help-26

[lost plover]

yeah

[subtle mountain]

try to ask in #calculus

[lost plover]

ok thx

[subtle mountain]

let's hope u get helped this time 😭

[lost plover]

lets hope😂

[main mauve]

@subtle mountain next time you see someone send something with the word fourier in it, i recommend you send them to #odes-and-pdes, because the normal help channels aren’t made for questions that advanced

@lost plover close the channel if you’re not using it anymore

[lost plover]

.close

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[lofty mauve]

what is the derivative of

[keen pawn]

i dont even know what a derivative is

[lofty mauve]

ok then don't answer?

its calculus

[keen pawn]

wow aggressive

[neon iron]

@lofty mauve are you familiar with the quotient rule?

[lofty mauve]

no i dont think so

[neon iron]

i think this will help more than I can

https://en.wikipedia.org/wiki/Quotient_rule

if it doesnt help ask here again

[lofty mauve]

alright thanks

[keen imp]

-(2/(x-1)^2)

[lofty mauve]

ye thats the correct answer

ty ill read the page

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[neon iron]

hi may i get help with this question, please?

[neon iron]

so i found that when B = 0, 1, or 3, it can be divisible by 3 and when B = 2, 6, it can be divisible by 4

with that being said, im unsure which values would be correct because i dont know if both numbers must work for both 3 and 4 in order to be correct

could you further explain what you mean by adding 12s please?

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[neon iron]

.reopen

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✅

[neon iron]

oh yes! i did find that when B is 2, the As are 1, 4, and 7 but i couldnt figure out the second B

thank you!

yes please, thats the one ive been stuck on

no worries!

theres 4!

every time i tried a diff number, id only get 3 A values

when B = 4, it wouldn't be able to be divisible by 4 no? bc following the divisibility rules, the number must be divisible by 3 and 4 i believe

yes! but the divisibility rule for 12 follows 3 and 4

the divisibility rule for 4 is the last two digits, so if B = 4, 14/4 wouldnt work

oh! i got 6 as well earlier! dunno why it didnt click that it was the right answer

thank u sm! i appreciate it!

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[junior leaf]

can someone pls explain this

Associative Laws: ¬p∨¬q ∨(p∨q)≡(¬p∨p)∨(¬q∨q)

[junior leaf]

I know associative low is like this ```

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[keen venture]

Basically, you can do ∨ in any order you want.

Parenthesis can go in any order you want

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[junior leaf]

can u pls explain more? because the low has only 3 parts p, q and r while in the example it has 4 parts. I just don't know how they combained it

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[pseudo remnant]

Help

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[fringe raft]

Hi can anyone help me on this question with steps?

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<@&286206848099549185>

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[dry summit]

I’m confused on how exactly I am to maximize an expected sum. Is there a formula ?

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[dry summit]

<@&286206848099549185> if anyone could give me some direction that would be much appreciated

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@dry summit Has your question been resolved?

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@dry summit Has your question been resolved?

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@dry summit Has your question been resolved?

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@dry summit Has your question been resolved?

[inner oracle]

Ask in #probability-statistics

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@dry summit Has your question been resolved?

[dry summit]

Ok thanks

[alpine rune]

It is solved i think?

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@dry summit Has your question been resolved?

[main mauve]

@dry summit bruh close the channel if you’ve asked in #probability-statistics

[dry summit]

I pressed thag my question is solved idk how to close a channel

i thought that was a mod thing

[sullen hazel]

@dry summit

press

the

✅

on the bot

[dry summit]

I did !

[sullen hazel]

do .close

[dry summit]

R hats what I’m saying

[sullen hazel]

I think .close works

[dry summit]

.close

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[sullen hazel]

[main mauve]

after 2 days

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[wicked hill]

Any sources to solve these type of problems?

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[wicked aspen]

if i take a loan of 2 000 000, with equal payments over the next 30 years, with an annual rent in addition to the total of the loan that is 2,1% (per year of the total sum to pay for), how do i formulate this? the first payment is supposed to be 90532. I tried to do

[wicked aspen]

we're also given the answer, it is supposed to be 90532 in payment the first year after loan is taken

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@wicked aspen Has your question been resolved?

[sacred sparrow]

Your issue may be that 2.1% is 0.021 not 0.0021 @wicked aspen

[wicked aspen]

ill try that

im supposed to get 90532 to pay for the loan the first year, basically 2 000 000 / 30 because of 30 years down payment + interest rate of original sum, that is 2,1% of 2 000 000

added together, those should make 90532

[sacred sparrow]

Can you show me the original question?

[wicked aspen]

it is in norwegian though

shall i

[sacred sparrow]

I'm swedish actually, so I should be able to understand. This gave it away lol

[wicked aspen]

okay one sec

9b)

[restive marlin]

Hey @wicked aspen, are you using an HP-12c?

PV = 2000000; N=30; i=2.10; FV=0; PMT

[wicked aspen]

i don't know what that is

[restive marlin]

The idea is that you are paying a fixed amount each year so that by the end of the 30 years you are done paying.

[wicked aspen]

but the answer you got was correct, how could i input what you did, but onto geogebra CAS?

wait youre right, maybe its supposed to be that amount every year

don't know how to calculate that myself though

we use geogebra

[restive marlin]

@wicked aspen

$2000000 = \sum_{k=1}^{30} {PMT \over (1+2.10%)^k}$

[thorny flame]

keepitalphanumeric

[restive marlin]

This is a geometric progression, that you can simplify... and get the result

[wicked aspen]

we use this

[restive marlin]

Never seen this before

[sacred sparrow]

So I just did some googling, there's this formula for it that looks like this and I got the right answer using it

S is how much you owe (2 mil), n is number of payments (30) and p is rent

[wicked aspen]

that looks familiar

thank you i think this is it

[sacred sparrow]

or this one they're the same thing

Just googled what "annuitetslån" was

Note that if you for example are paying monthly you'd have to divide the yearly rent by 12

[wicked aspen]

ill look at it in an hour when i have time

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[ivory pond]

pls help

[ivory pond]

<@&286206848099549185>

pls

ok

ima wait

ok

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[ivory pond]

please help

<@&286206848099549185>

[thorny flame]

TC159

[ivory pond]

alr thanks

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[dapper crow]

heyy does someone know how to intergrate this?

[subtle mountain]

so x is the variable

[dapper crow]

yes

and you want to have x isolated

so like a formula x = ..

an explicit solution

[wooden matrix]

you mean solve the DE?

it's a seperable DE

[topaz sinew]

@dapper crow Has your question been resolved?

[dapper crow]

yeah solve it

and then

isolate x

[wooden matrix]

yeah

it's a seperable DE

[dapper crow]

so that you have x = ....

i know a bit about substitution

just learned it

[wooden matrix]

You can't solve it with just basic integration.

[dapper crow]

but i have not really an idea how to solve it

hmm

is it possible you can help me with it?

[wooden matrix]

sure, so you have $\dv{x}{t}=rx^2-kx$

[thorny flame]

Mosh

[wooden matrix]

as I said, this is a seperable DE, so I can write it in the form $f(x)\dd{x}=g(t)\dd{t}$

[thorny flame]

Mosh

[dapper crow]

yeah

[wooden matrix]

namely $\frac{1}{x(rx-k)}\dd{x}=\dd{t}$

[thorny flame]

Mosh

[dapper crow]

yeah i got that aswell

but then i got stuck xD

[wooden matrix]

hence $t=\int\frac{1}{x(rx-k)}\dd{x}$

[thorny flame]

Mosh

[wooden matrix]

what technique is used on RHS?

[dapper crow]

ehmm

RHS are riemanns summs?

[wooden matrix]

??

[main mauve]

[dapper crow]

or what do you mean?

[wooden matrix]

The RHS is an integral, yes

I mean what technique

[dapper crow]

i know seperation

[wooden matrix]

u-sub, trig sub, IBP, partial fractions

[dapper crow]

or substitution

you asking me something there mate

[wooden matrix]

Yes I clearly asked you a question.

[main mauve]

mosh is asking you what technique you need to use to complete that integral

[wooden matrix]

[dapper crow]

yeah i mean its a hard question hahaha

ehm

i would say substitution

[wooden matrix]

Cause you need to be able to identify the adequete technique.

ok, why?

and what sub?

[dapper crow]

ehm

i think you want to isolate the x to one side right?

[wooden matrix]

Dont beat around the bush.

Answer what was asked.

[dapper crow]

yeah

thats why

and just with u

[wooden matrix]

u=what?

[dapper crow]

u = rx-k ...?

i think

[wooden matrix]

ok, try that

[dapper crow]

aight

btw

this is just the only method i know

a bit

so yeah

lemme try

[wooden matrix]

Then you shouldn't be attempting to solve DEs if you only know u-sub.

[dapper crow]

well i have to

[wooden matrix]

This isn't solvable w/ u-sub.

[dapper crow]

hmmm

[wooden matrix]

you partial fractions it.

[dapper crow]

I've heard of that

but never used it

[wooden matrix]

$\frac{1}{x(rx-k)}:=\frac{A}{x}+\frac{B}{rx-k}$

[thorny flame]

Mosh

[wooden matrix]

then solve for A and B.

[dapper crow]

ehmm oka

y

wait

so A would be rx-k in this case

and B would be x

right?

[main mauve]

no

[dapper crow]

ffs

[subtle mountain]

me seeing pfd 👀

[dapper crow]

then

i have no clue

[main mauve]

multiply both sides by x(rx-k)

[subtle mountain]

basically 1=A(rx-k)+B(x)

[main mauve]

then you have $1 = A\cdot(rx-k)+B\cdot(x)$

[thorny flame]

quantum

[main mauve]

didn’t want it to look like A and B were functions

@dapper crow do you know what to do to get A and B?

[subtle mountain]

capital letters are rarely used for functions I think

[dapper crow]

ehm

let me see

okay tbh no

im searching stuff up

[main mauve]

hint: see what you get when you set x = 0

[dapper crow]

ehmm

okay

[main mauve]

try pauls online notes

[dapper crow]

im there

xD

thats what i have in front of me now

wait

do you make A(0) for one thing

and B(0) for another thing

ehm

ohh wait

WAIT

[subtle mountain]

yes

[dapper crow]

rx-k = 0 and x = 0

[main mauve]

no

[dapper crow]

fuck why?!

[main mauve]

set x = 0

when x = 0, you have $1 = A\cdot(-k)+B\cdot0$

[thorny flame]

quantum

[subtle mountain]

you can do x=k/r after x=0 to solve B

[main mauve]

or you can just take what A is and put that in the equation

either works

[dapper crow]

do you always set x = 0?

[main mauve]

when we have x by itself like this, yes

[subtle mountain]

you just need to make one expression 0 to be able to solve for one/the other variable

[main mauve]

we try to first plug in numbers that will make one term 0

in this case x = 0 worked

also how are you doing odes but you don’t know pfd

[dapper crow]

because, uni's dont tell what you need for certain subjects

so you end up with this stuff

[main mauve]

anyways

what would A be?

[dapper crow]

we want to set A to zero aswell right

[main mauve]

no

[dapper crow]

this time

[main mauve]

A is what we’re trying to find

we can set x = something

A is a fixed value

after doing this we will know what A is, so we just substitute that back into the equation

[thorny flame]

quantum

[dapper crow]

btu so

but

for what was this then?

[dapper crow]

?

just to find a value that b = 0?

[subtle mountain]

to solve for a

[main mauve]

so we can find what A and B are

[dapper crow]

ahh so now you know what A must be

[main mauve]

if $1 = A\cdot(rx-k)+B\cdot(x)$, this will hold for all values of x

[thorny flame]

quantum

[main mauve]

since x is what can vary here

so we set x = whatever is convenient

which here would be 0

[dapper crow]

when would it not be 0?

[main mauve]

when x isn’t by itself

because then that does nothing for us

basically just read that page you have pulled up

[dapper crow]

from paul right

[main mauve]

yeah

that’s where i learned it

[dapper crow]

aight

i think i will do that then

i guess

[subtle mountain]

me gonna finally learn differential equations next week which will be final week then exams 😭

[dapper crow]

thnx anyways for trying ❤️

!close

[subtle mountain]

.close

[dapper crow]

.close

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[tropic elm]

Using derivatives, determine any local extreme points for the function f ( x ) = 2 ^x - 2 x .

[tropic elm]

how to solv this question ?

[void flax]

differentiate and find where f'(x)=0, if you don't know how to differentiate 2^x start by rewriting that into e^(something)

[tropic elm]

i will show u my solution

i didn't calculate anything. i just want to know if i did right ?

@void flax

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[neon iron]

Please don't write ln (LN) as "in" from next time.

,w 2^x ln(2) = 2

[thorny flame]

Results provided by WolframAlpha

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

Requested by TeamSeas.org#7284

[neon iron]

Looks good.

Well done!

[nocturne bane]

bruh can you help me out

help-24

[tropic elm]

thanks,

[neon iron]

#help-24

[tropic elm]

this is what i'm working with.

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[neon iron]

@tropic elm You have .close the channel if your doubt has been answered or you don't have any more questions.

[neon iron]

Oh wait no.

.close

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[neon iron]

If i have a negative ratio on a geometric number sequence and I want to get the sum of the 8th member, do i do it like a1 * (1-(-q^2)/1-q

[neon iron]

Or a1 * (1-(-q)^2/1-q

[coarse fulcrum]

The second notation

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[wooden matrix]

find the common ratio

[gilded needle]

how

ik how to if it was like 1 and 4 in the sequence but not 3 and 6

[noble scarab]

a3 should be a1*q^2

q being the common ratio

[wooden matrix]

how would you do it w/ a_1 and a_4?

[gilded needle]

a1 is the initial term, write a4 as the common ratio

[wooden matrix]

wdym "write a4 as the common ratio"?

a_4 != r

[gilded needle]

yeah i know, you solve to get the common ratio

im probably explaining it wrong

[wooden matrix]

Explain how the algebra goes if you're given a_1 and a_4

you would say $a_4=a_1r^3$ then do what?

[thorny flame]

Mosh

[gilded needle]

alr so
a1(r)^n-1

plug in a1 from a1, and then the number n for what ur solving so if it was a4 n would be 4, solve for r

[wooden matrix]

yep

apply that here

$a_3=a_1r^2 \ a_6=a_1r^5$ as you said

[thorny flame]

Mosh

[gilded needle]

i dont have 5 or 2

im confused

[wooden matrix]

Read what you literally wrote 2 messages ago.

you wrote the general term

[gilded needle]

sorry im stupid

[wooden matrix]

6-1=5 and 3-1=2.

[gilded needle]

yeah

60=a1r2

[wooden matrix]

r^2

not r2

[gilded needle]

160/9=a1r2

yeah i just write it like that

sometimes

[wooden matrix]

r^5

[gilded needle]

crap

[noble scarab]

a6=a3r3

[wooden matrix]

$60=a_1r^2 \ \frac{160}{9}=a_1r^5$

[noble scarab]

you know the value of a6 and the value of a3

[thorny flame]

Mosh

[noble scarab]

then you can find r3 then r

[gilded needle]

what do i do with that.. thats the issue

[wooden matrix]

you said you've solved it w/ a_1 and a_4

[gilded needle]

ive solved when i had a1 and a4

[wooden matrix]

yes.. How did you do that?

[gilded needle]

we dont have a1 here

or r

[wooden matrix]

answer what I asked.

You said if you're given a_1=something and a_4=something else, you could find r.

[gilded needle]

divided bothsides by a1 and then rooted to whatever power

[wooden matrix]

Yes

do that here

$\frac{a_6}{a_3}=\frac{a_1r^5}{a_1r^2}$

[gilded needle]

60/a1=r^2?

uh

oh'

[thorny flame]

Mosh

[gilded needle]

a2 = r^3?

[wooden matrix]

??

where did a_2 come from??

[gilded needle]

sorry im not good with manipulating variables

a6/a3

idk

[wooden matrix]

a_6/a_3 is just... a_6/a_3

which is a number you can compute.

[gilded needle]

sorry im a bit stupid

60/160/9 = a1r^5/a1r^2

[wooden matrix]

yes.

[gilded needle]

27/8=a1^r5)/(a1r^2)

[wooden matrix]

now simplify the RHS

[gilded needle]

rhs

?

[wooden matrix]

right
hand
side

[gilded needle]

sorry

a1 cancels

27/8 =r3

and then cube root

3/2

=r

thankas

[wooden matrix]

yes.

[gilded needle]

so to find a1

do i do
60=a1(3/2)^2 and solve for a1

[wooden matrix]

yes.

[gilded needle]

i got a=80/3

a1*

which looks about right

thanks so much

actually i thionk thats wrong

when i graph it for a3 its right

but for a6 i get 202.5

when its 160/9

@wooden matrix

[wooden matrix]

r=2/3

(160/9)/60 = 8/27

[gilded needle]

yeah i just recalculated it

ty

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[outer breach]

hey I could use some help with this one question:

You roll a die, winning nothing if the number of spots is odd, $3 for a 2 or a 4, and $7 for a 6.

(a) Find the expected value and standard deviation of your prospective winnings.

The expected value is
2.166666667 (Correct )

the standard deviation is _ The answer is supposed to be **1.7360555546666 ** for the standard deviation...

I need help to show how we are able to figure out that the standard deviation for this question is 1.736055...
because I am still struggling to understand how I'm supposed to do this?

[pulsar falcon]

By definition of variance

Then sd=sqrt(Var)

[outer breach]

i've been trying that till now but i'd fail to get the answer

until i used up all my tries for the question

and found out the answer was 1.736...

and i'm confused because idk how :<

[spiral flower]

You know how to calculate the variance ?

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[steep kelp]

I forgot how to do this

[topaz sinew]

@steep kelp Has your question been resolved?

[steep kelp]

<@&286206848099549185>

[slow zenith]

Start with 294 and get it down to its' primes: 2* 3 * 7 * 7

Do the same for your variables, and see if there are matching pairs you can pull outside of the square root (i.e: x^6 = (x^3)^2 so you can pull x^3 out of the square root

[steep kelp]

then do i multiply all of them by 3/4xy

[slow zenith]

Everything that you're able to pull out of the square root gets multiplied by that, yes.

[steep kelp]

so i multiply 7sqrt6 x^3 ysqrty sqrtz all by 3/4xy

[slow zenith]

....? Hang on ....let me draw this...

[slow zenith]

So, the 7 comes out, the x^3 comes out, and y comes out

So, you'll have 3/7xy * 7 * x^3 * y * √6y

Because left on the inside of the √2 * 3 * y

[slow zenith]

Does the drawing help you to see why?

[steep kelp]

but do you also multiply it by the x and y

[slow zenith]

Yes - I said that.

[steep kelp]

alright

I get this

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[icy pilot]

ahh I'm so confused

[icy pilot]

If A Is One, The Parent Function Is $f(x)=x^2$

[thorny flame]

geoxcaliber

[icy pilot]

So, Move From The Vertex Right 1, Up 1. Right 2, Up 4. If A Has A Value Other Than 1, Multiply The Up/Down Movement By A. Ex: If A Is -2, Move Up (-2)(1) = -2

That's What I Got From That

Now what's confusing me is the find other points by

What is meant by "using a"?

Because the a is not the same a is the one in vertex form right?

[leaden tusk]

you have three channels

you do not need three channels

[icy pilot]

I do

[leaden tusk]

no you do not

#rules #❓how-to-get-help

[icy pilot]

three different questions

[leaden tusk]

doesn't matter

[icy pilot]

can I ask all

[leaden tusk]

you can use one channel

[icy pilot]

okay

help needed 💯

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[loud elk]

Hello I am having trouble with these two problems that are on my math review sheet

[main mauve]

$(x-h)^2+(y-k)^2 = r^2$ is the equation for a circle with radius $r$ and center placed at $(h,k)$

[thorny flame]

quantum

[main mauve]

the domain of a function f(x) is all the values x for which the function is defined

[loud elk]

So with the coordinates I would have to put that into H&K and then for 5 I will have to put that into r?

[main mauve]

yeah

[loud elk]

Oh, okay

[loud elk]

Would you be able to explain that further?

[main mauve]

not really

not sure how i would

basically no square roots of negative numbers, no division by 0, no logs of 0 or numbers less than 0

stuff like that

[loud elk]

Oh okay, thank you so much!

[main mauve]

no problem

[loud elk]

😁

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[neon iron]

i remember having a problem like this

[neon iron]

how do i solve it?

Find all complex numbers $z$ such that $z^2 = 2i$.

[thorny flame]

crab

[frosty imp]

you can use polar form

[neon iron]

i didn't learn that

i dont htink i am supposed to use that

[frosty imp]

hmmm, ok

https://www.youtube.com/watch?v=Z49hXoN4KWg

try watching this

it's an algebraic solution

you should be able to apply your problem with what BPRP does here

in your case, use $\sqrt{2i}$

[thorny flame]

alias

[neon iron]

but that is not a complex number

[frosty imp]

it is though. you have $i$ in it, and it doesn't cancel or anything similar

[thorny flame]

alias

[frosty imp]

well, you can change a number like $\sqrt{2i}$ into the form $a+bi$

[thorny flame]

alias

[frosty imp]

the video i showed you does that too

[neon iron]

o

$\sqrt{2i} = a+bi$

[thorny flame]

crab

[neon iron]

then we square both sides

$2i = a^2+2abi+b^2$

[thorny flame]

crab

[neon iron]

group real terms on rhs

$2i=a^2+b^2+2abi$

[thorny flame]

crab

[neon iron]

divide by 2

$i=a^2+b^2+abi$

[thorny flame]

crab

[neon iron]

$0+1i = a^2+b^2+abi$

[thorny flame]

crab

[neon iron]

a^2+b^2=0

ab=1

b=1/a

a^2+1/a^2=0

lcm

$\frac{a^4-1}{a^2}=0

a^4-1=0

[frosty imp]

latex pro tip: put a $ on both sides of your equation. the beginning at the end. it's like how in programming you'll use quotes for a string

[neon iron]

$a^4=1$

[thorny flame]

crab

[neon iron]

a = 1

a= -1

$\pm1+b^2=0

$b^2=1$

[thorny flame]

crab

[neon iron]

or b^2=-1

b=1 or b = -1

@frosty imp is the answer 1-1i, 1+1i, -1+1i, -1-1i

[frosty imp]

it should be 1+i, since all the others squared are -2i

but yeah, good work! is there anything else i can help with

[neon iron]

i dont think so

[neon iron]

i dont really understand the last part

@frosty imp

[frosty imp]

which part?

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

since all the others squared are -2i

[frosty imp]

i think you made some sort of mistake on the way. remember that you wanted $\sqrt{2i}$, so your values for it squared should be $2i$

[thorny flame]

alias

[neon iron]

but i cancelled out the 2

i dont really see how to fix my solution @frosty imp

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@neon iron Has your question been resolved?

[neon iron]

<@&286206848099549185> @frosty imp

[rustic needle]

What is the question?!

[neon iron]

no, i was asking what about mya nswer was wrong

i didnt understand

[rustic needle]

Humm

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[waxen marten]

Do I just plug in the point in the gradient?

grad(T) = e^(yz) + zxe^(yz) + xye^(yz)

oh

wtf rolling

u cant do them all

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[dark swan]

.close

[waxen marten]

ye

dang

ill switch to another

[dark swan]

yeah use an open channel

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[steep perch]

62163

Bro nvm no repeating

[empty sail]

Don't given answers btw

[steep perch]

why

It was wrong anyway

[empty sail]

Because that's not the purpose of the server

You teach the person

[steep perch]

Oh

[empty sail]

Not give answers

[steep perch]

Ye ok nvm can't do thay

Sorry

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[celest glade]

how do I enter something like $$f(x)=\begin{cases}1,& \text{if } x \ge 1\0,& \text{otherwise}\end{cases}$$ into wolframalpha

[thorny flame]

illuminator3

[wooden matrix]

the cases option in math inputs.

[celest glade]

oh I see

.close

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[mortal jackal]

I can’t tell which question was wrong the grading was a bit unclear

[mortal jackal]

and can someone explain why it was wrong?

[neon apex]

bruh... aren't those tick marks... doesn't that means it's correct?

[mortal jackal]

i got points off

-2 and -2

i cant even tell which one of them is wrong XD

[neon apex]

but why the tick marks?

[mortal jackal]

thats why im confused

LOL

[neon apex]

hahaha

[mortal jackal]

best grading ive ever seen

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[neon iron]

Hello

[neon iron]

is the solution to 25-x^4=12 4sqrt 13?

what I did was do +x^4 so that I have 25=12+x^4 then subtract 12 and end up with x^4=13

then I do 4sqrt and end up with 4sqrt13, is that correct?

[restive inlet]

4sqrt doesn't mean what you think it means

[neon iron]

oh, what does it mean?

[restive inlet]

4sqrt(13) is interpreted as the product of 4 and the sqrt(13)

[neon iron]

oh

[restive inlet]

and not the fourth root of 13

[neon iron]

that's what I was trying to say

how would I say that?

[restive inlet]

there is no nice abbreviation for the fourth root and you're better using fractional exponents

like 13^(1/4)

however this will only be one of the real solutions

[neon iron]

ahh

[neon iron]

how so?

[restive inlet]

similar to how x=1 isn't the only solution to x^2 = 1

[neon iron]

ah

so 13^(1/4) and -13^(1/4)

[restive inlet]

those will be the real solutions

[neon iron]

sounds good, and is that because the exponent is an even number?

• • • • • • • = +

@restive inlet would my calculation be correct?

assuming that by "4sqrt 13" I meant 13^(1/4)

[restive inlet]

as mentioned that would only be one of real solutions

and you won't get full marks for it

[neon iron]

yup of course

I just forgot to add the -

but other than that my calculations seem to be correct

[neon iron]

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[neon iron]

.reopen

[topaz sinew]

✅

[neon iron]

Is the only correct solution to root(4x/9) = x/3 0?

I got 0 and 4

[restive inlet]

both 0 and 4 are solutions

[neon iron]

are they correct ones?

[restive inlet]

yes

[neon iron]

hmm

how does "punkt vor strich" work in cases like this

I mean for example that * comes before +

[restive inlet]

who's telling you otherwise

[neon iron]

nobody, it is just a matter of whether the root comes first or the calculation in the root

[restive inlet]

the root apples to everything within the parentheses

[neon iron]

yeah nevermind

I am stupid

[neon iron]

yup thank you, both 4 and 0 are correct answers

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[weak echo]

Hey, I took a math exam (and already completed it), but am getting far too anxious in waiting for my professor to grade it. I was wondering if anyone could take a look at my responses and let me know if I did anything wrong. This exam is a huge part of our final grade, so it's really stressful.

[weak echo]

Don't worry, I don't want to ask questions to help me on an exam or anything like that; I already completed the exam yesterday. I just want to know how I did before the professor grades it so I can know what to expect.

If this is off-topic or against the rules or anything like that, then I really do apologize and you can just disregard this (and close the question)

The exam itself is for Calculus 2 and is not very long with only 11 questions

I ask this rather than post the questions because I was hoping to go over them one by one with someone

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[broken glade]

why is the general case function in the primitive recursion operator defined like f(Succ(y),x1,...,xn) = h(y,f(y,x1,...,xn),x1,...,xn) and not just f(y,x1,...,xn)

[broken glade]

why does h need the y and all the xs

can't it just be defined as a function on the result of f?

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[hot cargo]

I need to scale a 20 sided dice(icosahedron), I need some help finding it's surface area

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[rocky pollen]

i understand the IVT but not how to use it with this table

wouldn't it just be every single value between n(0) and n(12)?

<@&286206848099549185>

someone pls help

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[thorny flame]

slump

slump

slump

$x=(2-y)/4$

[neon iron]

I then replace it in the second equation

[thorny flame]

slump

slump

[neon iron]

Is this right?

[nimble spruce]

Not quite after dividing by 4 you should get $4-2y+7y=6$

[thorny flame]

glittersparkles

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[neon iron]

4 was in the denominator, shouldn't (8-4y)/4 be 2-y?

[neon iron]

Ah I see I wrote 7 instead of y

[nimble spruce]

Ah yeah my bad. I divided by 2 lol

[neon iron]

But the end result is right yea?

[nimble spruce]

Yeah. And then go back and plug in what you got for y in either eqn to get x

[neon iron]

thx

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[forest rune]

so a^2 + b^2 = 25

[thorny flame]

Mohad

$2a\frac{dt}{da}  + 2b\frac{db}{dt} =  0$

Mohad

[forest rune]

after 5 seconds, a = 15, b = 20

db/dt = 4/3

is that right?

can anyone verify?

[forest rune]

meant da/dt

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@forest rune Has your question been resolved?

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[topaz sinew]

@formal fiber Has your question been resolved?

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@formal fiber Has your question been resolved?

[knotty stratus]

the cross product between any 2 vectors will give you something perpendicular to the plane they define in response, you can use that to calculate the height of the figure wrt the 3rd vector, it might be helpful to think about the 2d case first

[inner oracle]

And getting area of one plane side is enough here

[wooden matrix]

Volume of a parallelpiped is either the determinant of the natrix formed by the edge vectors, or the scalar triple product of the 3 vectors

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[livid raft]

A promissory note is a written statement agreeing to pay a sum of money either on demand or at a definite future time. When a note is purchased for its present value at a given interest​ rate, the note is said to be discounted and the interest rate is called the discount rate. Suppose a 10,000​$ note due 10 years from now is sold to a financial institution for ​4900$. What is the nominal discount rate with quarterly​ compounding?

The nominal rate is ?%

​(Type an integer or decimal rounded to two decimal places as​ needed.)

[livid raft]

<@&286206848099549185>

[main mauve]

@livid raft close the other two channels you have open

you can only have one channel open at a time

[livid raft]

ohh I am the new in the server but wait just a moment My friend is solving

[main mauve]

no

close 2 of your open channels now

[livid raft]

how can I close this one

[main mauve]

it’s .close

[livid raft]

.close

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[livid raft]

thanks

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[fading nexus]

can someone help me

a+2b=7

A-b=1

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@fading nexus Has your question been resolved?

[buoyant lance]

The answer is b = 2 but I don't know how to explain it

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[neon iron]

Hello

[neon iron]

Shouldn't the answer here four?

As limit from the left and right comes close to 4

[wooden matrix]

Slope, not y value

You're approximating the slope of the tangent at x=2

[neon iron]

Ohh

Thank you 🙂

[wooden matrix]

Also you could've just plugged in x=2 if they wanted the y value

[neon iron]

Yes, Thank you for the tip 😀

.close

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[livid raft]

https://cdn.discordapp.com/attachments/921081805623394355/921097316906172476/20211216_205030.jpg

[livid raft]

@chrome glen

[livid raft]

<@&286206848099549185>

someone help me

<@&286206848099549185>

[wooden matrix]

be patient.

[livid raft]

okay sorry

[livid raft]

can u help me

[chrome glen]

,w compound interest formula

[thorny flame]

Results provided by WolframAlpha

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

Requested by PapaBread#3820

[chrome glen]

$A=P(1+r)^{nt}$

[thorny flame]

PapaBread

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@livid raft Has your question been resolved?

[livid raft]

I was thinking it is

1458.42

what do u think

[livid raft]

@chrome glen

<@&286206848099549185>

someone help me

[chrome glen]

Nvm it's more complex than I thought

This class seems fairly hard

There's annuity formulas online

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[livid raft]

.close

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[lusty garden]

what did i do wrong

[bronze bison]

The last step seems odd

[lusty garden]

multiplied left side w x-1/x-1

right side with x+3/x+3

then there was 2 x-1 and 2 x+3 in the numerator

and one of each in denominator

so i canceled

and i got that

[bronze bison]

Ignore the above

I dont see where you can cancel stuff

[lusty garden]

hmm

i see

but why can't i cancel

like (x-1)^2

why cant i cancel with the denominator term

[bronze bison]

Denominator is the term below the numerator right? Or was it the other way around

The problem is that there is a sum not a product in the above term

[lusty garden]

yeah afaik its the bottom term

hmm

im not sure i understand

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[neon iron]

i have difficulties reading math questions and focusing in lessons in general but i have exams coming up in january and i cant remember a single thing about the area of triangles..

[eternal wing]

Area of a triangle is base * height / 2

Do you understand what a base and a height are?

[neon iron]

yeah im just confused since its slanted and im not sure

[eternal wing]

Tell me what the height is in this picture

[neon iron]

i think 8? im not sure because of the 4 being in the middle of the shape makes it look like height but the 8s going upwards

[eternal wing]

okay look, you shouldn't judge these things based on where they point towards

[chrome glen]

It shouldn't matter which you choose to be height

Even though it's objectively one thing

I suppose it'd be best to choose what's actually right

[eternal wing]

The height here is the line that goes from one of the vertexes to side opposite to it.

And of course, they must have a 90 degrees angle between them

the base is just one of the sides of the triangle

and when choosing a base and a height, make sure the height to a height to that specific base

[neon iron]

ohh

ok

[eternal wing]

For example here,

you can't just do 3 * 5 / 2

because the height is not going to that side

You need the height and the base that have a 90 degrees angle

[eternal wing]

So in here, you would need the base to be the side below the 3

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[grand wing]

i got a positive answer when u=sin(x)

where was i wrong. they are supposed to be the same right

help

[restive inlet]

recall the sub you used in part b)

also missing the constant of integration

[grand wing]

cos(x) ...

[restive inlet]

so how are you getting from
int u - du
to -1/2 sin^2(x)

and do you see your mistake

[grand wing]

not really

hmm

[restive inlet]

don't skips steps

[grand wing]

ohh

-1/2cos^2(x)

wait what

what trig identity should i use

sin(x)^2+cos(x)^2 = 1 does not seem to fit

nvm

yeah the integration constant

is -1/2

[restive inlet]

you can't conclude the value of the integration constant

[grand wing]

what

hmm

[restive inlet]

the best you do is represent it with a variable

[grand wing]

C = -1/2

[restive inlet]

no

you can't conclude the value of the integration constant

[grand wing]

...

i dont get it

[restive inlet]

note that both integrals have an arbitrary constant of integration

all that matters is that the results differ by a constant and are equivalent solutions

[grand wing]

ok so my answer for:
a is 1/2sin^2(x) + C
b is 1/2sin^2(x) - 1/2

would that be fine?

[restive inlet]

no

for the last time

you can't conclude the value of the integration constant

-1/2 cos^2(x) + d
and you could do some manipulation to get
1/2-1/2 cos^2(x) + d -1/2 = 1/2 sin^2(x) + d'
(where d' is a constant)

all this does is confirm that the solutions are equivalent

after reaching

-1/2 cos^2(x) + d
that's all you really need

[grand wing]

something like this

$\frac{1}{2}sin^2(x)+C\ = -\frac{1}{2}cos^2(x)+E \ \
\frac{1}{2}sin^2(x)+C\ = \frac{1}{2}(sin^2(x)-1)+E \ \
\frac{1}{2}sin^2(x)+C\ = \frac{1}{2}sin^2(x)-\frac{1}{2}+E \\
where -\frac{1}{2}+E \ is \ a \ constant \ \
\frac{1}{2}sin^2(x)+C\ = \frac{1}{2}sin^2(x)+E'$

[restive inlet]

use E' after combining the -1/2 + E

[grand wing]

ok. but is that what you mean

[restive inlet]

but like I mentioned this isn't really needed for the question

more or less yeh

[thorny flame]

aIex

[grand wing]

.close

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[dry oxide]

In this ques, ABC and CDE are congruent quadrants and CE(curve) is a semicircle. How can I calculate the shaded area?

[dry oxide]

<@&286206848099549185> pls help😔

[radiant marlin]

do you know calculus

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@dry oxide Has your question been resolved?

[dry oxide]

No

[radiant marlin]

you'll have to use trig to find the areas of these 2 triangles

[dry oxide]

Ok…but how do I get those angles?

I mean I’m facing prob with that semicircular portion

[radiant marlin]

hmm I'm thinking about how to get the angle at B