help-0

[normal frigate]

as so?

[quick wind]

yes

add the square bracket to the -4

like -4]

so we know its inclusive

[normal frigate]

oh sorry

[quick wind]

nah its ok

using ur notes and my advice hopefully u can attempt question 2 by urself

[normal frigate]

wait whats the K and vertex

nvm

who cares

im not turning it in

im just doing it so i can do a quiz

[quick wind]

just remember: find y intercept, make x 0. find x intercept make y 0. find vertex: if have brackets, (x+a)=0, h=-a, substitute -a to find k. IF NOT, use -b/2a, where equation is in the form ax^2 +bx +c =0. find domain: examine all x values. find range: use inequality with vertex given

[normal frigate]

yea naw

this is pointless

theres no c

or no b

idk

[quick wind]

math is pointless anyway

[normal frigate]

I know it is

[quick wind]

hey at least u got a bracket in question 2

[normal frigate]

unless I want to do something

[quick wind]

solve for (x+4)=0

[normal frigate]

ik but how do i do that

when i cant solve for H

if theres no b or c

idk which

probably no C

[quick wind]

the x value ur finding is h

IF HAVE brackets, (x+a)=0, h=-a, substitute -a to find k. IF NOT, use -b/2a, where equation is in the form ax^2 +bx +c =0

and this scenario u have brackets

so do the first option

[normal frigate]

dawg

what

is X=a

4=b

-1=c?

[quick wind]

ok forget the -b/2a for now

just make the bracket equal to 0 and ur golden

[normal frigate]

???

[quick wind]

make the inner bracket alone

equal to 0

to find h

[normal frigate]

(X+4)?

[quick wind]

(x+4)=0

we need to find the lowest value of y

if x is any other value other than (x+4)=0, the value of y would get higher and higher to infinity

[normal frigate]

Okay

[quick wind]

so x, aka h would equal to -4

and substitute -4 into x to find k

0-1 = k, so k=-1

[normal frigate]

I'm eating rn I'll be back in 5

[quick wind]

sorry its like 1am here now

i wanna sleep

yknow what dm me and we'll work it out

def would work better with a discord call and a proper whiteboard

[normal frigate]

okay

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✅

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[dense quail]

Between the two VA why is the function concave up? When I get the value of the second derivative withing that point, it's negative so should it not be downwards ?

Function: (-2x-8)/x^2-4

[coral steeple]

f"(x) <0 means concave down
f"(x) >0 means concave up

Make sure you study the sign well.

[dense quail]

I know that

[coral steeple]

$f(x) = \frac{-2(x + 4)}{x^2 - 4}$

[dense quail]

If you get the second derivative of zero, its negative, Zero falls within this domain(-2,2) so why is the function concave up there ?

[coral steeple]

Gimme f'(x) and f"(x)

[dense quail]

If you factored out -2 it should be -2(x+4)

[ocean seal]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[coral steeple]

Typo

[coral steeple]

.

[dense quail]

First Derivative

second:

[coral steeple]

R u sure about second derivative?

[dense quail]

yes

[coral steeple]

Mustn't it be -2x³ ?

[dense quail]

For what ?

[green shoal]

no it looks good, besides maybe wanting to change everything inside the parenthases to be positive and put the - outside

[dense quail]

Yh. You can factor out -4

[coral steeple]

$f"(x) = \frac{(4x + 16)(x^2 - 4)^2 - 4x(x^2 - 4)(2x^2 + 16x + 8)}{(x^2 - 4)^4}$

[ocean seal]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[green shoal]

I checked with the calculator too

[dense quail]

Yh this is right.

If you input 0, you get a -ve. But on the graph its concave up ?

[coral steeple]

Look at denominator

Negative at [-2;2]

[dense quail]

I see. Messed up my second derivative. Had -16

[coral steeple]

Did you find the answer?

[dense quail]

Well, still dont know how to graph it. Just know that it ic concave up

[coral steeple]

Did u study its sign?

[dense quail]

Yes

[coral steeple]

x³ + 12x² + 12x + 16 on [-2;2]

If it is concave up, -(x³ + 12x² + 12x + 16) must be negative

[coral steeple]

And this expression must be positive

[dense quail]

I get that now. There are different types of concave up. How do I know which one ?

And how does the graph look at the three different sections ?

[coral steeple]

U mean i, j, k?

U only have i and j

Just calcul f(-2, -1, 0, 1, 2) and draw it

[dense quail]

I have 3 parts becuase I have 2 VA. What will the graph look like at these points ?

[coral steeple]

Study f''(x) in [2;infty[

And ]infty; -2]

(Domain of definition)

[coral steeple]

Study f'(x) sign.
Positive means increasing
Negative means decreasing

[dense quail]

aii

Thank you for your help

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[daring breach]

I have a quick question and need some explaining.

How come the first photo is a real number but the next photo is not?

They both have negative in inside the radical sign. Can you also explain to me when it WONT be considered a real number and when it is considered a real number.

[daring breach]

The second photo doesn’t really explain it to me very well lol

[cursive ruin]

are you aware that raising any number to an odd power may give a positive or negative value
and raising a number to an even power will give only positive values

[daring breach]

Yes I’m aware. If n is an even positive number then it’s an absolute value

Wait

[heavy delta]

because odd power can give negative value
(-2)^3 = -8
but even power cannot give negative value
(-2)^2=4

same thing as root

[daring breach]

Are you saying in the first photo since 3 is an odd number, the result number can be positive or negative and inside the radical sign it’s -125, it works
But in the second photo since 4 is an even number, it won’t work before inside the radical sign is -16?

[heavy delta]

yes exactly

[daring breach]

Oooh! Okay!! And I have one last question.

Does that same rule apply to those problems as well?

[heavy delta]

yes

a. and b. is absolute value is because no matter the number inside ( )^2 or ( )^4 is positive or negative, it will turn into positive anyway

so it could be neg or pos if u use square root to cancel out the power

[daring breach]

For b, would it be considered wrong if I write it like this |x+2|

[heavy delta]

no

cuz it have a unknown variable, x inside

so just leave it there

[daring breach]

And then for the last one d) can you explain what they did there

I’m lost at why there’s an | | for x

[heavy delta]

because x is unknown variable, so u wont know it is pos or neg

but 25 and 5 is obviously positive

just think of x can be -4 or 4, but after square and square root, it should always come out 4

[daring breach]

Oooooh

I understand now!

Thank you so much!

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[median crater]

I got one of them wrong, I need with this

[fickle musk]

theres local max at 8

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[karmic pine]

I need help with linear algebra, I have a 3x3 matrix and I am being asked to find the basis for the null space. I was told to set up the matrix A with a 0 vector like [A|0] and then row-reduce to solve the system of equations.

[karmic pine]

the results I get should be a vector correct, if so is that vector the basis of the null space?

[placid zinc]

You shouldn't be able to reduce down to identity. There are many vectors that solve the system.

All vectors that solve that system are the nullspace.
The nullspace is a subspace.
As such, it can be expressed with a basis.

This shouldn't happen very often, but it can happen:
If there's a single vector solution, that vector is 0. The nullspace would then just contain the 0-vector, and would be 0-dimentional. The basis for such a space is empty.

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[tepid wadi]

yes i am that bad in math

[brisk ruin]

you want help with this question?

alright em, where to begin

[tepid wadi]

all i can do is like this

[tepid wadi]

I appreciate it if you can

i did this

[brisk ruin]

holy, um show me where you got this from?

[tepid wadi]

And then yapped a whole page and found out i did nothing

[tepid wadi]

from a game

[brisk ruin]

not the question, but

[brisk ruin]

this

[tepid wadi]

The last one?

[tepid wadi]

This?

[brisk ruin]

lets just start from the top

[tepid wadi]

I just realized it

from the question

i reached this

[brisk ruin]

so for these questions, first step is to combine the denomenators

[tepid wadi]

.

[tepid wadi]

yeah

[brisk ruin]

what is the LCM here?

"least common multiple" of 2x+10 and x+5

[bleak heath]

uhh why not take the numerator common first??

[tepid wadi]

Must be this

no?

[brisk ruin]

yes

you are correct

[tepid wadi]

nice

[brisk ruin]

now you want to move the 2x+10 to the other side

[tepid wadi]

alright

[brisk ruin]

therefore you ___ both sides by 2x+10

what do you do?

[tepid wadi]

multiple

i guess

[brisk ruin]

yes

[tepid wadi]

so far so good

[brisk ruin]

yes

now you want to get rid of the bracket

[tepid wadi]

i also can do this

[brisk ruin]

I mean square root

[tepid wadi]

i did this

[brisk ruin]

alright what did you get after squaring

oh you got 81(x+3)=4(x+5)^2

that is how you got this

alright

now you need to expand the brackets

what do you get on the left side

[tepid wadi]

so this

[tepid wadi]

ugh

now i am kinda lost

lets see

81/4 = (x+5)^2/(x+3)

[tepid wadi]

Are you there

[brisk ruin]

I am here

um

that is incorrect

[tepid wadi]

I see

[brisk ruin]

you can't go back to a fraction anymore

try to expand everything out

[tepid wadi]

Ok

[brisk ruin]

what is 81(x+3) if you take away the bracket

[brisk ruin]

yes

break the other bracket as well

[tepid wadi]

ok

[tepid wadi]

so i sum them all

-81x, -243?

to the other side

[brisk ruin]

yes

[tepid wadi]

Alr

[brisk ruin]

yes

and heck ugly numbers

[tepid wadi]

fr

[brisk ruin]

but eh, I think you can do the cross multiply method here

[tepid wadi]

hmm

[brisk ruin]

143=11*13

[tepid wadi]

Hmm

i dont think its this

The sum wouldnt be 41

[brisk ruin]

why?

4*13-11=41

[tepid wadi]

oh right

its 4x

[tepid wadi]

Haven’t learned this tbf with you

i know how if its x^2

not 4x^2

[brisk ruin]

it is the same thing

but instead with only the constant

noiw you are doing the x^2 term as well

so you want to multiply 4 and 143 together, and find two numbers with their DIFFERENCE (since it is -143) as 41

4*143=572

[tepid wadi]

I tried a trick i knew

but wasn’t as good as i thought

[brisk ruin]

no dont do it

that makes it harder

instead do this

[brisk ruin]

this

now

572, I know this is a hard number

it takes a bit of number sense to locate 52 and 11 as well

[tepid wadi]

Yeah

Maybe if with calculator easier

[brisk ruin]

I can teach you an easier method

if you know the formula

[tepid wadi]

I know it

[brisk ruin]

actually if it is easier is debatable

but anyways

[tepid wadi]

The right one is multiple and the middle one is the sum and guessing

[brisk ruin]

the cross multiply method

you break
4 -143

into

4 11
1 -13

if you cross multiply 4 and -13, 1 and 11, add them up, you get -41

[tepid wadi]

How do i choose numbers exactly? It could be 2 x 2

or -143 x 1

[brisk ruin]

that is up to number sense

there is no shortcut

you have to figure it out yourself

[tepid wadi]

so 41x is no related here too

[brisk ruin]

but like you can like estimate the range right?

no it is related

you cross multiply

[tepid wadi]

in last answer it should be -41

[brisk ruin]

multiply 4 and -13 you get -52

Hear me out!!!

[tepid wadi]

yes

-52

[tepid wadi]

sorry

[brisk ruin]

if you corss multiply 1 and 11 you get 11\

add -52 and 11 up

you get -41

[tepid wadi]

-41

i see

thats easier method

[brisk ruin]

and now that the cross is complete

[tepid wadi]

for hard questions

[brisk ruin]

you can just combine them

4 and 11 is in the same row

(4x+11)

1 and -13

[tepid wadi]

doesn’t matter no?

[brisk ruin]

no it does

x-13

[tepid wadi]

(4x+11)(x-13)

[brisk ruin]

you would get (4x+11)(x-13)=0

[tepid wadi]

two answers

[brisk ruin]

and yeah you would get two answer

now!!

[tepid wadi]

-11/4 , 13

[brisk ruin]

your original function

have some restrictions

it would be best to list them out

sqrt(9x+27)

obvious that x>-3

or =

[tepid wadi]

-11/4 is less then -3

ig

just a sense

[brisk ruin]

...

-11/4 is greater than -3

[tepid wadi]

oh

[brisk ruin]

cmon, know your numbers lol

[tepid wadi]

12/4 = 3
11/4 should be less no?

[brisk ruin]

it is negative!

negative is reversed!!!

[tepid wadi]

yes in negative its less so its greater

[brisk ruin]

and x+5 in denominator means x cannot be -5

fortunately, none affects your two answers

therefore this question does have 2 answers

[tepid wadi]

lets try them

[brisk ruin]

which is -11/4 and 13

[tepid wadi]

tbh

[brisk ruin]

yeah you can plot them into a calc

[tepid wadi]

9(/x+3) = 2(x+5)

should be easier now

36 = 36

It is 13

[tepid wadi]

thanks man i had struggled with it for all that yap

I thought -143 and 41 didnt have a relation

-41*

[brisk ruin]

lol, building up number sense is what ya need

[tepid wadi]

yea I should make sure before anything

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[zealous widget]

Can someone help me find the implicit differentiation dy/dx

[zealous widget]

I was thinking subtract y' and then factor it out?

.close

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[modest coral]

3b.. as we discussed whats happeniing is the total is initially 1, then 1+1, 1+2 so on until 1+5 then we add all those correct? i got 20 but the answer is 16. for part a it was correct; answer was 15

[modest coral]

@plucky trench

[plucky trench]

from last time we concluded that it would be total = x + 1 + 2 + 3 + 4 + 5 = x + 15

try to unwrap the loop to see whats going on every iteration

we first set total = x

then the loop begins

for the first run, i = 1

total = total + 1, which means total = x + 1

next loop, i = 2

total = total + 2, this time total = x + 1 so we're reassigning it to total = x + 1 + 2

after all the loops it would go total = x + 1 + 2 + 3 + 4 + 5 = x + 15

[modest coral]

ohhh

that makes a lot more sense tysm! & so whenever it says for i to whatever and variable = variable + i it’s just saying variable + all the values i can be plus it not individually?

ignore the image

i accidentally attached it

[plucky trench]

sure

it would make more sense to go through the loop

and see what i is every time

drawing a trace table might help also

https://www.101computing.net/using-trace-tables/

so you're going through the program like you're a computer

seeing what happens every step

[modest coral]

i might do that if i have some extra time but im trying to get through some questions ive got the test very soon for this 😭🙏

do u have some time for 1 more question

[plucky trench]

sureeee

i do encourage you to try out the trace table

it makes everything make so much more sense

[modest coral]

question 10 here i attempted it but im sure its off

[plucky trench]

mmmmmm

[modest coral]

oh we did something similar in class

[plucky trench]

i dont think this is up to the pseudocode standards of your book

[modest coral]

oh yeah

it isnt

one sec

[plucky trench]

imagine having a loop

and every iteration you update your xn variable to be

xn <- 3*xn + 2

so every iteration would be computing x_{n+1}

you can verify this by using a trace table

[modest coral]

i updated it sorta

[modest coral]

what do the _ and {} mean

[plucky trench]

just $x_{n+1}$

[ocean seal]

Deftioon

[plucky trench]

mmmm code doesnt like you defining variables like that

i get what you mean though, you're trying to do recursion

perhaps what the exercise wants you to do is to do a while loop

[plucky trench]

by doing this until xn > 1000

maybe you could think of a way to do that

[modest coral]

ok one sec lemme try that

how do we identify tho

what it wants us to do

is this good 🥲

oh i forgot to return the function just pretend thats there

[plucky trench]

hmmmmmmm

i dont think you need to make a function

[modest coral]

oh

[plucky trench]

just a variable xn = 4

[modest coral]

but it says defined by the rule

oh

[plucky trench]

and keep xn <- 3 * xn + 2

until its larger than 1000

[modest coral]

even if it says defined in the question we dont need a function?

[plucky trench]

you definitely could, if you wanted

but i dont think its needed for this question

as to why its because you can do it without a function

if you wanted a function, know that xn is a function that takes n as input

so you define a function

[modest coral]

ah ok

also

[plucky trench]

def x(n):
  if n = 1:
    return 4
  
  return 3 * x(n-1) + 2

[modest coral]

wouldnt this be x1 = 4 and xn= 0

before the while

[plucky trench]

would evaluate x(n)

[plucky trench]

you can keep x1 and xn in the same variable

[plucky trench]

this would probably be in your next chapter

recursion is in every cs book ever

[modest coral]

how

so this says ; initially its 4, then bc 4 is less than 1000 it runs, 4 is subbed into the equation and repeated until equation is over 1000 and when that happens, n is printed

i think i finally understand it :D

is that correct

[plucky trench]

ye this looks sound

but you havent defined n

just xn

[modest coral]

YESSSSS

[plucky trench]

keep a counter for n

and every iteration of the while update the n <- n+1

so you can count how many iterations its done

[modest coral]

oh, is that just n= 0, while in the loop its n+1

[plucky trench]

also n = 1 at the start not 0 thats just something to keep in mind

[modest coral]

.

why

[plucky trench]

cuz x1 = 4 not x0

[modest coral]

cus its multiplied?

[plucky trench]

define n = 1 outside the loop and n <- n + 1 in the loop

[modest coral]

ooooooh

[plucky trench]

uh no

[modest coral]

YEAH

[plucky trench]

remember the computer only reads what you say so

explicitly

[modest coral]

OK I THINK I GET IT NOW

THIS IS FUN

[plucky trench]

it does not know xn is for that sequence

it only knows xn is a number

and every loop i update it this way

[modest coral]

ooh so u have to do it seperately

[plucky trench]

ye

[modest coral]

so if u had like x+n = 1 too you’d have to define both first right?

like as an example…

or no

[plucky trench]

the computer doesnt understand what x + n = 1 means

it sees that and says

"I need to assign 1 to the variable x + n"

"but x + n isnt a variable, its an expression"

and oops it errors

[modest coral]

ohhh

okk i think i get it

tysm!

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[pulsar halo]

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@pulsar halo Has your question been resolved?

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[next crag]

how does one do this

[dim garnet]

Use the definition of directional derivative

Just saw it’s also the hint

[next crag]

how do i even start

[dim garnet]

Calculate the directional derivative

[next crag]

how

[dim garnet]

Plug in the information you have into the definition

[dim garnet]

Also the u in the definition is supposed to be a v

[lone heart]

@next crag Has your question been resolved?

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@next crag Has your question been resolved?

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[alpine sable]

is this solved

[ebon hornet]

please elaborate boss

[void nymph]

!done

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[modern pagoda]

trying to differentiate (4x+3)(2x^2+3x)^5

the thing written at top

can someone review my work?

I tried to use chain rule and product rule

this is the solution

[quick wind]

yes ur correct

[modern pagoda]

Okay I can't see how my solution is the same as this one

[quick wind]

just simplify the 5(4x+3)(4x+3)

[modern pagoda]

how do i rewrite

[quick wind]

into that quadratic

[modern pagoda]

why do i need to put ( ) around it in the final solution?

[void nymph]

because everything is multiplied by 5?

[modern pagoda]

here there is ( )

around 80x^2+120x etc

whyy

I have a feeling it needs to be there and it does but i dunno really why

.close

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[steady thorn]

can anyone help me understand why you can use 1-r and r-1 in geometric series equation?

[vale wigeon]

x/y = (-x)/(-y)

[steady thorn]

so it wont matter which one i use

[mental python]

no, thats why it says or

both work

[steady thorn]

ah ok

thx guys

.close

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[void nymph]

what the

the everyone ping doesnt actually ping everyone

[alpine sable]

what is this

[void nymph]

but what the

<@&268886789983436800> might wanna come say hi

[mental python]

nah

[void nymph]

the hell

[slim kite]

I think u need permission to ping everyone

[lone heart]

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[worn bane]

https://discord.com/channels/268882317391429632/1354445284138156052

help me please

[fickle crypt]

30 + 10

[lone heart]

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.

[worn bane]

?

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[golden pulsar]

hi

[golden pulsar]

I am stuck with Eigenvalues

I have this matrice:

(1 x)
(x 2)

then its (1-y)(2-y)-x^2 = 0

im stuck with the algebra here

why am i not allowed to do +x^2

i want to solve:
1-y = x^2 and
2-y = x^2

(if it matters, its for the condition number of matrice)

[slim kite]

Hi!

[golden pulsar]

that doesnt explain why my solution is wrong

i mean, AI says, i am not allowed to +x^2

my y_i are
y_1 = 1-x^2
y_2 = 2-x^2

and for x i get {-+sqrt(1), -+sqrt(2)}

i need the reason why its wrong

lol

nice help

prove this is right

yes i asumed thats what AI also did

no

i want an explenation why my is wrong

no

i know i can factor out the ()()

i want to know whats wrong with adding +x^2

and then solve 1-y = x^2

i already got he anweser from AI lol

you cant answer my origin question, its ok, thanks for help

yes im a cs student

i know this

this formula is 6th graqde

lol

it does not anweser my question

well i know but im too stupid to help others, thats why i joined this server for help

[winter light]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[golden pulsar]

you need your own thready

[raw vapor]

oh even you are having a question about matrices

[winter light]

You're allowed to do it, who says not?

[golden pulsar]

AI says im not

[winter light]

!nogpt

[lone heart]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[golden pulsar]

so i am allowed to do this

1-y = x^2
2-y = x^2 and solve it?

thats why i want a math professor

[winter light]

No, not like that...

[golden pulsar]

yes why not

[winter light]

Actually, here there's no need to add x² to both sides

You simply have to expand that product and solve for y

[golden pulsar]

but why can i not solve for y the way i did

i do know i can simply expand

[winter light]

Because that only works when the left hand side is factored and the right hand side is 0 (of course 😅 )

[golden pulsar]

so you mean if (1-y)(2-y) = 0 then i can 1-y = 0 and 2-y = 0

[winter light]

Yes

But I hope you know why

[golden pulsar]

but +x^2 is a valid aglebraic operation

[winter light]

Yeah totally fine. In equations (and also inequalities) you can add same thing to both sides, whatever that thing is

[golden pulsar]

is it because its another variable

[winter light]

Huh?

You can add a variable, a number, a constant, whatever, to both sides

The important thing is you do it on both sides

You should know this also before starting linear algebra, honestly 😬

[golden pulsar]

yeah that doesnt help me

i almost done with my cs degree

anyway thanks

.close

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[fierce barn]

(Don't mind polish I'll explain everything)

I need help with C) Find the area of the wall "PQR". idk what is the height for PQR. I know that |PQ| = 2*sqrt(5) but I don't know how to check if |PQ| falls 90 degrees on |QR| and if I can use it as the height. So my question is, how to find the height for PQR? (BTW point P seperates the side edge into 2 equal parts so 4/2 = 2)

[fierce barn]

ah wait nvm 😭 Im stupid, mb guys. Just had to look at it well

.close

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[last vault]

can someone explain to me rq why u dont knwo the exact value of x and y int for part c

[winter light]

How did you solve questions (a) and (b)?

[last vault]

well since for part a the x int doesnt change so it stays at 0

y int is when x=0 and like

since yk y moves down by -3

u do 2-3

which gives u -1

and similar concept for b

but x is (-2,0) and (5,0)

ye

[void nymph]

why cant you do that for the third too?

[last vault]

uh

well the answer says that

u cant find it

but wont x int just be -5 and 2

or am i missing something

[winter light]

How so you find x-intercepts?

[last vault]

when y=0

[winter light]

So you need to solve j(x) = 0, right?

[last vault]

hm yes

[winter light]

Therefore what do you get?

[last vault]

so f(x+2)-4=0
f(x+2)=4

[winter light]

Yep

[last vault]

uh

thats it ig

[winter light]

Yeah

But do you have info about f giving 4 as output?

[last vault]

wait but if u do that for lets say b so h(x) is meant to be 0

[last vault]

uh

wym

[winter light]

Solving f(x+2) = 4 means finding for which values of x the function f returns 4...

Do you know how functions work? 🤔

[last vault]

ye every input has one output

u cant have many outputs to one input

[last vault]

uh 2?

wait but that would be

hm

[granite crest]

yeah what is it ?

[last vault]

wait so the new x and y int is when the other is equal to 0

but u cant find what f(x)=4 is for the new x int

like if its a staright line it would cross y=4 somewhere but if its a porabola

we dont know if it ever crosses

and thats like the asme w y int

.close

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[alpine sable]

i need help

with the first question

i have no idea how to solve it

i tried everything i think

[vale wigeon]

including writing $z = \cos(\theta) + i \sin(\theta)$ and then doing double/half-angle BS to simplify $z \pm 1$?

[ocean seal]

Ann

[void nymph]

😭

[granite crest]

try this its right

[alpine sable]

.close

[lone heart]

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[vale wigeon]

uhhhhhhh

@alpine sable are you actually intending to commit suicide here or was that an exaggeration

[alpine sable]

oh sorry did that sound serious

[vale wigeon]

yes it did

[alpine sable]

mb

[vale wigeon]

you should not joke about it tho

[alpine sable]

sorry

[vale wigeon]

don't call me "sir" please.

[alpine sable]

i'm very sorry 😭

[lone heart]

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[paper fossil]

\

[paper fossil]

I belive I can do it I just dont know what the symbols mean in the second sentence

[tropic plaza]

which symbol?

AB||DE?

[paper fossil]

Yeah the first part of the 2nd sentence

[tropic plaza]

AB||DE means that AB is parallel to DE

[paper fossil]

Do the lines on top of AB and DE mean anything?

[tropic plaza]

ig it means 'line' AB

line AB is parallel to line DE

[paper fossil]

Ohh

Ok thank you

.close

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[wet magnet]

i get that n= 6 but its totally wrong

[vale wigeon]

mmm

what's n

[wet magnet]

like (9 over n)

[steel bison]

Binomial formula?

[vale wigeon]

right, and i take it you tried to rawdog it from this form?

here is a suggestion

[wet magnet]

i focused only on the powers equating it to zero

[vale wigeon]

can you show your work btw

it could be an arithmetic error for all we know

[wet magnet]

ya ill send it in a sec

[vale wigeon]

but failing this, i'll give my suggestion: rewrite $\frac{1}{3x^2} - \frac{x}{2}$ as $\frac{2 - 3x^3}{6x^2}$ so that your original expression becomes $$\frac{1}{x^3 (6x^2)^9} (2-3x^3)^9$$ or, after some more tinkering, $$\frac{1}{6^9} \cdot x^{-21} \cdot (2-3x^3)^9$$ from which you reduce this problem to finding the $x^{21}$ term in $(2-3x^3)^9$

[ocean seal]

Ann

[vale wigeon]

(the philosophy behind this sort of rewrite is that you should avoid handling negative exponents any more than absolutely necessary with this kind of stuff unless you are a sign error lover)

[alpine sable]

this is simple

[vale wigeon]

and that is an unnecessary thing to say in a help channel

,rccw

[wet magnet]

why do you just say it's simple without helping?

[steel bison]

Hey, I think I got it is the answer 36?

9 choose 7

[vale wigeon]

ok so you just forgor the 1/x^3 out front it looks like

[vale wigeon]

the answer will not be just 36 i don't think.

[wet magnet]

Ya I was thinking about that so it will be -3 - 18 +3 n?

So I would get n=7?

[vale wigeon]

yes

but see my suggestion also

[vale wigeon]

right here

[steel bison]

I think it’s the 8th term

[wet magnet]

alright, ill try my method first, but yours looks good first. but i look at awnser sheet and they say its supposed to be 9 over 2 not 9 over 7

[steel bison]

Oh wow

[wet magnet]

so is n 7 or 2

[vale wigeon]

$\binom{9}{2}$ and $\binom{9}{7}$ are one and the same actually.

[ocean seal]

Ann

[steel bison]

Ohh you’re right!

n choose k is the same as n choose (n - k)

[wet magnet]

oh true, but how did they get 2?

[vale wigeon]

well you want one thing ^7 and another thing ^2

whether you frame it as C(9,7) times some shit or C(9,2) times some shit doesnt really matter

[wet magnet]

Yes true. Sorry but it just bugs me of not being able to solve it the same way they did

hmm I maybe move on

Ya it did give the same value

[vale wigeon]

you should get used to problems having more than 1 correct/valid solution

[lone heart]

@wet magnet Has your question been resolved?

[lone heart]

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[slate sage]

anyone know a ytber that teachs calc 2 from the very beginning bc im like 4-5 lectures behind

[stiff trench]

very beginning as in from the beginning of calc 2 or calc 1?

[tacit arch]

https://en.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-7/e/finding-area-with-fundamental-theorem-of-calculus

[slate sage]

from indefinite integrals to integration of trigonometric functions

ill just search up each sections individually i think

[stiff trench]

u can do khan academy or organic chemistry tutor type stuff

[steel bison]

Maybe bprp?

[lone heart]

@slate sage Has your question been resolved?

[quick wind]

professor leonard

fantastic guy makes me learn so much stuff

[lone heart]

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[warped topaz]

Not really sure what to do here...

[vale wigeon]

a or b?

[warped topaz]

b sorry

Also, how is there only 2 points?

The red line is x = -1

The 4 blue lines are the 4 potential distances of 8, no?

[vale wigeon]

no

the distance from a point P to a shape S is the lowest among all possible distances from P to a point in S

and for a circle this closest distance will in fact manifest as a line that if extended would meet the center

so in fact the set of all points at distance 8 from c_2 is just a circle with center N and radius 5+8

[warped topaz]

1 moment I need to read this a few times to understand

[warped topaz]

But its not the lowest, right? There are points where the distance between x = -1 and the circle is greater than 8, and points where it is less than 8, right?

[forest marsh]

Let me read this rq

Wow i have no idea tbh

[warped topaz]

Was I at least right about there being 4 points?

[forest marsh]

Unless

Ann said it but you would have theses points such as the segment N to P is 13

Same for Q

[warped topaz]

Ok, makes sense

[forest marsh]

In that case the question is quite resolve

[warped topaz]

Theyre not straight lines though right?

Its 2 lines at an angle right?

[forest marsh]

They are cuz its triangle

[warped topaz]

Ah ofc lol

[forest marsh]

Else its anything else not a triangle

[warped topaz]

Yeye

[forest marsh]

So b*h/2

[warped topaz]

Wait

The angle between them would be 90 degrees right

Which means they would have slopes of 1 and -1?

Oh wait no

Nvm

[forest marsh]

Uh yeah probably

[warped topaz]

But we dont know the lines are touching

[forest marsh]

Not neccessarly

[forest marsh]

?

They both go to N tho

[warped topaz]

Ngl im really confused

Is the distance 8 between x = -1 and point n?

Or the circle?

point n makes way more sense

But it doesnt seem like thats what theyre asking

[forest marsh]

Between P and the circle and Q and the circle

But the circle is at 5 from n

[warped topaz]

Tbh I still dont know why there isnt 4 points.

[forest marsh]

Where are your points ?

[warped topaz]

The blue lines are the distances of 8

So the 4 intersections between the blue lines and the red line

[forest marsh]

Not from the circle

[warped topaz]

Why not?

[forest marsh]

The shortest way is perpendicular line to the tangent and so its not here

[warped topaz]

To which tangent?

And why does it need to be the shortest?

[forest marsh]

Any of the circle

[warped topaz]

Im sorry I gotta take a break my brain is sooooooo cooked

Thx for your help to this point

❤️

.close

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[dry cypress]

can someone PLEASE PLEASE tell me how do i do quadratic equations lecture in math

[dry cypress]

i have math exam tomorrow and im loosing my mind i cant fucking learn this shit

tag me if you answer

[tacit arch]

do you have an actual problem

from homework or lecture notes or something

[dry cypress]

i do: 2x and then the little number 2 on top of that and - 7x + 3 > 0

[tacit arch]

$2x^2 - 7x + 3 > 0$ ?

[ocean seal]

riemann

[dry cypress]

yeah that

[tacit arch]

,w roots 2x^2 - 7x + 3

[ocean seal]

Results provided by WolframAlpha

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

Requested by rie.mann

[dry cypress]

teach me like the most most important parts of that problem so i can just learn that and get positive grade

please

[tacit arch]

you can either use quadratic formula or try factoring

,tex .quadratic formula

[ocean seal]

riemann

[dry cypress]

yeah thats how they taught me in school

[tacit arch]

can you identify a, b, and c

[dry cypress]

i tried doing this with chatgpt but it couldnt do it

[dry cypress]

is it gonna continue?

[tacit arch]

!nogpt

[lone heart]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[dry cypress]

should i replace -b, b2-4ac with numbers im given?

[tacit arch]

yea try that

[dry cypress]

i did

now what?

[tacit arch]

did you get numbers for these two x valeus yet

[dry cypress]

huh?

[tacit arch]

they look similar but are actually different when b^2 - 4ac > 0

[dry cypress]

i just replaced two b's with number 7

[tacit arch]

yea do the same for a and c

[dry cypress]

instead of -b i put -7 and instead of b2 i put 72

i mean not 72 but like 7 and little 2

[dry cypress]

is a = 2 and c = 0 for me?

[tacit arch]

c is not 0

[dry cypress]

is it 3?

[tacit arch]

compare this

to this

yes 3

[lethal plinth]

Remember b=-7, not 7

[dry cypress]

i mean at the end it ends up looking like 423 but okay i guess

nothing goes in between those numbers ?

[tacit arch]

show

[tacit arch]

i see

$4ac$ means 4 times a times c

[ocean seal]

riemann

[tacit arch]

,calc 4 * 2 * 3

[ocean seal]

Result:

24

[tacit arch]

in this case $4ac = 4 \cdot 2 \cdot 3 = 24$ and not 423

[ocean seal]

riemann

[dry cypress]

i should write 4 * 2 * 3 and then = 24 under that

btw i cannot calculate 4 * 2 * 3 in my head in class without calculator but i guess i'll figure it out 💀

[tacit arch]

luckily multiplication can be done in any order

(4 * 2) = 8

then do 8 * 3

[dry cypress]

yeah thats what i always do

but if you were to give me like 32 * 17 i would never figure it out

like i could but it would take me like half an hour

you know what

thank you so much for this

but i cant right now

like i really really cant

listen tomorrow when im at the exam im maybe gonna send a picture of the eqasion and someone here please please please do it and make it really quick

i guess this discord is really active so i could just take a pic of it and send it to yall but if i cant then idk what i will do i will probably just get 1 and fail class and then quit school if i do.

i want to be a pc builder not a mathematic

[tacit arch]

yea don't do that

[lone heart]

@dry cypress Has your question been resolved?

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[lone heart]

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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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[alpine sable]

Hello

[vale wigeon]

you should just begin with your question next time

[void nymph]

!da2a

[lone heart]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[alpine sable]

Looking for this question for hours still cant even move my pencil🥹
İ would hapy if someone help..
Explaining:When the graphs of the functions f(x) and f'(x) are plotted in a computer program, the coordinate axes are deleted and a grid of equal squares is placed in the background, the following image is obtained.

According to this, what is the smallest value f(x) can take

[forest marsh]

Since f goes from decreasing to increasing then the derivative changes sign

[alpine sable]

🤔🤔

İ dont get is sir

[forest marsh]

Lasting now to know whats a square height

[forest marsh]

Which part

[alpine sable]

Oh nvm my bad

Pls contunie

[forest marsh]

.

Can't do anything without this

[alpine sable]

Hmm the question is wrong?

[forest marsh]

Its missing the value of a square

So if its not saying then yes the question is probably uncomplete

[alpine sable]

But it says isosquare

Maybe i translated wrong sry..

[crimson dawn]

I think it might be possible to solve for it

Ah nvm

[alpine sable]

Guys wanna see my attemps to solve this?

İ writed a bit

[forest marsh]

It should be saying a square side value is ...

Idt your translation is involved since there should be numbers in the question and there is none

[alpine sable]

Hmm

[forest marsh]

Try asking your teacher or tutor to know the truth about the statement of the exercice ig

[alpine sable]

Ty for your helps friend

[forest marsh]

Yw

[alpine sable]

@void nymph can u help?

[alpine sable]

.

[alpine sable]

İ stuck here

[vale wigeon]

i am asleep sorry

[sly mantle]

@alpine sable pls dont ping random ppl for help

[alpine sable]

<@&286206848099549185>

[alpine sable]

<@&286206848099549185>

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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Remember:
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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.

[viscid rain]

Hey I’m really confused choosing bounds and what I think they represent in 3d space and the volume they are covering could someone check these ans make sure I’m right I try checking with ChatGPT buts it’s always wrong or siffernt answers

[lone heart]

@viscid rain Has your question been resolved?

[lone heart]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[lilac vigil]

hello, just doing some trig questions on drfrost and have never come across a question like this, im not even sure how to begin so i would appreciate

[lilac vigil]

i thought about making a traingle using the radius to A and B But im not sure

[teal orbit]

notice that if you draw a radius towards the other tangent you get a kite

and that you have 2 right triangles in those kites

and that the line AO bisects angle CAB

so thats enough info

[lilac vigil]

AHHH

my goat

appreciate it 🙂

[teal orbit]

welcome

🫡

[lone heart]

@lilac vigil Has your question been resolved?

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Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[shell acorn]

.help

[lone heart]

Commands:

• clopen: .close, .reopen
• consensus: .poll
• factoids: .tag
• help: .help
• version: .version

Type .help <command name> for more info on a command.

[shell acorn]

need some help with this

[shell acorn]

its pretty easy im just confused on how to draw it

[teal orbit]

🤨

sum1 asked this yesterday bro

[shell acorn]

say ong

[teal orbit]

ong

[shell acorn]

LOL

yu got a ss fam

same class?

[teal orbit]

no

[shell acorn]

shi would b funny asl

[teal orbit]

idk bro i just saw it

😭

anyways

[shell acorn]

help me solve it

well

draw it please