help-0

[vale wigeon]

work backwards

there are essentially 5 problems here all unconnected to one another, which one would you like to have explained in detail?

[upper pebble]

oh so just perform the reverse operations on the result

[dim vector]

idk maybe the second pls

[vale wigeon]

okay

[dim vector]

like for example

[vale wigeon]

@alpine sable if you have a question of your own then please ask it in another channel. this one's occupied at the moment.

anyway

[upper pebble]

i think Ann will explain

[vale wigeon]

what we have here is that a mysterious number went into the "subtract 3" box

then what came out of that went into the "divide by 4" box

and out came the number 6

so let's consider that second box. the "divide by 4" box.

if the number 6 came out of it, what number went in?

i.e. what number divided by 4 gives 6?

@dim vector

[dim vector]

sorry

[dim vector]

24?

[vale wigeon]

are you asking me? or are you just not sure about your own answer?

[dim vector]

its 24

i think that

[vale wigeon]

that is correct. the number that went into the "divide by 4" box is indeed 24.

now, the number 24 came out of the "subtract 3" box.

so what number went into that?

what number, when you subtract 3 from it, gives 24?

[dim vector]

hmm 24-3?, 21?

[vale wigeon]

no

read carefully what i'm asking you

[dim vector]

27

[vale wigeon]

that's better.

when you said 21 earlier, you treated 24 as going into the -3 box rather than out of it as it actually does.

do you understand the ideas behind what we've done here?

[dim vector]

sorry

[vale wigeon]

...i wasn't expecting an apology here.

you're here to get help and you are getting help, part of which is pointing out the mistakes you make

[dim vector]

I understood bc of your explanation

[dim vector]

ty :)

I'm clumsy sometimes in math

[vale wigeon]

do you want me to take you through any of the other four problems or do you want to attempt them on your own?

[dim vector]

I would like to try it with the explanation you gave me, I hope it works out

[vale wigeon]

ok

[dim vector]

tysm

[alpine sable]

how did they get 60V for v2?

the 20kohm and 5kohm simplify to 1 4kohm

oh wait

fuck

nvm

[dim vector]

idk if i can write here, I am having a hard time doing the last exercise

7x5=35

and...

[vale wigeon]

yes

so what goes into the ×7 box is the number 5

so if the number 5 came out of the +7 box, what went into it?

what number, when added to 7, gives 5?

[dim vector]

ohhhhhh, -2

[alpine sable]

What does this mean

tan-1gamma

wait no that makes no sense

maybe its just 4

There should be an angle after tan right?

Nog a number

Not*

its arctan

so it takes a number and returns the angle

in this case i think its just 4 (for some reason)

And that can also be written like this?

[dim vector]

I could do it! thanks to you, tysm

[echo python]

was looking for ```cpp
xCoord += flySpeed * sin(PI * 2 * lrRot / 360);
yCoord += flySpeed * cos(PI * 2 * (180 + lrRot) / 360);

[alpine sable]

nope

thats not how it works

its not to the power of -1

its arctan

Okk

I'll google the arctan

[muted pelican]

i've drawn the points on a graph, how can i find the point to minimize it?

[vale wigeon]

write out the thing to be minimized

i.e. the sum of the squared distances from (a,b) to (-7,4), (6,-9), (7,0) and (-2,5)

expand and simplify

if you do everything correctly, you will find that you'll have the sum of two quadratic polynomials, one in a, one in b

[muted pelican]

ah alright

let me try

[gusty gate]

can someone help me with newtons third law of motion?
If lets say ball hits another ball how can I calculate the force and the direction of the ball that gets hit?

[vale wigeon]

that sounds like a collision problem to me

[gusty gate]

I am not sure how its called but if you say so

[muted pelican]

sorry to bother but is this the right way?

(7+a)^2 + (6-a)^2 + (7-a)^2 + (-2-a)^2 + (the b part)

[gusty gate]

it is momentum and collision, found the formula thanks man

[vale wigeon]

seems ok to me at a glance

[muted pelican]

alright i got 3a^2 + 6a + 4b^2 + 211

[surreal pumice]

I'm looking at the source code for Valve's Source engine and there's a function that "normalizes" a vector but I don't understand how it manages to do it

It outputs a decimal by taking the vector's square magnitude/length and multiplies it by its inverse square root

Does anyone know anything about that?

[muted pelican]

alright i got this already thanks

[ivory otter]

Bit confused om this one, om supposed to prove the trigonometrical identities

What did i do wrong?

[vale wigeon]

that second line is mega sus

[ivory otter]

Why

I just squared

[vale wigeon]

well how did you get from $\frac{1 - \cos(2x)}{\tan(x)}$ to $\frac{1^2 - \cos^2(2x)}{\tan^2(x)}$?

[ocean seal]

Ann

[ivory otter]

I just squared top and bottom

[vale wigeon]

okay there are two things wrong with that

(a) you didn't even do what you claimed correctly: $(1 - \cos(2x))^2$ is not the same as $1^2 - \cos^2(2x)$

[ocean seal]

Ann

[vale wigeon]

(b) and more importantly, squaring the num and denom of a fraction changes its value!

surely you wouldn't insist that 2/3 = 4/9?

[ivory otter]

No idea

Ah

Yes

Well hmm

But when can i do that

[vale wigeon]

do what?

[ivory otter]

Wait, do you think my idea atleast is on the correct path?

[vale wigeon]

no

as i said, your very first step is nonsensical

everything that follows is trash

[ivory otter]

Ok

Ye lol

[lethal vortex]

anyone can give me a hint on how to solve this?

[vale wigeon]

consider the inclusion-exclusion principle for two sets

and that the union of A and B is implied to be contained in the universe (xi)

[lethal vortex]

i do not understand

[vale wigeon]

do you know what i'm talking about when i say "the inclusion-exclusion principle for two sets"?

[lethal vortex]

im googling it

[vale wigeon]

$n(A) + n(B) = n(A \cup B) + n(A \cap B)$

[ocean seal]

Ann

[vale wigeon]

here it is stated in a 'symmetric' form which you might find useful

[lethal vortex]

oh never seen this before

[vale wigeon]

bruh

[lethal vortex]

[lethal vortex]

i got it now

14 and 50 :)

anyone mind telling me what topic or principle this lies in

[glass lichen]

perms and combs / combinatorics

[vagrant rover]

    A.    
power
    B.    
exponential
    C.    
neither because she needs a correlation coefficient of 1
    D.    
it doesn't matter, both correlation coefficients are close enough to 1```
Is this A?
Since the correlation coefficient is closer to 1?

[vale wigeon]

@alpine sable channel busy please move

[strong smelt]

B

[vale wigeon]

1. this question has been moved
2. even if it wasn't, don't give out answers.
3. especially don't give out wrong answers

[strong smelt]

chill

[lost cairn]

Berta’s teacher, Ms. Rose Harper tells her class that when sixty consecutive odd integers are added together, their sum is 4800 and asks the class to determine the largest of the sixty integers. Help Berta get the answer!

[glass lichen]

what have you tried?

[lost cairn]

x+x+2+x+4+x+6...

[vale wigeon]

...all the way to x+118 :P

while this isn't exactly invalid per se, you must keep in mind that if you write the sum out this way, x denotes the smallest and not the largest of your integers

[lost cairn]

x denoted the start of the 60 consecutive integers +2 +4 +6 is the continuation idk what to do next

[vale wigeon]

for lack of confusion let's stick with your choice of x.

it's nothing fatal, just a tiny bit more work at the end

anyway

you have sixty numbers being added, so once you collect all the x terms together you'll have 60x.

of course, you'll also have a constant added to the 60x, but we'll get to that in a moment.

do you understand what i've said so far?

[lost cairn]

Yes

[vale wigeon]

so now the constant

it's equal to 2 + 4 + 6 + 8 + ... + 118

or 2(1 + 2 + 3 + 4 + ... + 59)

[lost cairn]

yes

[vale wigeon]

do you know how to find the sum of the first n natural numbers?

[lost cairn]

n(n+1)/2?

[vale wigeon]

great, so you are familiar with that formula

why not apply it here, to find the sum of the natural numbers from 1 to 59?

[lethal vortex]

i started drawing dots and line thanks tho :)

[lost cairn]

k one sec

i got the answer 1770

[vale wigeon]

,calc 59 * 60

[ocean seal]

Result:

3540

[vale wigeon]

okay, you did just the sum

[lost cairn]

yes

[vale wigeon]

you're gonna have to multiply it by 2 anyway

[lost cairn]

i did 59*60/2

[vale wigeon]

so what you have here, after this arithmetic we've gone through, is 60x + 3540 = 4800

[lost cairn]

yes

[vale wigeon]

are you able to continue from here?

[lost cairn]

yes

thanks a lot! cant express my gratitude

[lost cairn]

@vale wigeon can I ask how you got 118 here

[vale wigeon]

59*2

[lost cairn]

sorry for ping

[lost cairn]

oh ok

[dull onyx]

how would i do this.. on the numerator

would i multiply with 2x - sqrt

[vale wigeon]

is that $x \to -1$?

[ocean seal]

Ann

[dull onyx]

yep

[vale wigeon]

so i take it you've verified that direct substitution gives you 0/0

[dull onyx]

well yes, but my tutor said theyre all gonna be 0/0 so i can practice

[vale wigeon]

trust but verify

anyway, yes, a reasonable way to go from here would be to multiply the numerator and denominator by (2x - sqrt(x+5))

[dull onyx]

ur right!

okay but then what do i do with x^2-x-2

quadratic?

[vale wigeon]

i would factor it

and given that you already know it gives 0 when x=-1 is substituted into it, you get one factor for free

from which the factorization of x^2 - x - 2 as (x+1)(x-2) is not hard to recover

[dull onyx]

yea i wanted to do it like that but my tutor said i should do the quadratic formula more but it takes me a while

and also i don’t understand how u can write -x as a difference 😵‍💫

[vale wigeon]

your tutor held you at gunpoint to use the quadratic formula?

[dull onyx]

yes😭

ok no

[vale wigeon]

did your tutor forbid you from using shortcuts in reasoning of the kind that i just presented?

[dull onyx]

but i asked him abt doing it like this and he said i should use the quadratic formula more

[vale wigeon]

if your goal's to practice the quadratic formula, there are better ways of doing that imo

[dull onyx]

hmm no but i don’t understand how u went to that

its rly not bc ive done it a thousand of times

[vale wigeon]

given that you already know it [i.e. x^2 - x - 2] gives 0 when x=-1 is substituted into it, you get one factor for free

the factor is, of course, (x+1)

[dull onyx]

😵‍💫

[vale wigeon]

we already know that -1 is a root of x^2 - x - 2

[dull onyx]

mhm

[vale wigeon]

so

yknow

the whole

back and forth between roots and factors

[dull onyx]

uhm

[vale wigeon]

it comes up a lot in algebra

[dull onyx]

sorry im kinda confused bc ive been taught all of this in greek and now im having a hard time

[vale wigeon]

:x

you know how, say, if you know that a quadratic polynomial has roots 11 and 7, then you can definitely write it as (some constant) * (x-11)(x-7)?

[dull onyx]

yup

[vale wigeon]

so you must know what i'm talking about

how the presence of (x-11) in the factorization gives you 11 as a root

[dull onyx]

OH yes

@vale wigeon thank u now i remembered what i would do to factor quadratics!! i literally forget things if i dont do them on a regular basis</3

[dull onyx]

@vale wigeon uhm another question

now i have 4x^2-x-5 in the numerator

[vale wigeon]

can i see the entire problem

[dull onyx]

,rotate

[dull onyx]

sorry abt the handwriting

[vale wigeon]

oh this is still that problem

well, you know that the numerator still produces 0 if you plug in x=-1

so (x+1) is a factor that you get for free

[upper pebble]

what a good deal

[vale sapphire]

and once that factor is canceled, I believe the limit can be directly evaluated

[exotic mortar]

How do you do this?

Topic:Sector area and arc length

[vale sapphire]

First of all, is it clear to you that you can easily get the length of the two semicircles that the string traces?

[vale wigeon]

semicircles?

are you sure they're semicircles?

the string will consist of two circluar arcs and two straight-line segments which are each tangent to both circles.

[vale sapphire]

Hmm, right

[vale wigeon]

it might be good to mark those points of contact on your diagram, and draw some radii, and maybe connect the centers of your two circles

[exotic mortar]

I dont think they are semi circles

[vale wigeon]

they are not semicircles.

[vale sapphire]

mb

[exotic mortar]

Makes sense if they are tangents it forms 90 deg

[vale wigeon]

anyway, as i said, you'll need a diagram

[robust phoenix]

can someone how to solve

[upper pebble]

start by getting rid of the radical

[pearl marlin]

Square both sides

[robust phoenix]

i did that

so its 6x-9=x^^2

[upper pebble]

the goal is to get it into quadratic form and then factor

[robust phoenix]

so it'll be

[pearl marlin]

Now just solve this

[robust phoenix]

x^^2-6x-9=0 ?

[robust phoenix]

yeah how

[upper pebble]

+9

[robust phoenix]

oh yeah +9

[upper pebble]

now you can factor the quadratic

[pearl marlin]

You can use , midle term split, quadretic formula

[robust phoenix]

how should i use them ?

isnt the quadratic formula ax^^2+bx+c=0 ?

oh nvm it isnt

sorry

[dull onyx]

yea but what abt da other one

[upper pebble]

i need to learn how to write on texit tbh

another way would be to split the middle term like learn4math mentioned

[dull onyx]

OH

(4x-5)?

[vale wigeon]

yes

[dull onyx]

wait sorry i forgot this is used

[upper pebble]

ask yourself what two numbers add up to the coefficient of the middle term and also multiply to the constant

[robust phoenix]

is it better to use it ?

[upper pebble]

i would rather use it in this case since it'd be much quicker

[robust phoenix]

I don't get it

[upper pebble]

$x^{2} - 6x + 9 = 0$

oops

[ocean seal]

cole

[upper pebble]

the coefficient of the middle term is -6

[robust phoenix]

and the 9 is the constant

[upper pebble]

correct

what two numbers add up to -6 and multiply to 9?

[robust phoenix]

-3 + -3

[upper pebble]

correct

[shrewd otter]

Right, this is just a perfect square.

(x - 3)^2.

[robust phoenix]

huh

[dull onyx]

@vale wigeon omg i solved it idk if its correct i got -3/4

[robust phoenix]

oh yeah it is

[dull onyx]

tysm tho!

[upper pebble]

you could indeed recognize that

[robust phoenix]

so what should i do with the -3 and -3

does that mean it has only 1 real root ?

[shrewd otter]

Yes, with multiplicity 2.

[robust phoenix]

wdym with that

[shrewd otter]

https://en.wikipedia.org/wiki/Multiplicity_(mathematics)

Because (x-3)^2 is (x - 3)(x - 3), the root has a multiplicity of 2.

[robust phoenix]

oh you mean it's written two times

[upper pebble]

[robust phoenix]

if it's (x-3)(x-4) it doesnt have a multiplicity of 2 ?

[shrewd otter]

No, it has two roots (3 and 4) of multiplicity 1.

[robust phoenix]

you mean the times it appears in the multiset ?

[shrewd otter]

Similarly x^3 has 1 root of multiplicity 3.

Yes.

[robust phoenix]

it means x appeared 3 times while multiplying ?

oh ok

I'm sorry i'm not that great at maths

[shrewd otter]

Well, not exactly, because sometimes you can't factor it into linear terms.

[vale sapphire]

(x-3)(x-4) : both 3 and 4 have multiplicity 1
(x-3)²(x-4) : 3 has multiplicity 2, 4 has multiplicity 1

[robust phoenix]

yeah i get it know

[robust phoenix]

is this advanced level maths ?

[shrewd otter]

Factoring? No.

Multiplicity? Yes.

[robust phoenix]

No i know factoring

uhuh

[pallid sail]

don't u call that a double zero

[shrewd otter]

I wouldn't know. It might be a colloquial term.

"Root of multiplicity 2" essentially just means double zero.

[vale sapphire]

In full generality, whenever you can uniquely factor an expression into a product of simpler terms, the multiplicity of a given factor is just its power in that unique decomposition

There's a slight technicality when only dealing with real numbers, because you can't write x²+1=(x-a)(x-b) without resorting to complex numbers

So a given polynomial isn't necessarily equal to α(x-a)(x-b)...(x-z) if you stay in the reals

[vagrant rover]

    A.    
power
    B.    
exponential
    C.    
neither because she needs a correlation coefficient of 1
    D.    
it doesn't matter, both correlation coefficients are close enough to 1```
Is this A?
Since the correlation coefficient is closer to 1?

[shrewd otter]

This chat is clearly already in use...

[alpine sable]

Sorry

[noble sinew]

No all you really need is correlation coefficient to be “high enough”

Where high enough depends on context

And certaninly both have very high, so which one to use shouldn’t depend on the very small difference in correlation coefficient

[vagrant rover]

Oh, so D?

[noble sinew]

Si

[vagrant rover]

Ah okay, and that's cause they're both high and close, right?

[noble sinew]

Well bigger doesn’t always mean better (can even be worse)

[vagrant rover]

Oh? How so?

[noble sinew]

For example overfitting

If I have 10 points I could make a function that pass through all 10

By simply using a degree 10 polynomial

This is probably not a good idea tho

[vagrant rover]

Oh, okay.

Thanks!

@noble sinew

A. True
B. False``` Is this False cause stem-and-leaf diagrams don't use classes or groups while histograms and frequency tables do?

[vale wigeon]

you could argue that stem-and-leaf diagrams group data too

like, the stems

[vagrant rover]

Would it be a good arguement orrr

Is it a good enough arguement to make it true?

[vale wigeon]

feels like a trick question you're asking me

[shrewd otter]

Feels like an overly vague question.

[vagrant rover]

Feels like I don't know the answer to the question.

[alpine sable]

yo

finally i can take

can anyone help me

[shrewd otter]

https://www.dontasktoask.com

[alpine sable]

simp, look above

[upper pebble]

[upper pebble]

Pythagorean theorem

[alpine sable]

yeaa

you know how to help me

[upper pebble]

do you know what the Pythagorean theorem is

[alpine sable]

yea

the hyp

and opp

[pallid sail]

cant he use the cosine law here

[alpine sable]

adj

sin rule and cos and tan rule

[upper pebble]

how would they use the cosine law

[alpine sable]

ik all

[upper pebble]

genuinely asking because idk

[alpine sable]

a squared plus b squared plus c squared minus 2bc

that cosine a rule

[shrewd otter]

The opposite side (let's call it c) is given by:

c^2 = a^2 + b^2 - 2abcos(x)

The Pythagorean theorem is a special case of this rule for x = pi / 2.

[alpine sable]

yea

but i dont how to get the angle

on the north

[shrewd otter]

It's... given.

[upper pebble]

i see

[alpine sable]

i mean side

my bad

[shrewd otter]

You plug stuff into the formula and find c.

Which is the side.

[upper pebble]

you can use the Pythagorean theorem though, right?

[alpine sable]

i can

[shrewd otter]

No, because the angle isn't pi / 2.

[upper pebble]

oh yeah it's not a right triangle

silly me

[shrewd otter]

Like I said, the Pythagorean theorem is a special case of the cosine law, and this special case doesn't apply here.

[vagrant rover]

So is this true or false?

I checked and they all group data into classes

[alpine sable]

can someone tutor

me

on how to do my assignment

lol

yall smart mashallah

[pallid sail]

why dont u just find a tutor wherever you live

[alpine sable]

nah

covid

[upper pebble]

well this server seems to be pretty helpful if you don't have a tutor tbh

[pallid sail]

yes this server is amazing

[alpine sable]

yep

[pallid sail]

it helped me a lot

[alpine sable]

yall math so advanced

it gonna be tough

look like greek language tbh

[vagrant rover]

Below are an AP Physics class test scores.  

     88, 92, 66, 74, 90, 80, 83, 85, 76, 74, 52, 65, 68, 70

Find the mean and standard deviation to the nearest tenth.  What percent of the scores differ by more than 1 standard deviation?```
Is this data set a sample or population?

[shrewd otter]

I believe it depends on the deviation.

[vagrant rover]

Well I need to know if it is a sample or population in order to get the standard deviation

If it is the entire classes' test scores then it should be population. right?

[shrewd otter]

The difference between a sample and a population is that a population is representative, while the sample is not.

Right?

[vagrant rover]

I thought the population was the whole and a sample was just a small, well... sample.

[vale wigeon]

how many people are enrolled in the class?

is it sensible to consider this data set of 14 points as comprising the entire class?

[vagrant rover]

It doesn't say

Yeah if it is the entire class then it should be population, and if not then sample, right?

[vale wigeon]

yes

[vagrant rover]

Ok, thank you

The quesiton is confusing though, right?

Since it doesn't specify if it is the entire class or not

How do I find this?

[shrewd otter]

Well, you have 7 distinct letters.

If you had 8 distinct letters, then it would just be 8!

But since you can swap the E's and get the same arrangement, half of the arrangements are duplicates.

So you divide by two.

[vagrant rover]

8!/2! ?

[shrewd otter]

Yes.

And in general if you had k duplicates, it would be 8! / k!.

[vale wigeon]

'k duplicates' is a little ambiguous

it could mean 'k letters all indistinguishable from one another' or 'k pairs of doubled letters'

the more general rule is: for every distinct letter that appears, divide by the factorial of the number of its appearances.

for those that appear only once, the division by 1! = 1 may be omitted.

[arctic wren]

What i'm doing wrong? If i use the chain rule i get the right answer but if i use the chain rule + the power rule+ chain rule i get the wrong answer, if i use one or another i must have the same answer, but i'm getting different answers

[vale wigeon]

$e^{\sqrt{x}}$ is not $(e^x)^{1/2}$

[ocean seal]

Ann

[alpine sable]

السلام عليكم ورحمة الله وبركاته
Peace and blessings be upon you

How can this question be solved:
e^2x - 3e^x - 4 = 0

[gray isle]

assuming that's supposed to be e^(2x),
you have a quadratic in e^x

[woeful forge]

I feel like a moron. Subtract cost from price means price - cost or the other way around?

[gray isle]

if you're uncomfortable working with that
consider doing a substitution and let u=e^x

[alpine sable]

I see now
Thankyou

[upper pebble]

subtracting cost from price is price - cost

are price and cost not the same thing though?

[alpine sable]

Just use an analogy for example and think how you would subtract 5 from 10

[alpine sable]

I think he means original cost

[upper pebble]

oh i see

now i feel like a moron

[alpine sable]

You shouldnt brother

[robust phoenix]

I don't get it can someone explain ?

and @upper pebble how did you learn math like that

[upper pebble]

math like what

[robust phoenix]

no i mean you are great at math

how old are you ?

[upper pebble]

i wouldn't say i'm great at math but i've taken interest in it

$W = \frac{1}{2}CV^{2}$

[ocean seal]

cole

[upper pebble]

so the problem is asking you to isolate C on one side

[robust phoenix]

yeah that's it i think

[upper pebble]

first, how do you move V^2 to the other side?

[robust phoenix]

-v2 ?

no never mind

idk lol

[upper pebble]

it's being multiplied by 1/2C. what's the opposite of multiplication?

[robust phoenix]

?2c/1

[upper pebble]

uh

[robust phoenix]

V^2=2/1C ?

2c

[upper pebble]

no

[robust phoenix]

ok

[upper pebble]

what's the opposite of multiplication

[robust phoenix]

division

[upper pebble]

yes

[robust phoenix]

I still don't get it fully

[upper pebble]

so you can divide both sides by V^2

[robust phoenix]

so

[upper pebble]

to get rid of V^2 on the right hand side

[robust phoenix]

i see

1/2C

V^2/W=1/2C ?

[upper pebble]

wrong positions on the left side

[robust phoenix]

my bad

[upper pebble]

W divided by V^2 = ?

[robust phoenix]

nope V^2 divided by w

[upper pebble]

you're dividing both sides by V^2, so it would be W/V^2

[robust phoenix]

yep

[upper pebble]

$\frac{W}{V^2} = \frac{1}{2}C$

[ocean seal]

cole

[upper pebble]

how do you get rid of the 1/2 on the right side?

[robust phoenix]

multiply W and V^2 by 2 ?

[upper pebble]

yes

multiply W/V^2 by 2/1

[robust phoenix]

2 * (V^2/W)=C

?

[upper pebble]

yes

[robust phoenix]

lets gooo

[upper pebble]

wait

[robust phoenix]

mhm

[upper pebble]

wrong positions again

it's W/V^2

[robust phoenix]

sorry in arabic we do that

my bad

[upper pebble]

oh

no problem

[robust phoenix]

if it's W/V does it mean W is on top and V is on the bottom ?

[upper pebble]

so we have $\frac{2W}{V^2} = C$

[ocean seal]

cole

[upper pebble]

yes

[robust phoenix]

mhm i see

Thanks sooo much i'm glad that you helped me

[upper pebble]

you're welcome

[robust phoenix]

do you have any recommendation that i can do to practice my math skills ?

i'm grade 10 going to grade 11

[upper pebble]

i recommend a website/app called Khan Academy. it's completely free. i think it's even available in Arabic if you prefer that

[alpine sable]

i need help

anyone spanish?

[upper pebble]

unfortunately i am not

[acoustic bay]

Does anyone know how to make a scatterplot of correlations in r?

[robust phoenix]

yeah i have an account there but idk which course to pick

[upper pebble]

maybe just look through them from the beginning, find something you're unfamiliar with, and go from there

or maybe find topics related to whatever math you learn in 11th grade

[arctic wren]

Why this is wrong ?

[robust phoenix]

Sure thanks ;3

[upper pebble]

no problem

[vagrant rover]

@vale wigeonRight, so 8!/2! would work here, right?

Why doesn't 8 permute 2 work?

[vale wigeon]

8P2 = 8!/6!

[vagrant rover]

Ah okay

ty!

    A.    
40,320
    B.    
6,720
    C.    
3,360
    D.    
64

THis is just 8!, right? So 40,320

[harsh girder]

no, should be (8!)/((3!)*(2!))

[lapis stump]

Help pls

[vagrant rover]

Wait, why?

[harsh girder]

Permutation of 3 clarinetists should be removed (I dont know how to express this)

[vagrant rover]

Ohhhh

Is that what they want though?

[still steeple]

add all sides of the sides of the triangle and make it equal the perimeter

then solve for x

[vagrant rover]

This question seems a bit ambigious, right?

[lapis stump]

Wdym

[still steeple]

so

[upper pebble]

perimeter = 82
perimeter is the sum of the lengths of the sides of the triangle
(2x + 3) + 2(3x + 4) + 3(2x - 9) = 82
solve for x and then substitute the value of x into each equation to determine the length of each side

[still steeple]

(2x+3)+2(3x+4)+3(2x-9)=82

then solve for x

yea what he said

[lapis stump]

How do I find x doe

[alpine sable]

blocked for posting one question on more than one channel

[upper pebble]

(2x + 3) + 2(3x + 4) + 3(2x - 9) = 82

[lapis stump]

82=x?

[upper pebble]

do you know how to solve that equation for x?

[lapis stump]

No that’s why I’m asking

[jagged trout]

https://www.youtube.com/watch?v=Z-ZkmpQBIFo

[still steeple]

I really dont know how to help u with that if u dont know how to solve for x

[lapis stump]

If I find x I find the whole solutions

I just don’t understand how to find x

[still steeple]

you can watch the video above

[vale sapphire]

Yeah, honestly take your time with that, knowing how to manipulate equations like that comes up everywhere

[still steeple]

I cant really teach how to solve for x in a discord text channel

do you have no idea how to solve for x? or do you know how to solve for x but just not that equation

[lapis stump]

I don’t have no idea to solve for x

When I get x I know what to do after

[still steeple]

then I don't think I can help you.

If this is from school then you should know how to solve for x. The teacher wouldnt give a question that absolutely requires how to solve for x without teaching it

[upper pebble]

welp

[still steeple]

if its not urgent you can alsways teach yourself from youtube videos

[upper pebble]

@lapis stump do you know what the distributive property and "like terms" are?

[lapis stump]

Yea

[upper pebble]

eh i wrote an explanation but you should probably properly learn how to do that

[desert kernel]

This is getting confusing

[urban canyon]

i have like

no clue

how to aproach this

[still steeple]

I havent done a question like this in a while

but im pretty sure

when the sides are all the same from b to c

anbd the triangles contain eachother

there is a pattern

like

I dont remember what it is exactly tho

[urban canyon]

ohh

ok tyy

[shell heron]

Hello guys. Does anybody have a good explanation as to why unit vectors are so special?

Like why is having a magnitude of 1 so special

[vale sapphire]

First of all 1 is nice

Second of all, whenever you multiply things by 1 the calculations look a whole lot simpler

[jagged trout]

@shell heron 1 := neutral element of multiplication

[shell heron]

What does ":=" mean?

[vale sapphire]

"defined as"

[shell heron]

oh

Cool

[vale sapphire]

And a lot of times, what happens with unit vectors is readily generalized for vectors of any other length, you just have to do multiplication. So then it's just a matter of arbitrarily choosing a single length to work on ; 1 makes things the cleanest

[ancient creek]

Yea, especially when dealing with linear transformations

[unique frigate]

I suppose it is 12 because the triangle is divided into 4 lines + the base (5 in total), so if AC (the base) is 20, the upper one is 16, then 12, then 8, then 4. This is because 20/5 = 4 soou reduce by 4 but Im not sure

[shell heron]

Thank you

[vale sapphire]

correct

[urban canyon]

tysm

[vale kayak]

Suppose p, q, and r are real number such that:
q = p(4-p), r = q(4-q), p = r(4-r). The maximum possible value of p+q+r is..?

So I tried finding the maximum value by seeing them as functions, in that case they are quadratics. As they all have a '-a' value, they have a maximum. The maximum of p(4-p) would be 4.
Why is it that the answer is not 12?

What am I missing?

[vale wigeon]

they can't all be equal to 4 at once

if p = 4 then q = 0 for example

[wicked ether]

basic algebra question here

[unique frigate]

I´m trying to solve it

[unique frigate]

Its long but not hard

[wicked ether]

how does factoring trinomials work?

I am a little confused

so

the question was

[shell heron]

the channel is already in use

can u go to another one

[unique frigate]

I think I got it

[unique frigate]

If is just real numbers, the max of p+q+r I found was 8.512177879

[still steeple]

for part b

[unique frigate]

I can´t assure you that it is correct

[still steeple]

oops sorry i didnt know there was a question already here

[unique frigate]

dont worry

[vale kayak]

hmm, it was a multiple choice question and all the answer choices were integers, 9 was one of them

[vale kayak]

oh very true

[alpine sable]

the answer is a right?

[vale wigeon]

no

[vale kayak]

2.4 / 6 would give 0.4

check the question again

[vale wigeon]

you're dividing by 1/6. this is not the same as dividing by 6.

[pearl marlin]

6 will get multiplies

[vale kayak]

yes
2.4 / 6 ≠ 2.4 / (1/6)

[alpine sable]

oh

so 14.4

[vale kayak]

right

[alpine sable]

thanks

[pallid sail]

y - 1 = 14 - 4y

[placid stone]

how did they get that answer in the video?

[vague coral]

what answer

?

the value of theta ?

[pearl marlin]

Not an easy task

[pallid sail]

to find the value of theta they had to find the arcus tangens of 8/6

[placid stone]

yea

[pallid sail]

thats the 2nd function of tan on the calculator

[placid stone]

idk I'm learning with videos on youtube rn

[vague coral]

$\tan^{-1}$

[ocean seal]

Herels

[placid stone]

ok

uhh

where do I find that on a calculator lol

[alpine sable]

A certain computer hard disk drive is rated to withstand an acceleration of 100g without damage. Assuming the drive de- celerates through a distance of 2 mm when it hits the ground, from how high can you drop the drive without ruining it?

I need help with this problem. The answers say that it is 0.2 meters, but I keep getting 0.202 meters

[pallid sail]

u press the 2nd function button and then the tangens button

[alpine sable]

Specifically, I am assuming that it can also drop the 2 mm along.

[vague coral]

just look at your calculator, you will find it

[pearl marlin]

You can use inbulit worlfram, but i have no idea how to use

[stoic pond]

hi can someone help me to solve this statistic problem pls 😦 thank you

wrong picutre... this is the one actually

[placid stone]

ok I found it tysm

[placid stone]

thank you!

[placid stone]

thankyou

[barren shoal]

A swimming race is to be 3 lengths of the pool but each length must be with a different stroke. If you can swim five different strokes, how many possible ways can you swim the 3 lengths?

this is a permutation question. my answer is: 5 x 4 x 3 = 60 possible ways

does this look correct? thanks for anyone responding

[vale ridge]

Find the centre of the circle that passes
through the points A(7, 4), B(4, 5),
and C(0, 3).

im not sure with this one

[solar pebble]

that is correct

[solar pebble]

find a locus for the first two then a locus for another two

[barren shoal]

@solar pebble thank you!

[stoic pond]

is there anyone who could answer this :((( thank you alot

[vagrant rover]

What formula do I need to use to find this?

[noble sinew]

number of favourable outcomes divided by number of total outcomes

[glacial tiger]

Anyone know this?

[noble sinew]

all the options are wrong tho so that is interesting

[ionic jewel]

try to think of a counterexample for each

[glacial tiger]

O

[ionic jewel]

3 of them won't have counterexamples, which makes them true

one of them will, so it's your answer

[glacial tiger]

K so

A is wrong

I mean

Right

[ionic jewel]

A is a true statement, yes

[glacial tiger]

B I think is right

Wait no

Confused 😔

[ionic jewel]

the "proof" of this one uses the fact a triangle can't have 0 length sides

do you see how that's useful?

[glacial tiger]

O

I see

So for b I have to think that the altitude is greater than 10

[ionic jewel]

is it possible for the altitude to be 10 (or more)?

[glacial tiger]

Uh

I think so

[copper wedge]

if i had 5/9 divided by -10/3, is it 5/9 x 10/3, or 5/9 x -10/3

like do u keep or drop the negative in a reciprocal

[ionic jewel]

what length of the base would do this?

[ionic jewel]

the second one, you never just drop negatives

[copper wedge]

alright thats what i thought

[glacial tiger]

Greater than 10

[pallid sail]

also its 5/9 x -3/10

[ionic jewel]

mind drawing the triangle and labeling the altitude, i think you are confused what it is

[glacial tiger]

Ok

?

[copper wedge]

if i have 32/27 / -6, where do i go after that

its all a big fraction

[vagrant rover]

Are you sure?

[glacial tiger]

Bunny?

[ionic jewel]

my internet is too slow to load images, someone that can check if that's right?

[noble sinew]

yes I am sure

[copper wedge]

ok but i only have 3 numbers

[pallid sail]

u can write a number as x/1

where x is the number

[copper wedge]

oh yea

[noble sinew]

looks fine

[vagrant rover]

How many meals can be created if you have 3 appetizers, 5 entrees, and 2 desserts to choose from?
    A.    
60
    B.    
84
    C.    
30
    D.    
720
``` Is this question ambigious?

@noble sinew

[noble sinew]

why would it be?

[vagrant rover]

Like can you have 3 appetizers

[noble sinew]

and anyway why you just speeding through questions

when I just told you none of the answers were correct

[vagrant rover]

Cause it's not the first time..

My school is shit and the practice sheets they give us are all trash

So I just send an email

And then don't get a response

For like 1 month

[noble sinew]

you can only have 1 appetizer, 1 entree and 1 dessert

[vagrant rover]

Oh right, that's one meal

I overcomplicated it

ty

[noble sinew]

anyway the answer to the one before is actually 1/15

[vagrant rover]

What's the math behind it so that I can include it in the email?

[ionic jewel]

sorry my internet awful

[glacial tiger]

Rip

Is it better?

[ionic jewel]

the altatide being 10 means the base would have to be 0

[copper wedge]

|3-2| is |1| which is 1 right

[ionic jewel]

no not at all my messages take like 30 seconds to send lol

[glacial tiger]

Oh

[noble sinew]

10^6 simulation and closed formula here:

[glacial tiger]

So b is right?

[ionic jewel]

but if you get this you should understand why

[glacial tiger]

No I’m confused

😔

[vagrant rover]

python best language

[noble sinew]

not for stats no

[vagrant rover]

Just in general

[noble sinew]

negative

[vagrant rover]

[glacial tiger]

Bunny mind telling me the answer and then solve backwards so I can figure it out?

Or no

U not allowed to do that

[ionic jewel]

b is always true, which means it's the wrong answer

yeah im sorry ur gonna have to get someone else, i can't help with this lag

[glacial tiger]

O Oke

[glacial tiger]

Lmao can u help me?

[vagrant rover]

shitnet?

I know the feeling

[glacial tiger]

Need some help here 😔

[noble sinew]

sup?

[glacial tiger]

Hey

Need some help lol

[vagrant rover]

    A.    
200
    B.    
184,756
    C.    
2,000
    D.    
96,712
``` This is `20 choose 10 = 184,756`, right?

[noble sinew]

si

[obtuse flint]

Can someone help with this

The median and lower quartile please

[dense spoke]

I think the median is 140\

[obtuse flint]

That’s the postion

[dense spoke]

and doesnt lower quartile mean the bottom 25% of the spread

[obtuse flint]

Yh

140 isn’t the score

Hats just where the score is located

Thats*

[alpine sable]

next time pls ask on one question channel @obtuse flint

[obtuse flint]

👍👍

[warped sapphire]

Hi! Can I ask a question?

Can anyone help me with a math problem? Is about mathematical analysis, specifically about Taylor serie

[quartz beacon]

guys, i have [x(x-5)]²-2[x(x-5)] so what else can i do on that

[shell heron]

simplify the brackets

[warped sapphire]

The problem is:
a) find the development in Taylor serie of f(x)=5 χ² e^-3x
in power of x

So I did the derivative first, f’(x) and f’’(x)

[quartz beacon]

how

one is at power of 2

also, nice pfp and nick bro

[shell heron]

so [x(x-5)]^2 = [x^2 - 5x]^2 = x^4 - 5x^2 right?

thats the first term

the second: 2[x(x-5)] = 2[x^2 - 5x] = 2x^2 - 10x

[quartz beacon]

(x-5)^2 should be x^2 - 10x + 25

[shell heron]

oh yeah

nvm then

[quartz beacon]

oh btw

wanna know wwhy i asked

[shell heron]

why

[quartz beacon]

because theres a second degree equation

look

x(x-5)^2 - 2(x(x-5)-25) - 24

i could say that x-5 is y

wait

x(x-5) = y

so y^2 - 2x -24

the roots of that are 12 and -2 i guess

[vagrant rover]

Elon Musk is the best human being alive. I pray to Elon Musk 5 times a day. @shell heron

[quartz beacon]

LOL

i like him too

[vagrant rover]

xd

Yeah, he's amazing. He does everything.

[shell heron]

ur gonna make me blush stop

[quartz beacon]

HAHA

[quartz beacon]

but contiuing, in order to that, it should be equal to 0

idk how to do that tho

thats where im stuck

[shell heron]

ok ok

lets do big brain stuff

[quartz beacon]

because it doesnt say that its equal to 0

[quartz beacon]

ok

[shell heron]

y^2 - 2x - 24 = 0

[quartz beacon]

but its not 0

[shell heron]

what is it then

[quartz beacon]

its not an equation actually

its an expression

[shell heron]

ok

so u want to simplify that?

[quartz beacon]

well

idk what i should do LOL

i want to solve it, but its not an equation, right? so i guess its impossible

also, you said lets do big brain stuff, so here you go

i just got this meme

[shell heron]

looool

[quartz beacon]

well, i think we can just simplify it

[warped phoenix]

if something outside of something inside of parenthesis denotes multiplication, then why is f*g(x) not equal to f(g(x))?

[glass lichen]

you mean (fg)(x)?

[warped phoenix]

well f(g(x)) = fᵒg(x) right?

[vague coral]

(fg)(x) is different of (f o g)(x)

[glass lichen]

yes

$(f\circ g)(x)=f(g(x)) \ (fg)(x)=f(x)g(x)$

[ocean seal]

Mosh

[warped phoenix]

oh wait g of x is not the same as g * x only in this scenario because we're talking about functions

right

🤦‍♂️

[glass lichen]

yes

[warped phoenix]

if it said g was a number and x was a number then it would be

[glass lichen]

g(x) is a function g w/ variable x

[warped phoenix]

ahhh, ty!!

[quartz beacon]

so, i need help again

im stuck in [5(x-5)]^2-2[x(x-5)]-24

i need to factorize that

[glass lichen]

what have you tried?

[quartz beacon]

well, actually i need to factorize that

[quartz beacon]

but i made it like that

[glass lichen]

ok so not what you wrote originally at all

$(x^2-5x)^2-2(x^2-5x)-24$

[ocean seal]

Mosh

[quartz beacon]

yes

[glass lichen]

does that look like something simpler you could factorize?

maybe doing a substitution would help see it

[quartz beacon]

$[x(x-5)]^2-2[x(x-5)]-24

[glass lichen]

Im gonna suggest not doing that

[quartz beacon]

oh

[quartz beacon]

i tried

i substituted x(x-5) by y

[glass lichen]

ok, and what did you get?

[quartz beacon]

and then i got y^2-2y-24

its a second degree thing

[glass lichen]

quadratic

[quartz beacon]

i could solve it?

ops srry

[glass lichen]

yes, you should be able to factor a quadratic easily

[quartz beacon]

so it is (y+4)(y-6)

[glass lichen]

yes

so $=(x^2-5x+4)(x^2-5x-6)$

[ocean seal]

Mosh

[quartz beacon]

noww my mind is buggy

[glass lichen]

it's just 2 more quadratics to factor

[quartz beacon]

hmm

i dont get it very well

sorry

[glass lichen]

you factored $y^2-2y-24$ perfectly fine... what's stopping you from doing the same process 2 more times?

[ocean seal]

Mosh

[quartz beacon]

but how did u get in (x²-5x+4)

hm

oh

[glass lichen]

undoing the sub

[quartz beacon]

x(x-5) = y right

[glass lichen]

yes

[quartz beacon]

and y should be (y+4)(y-6)

right?

wait

no

[quartz beacon]

thats where i got stuck

[glass lichen]

$(x^2-5x)^2-2(x^2-5x)-24 \ y=x^2-5x\implies y^2-2y-24 \ = (y+4)(y-6) \ = (x^2-5x+4)(x^2-5x-6)$

[ocean seal]

Mosh

[quartz beacon]

OHHHHHHHHH

GOT IT

[glass lichen]

Yep, and those are both quadratics which can be factored

[quartz beacon]

so actually we have x²-5x

OH OK

I GOT U

[glass lichen]

yep

[quartz beacon]

so yes, x²-5x = y

so

(y+4)(y-6)

just substitute y by x

lmfao

i understand now

[glass lichen]

just undo the sub, yes

[quartz beacon]

so

is it done?

[glass lichen]

you still have the remaining quadratics to deal with

[quartz beacon]

hmmm ok

so can i factorize x²-5x+4

hmmmm

wait

thats another quadratic expression

wtf

and the roots are 4 and 1

WTF

and x²-5x-6 is -6 and 1

ok

but how can i solve that

shall i get a z to substitute that?

or i don't need to

[alpine sable]

can i ask somebody a question

[quartz beacon]

sure

[alpine sable]

is anyone here good at cubic functions? i need help with a problem

[paper oar]

Just ask your question.

[quartz beacon]

@glass lichen i finally got it, it was easier than i thought hahah

[naive needle]

Is soemone avaible to help me here

[lunar relic]

How exactly do we use Gaussian elimination in the real world? It looks like row echelon form is kind of useless (since you need to perform back substitution) compared to reduced row echelon form?

[vague coral]

what do you mean by real world tho ?

[topaz scaffold]

I'm assuming applications

[vague coral]

Well, its used for matrix

and we use matrix basically everywhere

[warped phoenix]

"All constants have an exponent of 0" Shouldn't it be that they all have an exponent of 1? If something has an exponent of 1 then it is itself, but 5^0 = 1, which isn't the same as 5^1 = 5

[vague coral]

you are right, where did you see that "all constants have an exponent of 0" ?

[warped phoenix]

My book says "All constants have a x^0"

I'm not even entirely sure what they mean by that, it's in regards to defining whether or not a function is even or odd

[vague coral]

maybe they wanted to say that we can calculate, for all constants, x^0, except 0

[warped phoenix]

ohhh, i think they mean that all constants are raised to the power of x which is raised to the power of zero, essentially making that number equal to x^1, but they say y^x^0 instead of y^1 because x^0 is even..?

I'm not sure if that's right though

[vague coral]

i'm having a stroke while reading this

[warped phoenix]

LOL

one sec

[warped phoenix]

does this help? 😅

that's the only way what they're saying makes sense to me

unless what i am saying is also wrong

in which case i have no clue what the book is trying to tell me

[vague coral]

Can you send me the book ?

if it's possible of course

[warped phoenix]

WAIT

a constant * x^0

thats what they meant

like in the function, f(x) = 4x^3 + 7

the 7 is being multiplied with x^0

[vague coral]

well yes

x^0 = 1

[warped phoenix]

oh so you're using the power that the x is being raised to, not the actual number itself, like in that last function i said, if we recognized 7 as being raised to the power of 1, then the function would be odd

[vague coral]

dont think like this, it's easier than you think

[warped phoenix]

but in fact, the function is neither odd nor even, because f(x) = 4x^3 + 7 is equal to f(x) = 4x^3 + 7*x^0, and since there's an even and odd exponent, it's neither

LOL got it 😅

[vague coral]

a number (except 0) raised to the power of 0 is 1

that's all you need to remember i guess

[alpine sable]

,iamnot studying

[ocean seal]

Removed the studying! role from you.

[warped phoenix]

in the graph f(x) = |x|, why is the graph even and not odd since x has an exponent of 1 and 1 is odd?

[full canopy]

the definition of an odd function is f(-x)=-f(x) for all x, the absolute value function doesn't have that property.

its even because f(-x)=f(x) for all x

[warped phoenix]

ohhhh

[full canopy]

yeah the even odd power trick only works for x^n, cant be used on anything else

[warped phoenix]

ahh ok

[full canopy]

🙂

[warped phoenix]

ty! 😄

how is this graph being reflected across the x axis??

i dont see a second version of it literally across the x-axis...it's just one graph

[vagrant rover]

Jake has two different bags of candy. In one he has 12 red and blue candies, and in the other bag he has 22 green and orange candies. If he eats two, one after the other, out of each bag, how many ways can he eat the candies?
Here is did 12 choose 2 and then 22 choose 2 then multiplied the two results to get the answer. Is this correct? And if it is correct why do we multiple the two answers and not add them?

[glass lichen]

what?

x^2 is even, so a reflection of the graph on the y axis will be perfectly overlayed

[shadow edge]

Can someone help me with this problem : find the tangent equation

[glass lichen]

what have you tried?

[shadow edge]

ik i need to derivate the function but i cant

[glass lichen]

ok well have you done the implicit differenatiation?

[shadow edge]

what is that?

[glass lichen]

so no

check your notes on implicit

or related rates, as that's a similar concept, just the application side of implicit

[shadow edge]

idk what that is I am french