[tepid acorn]

the average is just equal to the average of a1 and an

[tepid acorn]

use the first equation to find a_n in terms of n

by plugging in values

[candid turret]

an = 11 + -2(n-1)
an = 13 - 2n?

[tepid acorn]

yeah

[candid turret]

okay

[tepid acorn]

and [(a1 + an)/2] * n = 36

[candid turret]

(11 + (13 - 2n)) / 2 * n = 36

do we use the an value there

of what its equal to

[tepid acorn]

yes

yeah then you get a quadratic in n

[candid turret]

n = 6

so we just plug that back in to the an equation?

an = 13 - 2(6)?

[tepid acorn]

nah that's our answer

[candid turret]

oh

wait ur right

[tepid acorn]

for the number of rows

[candid turret]

the n'

yeah

alright cool

yeah it worked

thanks

[tepid acorn]

np

[candid turret]

.close

[odd edge]

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[mystic saffron]

How do I find the domain of $\frac{f(x)}{g(x)}$

[clever fjord]

Matt

[mystic saffron]

g(x) is the straight line and f(x) is the semi parabola

[tepid acorn]

It’s defined where both f(x) and g(x) are defined except if g(x) = 0 at certain x which never happens

[mystic saffron]

so its just [-1, 4]?

[tepid acorn]

Both functions need to be defined

[mystic saffron]

oh

so

[-1, 3)

[tepid acorn]

Yeah

[mystic saffron]

ok ty

.close

[odd edge]

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[mystic saffron]

how would I solve $\int x^3(2-x^2)^{12} ,dx$ without int by parts, do you try to manipulate $x$ to equal something?

[clever fjord]

Retribution | ᵇᵃˢᵉᵈ

[mystic saffron]

if so, idk what to make it equal

<@&286206848099549185>

[open onyx]

you can directly attack this with binomial expansion

[mystic saffron]

no

[toxic monolith]

substituion is better

[mystic saffron]

no thx at least lmao

[toxic monolith]

but thikn how

[mystic saffron]

what abt $x^2=2-u$

[clever fjord]

Retribution | ᵇᵃˢᵉᵈ

[mystic saffron]

but idk

i'll verify

[toxic monolith]

yes

but x^3 = x^2 * x

and then all is ok 🙂

do you get it ?

[mystic saffron]

ah it does work $-\frac{1}{2} \int (2-u)u^{12} ,du$ should do fine

[clever fjord]

Retribution | ᵇᵃˢᵉᵈ

[toxic monolith]

$\int_{}^{}x^{2}\left( 2-x^{2} \right)x\text{ }dx=_{\cdots }$

[clever fjord]

Joanna Angel

[mystic saffron]

.close

[odd edge]

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[toxic monolith]

and pwoer i forgot )

[odd edge]

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[river lily]

how can I find the theta values to take the integral?

is the only way by graphing?

[odd edge]

@river lily Has your question been resolved?

[empty gate]

Not sure. Maybe it just goes once round?

Is it periodic in angle?

[odd edge]

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[river lily]

decided to draw it since it was relatively simple

thx tho

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[dull mortar]

What are remote interior angles of 1. The 1 is on the outside so I don't understand how it can be an remote interior.

[odd edge]

Please don't occupy multiple help channels.

[tawny wagon]

remote interior angles are on the inside

[crude carbon]

seems like this is test

[dull mortar]

I dont understand. So what are the remote interior of 1. Because 1 is on the outside

[dull mortar]

Math Tutor homework

online

[tawny wagon]

If its a test then i cant help you

[dull mortar]

As I said, it is not a test.

I really struggle with this.

I try to understand how this works

[tawny wagon]

Ok pretty much remote interior angles are angles that dont share the same vertex of a triangle with the exterior angle

[crude carbon]

can you show your work atleast

[dull mortar]

What?

[dull mortar]

So I believe that that would be 5 then?

Correct me if I am wrong

[tawny wagon]

no cause thats from the same corner

you are looking for a remote interior angle, so it has to be inside the triangle but not touching the corner of angle 1 vertex

[lavish jackal]

!show

[odd edge]

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

[dull mortar]

Aahh so 2 and 3?

Now I understand I think

[tawny wagon]

👍

[dull mortar]

Thanks man!

[odd edge]

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[spice mesa]

How would I write an equation and graph the problem "Each student must sell 2 different types of raffle tickets to earn $18. The raffle ticket to win a book costs $2. The raffle ticket to win a bag of candy costs $1.50"

[forest nest]

say x is the amount of books that cost 2$ and y is the amount of candy bags that cost 1.5$, what equation pops to your mind?

(y doesn't have to be isolated)

[spice mesa]

y=2x+1.5 something like that?

[forest nest]

ok how would get price of all the books

if you view x as the number of books, what would the price be

[spice mesa]

idk im rlly not good with this sort of stuff

[forest nest]

ok it's 2x

you can see that right

1 book is 2 dollars

2 books is 4 dollars

etc

you can say the same thing with the bags

1 candy bag is 1.5$

2 candy bags is 3$

etc

the price of the candy bags is 1.5y right

and we know that the price of the books + the price of the candy bags = 18

so how would you write that

[spice mesa]

yeah

that somewhat makes sense

it's just idk how to write the equation with those two different variables

and i'm not sure where the 18 goes

[forest nest]

you don't have to have y on one side at the start, at the end we'll make it y = something

right know i'm just writing as the total price = 18

or price of the books + the price of the candy bags = 18

u know what the price of books is

and u know what th eprice of the candy bags is

so u just replace right

price of the books is 2x

price of candy bags is 1.5y

[spice mesa]

so would it be something like 2x+1.5y=18

[forest nest]

yeah that's right

so now we want to isolate y

you know how to do that?

[spice mesa]

divide by 1.5?

[forest nest]

first move the 2x to the other side

you go in opposite order of pedmas

[spice mesa]

so what would i do

[forest nest]

subtract 2x from both sides

[spice mesa]

oh

so i'd have 1.5y=18-2x

[forest nest]

yeah

and then you divide

[spice mesa]

by 1.5?

[forest nest]

ye

[spice mesa]

so i'd have y=12-1 1/3

[forest nest]

yeah, i like writing it as y = 12 - 4/3x

[spice mesa]

oh

and then i just graph

[forest nest]

yeah, one thing to remember is x > 1 and y > 1

[spice mesa]

wdym

[forest nest]

x and y are the number of something sold right

and in the question sthey said each student must sell 2 different raffle tickets

so that means the amount of book tickets is at least 1

and the amount of bag candys is also at least one

in other words, x is bigger then 1, or x > 1

same with y, y > 1

[spice mesa]

yeah that makes sense

but does that influence my graph at all

[forest nest]

it just means your graph technically should start at 1

like when x = 1

your graph can't go more to the left then that

[spice mesa]

oh

so would 1 be the x intercept?

and cant go below that

is that what you mean?

[forest nest]

this is how the graph looks like

the red line

you can see it continues to the left of 1

we want it to start when x = 1

and as y goes down, we also want to make sure that y is bigger then one

so the only part of the graph that you draw is this

[spice mesa]

oh

because you dont have any less than 1

[forest nest]

ye

[spice mesa]

okay that makes a lot of sense thank you

i have one more question though

[forest nest]

shoot

[spice mesa]

how would i find the domain and range of it

i actually did learn that unlike what I asked you before, but I understand none of it still

[forest nest]

domain is just like what x's are being used

image is which y's are being used

idk if there's a nicer definition

so like imagine i have this

just a random graph

you can see clearly that the image is y >= 1

cause the graph is only above or equal to 1

for the graph we drew, what is the interval of y and x

you'll need to do some calculations actually

you know the "most left" of x is 1

to find the most right point, you must find when the equation = 1

im gonna dip

[spice mesa]

alright i think that makes sense

i appreciate the help bro thank you

[odd edge]

@spice mesa Has your question been resolved?

[odd edge]

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[mint forge]

I cant find the solution to this

[odd edge]

@mint forge Has your question been resolved?

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[left stone]

Q-Find most likely Y when X are Rs. 25, 20, 40 and 50. Information X YAverage 30 100SD 5 10Correlation between X and Y is –0.60.

[left stone]

How do I solve this?

[odd edge]

@left stone Has your question been resolved?

[left stone]

<@&286206848099549185>

[odd edge]

@left stone Has your question been resolved?

[left stone]

@rancid moat

[odd edge]

@left stone Has your question been resolved?

[odd edge]

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[left stone]

How do I solve this..

<@&286206848099549185>

[odd edge]

@left stone Has your question been resolved?

[left stone]

No

[odd edge]

@left stone Has your question been resolved?

[odd edge]

@left stone Has your question been resolved?

[odd edge]

@left stone Has your question been resolved?

[odd edge]

@left stone Has your question been resolved?

[mystic saffron]

ok <@&286206848099549185> fr this guy has bene here for 8 hrs

[uneven sable]

I’m in class I’ll take a look in a minute tho

[uneven sable]

Idk man- sorry

There isn’t enough context for me

[odd edge]

@left stone Has your question been resolved?

[ionic edge]

.close

[stiff shard]

@left stone I'm not an expert in the topic, but is the correlation between demand and price linear?

[left stone]

Yeppp

It is

[stiff shard]

that actually makes things easier

now, there's one more thing I need to ask

if the demand is zero

is the price zero too?

[left stone]

That's not given

[stiff shard]

okay, then we definitely don't need it

right, what does "Prices are Rs" mean?

[left stone]

Currency

Just like dollars

[stiff shard]

fair enough

[left stone]

Euro etc

[stiff shard]

now this is a bit weird

I add all the prices up

[left stone]

Yep

[stiff shard]

and divide by the number of prices

and I get 33.75

not 30

so (25 + 20 + 40 + 50)/4 = 33.75

[left stone]

What should I do...

[stiff shard]

whoah, is there only one demand value?

since it says "find the most likely demand (singular)"?

[left stone]

Yep

We've to find it for 25,20,40,50

[stiff shard]

yeah I'm quite confuzzled now - I understand what the question is asking for, but the processes behind the question are beyond me because I've never done this before

sorry about this

[left stone]

That's fine

Ahh that's fine

[left stone]

.close

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[odd edge]

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[cinder perch]

how to integrate tf(t)

[lyric moat]

you know newton leibniz theorem?

[solemn jay]

What’s the answer

[snow marten]

you dont have to integrate anything

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[odd edge]

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[cinder perch]

.reopen

[odd edge]

✅

[cinder perch]

It’s 3

I don’t understand the mechanism behind tf(t)

So if someone could explain it that would be nice

[cinder perch]

No

I’ve only been taught fundamental theorem of calculus

That’s what I need to use

But I don’t get it

Like for f(t) just sub in x but what for tf(t)

[odd edge]

@cinder perch Has your question been resolved?

[odd edge]

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[fickle cairn]

The question is as follows: Prove the function y=(x^2-6x+10)/(4x-12) has a minimum value on x ∈ (3; +∞) and find the lowest value on that range. I can prove it has a lower limit, because it is a hyperbola with an asymptote at x=3, but I can't grasp how to find the lowest value.

[odd edge]

@fickle cairn Has your question been resolved?

[fickle cairn]

<@&286206848099549185>

[fickle cairn]

<@&286206848099549185>

[copper frigate]

Have you done derivatives?

[cursive ruin]

sorry i cant help you with that im not covering this topic myself

[somber tree]

hello bakane

[somber tree]

that is a good catch; it is a hyperbola with an asymptote at x=3

that implies it having a minimum value that is the vertex of the hyperbola

[fickle cairn]

I haven't done calc

[somber tree]

do you know how to take the first derivative?

[fickle cairn]

not really, its pre calc school algebra

its supposed to be solved without calc

but the derivative should be 0 if im guessing correctly

i understand the concept but idk how to take them

[somber tree]

ok so y equals a fraction

when does y have its least possible value?

when the denominator is as big as possible and the numerator is as low as possible, you could set an inequality from these two bits of info

[fickle cairn]

highest denominator

least numerator

[fickle cairn]

like what?

[somber tree]

$x^2 -6x +10 > 4x - 12$

[clever fjord]

charles.exe

[fickle cairn]

ohh yeah

[somber tree]

so we get $x^2 -10x + 22 > 0$ when we move everything to one side

[clever fjord]

charles.exe

[fickle cairn]

the lowest solution of this

is the lowest point

right?

[somber tree]

let's see

[fickle cairn]

so D=100-88=12

[somber tree]

what is D?

don't say deez nutz pls

[fickle cairn]

$b^2-4ac$

[clever fjord]

bakane

[somber tree]

oh yeah we call it in Arabic the determinant

[fickle cairn]

thats what we use in russian schools

yea

[somber tree]

i don't know its name in english or i don't quite remember it

oh it is discriminant

[fickle cairn]

yeah

no whole solutions for this

[somber tree]

oh wait my bad sorry i remembered how we did it pre calculus

[fickle cairn]

this doesnt give much

idk

[somber tree]

wait sorry

the numerator quadratic function* can't be factored well

ok sorry but i can't help with this, i couldn't remember or find any way that isn't calculus related

[fickle cairn]

its alright, the teach does bring up problems that look remotely like this tho

[fickle cairn]

\frac{(x-3)^2+1}{4(x-3)}

\frac{(x-3)^2+1}{4(x-3)}

$\frac{(x-3)^2+1}{4(x-3)}$

[clever fjord]

bakane

bakane

[fickle cairn]

its basically this

but still

wtf

[odd edge]

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[fickle cairn]

.reopen

[odd edge]

✅

[fickle cairn]

$\frac{x^2-6x+10}{4x-12}$ Find the lowest point at x > 3

[signal shard]

use \inf ?

nope

unfortunately

life is hard.

[clever fjord]

bakane

[fickle cairn]

\just like this whatever

without calculus

[tepid acorn]

Idk if it helps but the top is equal to (x-3)^2 + 1

[odd edge]

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[fickle cairn]

whatever

ill ask the teach

[odd edge]

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[faint shore]

Anyone know how to do this

[restive delta]

,rotate

[faint shore]

Ignore the cylinder

[faint shore]

Its part of something else

This isnt part of school or anything

So?

[odd edge]

@faint shore Has your question been resolved?

[odd edge]

@faint shore Has your question been resolved?

[odd edge]

@faint shore Has your question been resolved?

[faint shore]

You know what

Forget it

[empty gate]

.close

[tepid acorn]

You could solve it algebraically, obtaining the dimensions of the rectangle necessary

And probably those lengths will be constructible (if you are meant to solve it with ruler and compass)

[odd edge]

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[drowsy heart]

Given the first 5 term of this sequence, find the nth term

[cold urchin]

What have you tried?

[drowsy heart]

at first i thought is was n^2/(n+1)^2 but it doesnt work for n=4

[cold urchin]

Lemme give u a hint

[clever fjord]

Pure

[cold urchin]

@drowsy heart

[drowsy heart]

isnt it just n^2/(n+1)^2

[cold urchin]

no

[odd edge]

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[marble vale]

hello

[marble vale]

$f(x, y) = \begin{cases}
\frac{x^2y}{x^4 - 2x^2y + 3y^2} & \text{if } (x, y) \neq (0, 0) \
0 & \text{otherwise}
\end{cases}
$

[clever fjord]

lilisworld

[marble vale]

how do i show that f is well defined

on R²

[boreal crag]

Show that (0,0) is the only place where the denominator is 0

[marble vale]

ok

$x^4 - 2x^2 y + 3y^2 = (x^2 - y)^2 + 2y^2$

[clever fjord]

lilisworld

[marble vale]

which is bigger than 0

or equal to 0

it is equal to 0 when (x, y) = (0, 0)

[marble vale]

but i dont understand what it implies

[tepid acorn]

the function can only be not well-defined if the denominator is 0

[marble vale]

mmh yes so it's enough? I just say it is well defined because it has a value when the denominator is 0?

[tepid acorn]

yes (the denominator is never even "equal to 0" since the function doesn't even use that expression except in cases where the denominator is not equal to 0)

[marble vale]

ok, so now they ask me to find the limit of g_m when x approaches 0

$g_m: \mathbb{R} \rightarrow \mathbb{R}, \quad g_m(x) = f(x, mx)$

[clever fjord]

lilisworld

[marble vale]

ye it's 0

so is f continuous at (0,0)?

[boreal crag]

That's not sufficient to determine that

[marble vale]

what steps do i need?

[boreal crag]

Maybe there's a lower bound and an upper bound and squeeze theorem applies

Try y=x^2

[marble vale]

ok

.close

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[boreal crag]

Did you solve it?

[boreal crag]

.close

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[marble vale]

yes thnks

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[frozen sail]

hello

[frozen sail]

can someone find the formula after the equals part

or explain what is going on

[mystic saffron]

have you done cofactor expansion before

[frozen sail]

no

[mystic saffron]

Okay lets start with, Find me the determinant of this 3x3 matrix
$$\begin{pmatrix}
1 & 5 & 3\
0 & 4 & 5 \
0 & 1 & 8
\end{pmatrix}$$

[mystic saffron]

have you computed the determinant before

[frozen sail]

yeah you row reduce it through coloumns

[mystic saffron]

thats one way, what about this way

[frozen sail]

yes i remember this way

[mystic saffron]

okay good, use this method for my question

but first how would you start

[frozen sail]

answer is -2

[mystic saffron]

i want your steps, can you send a pic of what you did

[mystic saffron]

thats another one, what about the one I gave you, but yeah thats the technique

[mystic saffron]

use it here now with 2-λ

[frozen sail]

what do you means?

[mystic saffron]

do the exact thing here
$$\begin{pmatrix}
2 -\lambda & 0 & 0\
1 & 2- \lambda & -1\
1 & 3 & -2 - \lambda
\end{pmatrix}$$

[frozen sail]

something went very wrong

[mystic saffron]

can I see

[frozen sail]

thats supposed to be the answer

[mystic saffron]

Factor and find the roots of
$$\lambda^3 + 2\lambda^2 + \lambda -2 = 0$$

[frozen sail]

oooooohhhh

that gives me the 1 2 and -1

but where did 1 1 1 come from?

[mystic saffron]

correct

[mystic saffron]

I usually use those when getting to eigenvectors, where you introduced to this as a eigenvalue problem? i wanted to get to geometric multiplicity

[frozen sail]

yes

[mystic saffron]

alr, in terms of algebraic multiplicity it would be number of times an eigenvalue has repeated and each are once

[frozen sail]

how to count the number of times repeated

[mystic saffron]

lets say we found the roots
3, 1, 1 instead

then 1 would have algebraic multiplicity of 2

@frozen sail anything else

[frozen sail]

sorry im trying to figure out the explanation u said

[mystic saffron]

okay lets say you have another matrix and the characteristic polynomial you get is (x-2)(x-2)(x-1)

epic fail💀

[mystic saffron]

what are the roots of my question

[frozen sail]

2,2,1

[mystic saffron]

right, so 2 has a algebraic multiplicity of 2

[frozen sail]

seems to make sense

[mystic saffron]

repeated twice

[frozen sail]

so since my roots only appear once its ks are going to be 1

[mystic saffron]

$k_2 = 2, k_1 = 1$

[frozen sail]

before you go can you please helo me understadn this

how did the matrix turn to this

[mystic saffron]

[mystic saffron]

these eigenvalues you got, 1,2,-1

[mystic saffron]

will be substituted here

then find the null space

[frozen sail]

that makes sense thank you very much for the help

[mystic saffron]

so you will have 3 matrices to work with correct?

[frozen sail]

wdym 3 matrices?

[mystic saffron]

you have three eigenvalues, subsituting each

[frozen sail]

what is an eignvalue

[mystic saffron]

since you haven't been properly introduced just the λ values you found

[mystic saffron]

@frozen sail sub the first what do you get

i have plenty of time to kill so we might as well do it I take that back

[frozen sail]

,rotate

[frozen sail]

no taksies backsies

[mystic saffron]

0,1,1 very good

next one

[frozen sail]

i think i understand it

thank you for your time

[mystic saffron]

good job

[frozen sail]

how do i achieve these emojis

:catThink:

[mystic saffron]

right click u shld see a favourite button

!done

[odd edge]

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[frozen sail]

.close

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[mystic saffron]

I was having an issue with this ACT statistics problem because I haven’t taken the class. How can I find out the number of combinations/permutations is possible if one of the spots is limited, like how the driver seat can only seat 3 of the 5 people?

[grizzled tide]

pick divers seat first, then assign the other 4 people to the other 4 seats

driver has 3 options, other 4 people have 4 permutations

your answer is right

@mystic saffron

[mystic saffron]

Ok, thank you. I got that correct by guessing but now I know. How would I calculate that answer in my calculator?

[lavish osprey]

first you choose between 3 of the 5 drivers, then the rest of the arrangements is a permutation of 4 items.

3 * 4! = 3 * 24 = 72

[mystic saffron]

Is a permutation of x items always x! Or are there different methods for different cases

[odd edge]

@mystic saffron Has your question been resolved?

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[thick skiff]

Hey, just a clarification question. The solution below takes the integral of g(x) - f(x), but I'm confused. Wouldn't this take the area of the shaded part above (f(x) - g(x)), and add the non-shaded area below?

[weary plaza]

Can someone help me with my math study guide?

[quasi sparrow]

Which non shaded area are you talking about

[weary plaza]

?

[thick skiff]

I sent my question before you btw

like split seconds before

i mean this part

(red)

[weary plaza]

Oh crap

U got that

[thick skiff]

.close

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[ember shell]

this is the question and this is my work

i just need help checking it that's all

<@&286206848099549185>

i sent this in a different channel but i accidentally deleted it

its been like half an hour 😭

[dry scarab]

!helpers

[odd edge]

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

[dry scarab]

!volunteers

[odd edge]

Helpers are just people volunteering their time to help you. Be polite and patient.

[ember shell]

ye lol

[ember shell]

ik it was my own channel

it was like kinda weird idrk how to explain it

but srry

[dry scarab]

ask admins if you suspect smth is wrong

!delete

[ember shell]

lol

[dry scarab]

there was a command for deleting etc

but i forgot rofl

ie when you delete accidentally

dont substitute before solving the problem symbolically!

ie solve with formula first

[ember shell]

uhh no it was just human error

[dry scarab]

then substitute constants/vars

ie you substituted P before writing it out fully

[ember shell]

Uhh

Wut

[dry scarab]

y/4=P(..)

solve

[ember shell]

Sorry I'm confused where this went lol

[dry scarab]

then substitute

[ember shell]

Oh I forgot to erase thst lol

Yeah uhmmm did I send the problem

I think because without the problem you don't know if I'm correct or not

Even if like I did the math right

If that makes sense idk

[dry scarab]

you did present the problem too

[dry scarab]

.

[ember shell]

Oh

Yeah I'm sorry lol I'm not in my mind rn

Uhh was what I got accurate

Or did I do something wrong?

[dry scarab]

im saying solve the formula first y/4=P() => y=4P() =>...

then substitute P=4000

[ember shell]

I have no clue what ur talking about srry

[dry scarab]

etc etc

[ember shell]

Like ok uhh

Do you mean this?

[dry scarab]

?

[ember shell]

That's the equation

[dry scarab]

yup

at the top you have the formula in its "final" form

[ember shell]

Right

Ic

[dry scarab]

no y/4=P() there

nice

[ember shell]

Uhhh

Why y/4

Because then at the end you multiply

[dry scarab]

.

[ember shell]

Ah I forgot to erase thst part

I did it differently before and I realized it was probably wrong

Since the answer I got was around 66300 or something

It didn't rlly sound right to me ino

Imo

[dry scarab]

well, i repeat, first solve the formula

then substitute

[ember shell]

Uhh ok well when I solved thst problem uhh

The y/4 thing I'll just solve it on a separate sheet hold on

[dry scarab]

hold tight lmao

[ember shell]

Ye np I'm just confused lol

And my discord keeps crashing

[dry scarab]

thats all there is to math

to be infinitely confused

[ember shell]

Literally

[dry scarab]

(and be ok with that, :P)

[ember shell]

Not when ur hw is due tmr 😭

[dry scarab]

weeeeell, homeworks come and go

confusion stays

[ember shell]

Fair

[dry scarab]

nonono

first solve y/4=p()

dont use numbers

use letters

[ember shell]

Wut

😭😭😭

And we find y then???

Thid?

This?

[dry scarab]

yup

[ember shell]

Kk

Well that's essentially the same thing that I did right?

Like uhm on the sheet I just sent

[dry scarab]

no

you substituted straight away

first solve formula

then substitute

[ember shell]

Oh ok

[ember shell]

So then I solve after substituting?

Uh...

@dry scarab ?

[dry scarab]

yes?

now just substitute

p=4000 etc etc

n=2? etc

[ember shell]

Uhh

Ok so I got yhh

[ember shell]

So is this the answer?

[dry scarab]

substitute all the values into the final formula you derived

[dry scarab]

yup

[ember shell]

Lol that was my original answer but it seemed so wrong

Ok ty

.close

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[fallow pond]

help a brother out

[light raven]

it's a cyclic quadrileteral

The opposite angles sum upto 180 degree

[fallow pond]

Ight ty

Let me check my answer first

[odd edge]

@fallow pond Has your question been resolved?

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[frosty sedge]

might be a stupid question but why is it 1

[frosty sedge]

is it right ?.. why is it 1..

why are.. n^2 - 8n + 16 equal to n^2 - 4n

is n-4 = n ??. . .

[ancient idol]

(n-4)^2 = n^2-8n+16

[frosty sedge]

yea i know that but why is the limit 1

[ancient idol]

but when you have two polynomial P(x) and Q(x) of the same degree, then lim(x-> inf) P(x)/Q(x) = 1

[wooden python]

@frosty sedge n^2 - 4n и n^2 - 8n + 16 сами по себе не равны

[ancient idol]

(n-4)^2 and n^2-4n have the same degree (2) with the same coefficient near it

[wooden python]

вообще формально предел находится так: $$\frac{n^2 - 8n + 16}{n^2 - 4n} = \frac{1 - \frac{8}{n} + \frac{16}{n^2}}{1 - \frac{4}{n}}$$ и тогда с чистой совестью утверждается, что $\frac{1}{n} \to 0$ и $\frac{1}{n^2} \to 0$

[ancient idol]

also, you can prove this just by dividing numerator and denominator by n^2

[clever fjord]

Ann

[frosty sedge]

аааааааа господи

спасибо

[frosty sedge]

thanks!

[wooden python]

ну или можно зазубрить правило, что если сверху и снизу одинаковая степень, то предел равен отношению старших коэффициентов

[frosty sedge]

аа

окей

[wooden python]

минздрав предупреждает: зубрежка без понимания сути и причин вредит вашему здоровью

[frosty sedge]

хахах

[wooden python]

ну или в данном случае видимо минобрнауки))

[frosty sedge]

.close

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[misty bane]

I need help with this please

[nimble blaze]

same idea as the previous question

$f(\underbrace{\blue{g(3)}}_{\text{find this first}})$

[clever fjord]

ℝαμΩℕωⅤ

[misty bane]

sorry im new to this and missed the days

is it harder or around the same thing?

[nimble blaze]

exactly the

same idea as the previous question

[misty bane]

okay will do

oooo i see

answer is 12

[nimble blaze]

yes

[misty bane]

okay thank your helping me understand

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[misty bane]

.reopen

[odd edge]

✅

[misty bane]

I dont understand for this problem. I got -1 while the answer is 7.

[nimble blaze]

what's your h(-2)

[misty bane]

umm sorry i dont undertand

[nimble blaze]

to evaluate that, you would've first done something like find
h(-2)

what did you get for that?

[misty bane]

umm this is how i did it

probably thats why i got it wrong?

[nimble blaze]

ah, you tried composing it first before substitution would is the other route
but the actual issues liies with how you're substituting in the -2

note that x^2 represents the square of the value x

[misty bane]

oh

[nimble blaze]

when substituting, what you have should still represent that,
in this case,
the square of the value -2, represented as (-2)^2 which will be 4

however you have -2^2, the negative of the square of 2, -4 which is different

[misty bane]

so what is the correct way?

[nimble blaze]

put parentheses around the -2

when substituting, what you have should still represent that,
in this case,
the square of the value -2, represented as (-2)^2

[misty bane]

oh becasue i didnt put paranthesis in -2 it came out different

[supple crater]

Yes

You should take x=-2

In h(x)

[novel hinge]

x is -2
so x^2 should be (-2)^2

[misty bane]

this goes with everthing not just this equation

oh okay

[supple crater]

Then take whats the value of h(x) into g(x) where x=h(x)

I am also getting 7

[misty bane]

got it

Thank you all for the help

.close

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[torn jungle]

How I solve this??

I already try but its wrong

This is my try

[livid storm]

,rotate

[livid storm]

,rotate

[torn jungle]

This is my attempt

[livid storm]

Original problem?

[torn jungle]

This is the original

We are task to identify it as a conditional or identity

[torn jungle]

But I see no problem with my attempt

[livid storm]

This is true

[torn jungle]

Its identity?

[livid storm]

How did -7 -2(5+3m) become -9(5+3m)?

[torn jungle]

-7-2=-9

Right??

[livid storm]

Yeah

But its -7 -2(5+3m)

not 7-2

[torn jungle]

Ohh yeah

Wait

Ohh okey now I see why im wrong

Thank you

How about this??

This is my attempt

[livid storm]

YOu cant just remove abs value like that

[torn jungle]

so how do I do it??

[toxic monolith]

look at such example, i made for you

$-3\left| x+4 \right|=-5\Leftrightarrow \left| x+4 \right|=\frac{5}{3}\Leftrightarrow \\x+4=\frac{5}{3}\text{ }\vee \text{ }x+4=-\frac{5}{3}\Leftrightarrow \\x=-\frac{7}{3}\text{ }\vee \text{ }x=-\frac{17}{3}$

[clever fjord]

Joanna Angel

[toxic monolith]

also remember this simple fact:

$\text{If }\text{ }a>0\text{ }\text{ then: }\\\left| x \right|=a\Leftrightarrow x=a\text{ }\vee \text{ }x=-a$

[clever fjord]

Joanna Angel

[torn jungle]

Is this the answer??

[odd edge]

@torn jungle Has your question been resolved?

[odd edge]

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[sweet cobalt]

is this the correct result for this question?

[shy smelt]

yeah

[sweet cobalt]

epic thank you 😄

.close

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[static shale]

How do i get 152

[restive delta]

Are you aware of the midpoint theorem?

[static shale]

No 😭😭😭

[restive delta]

How about BPT? Or Thales theorem?

[static shale]

Well maybe i just not sure what ur referring to

Im in math 2 academics idk

[restive delta]

Oh ok

[static shale]

😭😭😭😭

[restive delta]

It's nothin

Just that

[restive delta]

In a triangle, the line joining the mid points of 2 sides is parallel to the third side

And also equal to half of the third side

[static shale]

Rightt

[restive delta]

Then you may apply the property of parallel lines

Ykyk

[static shale]

Wait how would i do that tho

[restive delta]

Ok so did you understand how and why DE || AC?

[static shale]

Yeah

[restive delta]

Alr now

[static shale]

DE is half of AC

[restive delta]

Yeah

But DE and AC are parallel and AB acts as a transversal

So can you find any relation between the angles that BA makes with DE and AC?

[static shale]

Im not sure

[restive delta]

Have you heard of the term corresponding angles?

[static shale]

OH YEAH

[restive delta]

Nice

[static shale]

😭 sorry

[restive delta]

Don't be

[static shale]

I have a test today on this im really trying not to fail

🥲

[restive delta]

So what can you say about angles BDE and BAC

[static shale]

Their corresponding

[restive delta]

Yes

And so?

If they are corresponding what can we say?

[static shale]

Would i set them equal to eachother?

[restive delta]

Yes

[static shale]

But then i get 12=x

[restive delta]

Yeah

[static shale]

OMG

[restive delta]

It wants ADE...

[static shale]

I JUST DID IT

[restive delta]

Now what can you say about angles BDE and ADE

Oh you did?

[static shale]

So then i plug 12 into the equation and subtract that answer by 180

OK OK IM 25% MORE LIKELY TO PASS NOW

[restive delta]

Indeed

But be careful of which equation tho

[static shale]

Ok im probably going to have more questions so im not going to close the channel yet 😭 is that ok?

[restive delta]

Yeah ig

[static shale]

How about this one

i subtracted 70 and 60 from 180 and got 50 but why is that the answer

Ok forget this ine

How do i do this ONE

@restive delta

🥺🥺🥺

Pls come back ur saving me from my test rn

[restive delta]

It's similar

Use the corresponding angles thing and the fact that sum of angles in a triangle is 180⁰

[static shale]

Wait which one did u reply to

Mr. Lorentz please help me on #16

[restive delta]

I replied to 17

Ig

[static shale]

How do i do 16

[restive delta]

What does YZ equal to? I can't read it

[static shale]

YZ = 3x+1

[restive delta]

Oh

It's the midpoint theorem again

[static shale]

I set the equations equal to each other bc their parallel and corresponding and got 7 = 7x

😢 but then thats 1

[restive delta]

But the side lengths aren't equal

The line joining mid points is parallel, yes, but the length of it is equal to half the third side

[static shale]

Wait so what am i doing wrong

I have a feeling ur getting veryyyyy whats the word annoyed by me

🥲

[restive delta]

Nah, I'm just switching between chats that's all

[static shale]

Oh ok 😭

I think i got it now :3

But

[restive delta]

You said you equated the two equations as it is, but the side lengths aren't equal, YZ is half of MN

[restive delta]

Oh

Ok

[static shale]

How do i know this is none by none

[restive delta]

Same logic applies here

[static shale]

Im confused on how this is AA and SAS

Actually ignore all those other ones

Lets focus on this one

How is it 1/2 😭😭

[restive delta]

Scale factor= ratio between one pair of similar sides

[static shale]

How do i find that ratio

[restive delta]

How did you find 1/2?

[static shale]

I got the answers from my friends

🙂.

Pleaseee Lorentz hekp

[restive delta]

Lol

[restive delta]

Just find A'B'/AB

[static shale]

.close

[odd edge]

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[mystic saffron]

Does the Newton-Raphson method work, when choosing an interval with more than one solution?

[odd edge]

@mystic saffron Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mystic saffron]

Can someone please explain how the derivative at x=7 is undefined?

[ocean bramble]

3, 5 and 7 derivative 0.
9 derivative undefined

[hybrid ginkgo]

you said x = 7 is undefined but circled x = 9?

[mystic saffron]

I am talking about my teacher’s correction in red. I am asking why she is saying why the derivative x=7 is undefined

What makes it undefined

[hybrid ginkgo]

did yor teacher also circle the picture?

because then its probably a typo

[mystic saffron]

No, she did not. Anything in black was me

[torpid owl]

what about the thing in red? that is wrong

[mystic saffron]

Why is my teacher considering x=7 a critical number

You’re saying she’s wrong?

[torpid owl]

I'm saying "derivative undefined" for x=7 does not appear to be correct

the derivative at x=9 looks to be undefined

[mystic saffron]

Yes, because of the sharp corner.

Should the derivative at x=7 be 0?

[torpid owl]

it could be, sorta looks like it

[hybrid ginkgo]

could she mean that x = 7 is a critical point and that you forgot to define it?

[torpid owl]

I don't know; ask your teacher

[mystic saffron]

Maybe, Jonas. And x=7 would be a critical point because it equals 0?

Because the derivative* equals 0?

[torpid owl]

as I said, maybe. you need to ask your teacher; nobody here can know what was in her mind

[hybrid ginkgo]

yeah if she didnt make a mistake its the best guess i have, ask her.

[mystic saffron]

Thank you!

.close

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[odd edge]

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

[warped sparrow]

so i did this but i don’t think this is getting me anywhere

[viscid flint]

remember how you add matrices together, add each component separately

[warped sparrow]

wdym?

[warped sparrow]

how i add each component separately?

[viscid flint]

like add the top-left components together, then add the top-right, then the bottom-left, then the bottom-right

but start by distributing the coefficients so like you'll have $$\begin{bmatrix} 3x & 12 \ 3y & 3z \end{bmatrix} + \cdots = \cdots$$

[clever fjord]

hayley

[warped sparrow]

after i do that

i get two values for why

y*

[warped sparrow]

ya i get that

[viscid flint]

,rccw

[viscid flint]

it's hard for me to see where any of those equations come from

at least the top two

wait yeah what the heck

idk where the top two equations come from but the rest are good, and yeah it looks like there's no solution for y

[torpid owl]

7x = 14 is top-left, yeah

[warped sparrow]

so x = 2, z= -3

and y no solution

[odd edge]

@warped sparrow Has your question been resolved?

[warped sparrow]

so x = 2 and z = -3 and no solution for y

[viscid flint]

yeah problem is broken i think

[warped sparrow]

.close

[odd edge]

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