help-17

[simple mason]

So try substituting the first line with the values he gave you and you will get
Sin(-Q) on the right side
Use the identity he gave you that
Sin(-Q) = -Sin(Q)

So you have
cos(P) * -Sin(Q)
What will that result in

It is like
-Cos(P)Sin(Q)

Both are the same

[vocal sleet]

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[sinful magnet]

did i make a mistake

,rotate

[sinful magnet]

the exponent ^3 part im not sure whether its for the entire fraction

or just the numerator

can some one tell me that

[snow sapphire]

can you tell me what is the question

[sinful magnet]

Did i make a mistake

if not

the exponent ^3 part im not sure whether its for the entire fraction

[snow sapphire]

what is the math problem you are trying to solve for?

[sinful magnet]

the d)

x^3/sqrt(9-x^2)

[snow sapphire]

9 what?

[sinful magnet]

that

[snow sapphire]

ok

gimme a sec

ok

so first step

[sinful magnet]

i did the problem

[snow sapphire]

wait

why are you using sin

and trig

to solve this problem

if i have to do it

i probably wont use trig

i would just do it like this

[sinful magnet]

ik u sub

u sub with 9-x^2

but my teacher wants all trig

[snow sapphire]

what???

[sinful magnet]

my teacher wants us to practice

soo ye

[snow sapphire]

ok

alright then

im not really sure how you did it

but if i have to use trig

hold on

if you have to use trig

are you going to solve for an angle

[sinful magnet]

yes

[snow sapphire]

or something else

ok

[sinful magnet]

well adj/hyp

[snow sapphire]

ok

so you draw a right triangle

and then you put x^3 for hyp

and sqrt(9-x^2) for one of the side

because x^3 is probably bigger

now

there could be a lot of solution to this problem

so are you trying to solve for a range?

[sinful magnet]

i found the solution

[snow sapphire]

ok

[sinful magnet]

its just a question about the exponent

does it affect only the sqrt(9-x^2) or the 3 as well

in the answer below

the pic

[snow sapphire]

i think it affect both

but it could also affect just one

at a certain range

and after the range, it might affect both

[vocal sleet]

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[proud dirge]

Help please 🥲

[raven owl]

The degree of a polynomial is whatever the largest exponent is

The leading coefficient is whatever number is to multiplying x to the largest exponent

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[proud dirge]

/close

.close

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[jade stone]

I need help solving this problem

[jade stone]

Using mathematical induction, prove that 1^2+2^2+...+n^2=1/6(n)(n+1)(2n+1)

first is n=1

(1)^2=1/6(1)(2)(3)

which is true

2. assume that this is true for n+1

but idk how to proceed from here

I've turned the right side for n+1 and have 1/6(n+1)(n+2)(2n+3)

[weary sentinel]

you assume the sum from 1^2+2^2...n^2 is 1/6(n)(n+1)(2n+1),
then using that assumption show that 1^2+2^2+...(n+1)^2=1/6(n+1)(n+2)(2n+3)
hint:||by rewriting the latter (n+1)(n+2)(2n+3)/6 -> into the above + (n+1)^2, then subbing in 1^2+2^2+...n^2 in for n(n+1)(2n+1)/6||

[jade stone]

by subbing in wdym?

[weary sentinel]

basically we have

base case: $1^2=\frac{1}{6}(1)(2)(3)\$
inductive assumption $1^2+2^2+...+n^2=\frac{1}{6}(n)(n+1)(2n+1)\$
Given/using the above, show that $1^2+2^2+....+(n+1)^2=\frac{1}{6}(n+1)(n+2)(2n+3)$

[twin meteor]

Astral

[weary sentinel]

effectively, we turn the 1^2+2^2+...+(n+1)^2 into 1^2+2^2+...+n^2+(n+1)^2 and since we know that first part is just 1/6n(n+1)(2n+1) thanks to our inductive assumption, we know that it = (1/6(n)(n+1)(2n+1)) + (n+1)^2

make sense?

we literally sub in our assumption step

[vocal sleet]

@jade stone Has your question been resolved?

[jade stone]

yeah, but I see in my notes that it takes some equation and steps for simplificatiion

[weary sentinel]

the method depends

you can do it in various ways

the core of it is using the inductive assumption to prove f(k) -> f(k+1) in some way

[jade stone]

yeah but what do I do with the equation

how do I get to it

like

idk

[weary sentinel]

do you understand what I said here?

[jade stone]

wasn't it something like 1/6(n)(n+1)(2n+1)=1/6(n+1)(n+2)(2n+3)

[weary sentinel]

no

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[delicate jewel]

hi. i am having trouble understanding the concepts of probility. hopefully someone can help me solve this.

[vast shale]

gabennn

[lyric night]

!status

[vocal sleet]

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

@delicate jewel Has your question been resolved?

[delicate jewel]

i don’t know where to begin

[lyric night]

Ok

So

Let’s start with the first question then

We know there are exactly 2 female board members right

So how many ways are there to choose 2 female board members from a group of 13 female board members

[delicate jewel]

2/13

[lyric night]

Not quite

Has your class introduced choose notation yet?

[delicate jewel]

ooooh is that like the c2 thing orrr idk

[lyric night]

It’s like 3C2

[delicate jewel]

i don’t want to be difficult i’m just exetrenely clueless. i have been unable to go the past couple classes and i’m exetremely out of the loop

ok so it would be 2c13?

[lyric night]

Ok so

Choose notation is nCk

And it’s the number of ways to choose k things from a group of n things

[delicate jewel]

ok

[lyric night]

nCk=(n!)/((n-k)!(k!))

You can look up the derivation if you want

[delicate jewel]

okok got it thank you

[lyric night]

So then for question 1 for example, we choose 2 female board members and 10 make board members

So what choose expressions would those be

[delicate jewel]

2c10

[lyric night]

Well

We’re choosing 2 female board members from 13 female board members

And 10 male board members from 17 male board members

[delicate jewel]

11c10?

[lyric night]

Not quite

There should be 2 e pressions

One for the males and one for the females

[delicate jewel]

10c2

[lyric night]

Well

If there are 13 females to choose from

And we need to choose 2

There should be 13C2 ways to choose

Does that make sense?

[delicate jewel]

yes

[vocal sleet]

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[latent elk]

hello, i am a little new to group theory, can someone help me find the units and zero divisors of Z6 x Z

[latent elk]

i know the zero divisors of z6 are 2,3,4 but I dont know how to apply this

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@latent elk Has your question been resolved?

[latent elk]

<@&286206848099549185>

[thin vale]

maybe try #advanced-algebra ?

or #groups-rings-fields

[vocal sleet]

@latent elk Has your question been resolved?

[vocal sleet]

@latent elk Has your question been resolved?

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[mighty vapor]

could anyone check if the free body diagram i made is right?

[mighty vapor]

it never specified if there was a force moving it to the right but i just assumed that there was in order to get initial speed of 20m/s, but i honestly have no idea

i made the friction vector larger than the force vector because the crate comes to a stop

[vocal sleet]

@mighty vapor Has your question been resolved?

[lone linden]

it never specified if there was a force moving it to the right
I wouldn't put the Fc for that reason

cause if you think about it, the friction force will eventually cause v = 0 at some pt anyway

[mighty vapor]

should i just assume that the crate got its initial speed without a force? @lone linden

[lone linden]

I mean just cause a force initially applied the speed doesn't mean the force remains in contact after it applies said initial speed

[mighty vapor]

but doesnt initial speed infer that there was a force acted on it? @lone linden

[lone linden]

again, even if a force initially acted on it, there is no reason for the force to continue acting on it

[mighty vapor]

ohh i see

[mighty vapor]

also, i was wondering do you know how to find friction?

just in general

[lone linden]

I mean depends on the text

Ig as a basic building block you have $F_f=\mu F_N$ if you want, where $F_N$ is the normal force and $\mu$ is the coefficient of friction

[twin meteor]

Civil Service Pigeon

[mighty vapor]

okay tysm!

.close

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[fringe jewel]

Can someone please help me with this related rates problem

[fringe jewel]

I have tried setting the derivative to 0 and setting dy/dt = dx/dt in the derivative but I keep ending up with 0=0

[feral light]

show me ur steps when you set dy/dt = dx/dt

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[desert moth]

first break up the initial velocity into x and y components

v_y = vsin(theta)
v_x = vcos(theta)

[desert moth]

then you can use the equations to do x position and y position seperately

[pine coral]

srry i was doing other stuff

um ok

@desert moth wouldn't acceleration for one of the two to be 0?

and the other be -9.8

[desert moth]

acceleration in x direction is 0, acceleration in y direction is -9.8 correct

[pine coral]

im assuming thats always going to be the case when finding a right?

[desert moth]

in the future they may tell u about friction or air resistance where acceleration might not be 0

[pine coral]

oh ok he said we not doing that yet

[desert moth]

but for now it is 0

[pine coral]

so would it be the inverse of sin which = sin-1 O/H = Vo in y direction?

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[fast swallow]

In a question like this , why cant i just say that i will choose 2 questions from the first four and choose 4 questions from the remaining 6 such that answer will be 4C2 * 6C4 ?

[brisk moss]

that will count some ways more than once

[fast swallow]

i see, can you give me an example please ?

[vocal sleet]

@fast swallow Has your question been resolved?

[vocal sleet]

@fast swallow Has your question been resolved?

[pallid zenith]

well for one, you have at least 2 questions

you have some overlap in your cases here

why not break it down into some smaller cases

say that only 2 questions are from the first four, then only 3, then all 4, ...

[fast swallow]

well but doesnt the 4C2 guarantee that i'll choose 2 questions from the first four then i remove those 2 and 6C4 handles the rest of the possibilities ?

[fast swallow]

i see, i get it and this for sure easily makes sense, i am just still trying to disprove my initial intuition

[pallid zenith]

I think you have an issue here

because they are overlapping

like

lets just write them maybe this way

say you select the first 2 questions and the last 2 or whatever

well write xx oo oo xx

make sense

i know you have to select 6

okay, lets say you chose 2 of the 4

so you are at

ox ox oo oo

now you choose 4 of the last 6

whats a good duplicate case

this works actually

ox ox oo oo

to

ox Xx XX Xo

you are counting this here

but also here

ox xX XX Xo

double counted

make sense? @fast swallow

[fast swallow]

ooooh riiight, i see this way i ended up with the same set of questions answered since i can happen to choose 2 then 4 then on another way choose 2 that were part of the previous 4

[pallid zenith]

yea

this is why you need to keep those two sets disjoint

[fast swallow]

i see

[pallid zenith]

the other option is to figure out how many ways you are overcounting

and remove them

but this isnt always the easier option

here i dont think it seems easier

[fast swallow]

yeah

thank you mate @pallid zenith 😄

[pallid zenith]

np

[fast swallow]

.close

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[lofty hornet]

where did i go wrong

[sturdy lance]

Integral 0 to 1

Why F2 - F0

Incorrect

[lofty hornet]

if i sub in x = 0 and 1

is that just a nono

[sturdy lance]

Yes

[lofty hornet]

aww man

oh well

thanks lmao

back to analysis

.close

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[inland beacon]

i know the derivative of .1^x is .1^xln(.1)

but i am just confused on how to find the derivative of ln(6) and ln(x)

[sly sierra]

ln(6) is a constant

therefore..?

[inland beacon]

it doesnt exist

its 0

[sly sierra]

its derivative exists and it is 0

[inland beacon]

oh okay

[sly sierra]

what about the derivative of ln(x)?

[inland beacon]

thats what i just wanted to see how its done

[proven garden]

y=ln(x) then e^y=x

try to differentiate both sides of e^y=x

[inland beacon]

not gonna lie what you just said makes no sense D:

[river kettle]

Ya know log differentiation?

[inland beacon]

i dont remember

if i did learn it

which i prob did

[river kettle]

Look it up on YouTube

[inland beacon]

okay

okay i got it thank you guys

.close

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[fleet ivy]

I am having some trouble with trig and I am confused how
cos^2 theta divided by cot^2 theta is somehow sin^2 theta

[pale perch]

what is cot^2 theta

[fleet ivy]

its trig function identities

hold on lemme look i have it right next to me

[pale perch]

ik, what is it

[fleet ivy]

cos^2 theta/sin^2 theta

[pale perch]

so if you divide cos^2 theta by that, what are you doing

[fleet ivy]

i just realized that i forgot to do something

yea i realized my problem as i was typing that lmao

[pale perch]

[fleet ivy]

i forgot the flip part of that

[pale perch]

rookie move

[fleet ivy]

yea the linear and angular speed about killed me

doing a test review lol

[pale perch]

ah i see

[fleet ivy]

appreciate it tho

.close

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[pearl plaza]

Can someone help lead me a bit in the right direction with probability(?)
im stuck trying to figure out how to get the amount of combinations from a set that has repeat numbers (ex. 3 number combinations with {1, 1, 2, 3, 3, x})

[vocal sleet]

@pearl plaza Has your question been resolved?

[pearl plaza]

<@&286206848099549185>

this is already incorrect starting from just combinations that start with 1
just with that to start there are >10 combinations

112 113 11x 121 123 12x 131 132 133 13x 1x1 1x2 1x3

<@&286206848099549185>

[pearl plaza]

<@&286206848099549185>

[pearl plaza]

<@&286206848099549185>

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@pearl plaza Has your question been resolved?

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[ocean fjord]

.ask

.help

[vocal sleet]

Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help

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

[ocean fjord]

Is b) correct? Need to derivate

[paper depot]

for future reference,

when you send a message beginning with a . it PREVENTS a channel from being opened

you are supposed to just post your question directly

[ocean fjord]

yeah okay

[paper depot]

anyway

1. your handwriting is shit
2. your derivative is wrong on multiple counts

due to misapplying the power rule

$\dv{x} [x^n]$ is $n x^{n-1}$ and not just $n$.

[twin meteor]

Ann

[ocean fjord]

so add d/dx[x^n] on the x/2 and 3/x^2?

[paper depot]

no

like...

look

tell me: what is the derivative of 5x^3?

[ocean fjord]

15x^2?

[paper depot]

yes

ok now redo that derivative

and please make an effort to write with less shit handwriting!

[ocean fjord]

30x?

[paper depot]

redo it on paper and in full

you came here with the problem:

g(x) = 5x^3 - 2x^2 + 7x
find g'(x)

[paper depot]

wrong again

you are still not applying the power rule correctly

the derivative of 5x^3 is not 30x

and the derivative of 7x is not again 7x

[ocean fjord]

oh okay

like this?

[paper depot]

yes

[ocean fjord]

now derative of 15x^2? and 4x?

[paper depot]

no, why?

you're done...

you were only asked for the derivative of g(x)

not for its second derivative

[ocean fjord]

oh okay

can you help me with another one

[paper depot]

depends on what that other one is

[paper depot]

this one can be done with the very same power rule

[ocean fjord]

making the x? to 1? and x^2 to 2?

[paper depot]

no.

bad on multiple levels.

first off even if you had an x^2 term it would not be made into 2 it would be made into 2x

and second you don't have that anyway so it's irrelevant

$h(x) = 2x^{-1} - 3x^{-2}$

[twin meteor]

Ann

[paper depot]

this is your function

[ocean fjord]

okay do i have to solve the ^?

[paper depot]

what does "solve the ^" mean

[ocean fjord]

like solve the 2x^-1? and -3x^-2?

[paper depot]

"solve" can mean a thousand different things

i don't know what meaning you put into that

the next step is to apply the power rule

twice

to these two terms

each of which is in exactly the right form for that to happen

[ocean fjord]

i dont really understand how would i go about that?

[paper depot]

tell me: what is the derivative of x^n?

[ocean fjord]

1^n?

[paper depot]

wrong

the derivative of $x^n$ is $n x^{n-1}$

[twin meteor]

Ann

[paper depot]

do you have class notes? a textbook? presentation slides? anything?

[ocean fjord]

yeah class notes

[paper depot]

ok

can you show your class notes?

like you must have learned about derivatives in the somewhat recent past, yes?

[ocean fjord]

its in another language but i can show

[paper depot]

show it anyway

what language is it in

[ocean fjord]

yeah we've learned about it

norwegian

[paper depot]

ok yeah post your notes here

[paper depot]

so you have this rule here

[ocean fjord]

oh okay

[paper depot]

firstly do you understand the correction i just made to it

you made a typo when writing it down

[ocean fjord]

yeah cause it can vary

[paper depot]

ok

so

you know how to take the derivative of x^n

now tell me

what is the derivative of x^(-1)?

[ocean fjord]

x?

or no

[paper depot]

no

apply

[ocean fjord]

-x^-2

[paper depot]

the power rule

fuck

you have the rule right in front of you and it takes you two tries to apply it

come on

yes, the derivative of x^(-1) is -x^(-2)

now tell me also:

what is the derivative of x^(-2)?

[ocean fjord]

x^-3

[paper depot]

incorrect

$f(x) = x^n \implies f'(x) = nx^{n-1}$

[twin meteor]

Ann

[paper depot]

here is the rule again

so that you do not lose sight of it

[ocean fjord]

-2x^-3

[paper depot]

write it down somewhere like. idk directly on your arm or something

yes the derivative of x^-2 is -2x^-3 great

$h(x) = 2x^{-1} - 3x^{-2}$

[twin meteor]

Ann

[paper depot]

now take the derivative of this function

$f(x) = x^n \implies f'(x) = nx^{n-1}$

[twin meteor]

Ann

[paper depot]

in case you lost sight of it again

[ocean fjord]

-2x^-2-6x^-3

[paper depot]

mind your signs

[ocean fjord]

-2x^-2-6x?

[vocal sleet]

@ocean fjord Has your question been resolved?

[vocal sleet]

@ocean fjord Has your question been resolved?

[vocal sleet]

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[tribal holly]

40^6/20^5

[tribal holly]

I know subtract 6-5

but

Can you do that?

The 2 base numbers aren't the same

[sudden compass]

No u can't

[tribal holly]

so it will be 2

and then what happends to 6 and 5

[tribal holly]

= 1280

I have to put it in standard form

answer says 2 x 10^1

nah i dont understand

[vagrant plume]

You can only use those rules when the base is the same.

[tribal holly]

Ya so

how do i do it

[wary mantle]

Uh, I don't agree with the answer

,w (40^6)/(20^5)

[tribal holly]

why?

[twin meteor]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by Kepe#5235

[tribal holly]

which answer?

[wary mantle]

WA doesn't either

[tribal holly]

i know bro

but look

[wary mantle]

This

[vagrant plume]

Ok look

[wary mantle]

Is it really (40^6)/(20^5)?

[tribal holly]

20 = 1280????????

[vagrant plume]

I will tell you, and give you another problem to see if you understand

[tribal holly]

lol

[vagrant plume]

40^6/20^5

(2*20)^6/20^5

[tribal holly]

nah just says 4*10^6/40x10^5

[vagrant plume]

2^6*20^6/20^5

[wary mantle]

That's not equal to that expression

[vagrant plume]

Oh look they have the same base

[tribal holly]

alr one sec

2x20^1

????????

[vagrant plume]

I’m so confused

Can you wrkte it in latex

[tribal holly]

me too

wait i send img

[wary mantle]

Is this really exactly what it says? Since that should be 1.

[vagrant plume]

Fr

[wary mantle]

That's different...

[tribal holly]

how?

[wary mantle]

40*10^5 you said

in the denominator

[tribal holly]

ye i have to put 4000000

into

4*10^6

[wary mantle]

Yes, you can do that

[tribal holly]

ye and that is

40^6

[wary mantle]

No

[vagrant plume]

What

[tribal holly]

and 2x10^5 is 20^5

[vagrant plume]

😭

[tribal holly]

so 40^6/20^5

[tribal holly]

what?

[wary mantle]

Also not 20^5

$a^n \cdot a^q = a^{n + q}$.

[tribal holly]

oh wait boys

I have to use pemdas

[vagrant plume]

No you are mixing up the rules

[wary mantle]

Note that the two bases have to be the same

Also

[vagrant plume]

Fr

[tribal holly]

(10^5)*2

[wary mantle]

$a^n \cdot q^n = (aq)^n$.

[tribal holly]

ye ik that

ik those rules

[wary mantle]

Note that here, the exponents have to be the same

[tribal holly]

yep

[vagrant plume]

Also when you multiply an exponent by a number, the exponent only goes up if it is the base…

n*n^k = n^k+1

[tribal holly]

only base have to be same here

[wary mantle]

Yes

[wary mantle]

And here, only the exponents

[tribal holly]

so how do i use it in my problem?

the base isnt the same

i dont understand how you cant do 4*10^6 as 40^6

[polar herald]

what's the problem

[wary mantle]

You can rewrite 4000000 as 4 * 10^6

[vagrant plume]

Ohhh

[wary mantle]

Then you can cancel 4 with 2

[vagrant plume]

Ok you are thinking

[tribal holly]

use natrual form

[wary mantle]

Getting (2 * 10^6) / (2 * 10^5)

[vagrant plume]

Of (2*20)^6

Right?

Or are you saying 2*20^6

[tribal holly]

no

[vagrant plume]

Or whatever it is

[tribal holly]

2x10^6

= 20^6

[vagrant plume]

Write whatever it is with parenthesis

[polar herald]

?

[vagrant plume]

Please 😭

[polar herald]

oh shit

[tribal holly]

how wtf?

[polar herald]

so it could be more formal.

[wary mantle]

$\frac{4000000}{2 \cdot 10^5} = \frac{4 \cdot 10^6}{2 \cdot 10^5}$.

[polar herald]

and more easy to understand

[tribal holly]

ye

and that means

[wary mantle]

Take out a factor of 2

[tribal holly]

40^6/20^5

[wary mantle]

No

[vagrant plume]

(210)^6 = 2^6 * 10^6. Right?
But (210)^6 = 20^6, right?
And 2^6 * 10^6 doesn’t look like 2*10^6 does it

[wary mantle]

Only if it was 4^6 * 10^6

[polar herald]

oh fuck

[wary mantle]

Then it would be (4*10)^6 = (40)^6

[polar herald]

[tribal holly]

ar

alr

[tribal holly]

ye

ya*

[tribal holly]

how do i take out 2?

[vagrant plume]

So wat da problem ;-;

[tribal holly]

oh

[wary mantle]

$\frac{4 \cdot 10^6}{2 \cdot 10^5} = \frac{2 \cdot \Bigl(2 \cdot 10^6\Bigr)}{2 \cdot \Bigl(10^5\Bigr)}$.

[tribal holly]

10^6 / 10^5 = 10^1

4/2 = 2

2 x 10^1

[wary mantle]

Cancel 2 and cancel 10^5

[wary mantle]

Yes

[tribal holly]

ok

one sec

2 * 10^5 is not 20^5 because 2 doesnt have ^5

so you can only multiple togheter if they have same ^x?

(2 x 10)^5

but this works for everything?

cant muliply normal number with x^x?

[wary mantle]

yes

[wary mantle]

What do you mean?

[tribal holly]

so does this work for everything?

the rule

[wary mantle]

$a^x \cdot b^x = (ab)^x$ for all $a, b$ and $x$, yes.

[tribal holly]

10 x 10^6 not = 100^6

[tribal holly]

so

10^6 x 10^6 = 100 ^6

[tribal holly]

because you have to calulate 10^6 before multiplying with 10?

[wary mantle]

Yes

[tribal holly]

fact or cap

[wary mantle]

10 * 10^6 = 10^7, you can use the a^b * a^c = a^(b + c) rule

[tribal holly]

oh lol

e

ye

because

10^1

[wary mantle]

same base

yes

[tribal holly]

ye 1 + 6

but

if its diff number

3^1 x 10^6

[wary mantle]

Then you can't do anything

If it was 5 * 10^6, then you could do something.

[tribal holly]

I can't 30^7

[wary mantle]

Because 10 = 5 * 2

And so 10^6 = (5 * 2)^6 = 5^6 * 2^6

[wary mantle]

No

$5 \cdot 10^6 = 5 \cdot (2 \cdot 5)^6 = 5^1 \cdot 2^6 \cdot 5^6 = 2^6 \cdot 5^7$.

[tribal holly]

2 * 5

10^13

[wary mantle]

Though you'd usually keep it as 5 * 10^6, except if in the denominator, there is a factor of 2 or 5 and so you can cancel it

[wary mantle]

What?

From where did you get 10^13

[tribal holly]

lol dw

i multipled 2 and 5

but

its wrong ik

[wary mantle]

But yes, here, you couldn't really do anything

[tribal holly]

from 2^6 x 5^7

here you cant simplify more too

[wary mantle]

Yes

[wary mantle]

You could go back though

2^6 * 5^7 = 2^6 * 5^6 * 5^1

Now you have two same exponents

[tribal holly]

ty i understand because to multiply with a number that has expontent you have to have the same base

[wary mantle]

So that's 5 * (2 * 5)^6 = 5 * 10^6

That's where you started

[tribal holly]

and if you have the same base its the exponents + eachother

[wary mantle]

Yes

if its the same exponents, then you multiply the bases and keep the exponent

If it's the same base and exponent, you can choose what you want to do

[tribal holly]

ty also how long do you think it takes to learn from my noob level to differiental equations, geometry, advanced algebra, functions, trigometry, vectors, derivation in functions, integration and a bit more

if 18 hours a week

is 0,5 years enough?

if i did study efficent

[wary mantle]

It depends, many of those can go pretty deep (e.g. with advanced algebra, you could mean abstract algebra)

Which is a field many mathematicians do research in

[tribal holly]

Number follower
Arithmetic series
Geometric series
Certificate of Induction

google translate

this is minimum algebra i need

but i want to learn more so thats why i said advanced

[wary mantle]

A uni would usually take longer to cover those

for example, differential equations would be a course going a semester

[tribal holly]

wow

[wary mantle]

The others are usually covered in Pre-Calculus and Calculus

[tribal holly]

i got 1,5 years max

[wary mantle]

There are three calculus courses in the US, usually (I'm not from the US though, it's a bit different here)

[tribal holly]

to learn 3 math books and 2 physics books

[tribal holly]

ye im not too

[wary mantle]

I think Calculus 3 would be vector calculus, optimization and so on?

[vagrant plume]

Ye

[tribal holly]

one sec

Algebra

Number follower
Arithmetic series
Geometric series
Certificate of Induction

Trigonometry

3.4.1. General trigonometry - introduction
3.4.2. Trigonometric identities
3.4.3. Trigonometric equations(*)
The sine function
The function a sin cx + b cos cx
Periodic functions

3.1 Functions

Derivation of trigonometric functions
Function discussion
Modelling

    Linear modeling
    Non-linear modeling
    Modeling with spreadsheets

3.1.1. Integral (*)
3.1.2. integration
Antiderivation
Partial integration
Integration by changing variables
Integration by partial fraction splitting
Volume calculations

List of integrals - solved

Differential equations

Introduction to differential equations
Integral curves
Initial conditions
Direction diagram
Separable differential equations
Integrating factor
Second order differential equations
Practical problems where differential equations are the solution

Vectors

Vectors in space
Parameter generation
Vector product
Plan in the room
Lines in the room
Distances between points, lines and planes in space
Practical spatial geometry
Space figures

[vagrant plume]

Calc 3 is like everything in more than 1 variable

[tribal holly]

All that math in 1 year min

[vagrant plume]

Seems like calc 1/2

[tribal holly]

i dont know what calc is

[wary mantle]

That's a bit similar to the topics covered in grades 11 and 12 here in Germany in the AP (or atleast equivalent) math class.

Except DEs

[tribal holly]

i am grade 12

but

[vagrant plume]

DE is in AP

[tribal holly]

i dont learn this type of math in school

i need to learn this before end of grade 13

i started grade 12 2 months ago

900 hours studying

[wary mantle]

I think it's possible to cover those in a year, though I'd imagine most school courses taking a bit longer

[tribal holly]

in my school grade 11 is something easier grade 12 is something little harder then grade 13 is this i reply to

but i dont take the type of math in my school

so they use 3 years

[tribal holly]

420 hours

[vocal sleet]

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[fluid oracle]

Can someone please help

[vocal sleet]

@fluid oracle Has your question been resolved?

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[vast shale]

Can there be particular solutions of a differential equation with no initial values given

[viral copper]

wdym?

[quiet valve]

A particular solution is where there are no arbitrary constants like f(x) = ax + b is not particular because a and b are constants. But f(x) = 7x + 27 is particular.

So, if you can arrive to a particular solution without the need of initial conditions, that means that solution has no arbitrary constants and is the only solution to the differential equation.

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

Is this possible though

In particular

For y" + a(x)y' + b(x)y = f(x)

For this sort of a DE

Is it always so that

We get a particular solution?

[quiet valve]

iirc, If you arrive to a solution that is particular with no initial conditions then it’s an ODE (ordinary differential equation)

[vast shale]

We are only ever dealing with ODEs in this course...

[quiet valve]

If you arrive to a solution that is particular that it is an ODE, not if it’s an ODE it’s going to only have one particular solution with no initial conditions.

“A mouse likes cheese, if I like cheese am I a mouse?” Don’t get confused on the logic.

[vast shale]

Ohhh

I got it

[quiet valve]

For this, you may or may not get a particular solution without initial conditions, but not guaranteed without initial conditions.

[vocal sleet]

@vast shale Has your question been resolved?

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[vapid wedge]

find an isomorphism ¨ ϕ that ¨crosses¨ the nodes (a ÷ f)
ϕ→ (0 ÷ 5)!

[vapid wedge]

What does this mean?

[sharp mortar]

It would be better to send a screenshot of the original problem

[vapid wedge]

The first part is just concluding that they are isomorph

Which they are

After that i don't understand what they want me to do

[sharp mortar]

weird notation, I don't think its standard

But seems like they want you to find whether an isomorphism exists by explicitly defining a map between the nodes

e.g. f must map to 1 since they are the only nodes with degree 1

[vapid wedge]

As in showing which letter corresponds with which number?

[sharp mortar]

yes

[vapid wedge]

f = 1
a = 0
e=5
b=2
c=3
d=4

That's what i've written down, seems to check out?

[sharp mortar]

yeah, looks good

[vapid wedge]

sweet, tysm

.close

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[vast shale]

i can help you

is that algebra 2?

@unborn wadi

[unborn wadi]

yes

[vast shale]

ok

[unborn wadi]

im a bit uncertain here

[vast shale]

i did alg 1 so ill try to help u

[unborn wadi]

oh

this should be alg 1

dont worry

[vast shale]

ok

[unborn wadi]

what is the name in english of such functions?

[vast shale]

i did alg 1 in 8th grade and he was a pretty bad teacher so

[unborn wadi]

8th grade

pretty early

[vast shale]

i believe it is just functions

[lapis niche]

Piecewise function

[unborn wadi]

thanks

[vast shale]

ok

[lapis niche]

What are you uncertain about? What are we doing with it?

[unborn wadi]

if you can differentiate it x=1

[lapis niche]

Usually one would do left derivative and right derivative at the point to figure that out, do you know that or do we have to use the definition of the derivative?

[unborn wadi]

left and right?

do you mean up and down?

[lapis niche]

I mean left and right, e.g. left derivative at 1 would be the derivative as we approach 1 from the left

Hm, maybe in other languages they teach it as up and down, idk

[unborn wadi]

oh

[lapis niche]

From the left would be "down" in some way, as we gradually increase x towards 1

[unborn wadi]

so like a^- and a^+

[lapis niche]

Yeah, like taking limits at a^- and a^+

Since the derivative is a limit, one can also just take a derivative below 1 and above 1, they must be equal if the function is differentiable at 1

[unborn wadi]

yes that is the limit rule

limx->a^+ must equal limx->a^-

right

[lapis niche]

Yep, exact same idea applies to differentiability

So if you know derivatives, you can take the derivative of f directly and see if it's continuous at 1

If you are supposed to be using the definition, then you can just invoke that and do it at 1^- and 1^+

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[static mirage]

hello

[static mirage]

how do you figure this out?

(80km/h)

and how long would it take

[strong grove]

well u have speed and distance

[static mirage]

Yes

[strong grove]

distance = speed x time

[static mirage]

so 80 x 60?

[strong grove]

no?

[static mirage]

oh

oops

[strong grove]

u want time

[static mirage]

so 60 x something to 80?

[strong grove]

what?

[static mirage]

you said distance = speed x time

[strong grove]

20 km is distance
80km/hr is speed

[static mirage]

oh

oops

[strong grove]

where is 60 coming from

[static mirage]

its 12am my brain iisnt working

the hour

turned to miuntes

[strong grove]

wait u want to find the answer in SI units?

the standard unit would be meters and seconds , so convert everything into meters and seconds

[static mirage]

i dont even know

3b iii

[strong grove]

hm

how were u taught in school?

[static mirage]

my teacher doesnt teach

he just says to do something in the textbook

[strong grove]

well then he/she isnt a teacher

[rugged vortex]

Well

Technically they're doing heuristics

Despite doing a shitty job

Are you familiar with dimensional analysis?

[static mirage]

no

[rugged vortex]

Alright well it helps with shit with units

So let's look at 3ai

80 km/h is your speed. 3 h is the time

[static mirage]

yeah thats easy

240

[rugged vortex]

Yeah

The hours cancel out

[static mirage]

im just confused on b iii

[rugged vortex]

3biiiw is simply working backwards

[strong grove]

b iii is literally same as b i and b ii

[rugged vortex]

80 • x = 20

[strong grove]

just changed values

[static mirage]

those i can domentally

nvm

answers 15 right

[strong grove]

u can divide hundreds mentally but struggle with tens?

[static mirage]

Um

Bc its not a quarter

but rather just a half

or multiplication

like this is just

1 x 5

ii is just 1x4 + 40 cause its half

idkhow to explain it but

thanks i guess

.close

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[static mirage]

Nvm

.reopen

[vocal sleet]

✅

[static mirage]

how do you simplify this

[strong grove]

changed mixed into improper first

[static mirage]

so 3/8 : 7/8

4*

[strong grove]

this is correct

and cancel the 8 in denominator

same number in denominator can be canceled , so u are left with 3:7 which is simplified

[silent burrow]

no

its 3/8 :7/4 as he said

[strong grove]

oh yeah

[silent burrow]

which is 3/8 :14/8

[static mirage]

u cant simplify that

ion think

[silent burrow]

and if u divide by a number, you multiply by its reciprocal

so (3/8)*(8/14)

and now u cancel them

[static mirage]

What

how do u

canel them

so 3:14?

[silent burrow]

well, u divide by 8 then multiply by 8, so u can just leave that out

[static mirage]

so is the answer

3:14

[silent burrow]

yeah

[static mirage]

Thaks

Goodnight

.close

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[vast shale]

Hello okay so I have no idea what c is asking for

I mean d

[flat whale]

c is a number

[vast shale]

So I got

[flat whale]

oh

[vast shale]

What

[flat whale]

if you did c, ignore my comment

[vast shale]

I’m not sure how you get the inflection points of this graph because there is an integral does that like change everything

[flat whale]

yes

g''(x) = ?

[vast shale]

So you can say when function changes to positive to negative

Can’t *

Cause I was thinking 2 and 5

[vast shale]

hm?

[flat whale]

what definition of inflection point are you using

[vast shale]

I’m using if the function changes sign it is an inflection point

When it’s cocance up or down

[flat whale]

function changes sign isn't correct

y = x changes sign from x < 0 to x > 0, but there's no change in concavity at x=0

do you know when a function is concave up?

[vast shale]

Yea

When it changes sign

Positive to negative

No

Opposite

Of what I said

[flat whale]

when what changes sign?

[flat whale]

your response should not fit into this counterexample

[vast shale]

The function f’

[flat whale]

f' is the derivative of the function f

[vast shale]

Yes

[flat whale]

so calculate this

[vast shale]

That’s f’

Is that what is?

[flat whale]

yes it is

[vast shale]

Ohhhhhh

So this is easy

[flat whale]

the calculations are easy yes

[vast shale]

Okay wow I’m not smarty so it’s x = 2,5

F’ changes signs at those points

[flat whale]

you got it

[vast shale]

yay at

thanks you

close

[flat whale]

.close

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[regal dune]

Start by calculating the rate of change for the function h(x)=x^2-1 aka. take the derivative of the function.
Then insert the intervals in the h'(x), add them up and get the average rate of changee

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[night river]

I need help with both parts

I know ur meant to show that LHS is subset of RHS and vice Vera’s

But idk how

[hybrid flicker]

Here's an example with i. first "subset"

Let x be in (A\B) U (B \ A)

If x is in A\B, then...

If x is in B\A, then...

[night river]

x is in A and x is not in B right

[hybrid flicker]

yes

[night river]

or x is in B and x is not in A

But idk how to continue

[hybrid flicker]

if x is in A, then x is in A U B

[hybrid flicker]

and if x is not in B, then...

[night river]

It’s not in A intersect B

[hybrid flicker]

yes

which means x is in...

[night river]

The RHS

[hybrid flicker]

yes

[night river]

Ah yeah that makes sense

[hybrid flicker]

then other case

pretty much the same

[night river]

Okay let me try writing it out and I’ll come back if I have a question

Thanks

Right but idk what I should write for the next line

If the left implies x is in A union B and not A intersect B and so does the right thing

@hybrid flicker sorry for pinging

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[night river]

Do I do this

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@night river Has your question been resolved?

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[abstract pumice]

Alright, so this is just getting ridiculous.

How do I do this power set?

[hard atlas]

well its a set which contains only one element

the element being {emptyset}

[covert raft]

$\mathbb{F}_{\text{un}}$

[twin meteor]

sakka ismail

[hard atlas]

if you want you could call that a={emptyset}

then you are asked for P({a})

[covert raft]

First questions plz

[hard atlas]

!help

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