help-0

[surreal meadow]

do you know about permutations/combinations

[slow canopy]

yes (but terrible at them)

but I know the formula for choose

[surreal meadow]

nCk is n choose k which is the number of ways to pick out k elements out of a total of n, without taking order into account

which is what we were doing when we did 2 * 3, 2 * 5, 2 * 7, 3 * 5, ...

picking out 2 elements out of our 4

[slow canopy]

ohhhhh

so with n = 4

[surreal meadow]

and we sum up the total number of ways to pick out 0 elements (factor of 1), 1 element (each prime), 2 elements (any product of 2 of the primes), ... n elements (product of all the primes)

[slow canopy]

4C0 = 1 which is where 1 comes from

[surreal meadow]

the 1 doesn't come from there

but it represents picking "none" of the primes

so it works out 😅

[slow canopy]

...lol

[surreal meadow]

we could also just say

[slow canopy]

and then 4C1 are the {1, 2, 3, 5, 7}

then?

[surreal meadow]

1 + nC1 + nC2 + ... + nCn

no. 4C1 = 4

[slow canopy]

oh duh

[surreal meadow]

which represents {2, 3, 5, 7}

[slow canopy]

let's go with this

[surreal meadow]

sure

now that 1 doesn't represent the factor of 1

but it represents that the factor of 1 adds another factor to our total number of factors

because that expression represents our total number of factors

regardless, this expression (should) work out, now the task is to justify why it works out

[slow canopy]

ok let me re-read the initial problem lol

[surreal meadow]

probably want to use induction here

[slow canopy]

I'm god awful at formal proofs

[surreal meadow]

i feel an informal proof should suffice

they said justify carefully so justify it as best you can

[slow canopy]

oh

[surreal meadow]

but a formal proof doesn't seem required

[slow canopy]

he gave us this

can't say I understand this justification

[surreal meadow]

since each prime does not have any other prime as a factor, the product p1 * ... * pn has at most a single divisor for any prime in {p1, ... , pn}

[slow canopy]

I think he means their product

[surreal meadow]

so any divisor can, at most, have any prime p_k in {p1, ..., pn} as a factor once

[slow canopy]

otherwise he'd use commas

hm

[chrome salmon]

Can ai be equal to 0

[surreal meadow]

yes

[slow canopy]

presumably?

[sour scaffold]

sorry for slow respond,, thank you so much ❤️

[chrome salmon]

If all ai are 0 then how would we get 2^n

[surreal meadow]

there's 2^n choices, since there's 2 choices for ai for any of the n primes

[chrome salmon]

Ok so this is divisor not the thing that's getting divided right

[surreal meadow]

divisor is the number dividing the dividend

@slow canopy take p1 as a focus point for our number:
p1 * (p2 * p3 * ... * pn)

you can see that if we were to divide our number

[ocean seal]

it's Sam

[surreal meadow]

@chrome salmon

[chrome salmon]

Yeah 2ⁿ

[surreal meadow]

if we were to find divisors for our number, p1 can only be a factor once, as (p2 * p3 * p4 * ... * pn) does not contain a factor of p1

[ocean seal]

it's Sam

[chrome salmon]

But I get what the question is

[surreal meadow]

does this make sense to you @ poop

[chrome salmon]

This

[slow canopy]

I'm a bit lost

[chrome salmon]

Did you solve it?

[surreal meadow]

does p1 divide (p2 * p3 * p4 * ... * pn) @slow canopy

[slow canopy]

No

[surreal meadow]

exactly

so then our composite number p1 * ... * pn

can only have, at most, 1 factor of p1

so if we find a divisor, it can either have (p1)^0 or (p1)^1 as a factor

[slow canopy]

so you're saying if we factored out our composite number we'd only have one p1 at the bottom of that factor tree

[surreal meadow]

yes

because every factor is a prime

so no other prime has p1 as a factor by definition

same idea applies to any prime in our set, so then p2 can be a factor in the divisor at most 1 time, and same with p3, ... pn

and so we can write the divisor as p1^a1 * p2^a2 * p3^a3 * ... * pn^an, where ai is either 0 or 1

[slow canopy]

makes sense since we're multiplying one of each to make this composite number

[surreal meadow]

since it can be a factor no times (0) or once (1)

[slow canopy]

so n instances, 2 possibilities per instance

[surreal meadow]

yes

and we talked about where does quantities come from above

[slow canopy]

this is the only part I'm a little hazy on

[surreal meadow]

the divisor is another composite number

and it's factors can only be the primes that comprise the larger composite number p1 * p2 * ... * pn

and as we said above, each of those primes p1, p2, ..., pn

can only show up once

since it's multiplied into the composite at most once

[slow canopy]

I just don't get the ^0/1 thing

if you write the divisor with any of these parts being ^0 it just becomes 1 and changes the outcome

[surreal meadow]

it doesn't change the outcome though

and thats a completely reasonable divisor

[slow canopy]

ohhhh I get it

I'm so ready to be done with discrete math lmao

ok

because you can change any of those primes to 1 and the resulting number will still be a factor

[surreal meadow]

yeah basically

[slow canopy]

I get it now

Thank you so much for walking my peanut brain through this

[surreal meadow]

peanut brains can't do discrete math, don't do yourself a disservice

[slow canopy]

I just need to power through it, once I'm past these classes I'll more or less never see any of it besides the logic stuff ever again

Anyway, all my questions have been answered so

.close

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[warped jay]

how many interest in 10m 0.1%

[lone heart]

@warped jay Has your question been resolved?

[misty ice]

?

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[alpine sable]

Help

[alpine sable]

help me guys

[raw shard]

literally count the number of terms

[alpine sable]

so
#1 is monomial
#2 is multinomial
#3 is multi
#4 is trinomial
#5 is binomial?

[raw shard]

3 isn’t multi

everything else is right

[alpine sable]

oh

oh

[alpine sable]

Is it monomial?

[raw shard]

no

ignore the fraction if you need to

since the denominator is a constant

[alpine sable]

So it's a trino then

@raw shard quantum #3 is trino then

[raw shard]

yes

do you understand why

[alpine sable]

x2+x4xy-y²

that's 3 terms total by my count

[raw shard]

@alpine sable close the channel if you’re done

[alpine sable]

.close

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[amber cedar]

I'm a bit confused as to how my professor got this answer.

[amber cedar]

More specifically I should say I see where the numbers are directly coming from, but where are they in a general sense?

[chrome salmon]

Have you done questions like
Number of ways to choose 4 positive integers such that they add to 49

[severe sluice]

also

because you have to choose 8 apples

you can only "freely" choose the other 41 fruits

[amber cedar]

I can't say I have no.

[chrome salmon]

Ok I think KGAA is explaining

[amber cedar]

Okay.

[chrome salmon]

You have to basically find number of ways for this x+y+z+w=41

[amber cedar]

Wait but I thought it was adding up to 49 here

And just like one of them has to be 8.

[severe sluice]

they're asking for the number of ways you can choose the fruits, right?

[amber cedar]

Yes.

[severe sluice]

so

with the 8 apples

you must choose them

there's no other way

right?

[amber cedar]

When you say choose do you mean pick? Or do you mean choose in the mathematical sense?

[severe sluice]

yeah, i mean pick

[amber cedar]

Okay. Then yes.

So you have 3 other fruits, x y and z and they have to add up to 41

Right?

[severe sluice]

no?

[amber cedar]

But you're buying 8 apples.

[severe sluice]

other than those 8 apples, i think you can buy more apples

[amber cedar]

Yeah it says at least.

Ooooooh wait

Okay I get it.

.close

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[low pewter]

absolute value of a and b are > 1

[severe sluice]

uh
just take the term with the highest power
what do you have?

[low pewter]

an / bn ?

or do you mean that i need to make seperate lim to a and b highest power ?

[chrome salmon]

You can ignore the elements with power less than n

[low pewter]

ok

makes sense

but what do i need to do with an/bn ?

[chrome salmon]

If a>b then it will diverge

[low pewter]

i know that it will diverge when a >b and converge if b>a but i need to calculate the lim

can i make (an+1/bn+1)/(an/bn) ?

(an+1 x bn) / (an x bn+1) ?

nah that wont help

[noble sinew]

What is that gonna do for you?

Lim n->inf of a^n/b^n=lim n->inf of (a/b)^n

[low pewter]

then thats just inf

if you put it that way

[noble sinew]

No depends on values of a and b

If b>a then a/b is what?

[chrome salmon]

<1

[low pewter]

0

[noble sinew]

2/3=0?

[low pewter]

(2/3)^inf is approaching zero

(3/2)^inf is approaching inf

[noble sinew]

Bad notation but yes that is the idea

[ocean seal]

it's Sam

[low pewter]

if c (1 , inf) it is inf

if c is 1 its 1

if c <1 its approaching 0

if c is <0 its divergent

but a and b absolute values are 1<

how do i work with negative numbers ?

[noble sinew]

Can you decide?

And wdym with how do you work with negative numbers

[low pewter]

how do i answer the question if the value of a is positive and b is negative number and a>b then the sign of inf is determined by the n

[noble sinew]

So do you think the limit exists then?

[low pewter]

oh

so if i get (negative number)^n the limmit does not exist

[noble sinew]

No

[low pewter]

then the infinite series is divergent

[noble sinew]

No?

[noble sinew]

This isn’t true

[low pewter]

Ehhhhhh

i am sorry

the language barrier is big for me

so thank you for you help

.close

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[devout summit]

Can't |b|>|a| , b<-1 and a>1 give us converging?

[chrome salmon]

I was just talking about positive at that moment for them to understand

Didn't mentioned it but that was the task for the moment

[devout summit]

Understood

.close

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[chrome salmon]

That would've just aroused more questions than answers

[devout summit]

But did chernobog understand the case when b<0, a>0 though?

[chrome salmon]

Idk scapeprof continued so I didn't see anything

[lone heart]

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[valid ivy]

hm

[valid ivy]

i got a question

[bleak ridge]

Wots this question

[valid ivy]

which one is right

[severe sluice]

1

[bleak ridge]

The first one ye

[tiny minnow]

1

[valid ivy]

so we do the lil line divide first?

[tiny minnow]

yes

[bleak ridge]

If the line between a and b was bigger it'd be the other one though

[tiny minnow]

the biger

[bleak ridge]

It's really just what you make it

[valid ivy]

so a/b/c=ac/b?

[gray isle]

no

[bleak ridge]

There's no specificity to that

[valid ivy]

wdym

[gray isle]

a/b/c
is bad notation and as written would be interpreted as (a/b)/c which is a/(bc)

[valid ivy]

i mean this

[bleak ridge]

Yes

[valid ivy]

ight

[gray isle]

the fraction line is long enough that
a/(b/c)
is implied

[valid ivy]

so if for example i got 6^x*6/ 3^x * 3 its like 6^x * 6 * 3 / 3^x?

[bleak ridge]

You need to use parentheses for in text stuff usually

That would imply

[gray isle]

its better if you write it out
or use sufficient parentheses
or use texit properly

[bleak ridge]

$6^x * \frac{6}{3^x} * 3$

[ocean seal]

PapaBread

[valid ivy]

wouldnt it be easier to get the 2^x and then 18?

to do 6^x/3^x in order to get that 2^x

then 6*3=18

[bleak ridge]

You can't do that

With exponent stuff

[valid ivy]

why cant u do that

u could divide 3^x on every one u choose u just need to have 1 divided by it

[gray isle]

its better if you first clarify what you actually have

[valid ivy]

so wont it be easier to do 6^x divided by 3^x

?

or i cant

i think i can

[bleak ridge]

I'm p sure 3^x is equivalent to 6^sqrt(x)

[gray isle]

https://discordapp.com/channels/268882317391429632/490557019623915520/917417000328900659
is that what you have or is is something else

[bleak ridge]

So 6^x/3^x is 6^(x-sqrt(x))

[valid ivy]

gimme a sec to show ya rq

[raven rover]

Test x = 4, this is actually false

[bleak ridge]

Not 2^z

[raven rover]

81 vs 36

[gray isle]

if you're talking about
$$\frac{6^x}{3^x}$$
then yes, that will simplify to $2^x$

[ocean seal]

ℝamonov

[bleak ridge]

Hmm

[raven rover]

^

[valid ivy]

so then 2^x +18

bc u have that 3 * 6

lemme show ya

just a min

[raven rover]

2^x ***** 18

[valid ivy]

ye oops

[raven rover]

$6^x \cdot \frac{6}{3^x} \cdot 3$

$\vspace{10pt}$

$\frac{6^x}{3^x} \cdot 6 \cdot 3$

$\vspace{10pt}$

$2^x \cdot 18$

[valid ivy]

💯

[ocean seal]

Shen

[valid ivy]

is this right

[gray isle]

um...

can you fix that handwriting

[raven rover]

Can you write it a little more neatly?

[valid ivy]

oof

il try

[gray isle]

its hard to distinguish whether stuff is supposed to be part of the exponent or not

[valid ivy]

this is what we got

this is what we need to find

[raven rover]

You can basically undo the steps we outlined above

$2^x = \frac{6^x}{3^x} = \frac{b/6}{3a}$

[ocean seal]

Shen

[raven rover]

3a = 3^x

b/6 = 6^x

[valid ivy]

whats the answer

lemme write it on a paper

ight

[gray isle]

you could continue from the work you did where you reached
$$\frac ba = 18\cdot 2^x$$
and getting $2^x$ in terms of $b$ and $a$ is just 1 step away

[valid ivy]

tell me if its right

[ocean seal]

ℝamonov

[gray isle]

no, algebraic error at the end

[valid ivy]

?

what is it

[gray isle]

what exactly are you doing from:
$$\frac ba = 18\cdot 2^x$$

[ocean seal]

ℝamonov

[valid ivy]

dividing 18 both sides

so i will get 2^x =c

c=b/a/18

?

[gray isle]

better if you put parentheses around the (b/a)/18

[valid ivy]

oh

ok

[gray isle]

on the page you somehow swapped it to a/b and also messed up the other order of division

[valid ivy]

yh

this supposed to be b/a

mb

so 2^x=a/18b?

[gray isle]

no

[valid ivy]

then whats the answer

[gray isle]

how are you getting a/18b

[valid ivy]

just a sec

b/18a

2^x=b/18a

?

[gray isle]

parentheses around the denominator when typing it in text here

2^x = b/(18a)

[valid ivy]

i have to

?

[gray isle]

that's fine

[valid ivy]

order of operations

[valid ivy]

thx

ight

thank u man

[raven rover]

.close if appropriate

[valid ivy]

.close

[lone heart]

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[valid ivy]

.reopen

[lone heart]

✅

[valid ivy]

got another small question

same thing but i need to find 18^x

gimme a sec to try

hmm

stuck here

how do i continue

[tiny minnow]

u get until $\frac {3^x}{3} \cdot 6^x \cdot 6$?

[valid ivy]

yes

[ocean seal]

IVMC Gaming CH

[valid ivy]

could ya help me out what to do next

[tiny minnow]

= $3^x \cdot 6^x \cdot 2$

[ocean seal]

IVMC Gaming CH

[valid ivy]

ohh yea

[tiny minnow]

= $18^x \cdot 2$

u get it?

[valid ivy]

yea

[ocean seal]

IVMC Gaming CH

[tiny minnow]

If ur done u may do .close

[valid ivy]

18^x *2 = ab
ab/2 = 18^x

?

[tiny minnow]

yes

[valid ivy]

ight thx bro

[tiny minnow]

np

[valid ivy]

appreciate that

.close

[lone heart]

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[void swift]

You roll 5 dice at once, and you must get at least two “4”s to win. What is the probability that you will win?

This question came up in our chapter on discrete probability distributions, but I'm not sure how to solve it with distributions.

[noble sinew]

Probably easier to calculate the complement

[void swift]

I began by calculating the chance of getting no 4s and the chance of getting one 4, and subtracting those from 1

Is that relevant to distributions?

[noble sinew]

No that is just a property of probability

[void swift]

Oh, weird... what does distributions come in here then?

By the way, afterwards, the question asks: expected number of trials to win?

[noble sinew]

When calculating prob of 0 4’s

And of 1 4

[void swift]

I just did
No fours:
(5/6)^5

One four:
(5/6)^4 * (1/6) *(4C1)

[noble sinew]

Yes you used a distribution there to calculate those probabilities

[void swift]

Does it have something to do with this?

[noble sinew]

Yes that is what you used isn’t it?

[void swift]

No... haha

I don't know what it's called, I just used the formula we used when doing "from x choose y items" questions

[noble sinew]

Which is exactly a binomial distribution

So yes you did

[void swift]

But let me try starting by putting it in the formula because that's what we're supposed to use

Alright, cool. The question tells me each roll (of rolling 5 dice at once) takes 10 seconds, and asks me for the expected time to win the game.

I'm thinking, if P=probability of winning, 1/P is expected number of trials, right?

And then you just do 1/P * 10 seconds.

[noble sinew]

Si

[void swift]

[lone heart]

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[alpine sable]

if we cut the triangle in half and then get the sin of x on both sides and then add them together does it work ? or we need to use the cos rule

[alpine sable]

i hope someone understand me 😫

[wary stream]

What's the full question?

Because it says "use the cosine..." and gets cut off

[raw shard]

law of sines

[wary stream]

Cosine and sine rule as in law of cosine and law of sines?

Law of cosines works better

[raw shard]

why is that

[alpine sable]

ik but ive got an idea to not use the formula and instead use this thing

[wary stream]

Because you need another angle for law of sines

[raw shard]

makes sense

[wary stream]

Cosine rule is law of cosines, I believe

So that's what you need

Also, it says to "find the indicated missing angle/side" and that problem is missing a side so the only option is law of cosine. You don't have to use both rules, it's based on the case you have

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[daring schooner]

"If angle CAB is equal to 22 degrees and line AB is parallel to the chord with a length equal to 380 m." which is 380m AB or the chord?

[knotty garnet]

Thats not really a math problem but that's not your fault

That is quite ambiguous but I think it might be more likely that it's referring to the chord, but without more context probably can't tell

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[simple elm]

deriving f(x)=(200x)/(x^2+1) and getting f'(4) with central quaote thing and h=0,001

[simple elm]

i cant derive this

[bleak ridge]

Are you using the limit definition?

[simple elm]

im supposed to use the central quote way

[knotty garnet]

Close this one

You already have a channel

[simple elm]

.close

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[surreal abyss]

Hi, Can somebody help me ? I have a question about how do we find the directrix of a parabola with a graphic, for example this image ?

[devout summit]

Didn’t you already draw it?

[surreal abyss]

Yes I forgot how did I find it ? 🙈😅

[devout summit]

What all is “given”?

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@silver flare Has your question been resolved?

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[prime flax]

hi is someone able to explain to me how to find the exact and approzimate roots please, for - 10 sqrt 100+104/4

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[fickle dock]

Hello, would anyone mind explaining to me what is happening when the series gets changed to (-1)^n? I don't understand why that would work, it's the whole numerator multiplied by -1, not just half of it, no?

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[fickle dock]

Hello, would anyone mind explaining to me what is happening when the series gets changed to (-1)^n? I don't understand why that would work, it's each term in the numerator multiplied by -1, not just half of it, no?

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[daring schooner]

Here the diagram and the full question "The PI of a highway is located in a lake at point C. Stations A and B are selected to replace the inaccessible PI, which is lying along a line through PC and PT respectively. The stationing of PC is 15+140 while that of A is 15+410. If angle CAB is equal to 22 degrees and line AB is parallel to the chord with a length equal to 380 m."

[daring schooner]

I'm not sure which is the 380m.

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[alpine sable]

can someone explain how to start this?

[alpine sable]

fully factored the (x^9-4)^4

then multiplied by x^8

yea

but i wasnt able to get ln so i erased

[glass lichen]

Yeah ln never comes up

[alpine sable]

i think just the basic ones but im assuming for this i would get to 1/x dx

[glass lichen]

you dont

[alpine sable]

really?

[glass lichen]

I can tell you with certainty ln(u) would never show up unless you royally fucked up

[alpine sable]

what do you mean by u-sub

[glass lichen]

the technique of u-sub

aka reverse chain rule

[alpine sable]

oh yea

i dont think i have been taught u-sub

so i wouldnt be able to use it

[glass lichen]

then just expand everything out again

[raw shard]

nothing like expanding out a 4th power

imagine doing ibp on this

bruh

they just haven’t learned it

nothing bad about that

[alpine sable]

no im checking my notes for a list

I know power, constant, constant multiple, sum/difference

that should be all

but ik how to integrate an exponetial function and a log function

i havent done it so no

okay

could i come back with some work

and could you check?

Could you explain what the directions mean?

im talking about the assume u>0 when ln u appears

no your right

my bad

yea thats my bad ive just been working on this sheet for a while

but other than that is it good?

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[loud oyster]

might be a dumb question but... how would I get started to solve this system of equation?

[loud oyster]

I tried equaling them, didn't work. substitution made it really complex

[placid zinc]

Substitution shouldn't be so bad. The second one can be written as:
z = -2x + 7y - 24

[loud oyster]

I got 13x-29y=-123 from that

but where do I go from there? substitute again?

I can see that but this is the answer for this question

[turbid shuttle]

Aren’t u suppose to do a cross product?

[placid zinc]

Note that 13x-29y=-123 is, as far as I'm concerned, a perfectly good answer to your original question

They just want a different form

[loud oyster]

yeah you're right lol

I think they do want to cross product, or at least this question does

like getting the normal vectors of the two planes and then cross product to put into the equation for a line

I think the intersection is to find the point of intersection

[turbid shuttle]

U just need a point now

[placid zinc]

There's a line of intersections, not a point.

You can use any point on the line, though

[loud oyster]

so I guess like just use 13x-29y=-123 to find a point assuming z = 0?

[turbid shuttle]

U can just set any variable to 0 and it becomes 2 var

Yea

I’m taking a shit so I don’t have pen an paper but u have 2 variables and 2 rams

Eqn

[loud oyster]

lol yeah thank you all for the help

!close

.close

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[atomic lodge]

Here’s my work

The correct answer is 162x^4 im getting 486x^4

[raw shard]

don’t ping helpers immediately

[atomic lodge]

sry!

[raw shard]

rewrite it as $\int^{3x}{a} - \int^{-3x}{a}$

[ocean seal]

quantum

[atomic lodge]

can't I just use second fundamental theorem

[raw shard]

yes

[atomic lodge]

So I did that but unable to get the correct answer

[raw shard]

you have to use the chain rule

[atomic lodge]

Hold on
Lemme try again

Well so [(3x) ^4 * 3]- [(-3x)^4 *-3]

Derivative of 3x is 3

I don’t see any chain rule

@raw shard

[raw shard]

3x is a function in a function

the outside function is the integral

[atomic lodge]

I don’t get what u r trying to say

[raw shard]

K(x) = $\int_{a}^{x}$, $g(x) = 3x$, $\int^{3x}_{a} = K(g(x))$

[ocean seal]

quantum

[raw shard]

function composition

@atomic lodge

[atomic lodge]

We don’t have a constant in the bottom number

We have 2 functions

[atomic lodge]

I’m in calc ab u sure this is calc ab stuff

[raw shard]

i know what i did

you can split one integral into two integrals

[atomic lodge]

I don’t get it I’m sorry like u multiples the upper limit by 3 but how did that split it

[raw shard]

$\int_{a}^{c} = \int_{a}^{b} + \int_{b}^{c}$

[ocean seal]

quantum

[raw shard]

i didn’t do anything to the limits

i just split it into two integrals

[atomic lodge]

Ohk

I kinda get it

[raw shard]

remember that $\int_{a}^{c} = F(c) - F(a)$

[atomic lodge]

So how would u solve that problem

[ocean seal]

quantum

[raw shard]

i already said how i would

[atomic lodge]

1 fundamental Theorem

[raw shard]

scroll up

[atomic lodge]

I think that question won’t be ask
A friend of mine is getting the same answer

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[shell ridge]

help please

[median dirge]

Hi @shell ridge

[shell ridge]

hi

ive done every other question and got it right but im kind of stuck with this one

i dont know which ones to switch

[median dirge]

Which one is it

[shell ridge]

d and e

i did the rest in my book btw

[median dirge]

Yeah,what rule did you get for the volume of water

[shell ridge]

v = -200t - 1000

[median dirge]

Yes, and whats V, and whats T

[shell ridge]

omg sorry

i think i read it wrong before

[median dirge]

Oh, its okay, did you get how to do it

[shell ridge]

yeah

[median dirge]

Nice.

If you like, you can share your work once youre done!

[shell ridge]

v = -200 * 3.5 - 1000 right?

[median dirge]

Yeah!

[shell ridge]

thanks mate!

[median dirge]

Welcome

[shell ridge]

I need help with e now

[median dirge]

Sure

[shell ridge]

I don't know which ones to flip

[median dirge]

The volume is given

And time is unknown

So you can substitute V

And find t

[shell ridge]

oh is it 1.25 minutes

i just used the unitary method

because 750 = ? + 1000

? must me -250

and -200 * 1.25 is -250

[median dirge]

Yeah exactly

You can do it this way too

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[daring egret]

sin x - (sin x cos^2 x)
how do I simplify this one?

[median dirge]

Hi

Again

[ocean seal]

Muhammad Hussaini

[median dirge]

Is this your question??

[daring egret]

yes

[median dirge]

You can

Try the pyth. identities once again

Write all of it in terms of sin(x)

[daring egret]

you can't change cosine to sine randomly

[median dirge]

It is cos^2x

So you can use

$sin^{2}x+cos^{2}x = 1$

[ocean seal]

Muhammad Hussaini

[median dirge]

Did you get it

[daring egret]

I don't know

[median dirge]

Well... Lemme show you

Now try

[ocean seal]

Muhammad Hussaini
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[median dirge]

Can you do it now @daring egret

[daring egret]

is it just sin cubed theta?

[median dirge]

Yeah!!!

[daring egret]

thankssss

[alpine sable]

.close

[median dirge]

.close

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[lone heart]

@grave urchin Has your question been resolved?

[grave urchin]

<@&286206848099549185>

[vale wigeon]

"ah yes let me post this problem with no explanation of what work i've done or where i'm having trouble and then wait around like an idiot"

[grave urchin]

well i divided 72 with the year given and got 3.512

.close

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[alpine sable]

There are 6 old and 12 new model cars in a gallery.

a) On a random day, if we know that three cars have been sold, what is the probability of those cars to be 2 new and 1 old?

b) What is the probability of at least one new car has been sold?

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[slow canopy]

Can someone walk me through this?

[severe sluice]

well

expand i(i+1)

then the rest would be obvious

[slow canopy]

I was given this as a solution but I don't know how I was suposed to figure out how the final equation equaled the sum of the first two to begin with

[slow canopy]

i^2 + i?

oh

lol

jesus christ

thanks

.close

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[peak tiger]

i have no idea how to approach this

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[velvet pelican]

you'll probably need 2 things

1. Sum of all the probabilities is 1
2. E(X) = Sum[ x * P(X=x)]

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[covert breach]

how do they get -512, +512, etc as the answers there?

like how do they evaluate this integral?

[naive parrot]

Does anyone know why we log a time series? Just curious

[covert breach]

@naive parrot im asking a question here already

[naive parrot]

alright relax

[covert breach]

<@&286206848099549185>

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[covert breach]

<@&286206848099549185>

https://cdn.discordapp.com/attachments/490557019623915520/917721532980133918/unknown.png

how do they get -512, +512, etc as the answers there?
like how do they evaluate this integral?

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@covert breach Has your question been resolved?

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@covert breach Has your question been resolved?

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@covert breach Has your question been resolved?

[grim void]

<@&286206848099549185>

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[placid zinc]

log(xy) = log(x) + log(y)

Basically just apply wherever possible

Oh wait, the bases are all different

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[edgy sand]

how is this wrong? anyone know?

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[edgy sand]

how is this incorrect?

[jagged imp]

The area of the rectangle isn't equal to the area under g

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[edgy sand]

would it be the bottom right one then?

[jagged imp]

The bottom right one has both the wrong graph for g and the wrong rectangle

[edgy sand]

hm so its the first one then but how would I know

[jagged imp]

First, notice that only the top left and bottom left have the correct graph of g. Then, the bottom one can't be right since the rectangle is strictly under g, so its area its less than the area under g

which means it can't have the same area as the area under g

so it must be top left

Also, a rectangle with the same height as the average over that interval is always going to have the same area as the area under g. the top left rectangle is the only one with that averaage height (30)

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[void sable]

is there any way to take a "modular average"? using a clock as an example the average of 1 o clock and 9 o clock would be 11 o clock, another average could be 5 o clock but that's farther away from 1 and 9 than 11.

what i want to figure out specifically is how to get an "average point" on a circle, i have some points on a circle and i want the point who's angle is the average of all the angles. ive tried just doin regular mean but for like, (1,0) (-1,0) and (0,-1) you get (cos(5pi/6),sin(5pi/6)) which diffidently doesn't look like the average

[severe sluice]

that's a bit ill-defined...

[void sable]

ill draw a diagram on sec

so like the "average" of the 3 black points on the circle would be the red point on the circle

the red point is in the middle of the 3 points

also should have specified that im working with the unit circle

[severe sluice]

how do you define that?

[void sable]

given a set of points P on the unit circle, what is the point A on the unit circle that minimizes the sum of the distances from A to the points in P

[severe sluice]

uh... right.
seems hard
working on it (i'm not sure if i can do this)

i don't know if there's a general formula for this

but i think we can use polar for the circle (so that there's only 1 variable: theta)

then just do the arithmetic mean of all the points

then calculate the total distance

after that, add pi to the angle of the mean

and see if the distance decreases

i mean

we'll check both of those

[void sable]

ah nice!

thank you, sorry if the way i asked it was weird, but i tried this and it totally works

.close

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[worthy field]

Need help with this

Do I find the zscore of 7.4 and 6.5 first

[subtle vortex]

yep, you want P(6.5 <= weight <= 7.4)

find the z score of 7.4, find z score of 6.5

then, you can use the z table to find the probabilities, and subtract them to get the interval

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@worthy field Has your question been resolved?

[lone heart]

@worthy field Has your question been resolved?

[worthy field]

I got

7.3 | .65
7.2 | 0.45

What’s next

[subtle vortex]

what is 7.3 and 7.2

[worthy field]

U

[subtle vortex]

you shouldve found the z score for 7.4 ( the upper bound )

and 6.5 (the lower bound)

[worthy field]

So that’s not correct

[subtle vortex]

so 7.4 - 7.3 / .65 and 6.5 - 7.3 / 0.65

i dont think so

[worthy field]

7.4-7.3/.65 is .153

And the second one is -1.23

[subtle vortex]

mhm, now look up the probabilities for 0.153 and -1.23 in the z table

and subtract the two and thats your answer

[worthy field]

I got .45031

so for a I right 7.4, and .153

B 7.3, -1.23?

And then c .45031?

Oh wait is it 6.5, and -1.23

@subtle vortex ?

<@&286206848099549185> think he fell asleep in the high point lol

But can someone chip in^

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@covert field Has your question been resolved?

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@covert field Has your question been resolved?

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@covert field Has your question been resolved?

[raw shard]

@covert field it shouldn’t take too long, just remember the area formula for a square and circle, and remember what percent of the big square the smaller squares each take up

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[gritty knoll]

before asking the question, i want to apologize. this is a physics question. i asked a physics discord server and it's kinda deserted. i asked for permission to ask physics in this server and a mod allowed it

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[true wharf]

So theres no water in the sphere?

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@gritty knoll Has your question been resolved?

[gritty knoll]

no, just air

[true wharf]

Do we care about the thickness of the shell?

I think your missing some part of your question, since if theres no water in the shell, wouldn't the mass just be air?

Not sure why the mass would need to take into account 'wetness' or 'liquid', unless your considering liquid on the shell?

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[copper spruce]

Hi

[copper spruce]

Hello could someone help me with this. In wich point from the first quadrant , on the parabole y=4-x², will de tangent from the parabole with the x and y axis form a triangle with the lowest area?

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[robust flame]

Hey! Can someone help me w this pls?

[pale spire]

i think cos will be positive

and sin will be negative

[robust flame]

Thanks! Can you also help me w b and c?

[pale spire]

sin cos and tan are used to find the ratios of the lengh of the sides given an angle

and u can do the opposite

u can say sin ∂ = opp/hyp

and so if u get the sin inverse of the fraction u get urself an angle]

draw you triangle out and put the measurements in, it ll make it so much easier!

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[alpine swift]

I need help

[alpine swift]

How do I do questions like this

<@&286206848099549185>

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[alpine swift]

Hey

.reopen

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[mild gate]

What are you struggling with?

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[lethal lichen]

How do I expand $$\sqrt3cos(\theta-30)$$

[ocean seal]

NiLo

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@lethal lichen Has your question been resolved?

[lethal lichen]

<@&286206848099549185>

[mild gate]

Cosine angle addition formula

[lethal lichen]

ok

but what would a and b be?

[mild gate]

Theta and -30

[lethal lichen]

so

$$\sqrt3cos(\theta-30) = \sqrt3cos(\theta) - 30sin(\theta)$$ ?

[ocean seal]

NiLo

[lethal lichen]

@mild gate

[mild gate]

That is not how the formula goes

Try doing it without the sqrt(3)

[lethal lichen]

im not sure

i cant find the formula

@mild gate

[mild gate]

$$\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$$

[ocean seal]

Violeta

[lethal lichen]

ok

so $$\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)$$ ?

[ocean seal]

NiLo

[mild gate]

Yep!

[lethal lichen]

but what about R?

[mild gate]

What R?

There’s no R in here

[lethal lichen]

in Rcos theta - 30

@mild gate

[mild gate]

There is no R in here

I don’t know what you’re talking about

If you’re talking about the circumradius of some triangle, neither your problem nor the formula I’m giving you depend on that

[lethal lichen]

oh ok

[lethal lichen]

so once i have this formula

what do i do

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[dapper patio]

what does the (2 over -1) mean?

[dapper patio]

.close

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[ember sky]

i was thinking to making both equations equal to each other and then rearranging
but that seemed to simple

any help plz?

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@ember sky Has your question been resolved?

[solar merlin]

i'll break it down step by step: they both meet at $(-\sqrt{2}, 1)$ and $(\sqrt{2}, 1)$

[ocean seal]

alias

[raw shard]

that left function is an inverse trig derivative i think

just so you know

[solar merlin]

from here, you can calculate the area under the graph at $\ 3/1+x^2$ from $(\sqrt{2}$ to $(-\sqrt{2}$, and add it with the area of the parabola from $(\sqrt{2}$ to $(-\sqrt{2})$

[ocean seal]

alias

[raw shard]

if you’re confused on something i can maybe help alias

since you seem to be editing that message a lot

[solar merlin]

nah lol i'm just shit at latex haha

[raw shard]

understandable

[solar merlin]

visualisation:

from here, if you just add up the areas with some definite integrals, both from $(\sqrt{2}$ to $(-\sqrt{2})$, you should get your answer

[ocean seal]

alias

[ember sky]

ohh right i see

thanks

then its just a simple integral right?

[solar merlin]

yeah. btw:

the integral of 3/1+x^2 dx = 3 arctan x + C

that should help

[ember sky]

Can i not make both of the equations equal to each other?

[solar merlin]

to get the points at which they intersect? yeah, that's exactly how you should do it

i was just lazy and used a graphing calculator to show it lol

[ember sky]

right right

okie thanks

[solar merlin]

np bro

tell us if you need any more help

[ember sky]

can i close the page but if i get a further question i can dm u ?

[solar merlin]

ofc! feel free to

[ember sky]

can u send me a message i cant dm u

i think u have ur setting off

[solar merlin]

done!

[ember sky]

.close

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[candid minnow]

how do I know how to setup the integral for E(Y1,Y2)

and how do I know the bounds for a problem like this if I wanted to intergrate w.r.t.y

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[alpine sable]

Hi, I need to verify a proof by natural deduction

[alpine sable]

I have ${P\longrightarrow Q,P\longrightarrow R}\vdash P\longrightarrow (Q\wedge R)$

[ocean seal]

Frederic Fitch

[alpine sable]

.close

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[ember sky]

Hi, im having trouble with part c of this question

[ember sky]

I allready got part a and b, but i have no idea how to approach part c

i tried doing the chain rule on the RHS, but didnt get anywhere

Any idea?

[placid zinc]

Compute the left hand side, and compute the right hand side

So what's d²y/dx²?
And what's (1 - dy/dx)³?

[ember sky]

sorry i shouldve added part a and b

gimme a sec

[placid zinc]

No no you're fine

I'm not actually asking what they are, but I'm asking if you've found them yet

[ember sky]

so, since part b gives us 1-dy/dx

i expanded it to ^3 once, that was pointless

and then i did chain rule but ended with 4(d^2y/dx^2)=-3(dy/dx)(d^2y/dx^2)

pls

<@&286206848099549185>

also, cubing the rhs took me like 15 min, there must be a better way

<@&286206848099549185>

someone, pls help, im beating myself over this

<@&286206848099549185>

bro

<@&286206848099549185>

cant i ping a moderator?

<@&286206848099549185> <@&286206848099549185>

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@ember sky Has your question been resolved?

[ember sky]

<@&286206848099549185> please :(

[placid zinc]

@ember sky
Back. So, I asked what d²y/dx² is as well kek

Have you found that?

Again, I'm not looking for your work, just asking if you've gotten both

[ember sky]

yep

it would be the firdt pic

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@ember sky Has your question been resolved?

[raw shard]

@ember sky what part is confusing you?

[ember sky]

part c

ive tried everything

what am i supposed to do

[raw shard]

exactly what it says?

find $\dv[2]{y}{x}$, then do $(1 - \dv{y}{x})^3$

[ocean seal]

quantum

[raw shard]

and see if they are equal

ping me next time you respond, or else i’ll probably forget what channel you’re in

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@ember sky Has your question been resolved?

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