help-38

[gusty bone]

so what is x when cos(x) = 0?

[lone elbow]

nevermind, found it

cos(x) = 0 whenever x = 90

1/cos(270) works as well

jesus christ

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[lone elbow]

@devout drift @gusty bone @ionic pendant thank you for trying to help me with this problem 🙏🏻

[devout drift]

You know 90 degrees is just pi/2 in radian measure

[lone elbow]

nope i did not realize that F

[devout drift]

I think I should have just used degrees

[lone elbow]

For some reason i never made the connection LMAO

[devout drift]

And since cosine function is periodic

[lone elbow]

maybe it would’ve been easier

[devout drift]

Yeah but anyways

You understood

It

Right?

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[delicate lance]

what does g(1) equal?

[naive pilot]

-4

[delicate lance]

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[vague sinew]

right now i am having trouble with what to do after i get to the integral of 9 sec

i will send my work

to make sure i did not do anything after that point wrong

or before

any help is appreciated

what is S?

how did you get that

is that the answer

what are you trying to say exactly?

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[wise yarrow]

Can someone help verify that this is correct?

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[echo jasper]

how to graph this againa

like ;/

is it just

the points of y=x^2

and just make them go up 2 and right 1

[gusty bone]

no

complete the square

giving

y = (x+1)^2 -1

So the vertex is at (-1,-1)

[echo jasper]

ah

[gusty bone]

So a downward shift of 1 and a leftward shift of 1

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[azure thistle]

can anyone explain what p is the foot... part means?

[umbral maple]

where the height of the triangle meets the base

so draw a line from b

and it should go straight through ac

[azure thistle]

smt like this?

[umbral maple]

ya

[azure thistle]

also after finding the equation of BP, do u know how i could find the cordinate of P?

[umbral maple]

do you have the equation of AC

if yes then you can just set them equal to each other to find their intersection

[azure thistle]

oh ok

ty

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[bold matrix]

Hi, how do I start? I have the gradients and midpoints of the sides, but how do I find the gradient of the mediator?

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[bold matrix]

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<@&286206848099549185>

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[bold jay]

any chance you can use the fact that there are only two groups of order 6 up to isomorphism?

probably not

[alpine fern]

elab?

[bold jay]

no need, you can't use it if you don't know what i'm talking about

[solar quest]

so, what is the geometric intuition for D_3

[alpine fern]

a triangle

[solar quest]

not quite a triangle

the rotations of a triangle

now what happens if you label each of the vertices of this triangle and apply various transformations from this group

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[terse field]

There are 52 cards in a deck. I will draw 7 times from the deck. The drawn card will not be reinserted into the deck. What's the probability of drawing 3 spades, 2 clubs, 2 diamonds and 0 hearts?

The order does not matter. eg: (AAB & BAA & ABA are the same outcome)

I'd like to know the working for this. Is there a formula to calculate the probability of all outcomes quickly without using the probability tree? I only remember using the tree. Even pointing to a youtube tutorial is fine.

[neon dirge]

calculate the prob of one path

then multiply it with the number of paths

[terse field]

So, it has to be done manually with the tree?

[neon dirge]

well what's the prob that you first draw a spade?

[terse field]

13/52

[neon dirge]

yes, now what's the prob that you draw a second spade

[terse field]

12/51

[neon dirge]

third spade?

[terse field]

11/50

[neon dirge]

now a club?

[terse field]

13/52

[neon dirge]

careful

[terse field]

13/49

[neon dirge]

now another club?

[terse field]

12/48

[neon dirge]

then a diamond

[terse field]

13/47

[neon dirge]

and lastly another diamond

[terse field]

12/46

[neon dirge]

13/52 * 12/51 * 11/50 * 13/49 * 12/48 * 13/47 * 12/46

is your probability

for one path

if you can find the number of paths which fulfill the requirements and multiply it by that probability, you get the desired probability for the solution

[terse field]

And that's one path. And there are other paths since you can draw a mix of clubs/spades/diamonds in a different order.

[neon dirge]

ys

[terse field]

Is there a way to simplify the process?

That's a lot of paths.

[neon dirge]

sure

there's two convoluted steps put into one problem

currently we have one path

but there are paths for all arrangements of the types: Spade/Club/Diamond

and there are paths for different spades, clubs, diamonds we draw

ok so firstly, we drew SSSCCDD

S=Spade, C=Club, D=Diamond

in how many ways can you arrange SSSCCDD?

same letter is seen as same object

[terse field]

A lot. I'm typing it manually in excel.

[neon dirge]

nono

ok in how many ways can you arrange SSSSSSSSSSSSSSSSSSSCCDD

:D

[terse field]

I'm lost on that.

[neon dirge]

k, are you familiar with permutations?

and combinations

arranging SSSCCDD is the same as arranging 7 elements in a line, but there are duplicate groups of size: 3, 2, 2

[terse field]

I know combinations are the total amount of paths there are. Permutations I can't recall but it's related to combinations.

[neon dirge]

kk, if for instance you were to arrange the letters

ABCDE

you have 5 distinct letters

the number of ways to arrange them thereby is 5!

5! = 5 * 4 * 3 * 2 * 1

which is a permutation

and we do the same above with SSSCCDD

we have 7 elements

[terse field]

Which is 7!

[neon dirge]

yup

and now we account for the duplicates:

7! / (2! * 2! * 3!)

this principle always works

for arranging objects (and duplicate groups)

so now we know that there are 7! / (2! * 2! * 3!) possible paths for arranging SSSCCDD

now we only need the number of paths for the different cards within Spades/Clubs/Diamonds

following so far or is a step unclear? @terse field

[terse field]

So it's (7654321) / (321)(21)(21)

[neon dirge]

yup

[terse field]

So it's (7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1)(2 * 1)(2 * 1).

[neon dirge]

discord turns STARtextSTAR into cursive

[neon dirge]

as you see this principle makes finding the paths quite easy

[terse field]

Just for extra knowledge. If that works on dependents like card drawing, what happens if you reinsert the card into the deck and it becomes independent?

[neon dirge]

same principle for these

the number of paths wouldn't change

since you can still arrange SSSCCDD in the same number of ways

however your path probability, that we calculated at the start, would change

since you put them back

[terse field]

What do I search for if I want to learn a bit more on this on google/youtube?

[neon dirge]

combinatorics basics

permutations / combinations / case differentiation

and binomial coefficient

[neon dirge]

but lastly onto the remaining paths:

we want to know how many paths there are for drawing the different Spades for instance

we've drawn three spades

the first one can be 13 variations

second one 12

third 11

so for the spades there's 13*12*11 paths

likewise for Clubs:

13*12

and for Diamonds:

13*12

so the number of paths for the different card outcomes is:

13*12*11*13*12*13*12

ok and lastly:

Probability * All paths

13/52 * 12/51 * 11/50 * 13/49 * 12/48 * 13/47 * 12/46
times
7! / (2! * 2! * 3!)
times
13*12*11*13*12*13*12

@terse field

[terse field]

And that makes a really big number.

[neon dirge]

yop

[terse field]

8769720960

oh wait

[neon dirge]

hm wait did I do something dumb

yea sry the second paths step doesn't have to do with the problem lol

it's just

13/52 * 12/51 * 11/50 * 13/49 * 12/48 * 13/47 * 12/46
times
7! / (2! * 2! * 3!)

[terse field]

0.00006 * 210

[neon dirge]

k so 0.0126

= 1.26%

weehee

[terse field]

Those are very low odds.

Thank you. I'll self-study on it a bit more myself.

[neon dirge]

have you rounded heavily btw?

I get 0.0130061645379706

[terse field]

I rounded heavily

[neon dirge]

kk

[neon dirge]

np

[neon dirge]

yea it's a very specific request to draw that arrangement

even drawing no hearts from among 7 cards is already a little rare

[terse field]

It's a variation of deckbuilding for trading card games

[neon dirge]

kk

[terse field]

To simplify, there are 3 categories- (bricks)card you do not want to draw in the opening hand, (engine)cards you want to draw in the opening hand but you only want to draw 1 or 2 out of all of them, (other) supplementary cards- more is good, but you want an engine card or they're useless.

Different decks have different ratios. So, it's up to the player to consider the risk of drawing a bad hand.

[neon dirge]

neat

[neon dirge]

and you go through minmaxing a bit? :3

[terse field]

Then you minmax.

[neon dirge]

k

[terse field]

Alright. Thank you so much. I shall research it further myself. Bye

[neon dirge]

🦇

[terse field]

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[subtle rapids]

how do you answer thiis?

[hallow wren]

what happens when you put in 0 bro? 🙂

foe x

like it says

[subtle rapids]

1/0 - 4/0

[hallow wren]

yea, so?

[subtle rapids]

what's the answer

[rough goblet]

"yea, so?"

!noans

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[hallow wren]

was I doing that??

[rough goblet]

no he was

[trail ingot]

💀

[hallow wren]

oh ok, cuz you quoted me

[subtle rapids]

is it infinity?

[hallow wren]

what does it mean if you have 0 in below the division sign?

[subtle rapids]

dne

does not exist?

[hallow wren]

yeah

that's the answe

[trail ingot]

💀

[hallow wren]

write undefined or something like that

[subtle rapids]

oh okay thanks

[gritty harness]

What

[vernal warren]

That is not undefined

[gritty harness]

@subtle rapids subtract those terms

The X's will get cancelled

It's not undefined

[hallow wren]

oh.. sorry lol

I was just doing this stuff haha

[gritty harness]

Limits fun

[hallow wren]

I still don't get it lmao

[rough goblet]

@hallow wren if you don't know the topic, don't say anything

this is limits--precalculus

you might accidentally mislead someone who's looking to get help

[hallow wren]

Well this is exactly what I'm studying right now.

[rough goblet]

okay-

but what you said was most definitely incorrect

@subtle rapids factorize, and make sure the fractions have the same denom

[devout drift]

How so?

[rough goblet]

he said just write undefined

lmao

[rough goblet]

^^

[devout drift]

Makes sense

[rough goblet]

shrugs

[hallow wren]

Well ty for pointing it out

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[versed crypt]

how do u do part 2 and 3 of this

[left oriole]

you should have enough to compute P(A ∪ B)

have you tried that?

[versed crypt]

im not sure how to, is it like the addition rule? P(A or B) = P(A) + P(B) - P(A and B)

i got confused cus of the conditional probability

[left oriole]

yes that rule

you can compute P(A) and P(B) from the three given items

[versed crypt]

ohhh ok

[versed crypt]

so for part 2 its just the complement of whatever this right

[left oriole]

right

[versed crypt]

alr ty

also what do they mean by

"largest possible interval"

[left oriole]

i guess it just means, what's the smallest and largest possible value that p could have

[versed crypt]

ohhh ok got it

thanks for ur help 🙂

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[marsh socket]

i need help w b

[sacred sapphire]

differentiate the equation of the curve

[marsh socket]

-6x+2y/2x+3y

[sacred sapphire]

then just find the slope of the tangent line at (1, 2) by putting those points in there

then find the equation of tangent line

[marsh socket]

-5/4

[sacred sapphire]

good then just find the intercept of the tangent line and you're done

[marsh socket]

how do u od that part

[sacred sapphire]

equation of straight line is y = mx + c

you know that the line must pass through (1, 2)

and you know m = slope = -5/4

put all of those in and find c

[marsh socket]

so

2=-5/4(1)+c

i got 3 1/4

[sacred sapphire]

then just rewrite your straight line equation

[marsh socket]

y=3 1/4

wait

[sacred sapphire]

no..

[marsh socket]

im lost

[sacred sapphire]

you found c

then just rewrite it in y = mx + c

[marsh socket]

yes

[sacred sapphire]

you know m and c

put those in

and you're done

[marsh socket]

y=-5/4x+3 1/4

[sacred sapphire]

no

leave y and x as it is

only put in the constants

y = -5x/4 + 3¼

[marsh socket]

why do we keep x and y like that

[sacred sapphire]

because in the straight line equation, only m and c is constants

[marsh socket]

how arent x and y constants if we have them

[sacred sapphire]

x and y are not constants

y depends on the value of x

and x is also not a fixed value

its a variable

not a constant

we only know what y is because we have x

[marsh socket]

but they r both given

[sacred sapphire]

yes but we're trying to find an equation

[marsh socket]

alright

thanks

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[hot prawn]

a rectangle shaped room of $4.5m4m$ would be installed with $40cm40cm$ sized tiles (tile cutting is allowed), the minimum area that isn't covered by whole tile would be ... $m^2$

[solid kiln]

sho

[hot prawn]

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[analog shale]

you did not get an answer 🤔

[analog tusk]

I need help w this

Determine the possible points of discontinuity of the following functions and the type of discontinuity exhibited. Remove any removable discontinuity. Sketcg graph of f(x) to verify your answer

a. f(x) = cos x, x ≠ 2kπ, where k is an integer

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[analog tusk]

<@&286206848099549185>

[light berry]

yes mortal @analog tusk

[analog tusk]

I need help with this please🙏

Determine the possible points of discontinuity of the following functions and the type of discontinuity exhibited. Remove any removable discontinuity. Sketcg graph of f(x) to verify your answer

a. f(x) = cos x, x ≠ 2kπ, where k is an integer

[analog tusk]

.

[tranquil widget]

sketch the graph of f(x)

[analog tusk]

thats the problem, i dont know anything ab that😭

[tranquil widget]

oof

uhm

have yall not been taught

it

or do you just not know it

oh wait

theyre literally asking you to do it in the q

well okay so you need to know the graph of f(x)=cosx

[analog tusk]

he forgot to teach us this

[tranquil widget]

thats just

something you memorise ig

this might help

[analog tusk]

thats what i was trying to do earlier

[thin rune]

Hmm..

[tranquil widget]

ignore the poor crop

2k pi basically means

[analog tusk]

and i was focusing on the (0,0)

[tranquil widget]

whenever you have an integral multiple of 2pi

[analog tusk]

its all continuous

[tranquil widget]

so at those points erase the graph bc x ≠ 2kπ

[tranquil widget]

not if youve got bits missing

[thin rune]

Yeah Goodyear job

Good*

[analog tusk]

how do I find where its discontinuity

sorry english is not my first language

[tranquil widget]

wherever x = 2kπ

the graph is missing

like uh

that point is not there

so it is discontinous there

so when u sketch f(x) exclude all the pts where x = 2kπ

the pic i sent does not show removed bits

[analog tusk]

there's no equation?

[tranquil widget]

?

what do you mean

[trim jolt]

@analog tusk Has your question been resolved?

[analog tusk]

I do not understand

is x = 2kπ and its multiples the discontinuity itself?

like this?

please correct me

[thin rune]

yes.

@analog tusk

[analog tusk]

is it correct?

[thin rune]

yes

[analog tusk]

how

[thin rune]

i think it is

hey

[analog tusk]

I don't understand

[thin rune]

omg

[thin rune]

it is correct

<@&286206848099549185>

[thin rune]

is it correct?

[analog tusk]

<@&286206848099549185>

[thin rune]

what

[analog tusk]

help me please😭 🙏

[thin rune]

why just me in here

[thin rune]

i am.

[analog tusk]

thank you

literally about to cry

[thin rune]

i said : it is correct

okey

[analog tusk]

is it really

like

sure?

[thin rune]

yeah

[analog tusk]

my math teacher might say otherwise if its not

how sure

[thin rune]

i said "i think"

[thin rune]

look

[analog tusk]

thats why we need to be sure

man

gonna cry

this is whats gonna ruin my grades

[thin rune]

i think your teacher is right

[analog tusk]

ofc he's always right

[thin rune]

Now that I think about it, I think it's wrong

[analog tusk]

whats wrong please say whats wrong

[thin rune]

not your teacher

[thin rune]

your problem

[thin rune]

this

[analog tusk]

whats wrong w it

Thats what i was thinking at first but I know my teacher

man probably analyzed a hundred times before giving that to us

[thin rune]

your teacher said it is wrong

yes or no

?

[analog tusk]

I do not know

[thin rune]

what

What did your teacher say about your problem?

@analog tusk

[analog tusk]

nothing

he saidd to solve it

it is 40% of our grade

[thin rune]

Did he say true or false?

[analog tusk]

nothing he said nothing

I know that man

[thin rune]

i am 🇹🇷

what else

.......

[analog tusk]

I don't even know why an engineer became a high school teacher

[thin rune]

off..

[thin rune]

😄

[analog tusk]

I don't even know why im studying math when im not even gonna be an engineer

[thin rune]

how old are you

[analog tusk]

16

[thin rune]

🥶

[analog tusk]

I thought basic calculus would be basic

[thin rune]

I'm 12 years old but I know a lot about math. and ingilish

[thin rune]

what

[analog tusk]

it would be basic if he taught us how to solve this

[thin rune]

I think so too😄

[analog tusk]

Thats what I thought when I was not studying this subject

[thin rune]

What do you want to be when you grow up?

[analog tusk]

A dermatologist

wuld be good to be a researcher

[thin rune]

yes i think

[thin rune]

good i want to be a neuroscientist 🧠

[analog tusk]

cool

my classmate wants to be one too

all my classmates are gonna go to medical field why are they making us take this subject

I used to like math

[thin rune]

at my girlfriend But we don't even talk much

[analog tusk]

she maybe busy

your too young

12 is too young

[thin rune]

We're not like lovers anyway

[analog tusk]

i had a relationship at that age but I broke up w him after one day

he was creepy

turns out he was 16

and like why would he even talk to a 12 year old romantically

[thin rune]

I'm not like that😄

[analog tusk]

ye but how old is your gf

[thin rune]

i think he hasnt brain

[thin rune]

12

bb

bye

[analog tusk]

aight gonna rewrite my math problem

I need help with this please🙏

Determine the possible points of discontinuity of the following functions and the type of discontinuity exhibited. Remove any removable discontinuity. Sketcg graph of f(x) to verify your answer

a. f(x) = cos x, x ≠ 2kπ, where k is an integer

is this even correct

[thin rune]

püff..

[trim jolt]

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@analog tusk Has your question been resolved?

[tranquil widget]

it can go

to the negative side too

since k is an integer

but yeah now that you have the basic graph

can you identify the type of discontinuity?

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[sacred socket]

Why does the uniqueness of a differential equation depend on the partial derivative of f with respect to y?

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@sacred socket Has your question been resolved?

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@sacred socket Has your question been resolved?

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@sacred socket Has your question been resolved?

[sacred socket]

<@&286206848099549185>

[lofty sierra]

well the uniqueness of a differntial equition depends on the partial derivative from/ of f and also looking at / with repsect to y

because that ensures the existence of the unique solution when it is like continuous

[trim jolt]

@sacred socket Has your question been resolved?

[sacred socket]

What about it ensures that there is a unique solution?

[analog tusk]

Kinda solved it now but I'm not sure about my answer and I identified as a removable discontinuity then removed the discontinuity by finding the limit from both sides and reworded the function

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[wild quail]

hi

[wraith hinge]

yo

[wild quail]

so i got a question in chemistry and its about finding equilibrium constant and the last step is like this
log base 10 kc = 15.6
and the final answer is like. kc= 3.92 X 10^15

how did we get the answer

[wraith hinge]

you raise both sides with 10 as the base

[wild quail]

what do you mean

[wraith hinge]

to get rid of the log, it's 10^15.6

[wild quail]

what about the 3.92

[wraith hinge]

you can either use a calculator or use log properties but the answer is approx 4 x 10^15

3.92 is wrong

[wild quail]

no but how do I obtain its value ?

[wraith hinge]

<@&286206848099549185>

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@wild quail Has your question been resolved?

[devout drift]

Did you understand till $\log K_C = 15.6$?

[solid kiln]

ColdTee

[wild quail]

Yes

[devout drift]

Are you familiar with $\log_a x = y \iff a^y = x$

[solid kiln]

ColdTee

[wild quail]

yeah

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[upbeat pike]

can someone please help me solve this for y

[upbeat pike]

I'm pretty sure this is a bernoulli equation but idk how to use the formula

i've tried it but got stuck

[granite cove]

Can't you just use separation of variables?

[runic dew]

If you think it is the Bernoulli equation then you can just search it up and find the appropiate substitution

[upbeat pike]

How would that work

[upbeat pike]

I tried but failed

[granite cove]

Get the y to the other side and divide by y^(-2)-y

Then get rid of the 1/y^2 in the denominator

[upbeat pike]

What about the lhs

[granite cove]

What?

[upbeat pike]

It’s gonna be y’ dividded by what you just said

[granite cove]

Yes, y'/[1/y^2-y] = 1

[granite cove]

Then you need to integrate

[upbeat pike]

How in gods earth do you integrate that

[granite cove]

Multiply num and denom by y^2

In LHS

[upbeat pike]

Doesn’t that make it even messier

[granite cove]

Then you have y`•y^2/[1-y^3]?

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[proven hound]

Just add up the areas under the curve

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[solar pelican]

how does that one "x" change into +1

i can send the thing as a whole

[spiral socket]

what is any number divided by itself?

here you simply divide x by x

[nova minnow]

you factor x+xsomething to x(1+something)

[solar pelican]

the x cancel the other x though

[spiral socket]

yes canceling is division

in this case

if you had -x + x + 1 then yes -x + x = 0

[solar pelican]

yes so the x disappears. how does it affect the other x which gets changed into +1 ?

[nova minnow]

sorry it was meant to be x * (1 + something) is the same as x + x * something

and then you simplify both the numerator and denumerator by x

[solar pelican]

there are two exes down there

and it cancel them both

how

[spiral socket]

because they factorised x

xa + xb = x(a+b)

[solar pelican]

ohhh

[spiral socket]

in your case, a is x

[solar pelican]

i think i got it

[spiral socket]

and b is the square root

[solar pelican]

how should i realize to do that by myself intuitively without help xdd

[nova minnow]

if you see a fraction and they have the same stuff in the numerator and denumerator, you can try to factor it

[spiral socket]

for factorisation just write x and inside the parantheses, all the terms that “used” to contain x

let me give you an example

[nova minnow]

for example:
(n + n * m) / (n * n + 3 * n * x)

[spiral socket]

$2x^2+3x$

[solid kiln]

dqvidutzul

[solar pelican]

hmmm okay okay

[spiral socket]

do both terms have a common variable?

[solar pelican]

x(2x^2+3) right

[spiral socket]

careful at the square

you have 2x^2 divided by x

[solar pelican]

x(2x+3)

yeah

[spiral socket]

yep

[solar pelican]

but alr thx guys

[spiral socket]

same for multiple terms

hope you understood

[solar pelican]

got it

.close

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[inland bear]

why do i have to sub -1 in and so on? where did they get the -1?

[stable totem]

f''(-1) and f''(1) allows them to determine the concavity near 0

they couldve also set it to -0.1 and 0.1 it would still give the same result that concavity changes

essentially they picked -1 and 1 for convenience

[livid thunder]

im pretty sure its a horizontal point of inflection if f'(a)=0 and f''(a)=0

don't know why the substitution is necessary

[stable totem]

not always take x^4

[livid thunder]

right my mistake, still the substitution is unnecessary as 40x^3 isnt always >=0

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[inland bear]

thanks

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[empty basin]

Can anyone help me with maths?

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@empty basin Has your question been resolved?

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[dreamy magnet]

Studying the points of non derivability of the function f(x)=|x+ln(x)|
The function is non-differentiable when x=-ln(x) which holds for a certain value x=a
Now I want to find what kind of point x=a is with the definition of derivative with the limit lim(h->0) (f(x'+h)-f(x'))/h which turns into lim(h->0) (|a+h+ln(a+h)|-|a+ln(a)|)/h. To find the two values I split the limit into the left and right limit.
Right derivative = lim(h->0+) (|a+h+ln(a+h)|-|a+ln(a)|)/h.
My problem is solving this limit, because the second term of the numerator is by definition 0, but if I simply delete it I get a different result (infinite) than by keeping it (the correct result 1+1/a)

[vernal briar]

You said a is the point where a = -ln(a)

This means f(a) = 0, and you can know the sign of f on the right side and left side of a.

Use this to get rid of the absolute values.

Also, what are you trying to study exactly?

I think it's pretty clear what the function looks like around that point

[dreamy magnet]

I don't think that really answers my question.
a is the point where a=-ln(a), so in the limit lim(h->0+) (|a+h+ln(a+h)|-|a+ln(a)|)/h I would immediately delete |a+ln(a)| because it's 0, but I don't understand why this is wrong

[vernal briar]

Is it wrong?

I think it's right to delete it

[dreamy magnet]

you are right
my mistake was using a calculator for the resulting limit, putting a placeholder for a but ignoring the fact that a+ln(a)=0

[vernal briar]

Yup

[dreamy magnet]

ok thanks for the help

.close

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[dreamy vapor]

I need some help

[dreamy vapor]

I have an assignment

a) Determine the monotonicity conditions for f.
For x = 1.2, the graph of / has a tangent, t.
| b) Show that the equation for t is given by y = -0.44x + 2.152.

It is important and must be resolved within an hour

[gusty raptor]

broski def is doing an exam rn 💀

[rough goblet]

@dreamy vapor

is this a test?

[gusty raptor]

Looks like it

[frail heron]

use Taylor series to transform f(x) into f(x-1.2)

[dreamy vapor]

Yes

[frail heron]

sure, we can help you, but we can't directly give you the answer

do you agree?

[dreamy vapor]

I do not know that. Isn't it better to def

[dreamy vapor]

Yes

[frail heron]

def?

[dreamy vapor]

If you can help me, it's worth everything

[dreamy vapor]

so we can differentiate

[frail heron]

this question is basically in the field of calculus

[dreamy vapor]

Calculus?

How will you solve it?

[dreamy vapor]

Ahahahaa

[dreamy vapor]

@rough goblet

[frail heron]

use taylor series formula to transform the function into
-1/3(x-1.2)^3 + a(x-1.2)^2 + b(x-1.2) + c

[dreamy vapor]

i don't know about taylors

[frail heron]

I see

[gusty raptor]

"Ahahahaa" maniac vibes 💀

[dreamy vapor]

You have to make it simple for me

[dreamy vapor]

^

Can we differentiate the equation?

[frail heron]

sorry, I don't use such method on this question

[dreamy vapor]

Bro...

[frail heron]

probably next helper could help you

[dreamy vapor]

Wow

<@&286206848099549185>

I need some help

I have to hand in the assignment soon.

I need all the help you can get

We need to differentiate the equation I think

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[glossy gale]

Can anyone help with these two problems? I literally dunno how to do them at all

[indigo ferry]

!ask

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[candid flame]

Can anyone help me

[brazen forge]

hi what you want to know?

[mellow tendon]

Just Ask your question when you occupie a room, without saying if anyone can help you

[candid flame]

Solving this

[brazen forge]

with both?

[candid flame]

Yes

[brazen forge]

lets start with y=2x-8

do you know how to start?

[candid flame]

Can’t we just combine both

[brazen forge]

both equation?

[candid flame]

Yes

[brazen forge]

arent they separated?

[candid flame]

They are but you are supposed to to

Add things to sides subtract

[brazen forge]

wait im stupid sorry

can you say full question youre asked here?

[candid flame]

I don’t get what you mean

[brazen forge]

its your hw or something rigth?

[candid flame]

Yes

Solving algerbraticlly

[brazen forge]

for x and y?

[candid flame]

I think

[brazen forge]

ok

[candid flame]

Do you know the x

[brazen forge]

im guessing its the system of equations

[candid flame]

Can you try and solve this

Here is a example except the 2 equations are mixed already

[brazen forge]

i solved it

[pearl tendon]

You have a definition of y

put that in where you see y in the second equation

[brazen forge]

put 2x-8 instead of y in the 2nd equation

[pearl tendon]

combine like terms

[candid flame]

Can you guys write the steps so I can add them to my notes

[candid flame]

Example problem

[brazen forge]

you have to do it yourself

[candid flame]

What

[brazen forge]

i wrote you what you do

and solve for x in the 2nd equation

when you solved for x you get two answers

[candid flame]

7 and 2

[brazen forge]

2 and 14

[candid flame]

I got 2 not 14

[brazen forge]

you got two answers for x right?

x = 2 or x=14

7

of

im tired sorry

youre right

XDD

x=7

now put in the first equation x=2

and tell me what you got

after that put x=7

[candid flame]

It’s right

Can you help with this one now

[pearl tendon]

Do this again

But with your new problem

[candid flame]

Y= x squared - x -2x -8

Is that right

[pearl tendon]

No

[candid flame]

How do I combine them then

[pearl tendon]

Exactly like you did in the problem I highlighted - the 2x + 10 replaces y

[candid flame]

So -2x -8 = x squared -c

X

[pearl tendon]

Now you can add/subtract terms from each side

[candid flame]

Is this right

[pearl tendon]

Yes, that's why I gave you the next step

well.. minus the "c" (which I assumed that's what you were trying to correct when you just typed "x")

[candid flame]

Yes

[pearl tendon]

Also, just to help you speed up your typing, Shift+6 gives you this little character: ^

that means "raised to the power" so you don't have to type out "squared" every time

x^2

[candid flame]

Ok from the equation add the 8 to 2

[pearl tendon]

Those aren't like terms

You can't add them

[candid flame]

X^2 and x

[pearl tendon]

Those aren't like terms, either

[candid flame]

None are

[pearl tendon]

x and 2x are like terms

[candid flame]

So as 2 x

And 3 x

[pearl tendon]

I'm really worried once we get to factoring the 8, bud

If you're struggling with this part, I mean

[candid flame]

Let’s just keep going

-8 = x^2 = 3x

Is that right

[pearl tendon]

No

Here you go

[candid flame]

What is it

[pearl tendon]

https://www.youtube.com/watch?v=qeByhTF8WEw

Peace

[candid flame]

Can you just do this equation for me

Then this will be over

Can anyone help

[elder ingot]

uh no this server is to help you understand the problem clearer not do your homework for you

[candid flame]

I need help getting started

I don’t understand it

[elder ingot]

what's the exact problem you're having?

[candid flame]

This

[elder ingot]

FOIL it out

aka factoring

[candid flame]

I know

[elder ingot]

ok what is your factored equation

[candid flame]

-2x -8 = x^2 -x

[elder ingot]

what are the directions do you have to find x or just prove y=2x+10

[candid flame]

I think solve algebraticlly for x and y

Do you get the steps

[elder ingot]

yes

[candid flame]

So what do I do next

Combine like terms?

[elder ingot]

bring the 2x+10 to the other side and set the whole equation equal to 0

[candid flame]

It’s 2x - 8

[elder ingot]

y=2x+10

[candid flame]

This

[elder ingot]

oh alrr

same principle

[candid flame]

-2x -8 = x^2 -x

[elder ingot]

no

[candid flame]

What is it

[elder ingot]

x^2-2x-x-8=0

combine like terms

[candid flame]

Then what

[elder ingot]

try to factor

[pearl tendon]

Starting to get the feeling Megaz is just a troll

[elder ingot]

possibly

the equation dosent factor lol

[candid flame]

I’m not

Exactly

[pearl tendon]

I've been gone 20 minutes, and you're still at the same point

[candid flame]

Yeah cause no one will help

[pearl tendon]

I've helped, whitename has been helping

The Snake helped

Several people have helped you

[elder ingot]

i do not believe the variables are solvable with your current equation

at least not by factoring

[candid flame]

Can you guys help me out still

They should

[candid flame]

We want to solve it like this

[elder ingot]

do you know quadratic equation

[pearl tendon]

I like your optimism

[elder ingot]

lmao

[candid flame]

John do you know even how to solve this

[elder ingot]

there's def some imaginaries in there

[candid flame]

Pls actually help

[elder ingot]

mega

do you know quadratic formula

[candid flame]

It’s not that complicated

[elder ingot]

so use it to solve lmao

[candid flame]

It doesn’t involve that

[pearl tendon]

Yes, it does

[elder ingot]

it dose

[candid flame]

Oh

[elder ingot]

there are imaginary numbers there has to be

[pearl tendon]

funny you should say this, because it actually is a complex solution

[elder ingot]

Mega what math are you in?

[candid flame]

It’s 6 and 8

The answer

[elder ingot]

photomath is crazy

[candid flame]

Why would I waste all this time with you two when I could have just used Photomath

[elder ingot]

tf jus happened

[pearl tendon]

x = [−3 + sqrt(23​i)] / 2
and
x= [-3 - sqrt(23​i)] / 2

That's your answer

[candid flame]

That’s not the answer it can’t be square root

[pearl tendon]

lol... you've got an i in there, and you're hung up on the square root... roger that

[candid flame]

Idc

How many people did you help with math

1 probably

Your 4 year old cousin

[elder ingot]

funny how he keeps dodging my question on what math he's in

[pearl tendon]

Right?

straight up gave him the answer, and things spiral into namecalling.. very classy

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[vernal fern]

did i do this right

[fresh knoll]

depends on if you actually did something

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[devout token]

The graphs of the parobalas f(x)=x^2 and g(x)=-x^2 +bx+c Intersect at the origin (0,0) and at point B
g(x) also Intersects the X axis at (3,0) I need to find the equation of g(x)

[devout token]

And I've no clue how to do it

I mean, I've got this

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[devout token]

<@&286206848099549185>

[burnt spade]

wkt g(0)=0 and g(3)=0. performing this substitituon,

(0)^2 + b(0)+c=0

c=0

(3)^2+b(3)=0
b=-3

[devout token]

Oh

I see

I'm stupid

[devout token]

Thanks

But

Wouldn't this make meant that g(x)<0

Which it clearly isn't?

Oh never mind

I suppose if x is negative then it won't be the case

[devout token]

But I mean, that doesn't align with the graph

Because g(x) is greater than 0 when 0<x<3

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[last dawn]

How do you solve these types of problems with functions inside other functions when you want to integrate

[last dawn]

Like i get that you gotta derive the thing inside and play around with them and put something in front but like i cant use it in any example cuz i have no idea what im doing

[vernal briar]

u-substitution

[last dawn]

?

[vernal briar]

Have you learned u-sub?

[last dawn]

Im not learning math in english

[vernal briar]

Substituting a variable

Changing the variable

[last dawn]

My math book does this kinda thing

[vernal briar]

Well that's basically u-sub without doing u-sub

But yeah that's the way

[last dawn]

So can u explain. Why we are doing this

[vernal briar]

We are trying to undo the chain-rule

[last dawn]

Why do some stuff dissappear

Which is what

[vernal briar]

What stuff?

Chain rule is:
(f(g(x)))' = f'(g(x)) * g'(x)

I don't really a way to tell you how to "notice" it. It just comes with experience and solving a lot of integrals

[last dawn]

I mean you

1. derive the inner thing
2. Move the 1/front number to the front
3. Make half the derivative dissappear (All the x stuff)
4. Solve some stuff

LIke WTF

[vernal briar]

You just manipulate the integral, so it will be of the form:
f'(x) * (f(x))^n

in this case at least

There are some constants you need to move around

Like, if I integrate:

x(x^2 + 3)^4

Then I would write it as:

$\int x(x^2+3)^4 \dd x = \frac{1}{2} \int 2x (x^2 + 3)^4 \dd x$

[solid kiln]

RedstonePlayz09

[vernal briar]

Why did I do that? Because now that 2x is exactly the derivative of x^2 + 3

So that integral is exactly:

$\frac{1}{2} \cdot \frac{(x^2+3)^5}{5} + C$

[solid kiln]

RedstonePlayz09

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[topaz pasture]

So I have this question, where I don't know what I'm doing wrong..

[topaz pasture]

Translation: A copper pipe has an outer diameter, D = 3 cm, a length of 2.8 m, and a wall thickness of 2 mm.

Determine the mass of the pipe when the density of the copper pipe is = 8600 kg/m^3.

We've been given this formula

[topaz pasture]

The (4,24kg) is the answer, but I can't seem to get it.

I've tried multiple times, but can't seem to get the answer i want.

I know what my volume is (i know the answer), i just wanna know how to get there, and what i'm doing wrong.

<@&286206848099549185>

something must be wrong with the question

or i must need glasses

<@&286206848099549185>

[hallow wren]

I don't think I can help you BUT

You have to show your work

[topaz pasture]

😭

[hallow wren]

do you do math with a keyboard?

is that your work?

[topaz pasture]

what??

[hallow wren]

I was saying you have to show your work

people aren't gonna come in here and see that and know what is causing you to get the wrong answer

[hallow wren]

show....your....work... what do you mean bro

so people can check your math

are you expecting someone to just solve it and show you how?

[topaz pasture]

...

What are you waffling about