help-27

[dense cradle]

-1/3= 10

i got rid of x on the numerator and denominator

all i had remaining was

1/-3

and on the other side i did the same

all i had left was

2+8/1

@prime egret

[prime egret]

That’s not how you solve it

You can’t just cancel the x

[dense cradle]

how

why not

[prime egret]

Cross multiply

[dense cradle]

oh

so i do x^2+1+x+1

=

3x-6x+8x-24

right?

[prime egret]

(x+1)(x+1) = (2x+8)(x-3)

[dense cradle]

do you want me to simplify it now

[prime egret]

Then expand it

[dense cradle]

i just expanded it tho

[prime egret]

You didn’t get the right expression

[dense cradle]

did i expand correctly?

[prime egret]

Doesn’t seem so

[dense cradle]

okay give me a sec

x^2+x+x+1=2x^2-6x+8x-24

[dense cradle]

is this correct then?

[prime egret]

Yes

Now simplify and solve for x

[dense cradle]

okay

wait

sorry i had to do smth

2x+x^2+1=2x^2+2x-24

@prime egret

[prime egret]

Simplify that expression

You should get x^2=25

Do you see why?

[dense cradle]

can you explain how you simplified it

[prime egret]

Okay so

$x^2 + 2x +1=2x^2 + 2x -24$

[woven radish]

Pure

[prime egret]

Substract 2x from both sides;

[dense cradle]

right

okay

[prime egret]

$x^2 +1=2x^2 -24$

[woven radish]

Pure

[prime egret]

Subtract x^2 from both sides;

[dense cradle]

what do i do with the 2 then

[prime egret]

Which 2?

[dense cradle]

2x^2

it has a 2

in it

[prime egret]

Ok so if you subtract x^2 on from sides

$x^2 +1 -x^2 = 2x^2 -24 -x^2$

[woven radish]

Pure

[prime egret]

2x^2 - x^2 is x^2

So

$1=x^2-24$

[woven radish]

Pure

[prime egret]

Add 24 to both sides

$25=x^2$

[woven radish]

Pure

[prime egret]

Does this make sense?

[dense cradle]

wait im trying to process this

ohhh

okay

i got 5?

but the question is it wants another value of x thats not 5

[prime egret]

There’s another value

x^2 = 25

What happens when x is -5?

[dense cradle]

ohhhh

OHH

OKAY

thank you so much man

[prime egret]

Np

[dense cradle]

i have one last question

i just want to know if its right or not

really quick

[prime egret]

Ok

[dense cradle]

just the B)i)

[prime egret]

Lemme check

Okay so

n is not 30 in this case

Because we started from the 4th term

[dense cradle]

why not

[dense cradle]

oh

[prime egret]

the number of terms here should be 27

[dense cradle]

okay?

i did 7a correct tho right?

[dense cradle]

wait wait

[prime egret]

7a is correct yeah

[dense cradle]

okay

why do i do 27

what does r=4 mean

isnt 2^4 the first term of the series

since thats the formula

[prime egret]

So you have the sequence2^4 2^5 2^6 … 2^30

n is how many terms you have

[dense cradle]

so its 26

why 27

[dense cradle]

.

[prime egret]

If you think about 2^4 2^5 2^6

6-4 is 2

But you have 3 terms

So 30-4 is 26

But you have to add 1

[dense cradle]

right right

okay

27

[prime egret]

Yes

[dense cradle]

so everythings right

but i should replace 30 with 27

[prime egret]

Yes

[dense cradle]

s27=16(2^27 -1)

my bad

[prime egret]

And you could simplify this further to 2^31 -16

If you want

[dense cradle]

where did that come from

[prime egret]

16 is 2^4

[dense cradle]

ohhh

no

now all i have to do is solve

not simplify

like i plug it into a calculator

because its asking for the value

[prime egret]

Okay that’s fine

[dense cradle]

thank u so much man

i mean it

[prime egret]

Np

[dense cradle]

i really really appreciate this

[prime egret]

[dense cradle]

just a question

how old are you

im in 11th grade

[prime egret]

18

[dense cradle]

ah nice

so what're u doing now

u got a job or just go to uni

[prime egret]

Eating lol

Oh

[dense cradle]

🗿

lmao

[prime egret]

Im sending my uni application on 15 October

[dense cradle]

ah okay nice

planning to get into a big uni

?

or a local one

[prime egret]

Cambridge I hope. But also other unis in london

[dense cradle]

damnn

impressive bro

ur in the uk?

[prime egret]

Yeah I live in London

[dense cradle]

nicee

im taking IB

Math aa sl

im from saudi arabia

yk what ib is right

[prime egret]

Yeah

[dense cradle]

do u think a 5 is enough?

to get into a top 20 uni

like just get accepted not tuition

[prime egret]

Idk tbh I’m not familiar with grading system in ib

[dense cradle]

ah okay

anyways i gtg study physics now

my quiz is on sunday

and math quiz on monday

[prime egret]

Alright

[dense cradle]

thank u so much man

[prime egret]

Good luck with those

[dense cradle]

good luck with the applications

[prime egret]

Thanks g

[dense cradle]

have a nice one

[prime egret]

U too

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[modest spear]

I need to find the derivative of inverse function of f at point y=e^2

[modest spear]

I tried to do it via some help and yt vids

But I dont think Im getting anywhere

Am I doing it right? Beacuse I feel like Im not 💀

[crystal rune]

@modest spear If f(a) = b, what is f^-1 (b)?

[modest spear]

f^-1(f(a))

[crystal rune]

Or just a

You have f(e) = e^2 = y_o. What is f^-1 (e^2) or f^-1 (y_o)?

[modest spear]

Lemme write that down real quick so I can understand it better

Its f^-1(f(e))

or just e?

[crystal rune]

Yes just e.

To find the derivative of the inverse at y = e^2, you can just find the reciprocal of the derivative of the function at x = f^-1 (e^2) = f^-1 (y_o) = e

So all you need is just 1/f'(e)

[modest spear]

so It would be

gimme a sec

this?

[crystal rune]

Yes

Which is just 1/(3e)

And ur done

[modest spear]

Aight I get it now

Thanks

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[fickle drift]

what is the best way to solve this problem?

[brisk prawn]

Does the dot represent multiplication

[fickle drift]

yes @brisk prawn exactly

[brisk prawn]

Intuition and brute force

[fickle drift]

hmmm

my intuition is silent in this case

[brisk prawn]

Theres a -3 and a -2 which u can multiply to get a 6, there's also a -6 which u can add to the +6 to get 0 then ur peft with 12

[fickle drift]

so you are telling I will try with all numbers and search for possibilities?

[brisk prawn]

Yes

[fickle drift]

yes, I reached to 12

But it was so hard to reach 21

cant I reach without losing time?

[fickle drift]

not hard but time wasting

[devout snow]

@fickle drift Has your question been resolved?

[devout snow]

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[wary thunder]

Could anyone give me a hint on how to show the implies injective part?

[wary thunder]

Here $\sigma (u) = \sigma \left( \left{ u^{-1} (A) \colon A \in \mathscr{B} (\mathbb{R}) \right} \right)$

[woven radish]

CoffeeMan

[devout snow]

@wary thunder Has your question been resolved?

[stone stump]

if u is not injective and u(x)=u(y), then for any set A in sigma(u), x in A implies y in A

you can probably show this using some argument with dynkin systems and then using that lemma that certain dynkin systems are sigma algebras

[wary thunder]

Our prof decided to skip the chapter on dynkin systems

[stone stump]

its been some time since I've done measure theory but I think that should work

[wary thunder]

We're going through that chapter at the end of the course.

[stone stump]

oh. hmm. they are super useful for a few proofs tho

[wary thunder]

Damn. I'm not a fan of skipping chapters either, but well...

[stone stump]

maybe you can just show this by hand

[wary thunder]

Yeah, I was trying to as well; I just don't know how to argue that since any preimage of a set containing u(x) = u(x) must contain both x and y, any set closed under intersections and complements must either contain x and y or neither. I'm trying different things though.

But I've been stuck on the problem for a little over an hour, so I'm also considering just skipping it for now and coming back to it later.

There's a solution in the book, but I'd feel defeated :...D

[stone stump]

well the book didnt skip the chapter, so maybe it used dynkin systems

[wary thunder]

I'd be surprised since the professor put this problem on our problem list

Would be a huge troll

[wary thunder]

Here's a pic of the solution.

Haven't looked at it.

Could you check if it uses dynkin systems?

Or some crazy trick that one would never think of oneself

[stone stump]

so basically they handwave it

saying we can't "produce" it

what a letdown

[wary thunder]

The set ${ x}$?

[woven radish]

CoffeeMan

[wary thunder]

Ok, might as well look then.

Damn

That sure is a letdown

Thanks anyhow man, have a good evening/day

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[mild basin]

When you see this does it mean x^10 + 3^5?

[torn vessel]

no

[mild basin]

Then why are we allowed to do this?

[torn vessel]

it means (x^2+3)(x^2+3)(x^2+3)(x^2+3)(x^2+3)

[mild basin]

if x^2 is allowed to multiply why isn't 3?

[main gull]

Does (2x + 3)^2 = (2x)^2 + 3^2?

[main gull]

Because you don't care about the 3 from there. You're determining the highest power, which is (x^2)^5

[pine patio]

No

[mild basin]

so this is an illegal operation in math? normally you would never do this, it's only to find multiplicity?

(the ^2 * ^5 at the end)

the way i understand +-*/ operations, and correct me if I am wrong: but any time addition or subtraction is involved with multiplication or division gonna have problems unless there's distribution or factoring involved

because (a+b)^2 is not a^2 + b^2

[hollow pollen]

yeah thats not quite right

[mild basin]

hmmmm

[hollow pollen]

what did you want to do anyways?

[mild basin]

just to better understand how (x^2 + 3)^5 is able to get x^10, as per the screenshot above

[mild basin]

it's weird for me to do that because I'm also aware that the + 3 is there in the parantheses

[hollow pollen]

what is the question

[mild basin]

just to better understand how (x^2 + 3)^5 is able to get x^10, as per the screenshot above

[hollow pollen]

like if you want to find the highest power then thats x^10

[hollow pollen]

because this

if you just expand that youll see it works out nicely to x^10 + a bunch of stuff

[mild basin]

wouldn't 3 make powers too?

oh but when it comes to 3 to the power of whatever it is, you are saying it's lower power, and we are adding powers, not multiplying powers

when we add powers we take the highest power

when we multiply powers we take combined sum of powers

[pine patio]

Hope this helps

[mild basin]

pen and paper = no mistakes allowed 😉

[mild basin]

I think so..

I will try to review this to better understand it...

[pine patio]

The first lines expanding

Then writing a^5 as a^2 × a^3

Using whole square and cube identity

Then simplfying the rest

[mild basin]

I don't think I have learned cube identity yet

hard for me to read but still trying my best..

3rd line is where i am still stuck

I will save this and review lateer

[pine patio]

Wait lemme help

Replace them with the identity

[pine patio]

Is this better?

[pine patio]

Can you type out the text, the image isn't clear

[mild basin]

haha yeah i was going a bit blind, thanks for the repost

This is the cube identity?

[pine patio]

Yes

[mild basin]

good to know, never used it before

[pine patio]

If yoy want you can use the square identity instead of this

All the identities you will ever need

[devout snow]

@mild basin Has your question been resolved?

[devout snow]

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[devout snow]

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[unreal saffron]

$4x^2 - 25$

[woven radish]

Gigabyte

[unreal saffron]

how do I factorize this expression?

[wary thunder]

add butter

[umbral creek]

u can use difference of square formula

[umbral creek]

HAHA

[wary thunder]

that'll work too

[unreal saffron]

let me like look that up

[umbral creek]

okay

[unreal saffron]

thanks coffeeman

[umbral creek]

bread and butter

+coffee

[wary thunder]

any time brother

always coffee

[umbral creek]

trueee

[neon aspen]

Could you explain the joke btw or is it just funny coz it's unexpected

[umbral creek]

yes

[wary thunder]

Not a joke

Dead serious

[neon aspen]

Cool

[umbral creek]

use butter when stuck on a problem

you’ll slide right of it

[wary thunder]

Imagine trying to solve the problem by some crazy roundabout ways tho

Like the above one

[unreal saffron]

didnt expect this from a math server tbh

[umbral creek]

HAHAH

#chillserver

[wary thunder]

Imagine being like: well, naturally, we must check quadratic residues first

[umbral creek]

oops didn’t know that was a channel

[neon aspen]

Butter could make the problem difficult to grasp tho

[wary thunder]

Niiiice

[umbral creek]

HAHAHAHHA

it’s a good thing

[unreal saffron]

anyway thanks i get it now

[umbral creek]

who wants to hold onto a problem

[umbral creek]

no prob!

no pun intended*

[unreal saffron]

.close i guess

[devout snow]

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[unreal saffron]

what do you guys study btw

[wary thunder]

math

[tropic dune]

Not butter?

[unreal saffron]

yeah i figured he would be chef

[wary thunder]

Not unless we talking shapes

meth

[devout snow]

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[full moss]

can someone help me identify what I did wrong here? I got nT=253 and nS=0, which seem horribly wrong, but I can't see my mistake.

[full moss]

I see where I forgot to square .0005, but that only seems to make it worse

<@&286206848099549185>

im dumb

.close

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[boreal leaf]

is that one right?

[sand dove]

yes, because the scalar product is between two vectors and outputs a scalar

[boreal leaf]

ok thanks

If
V=(2, 10, 8), what is a vector perpendicular to
V?

[sand dove]

any vector W such that the scalar product of V and W is null

[boreal leaf]

(-20, 4, 0)

b)

(1, 5, 4)

c)

(-8, -10, -2)

d)

(4, 100, 64)

those are the options

[sand dove]

if W = (x,y,z), that means that 2x + 10y + 8z = 0. Up to you to find any x,y,z that satisfy this

[boreal leaf]

is it a

[sand dove]

it is

[boreal leaf]

ok thanks

a is (-20,4,0)

A boat wants to travel straight across a river. The current in the river is 15 km/h, and the boat can travel at a speed of 29.6 km/h relative to the water. What heading upstream, relative to the bank, should the boat take to end up directly across the river? Round your answer to to 1 decimal place.

.colse

.close

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[sand dove]

it's easier to start finding how many permutations do have six consecutive numbers in a row

to try to find one of those permutations, we have to choose these parameters :

• where does the sequence of consecutive numbers start ?
• which number does it start with ?
• how do you arrange the remaining digits ?

if it helps you

at least 6, because it is also implied "at least" in the reciprocal

[sand dove]

if you count correctly you should find 14 as the answer to this. If your answer is 18, that means you counted some permutations twice or thrice

you don't have to do that

[sand dove]

you can also choose how to get them with these parameters

for example :
"with which number does the sequence start ?" For the sequence to have at least 6 consecutive numbers in a row, the sequence must start with either a 1, 2 or 3

"where does the sequence start ?" the same reasoning brings you to the fact that the sequence has to start either in 1st, 2nd or 3rd position

and finally, "how do you arrange the remaining numbers ?" Anyway you like, as long as you don't count the same permutation multiple times

Example : the identity permutation (or 1 2 3 4 5 6 7 8), can be seen as "sequence starting from 1 in first position" OR "sequence starting from 2 in 2nd position" OR "sequence starting from 3 in 3rd position"

Anyways, 14 is the correct answer for the reciprocal set

So the answer to this question is ?

yes

so the result is ?

good answer !

exactly

you're counting the sequences (2 3 4 5 6 7 8 1) and (8 1 2 3 4 5 6 7) twice, as well as (1 2 3 4 5 6 7 8) thrice

so that 1 + 1 + 2 too many counts

and you get 14

the only sequences you won't count multiple times are the sequences with exactly 6 consecutive numbers

so any sequence with 7+ consecutive numbers will be counted multiple times

well, for sequences like this

you're exactly overcounting sequences with "exactly one more consecutive number" once, sequences with "exactly two more consecutive numbers" twice, etc...

yeah

only thing that changes is the total number of permutations

no, they get counted twice

so overcounted once

because you can either start on the actual first or second term of the sequence

[sand dove]

Yes 3 factorial

Oh right sorry

[solid sparrow]

!close

.close

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[eternal adder]

idk what to do

[eternal adder]

the table is quite confusing to read for me

[main gull]

Those times are in 24 hr format

Meaning 1300 = 1pm, 1400 = 2pm, etc

[topaz beacon]

They should label it on the top bus 1, bus 2, etc.

[gleaming socket]

This looks awfully similar to my local bus timetables 😭

[gleaming socket]

They actually don't in real life

[eternal adder]

i know that

[eternal adder]

thats what i did just now but it didnt help

[topaz beacon]

bus2, newton

[gleaming socket]

Bro it's literally 16 41

[eternal adder]

i dont know what the time means

[topaz beacon]

:l

[gleaming socket]

Wdym?

[topaz beacon]

You said you knew that

[eternal adder]

does the time mean the time they reached the location or does the time means the time they left

[eternal adder]

i know the time

im saying i dont know what the time indicates based on this table

[topaz beacon]

Departure

[eternal adder]

and how did u know that?

[topaz beacon]

Unless otherwise told so, just assume the problem gives you what you want

[eternal adder]

ok

?

so thats the answer

[gleaming socket]

Atomic bro

[eternal adder]

yes whta?

[gleaming socket]

Which country you live in?

[eternal adder]

why?

[gleaming socket]

Because in Europe this kind of timetable is very common

[eternal adder]

oh ok

hmm so its 16 41?

[gleaming socket]

Yesssir

[eternal adder]

but the question is not asking for the time of the second bus left right?

because they are asking when the second of these buses leaves Newton

the question is quite confusing

[main gull]

Not really

It's a chart of departure times and it's asking what time the second bus leaves Newton

[gleaming socket]

Again, it's perfectly clear to me because I see these timetables everyday

[eternal adder]

hmm so i am correct

[eternal adder]

ow

[gleaming socket]

So depends on where you live

[main gull]

So you go to the column for the second bus, row for the town, and that's the departure time

[eternal adder]

the marking scheme says otherwise

[topaz beacon]

???

That has like 0 correlation wtf

[main gull]

That's not even a time on the table

[eternal adder]

ye im a confused

i think the question is asking for another thing

cause it stated the second of these buses

if they wanted to know the second bus they would simply ask what is the departure time of the second bus

[main gull]

Can you post a full screenshot of the question page and then the answer key?

[topaz beacon]

Good idea lol

[gleaming socket]

I consider answer sheets divine but in this case it's wrong

[main gull]

Maybe you correlated the wrong answer to the wrong question

[topaz beacon]

Yeah no

The answer to b is wrong too

[gleaming socket]

The exam maker must be on drugs

[eternal adder]

hmm thats strange

[main gull]

You probably got the key for a different version, maybe

[topaz beacon]

Yeah thats what im thinking too

[eternal adder]

ur right

i confuse the marking schemes with paper 1 and 2

[main gull]

Lmao

[gleaming socket]

Atomic bruh

[topaz beacon]

Oof

[eternal adder]

my bad

[gleaming socket]

You played with us

[eternal adder]

it wasnt intentional i swear

[gleaming socket]

😭

[topaz beacon]

All good man just check with the other one

[main gull]

Does the proper answer key have the correct answers that you think they are? Like q1 should be 16 41, does it have that?

[gleaming socket]

Wait till he says no

[eternal adder]

yep, its right

[main gull]

Those look like the right answers now

[topaz beacon]

Yup

[eternal adder]

ok

thank you

have a nice day!

.close

[devout snow]

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[potent storm]

a battery tester takes 2 batteries out of a pack of 12. If those two batteries are defective, the pack is thrown away. If the batteries both work, the pack is accepted. If one battery works and the other is defective, the battery tester takes two new batteries out of the pack and repeats the process. In a pack with 3 defective batteries, what is the chance the pack will be accepted?

I am 90% sure the answer is 52/55 but i want an expert opinion/explanation.

<@&837645748744224799>

[devout snow]

@potent storm Has your question been resolved?

[devout snow]

@potent storm Has your question been resolved?

[short citrus]

,calc 1-3/12 * 2/11 - 2 * 3/12 * 9/11 * 2/10 * 1/9

[woven radish]

Result:

0.94545454545455

[short citrus]

,calc 52/55

[woven radish]

Result:

0.94545454545455

[short citrus]

yea looks right

I did 1- P(the pack is rejected)

[potent storm]

cool thanks

[topaz axle]

this is ambiguous

cuz you repeated it once, maybe the tester does it again

in fact if he doesn't it's not even clear what he does

[devout snow]

@potent storm Has your question been resolved?

[potent storm]

@topaz axlehuh????

[topaz axle]

You're saying "if on the repeat the tester gets one working and one defective battery the pack is accepted"

like why

maybe it's not like that 🤷‍♂️

hm

oh you're right

if it's not accepted immediately then, it will be accepted eventually because there is not enough defects left

[devout snow]

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[devout snow]

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[candid urchin]

i got D from just graphing and trial and error. but idk how to get it jsut from question

[inland seal]

Well, first of all you know that the range is 0 <= y <= 1.

arccos(x) will always give you a value between 0 and pi, so sin(arccos(x)) will always be positive.

[candid urchin]

yes

[inland seal]

And when arccos(x) = 0, sin(arccos(x)) = 1. This happens when x = 1, or in other words when ax - 1 = 1 so when x = 2/a

So there is a point where our function is 0, and where it's 1, and we know sin(arccos(x)) does not go above 1 and sin(arccos(x)) does not go below 0.
That's how we get the range to be [0, 1]

Now try to find a for which the domain is also [0, 1]

@candid urchin Try thinking about arccos(x). Where is it defined?

[candid urchin]

from -1 to 1

[inland seal]

Correct

So can you find the domain?

You want ax - 1 to be between -1 and 1 (including -1 and 1)

And you want the solution of this inequality to be 0 <= x <= 1

[candid urchin]

so.. -2/a<=x<=2/a

[inland seal]

Try to split it into cases where x > 0 and x < 0

Dividing by a isn't good since you don't know if it's positive or negative

[candid urchin]

oh mb. x>0 , x<2/a

[inland seal]

You mean 0 <= x <= 2/a

But yes

[candid urchin]

ye

so 0<=x<=2/a is also the range?

[inland seal]

Well that's what you want, yes

[candid urchin]

so

[inland seal]

The range is 0 <= x <= 1

[candid urchin]

oh

[inland seal]

And you want the domain to be the same

[candid urchin]

yess, i see

[candid urchin]

wait can u explain this again

how is sin(0) = 1

[inland seal]

I mean, arccos(x) = pi/2

Wait

Now I'm confused give me one sec

I mean arccos(x) = 1

Yeah.

WAIT

No

YES WHEN ARCCOS(X) = PI/2

my god

[candid urchin]

xD

wait, why pi/2 xD

like

why did u come up with pi/2

to get the range

oh

[inland seal]

And this happens when x = 0, so ax - 1 = 0, x = 1/a

[candid urchin]

nvm idk

[inland seal]

I just showed you that there is a point at which sin(arccos(ax - 1)) = 1

When x = 1/a

Yeah I made a mistake there

But it shouldn't matter

The point is:
There is an x for which the function is 0, there is an x for which the function is 1, and the function is always between 0 and 1.

So the range is [0, 1] since it takes all values between 0 and 1 (including 0 and 1)

[candid urchin]

wait just to clarify, sorry

oh nvm

wait

why is the function always between 0 and 1

sorry

i know that u said, since thers a x for 0 and 1

proving thats its 0 and 1 is a value

[inland seal]

Because sin(x) is never above 1,

[candid urchin]

oh yes

yes

yes

yes

sorry

[inland seal]

and Since arccos(x) is between 0 and pi, sin(arccos(x)) will not go below 0

[candid urchin]

yes

thank you

thank you alot xD

.close

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[inland seal]

No problem!

[devout snow]

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[pallid tundra]

Hello

[pallid tundra]

How do I go about solving #2?

[grim burrow]

what have you tried?

[pallid tundra]

Nothing thus far

[grim burrow]

well do you have in mind what you need to find in order to establish a parametric equation of a line?

[pallid tundra]

This?

[grim burrow]

sure, that's a formula, but i need you to understand how that works

do you know what v1, v2 and v3 represent in this?

[pallid tundra]

The components of a vector that's parallel to the line.

[grim burrow]

yes, the direction vector

and you know that the line goes through two points

so can you find this vector using those two points?

[pallid tundra]

I think so

[grim burrow]

which is?

[pallid tundra]

Give me a sec

<1, 0, -2>

Right?

[grim burrow]

no, not quite

[pallid tundra]

Hm

[grim burrow]

do you agree that if the line goes through P and Q, then the vector spanning from P to Q (i.e vector PQ) is the vector parallel to this line?

more than that, it lies on this line

[pallid tundra]

Yes

[grim burrow]

so can you find me vector PQ?

[pallid tundra]

^

[grim burrow]

.

[pallid tundra]

Ah

Wait, how would it not be?

[grim burrow]

because (1, 0, -2) is not the direction you should be heading from P to get to Q

[pallid tundra]

So I have to do it the other way around?

[grim burrow]

vector PQ shows you the direction to go from P to Q, so the components of the vector tells you the distance to travel in

[grim burrow]

i dont know what you did....

you showed no work

[pallid tundra]

<(-1 + 2), (0-0), (1-3)>

I subtracted the coordinate points

[grim burrow]

you seem to be getting random numbers here

these are your points

[pallid tundra]

Yes

[grim burrow]

i dont see any points with coordinates (-2, 0, 3) on there

[pallid tundra]

Oh, sorry

I wrote down the wrong point

<-2, -2, 2>

Is it good now?

[grim burrow]

yes

[pallid tundra]

Ok

My bad

[grim burrow]

and im sure you know what to do next here

[pallid tundra]

I was doing it with (-2, 0, 3)

[pallid tundra]

Uhm

Plug it into ...

[pallid tundra]

This?

[grim burrow]

yes

its basically just the number 1 exercise now

[pallid tundra]

Hm

So once I plug everything into that equation, what do I do next?

I got x = 1 - 2t, y = 2 - 2t, z = -1 + 2t

[grim burrow]

everything seems good

[pallid tundra]

Don't I have to create a restriction for t?

[grim burrow]

no

[pallid tundra]

Oh, ok

I was just going off of a YT video

Ok

So now that that's out of the way.

What differentiates it from these perpendicular ones?

[grim burrow]

nothing, still the same old find the direction vector and thats it

you just need to know your geometry

[pallid tundra]

Would I have to do the dot product?

[grim burrow]

no

if a line is perpendicular to a plane, can you guess what kind of vector would be parallel to the line?

[pallid tundra]

No, sorry

This is all very new to me.

[grim burrow]

what do you call a vector that is perpendicular to a plane?

[pallid tundra]

A normal

[grim burrow]

yes

and the line is also perpendicular to that plane

so what conclusion can you draw between that line and the normal vector?

[pallid tundra]

They are the same?

[grim burrow]

no

a vector is a vector,

a line is a line

they are not the same

[pallid tundra]

Same direction?

Idk

[grim burrow]

sure

so the normal vector of that plane is the direction vector of the line perpendicular to that plane

so for example, in exercise 8, what is the direction vector of the line?

[pallid tundra]

Uhm

(I'm assuming you're asking me to do the same process I did in #2)

[grim burrow]

no

[pallid tundra]

Idk then

[grim burrow]

what is the normal vector to the plane in exercise 8?

[pallid tundra]

No clue

[grim burrow]

ok, then i suggest you go review again

this should be something you should know, it wont take too long

[pallid tundra]

Is a normal vector N with a vector line over it?

[grim burrow]

im not sure what you mean by that

[pallid tundra]

I figured it out.

Thanks

Guess all I needed was a little review.

.close

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[dusk umbra]

Hello I have a problem, I have to tell wether that function is derivable and continuous in the entire real numbers set. The problem I have is that I know by replacing that it's possible to have a and b with different values than what i have defined but still i am not sure, but if the answer is still a yes i dont know how to prove it

[dusk umbra]

oh sorry

i guess i didnt exported it correctly

hold on

.close

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[dusk umbra]

.close

.closeeee

sadasd

[devout snow]

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[fickle drift]

(x-y) . (x+y) = 40

y = x + 2

x + y = ?

[sonic smelt]

if y = x + 2, what is x - y?

[fickle drift]

also x and y are odd numbers.

[fickle drift]

question is x + y = ? @sonic smelt

[sonic smelt]

ik

[fickle drift]

in numbers

[sonic smelt]

Just answer first

[grim agate]

well answer the bean’s question

[fickle drift]

x - x + 2

2

[grim agate]

is that x-y or y-x?

[sonic smelt]

if y = x + 2, then x - y = -2
So (x - y)(x + y) = -2(x + y) = 40

x + y = -20

[grim agate]

[visual moss]

🗿

don't answer the question straight away

[fickle drift]

its hard to understand

[visual moss]

tell them a way to understand and complete it themselves

explain it

[visual moss]

so this is your system

[fickle drift]

yes

[visual moss]

you know that y = x + 2

you want to pick that result to express the first line only with xs

try to replace y by x + 2 in the first line

(x-y) . (x+y) = 40
<=>
||(x-(x+2) . (x+(x+2) = 40||

[fickle drift]

im writing to my notebook hold on a second please...

[visual moss]

reveal once you're done

show us the result before

you should be able to find an x value out of this equation

then the rest is most likely done

[fickle drift]

(x - x + 2) . (x + x + 2) = 40

yessss!! correct

[visual moss]

put the "x+2" in parentheses

because it's going to change the sign

it gives (x-x-2) .(x+x+2) = 40

[fickle drift]

[visual moss]

reduce the expression

[visual moss]

Did you catch why ?

[fickle drift]

yes i got it!

[visual moss]

then reduce the expression

you can delete some x in it

it will give you a simple calculation

[fickle drift]

2x = 4 and x = 2

[visual moss]

||(-2).(2x+2) = 40
-4x-4 = 40
-4x = 44
x = -11||

that's what i got

[fickle drift]

oh I forgot to multiply

[visual moss]

in the first parenthese you can supress the two x's

it gives the expression : (-2)*(2x+2) = 40

[visual moss]

then you follow the steps above to find the x value

[fickle drift]

yes, correct x = -11!

[visual moss]

you can run the calculation again to confirm my result if you want

then you can insert the x value in your second expression : y = x + 2
then find out what is x + y =

simple now !

[fickle drift]

exactly, thanks a lot for your help! Is this called algebra?

[visual moss]

you should find something like ||y = -9||
||x + y = -20||

[visual moss]

I believe, but what we just did is solving a system equation i'm pretty sure

check on the internet i may be incorrect

[fickle drift]

So system equation is a sub topic of algebra?

[devout snow]

@fickle drift Has your question been resolved?

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[red tartan]

Need to know how to do these

Plz help I think it’s simple but I just can’t figure these ones out

[grizzled pulsar]

is it e

The cos -1 one

[red tartan]

yeah

i figured that one out

the other 2 im still stumped

i feel like they might be none of the above

[grizzled pulsar]

i never seen a tangent equal to 6 by its angle

[red tartan]

but not sure

[grizzled pulsar]

Maybe in a triangle but like prob max value of tangent is 1 by any given angle idk

Tangent means sin / cos

[red tartan]

yea

ill figure it out later if you dont know

which one?

[grizzled pulsar]

is the answer e of sin

[red tartan]

for what question

[grizzled pulsar]

First question

[red tartan]

it should be

all of them are sin-1 i thibk

think

[grizzled pulsar]

Can you check the answers of the questions

[red tartan]

no i cant

[grizzled pulsar]

i feel like sin one is e tangent one is undefined and the last one e i cant think of a triangle where two non hypnotuse side is 6x of one and other

[red tartan]

hm

im not really sure either

ill probably ask my teacher next class

.close

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[devout snow]

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[ivory depot]

i dont get this

[umbral creek]

uhhh

is it similarity and difference in how you pronounce

[prime egret]

Weird question

[umbral creek]

HAHA

[ivory depot]

ahah

wait let me check

this is the full question

.close

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[lament glade]

I tried to do: a_n=2+1/n

b_n=2-1/n

but it didnt help because the numerator reset to 0

[stone stump]

dont make people download random files to help you

[devout snow]

Channel closed

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[lament glade]

sorry, forgot to add png

.open

[stone stump]

open a new channel, this one will close soon'ish

[lament glade]

ok, thanks

[devout snow]

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[vocal lark]

How do I filter the column A such that data only from half hours such as 10:30, 11:30, 12:30 etc appear?

[vocal lark]

In excel

There are about 15000 rows like this...

[devout snow]

@vocal lark Has your question been resolved?

[vocal lark]

<@&286206848099549185>

[real trench]

Excel operations seem outside of the scope of mathematics. Check excel documentation on how to use excel

?

[devout snow]

@vocal lark Has your question been resolved?

[vocal lark]

.close

[devout snow]

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[devout snow]

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[rapid oasis]

I need help understanding horizontal stretches/compressions of a parabola, starting in y=x^2

[rapid oasis]

.close

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[restive river]

multivar help wanted: I want to know what I'm doing wrong and what the right answer is

[restive river]

because I got the partial derivative in respect to x at (x,y) = (7,8) as -131
and partial derivative in respect to y at (x,y) = (7,8) as 124

and we want to find a plane tangent to the point (7,8), right?

[devout snow]

@restive river Has your question been resolved?

[restive river]

<@&286206848099549185>

[grand flare]

yes.

[restive river]

hm

yeah that's where I'm confused/stuck now lol

wait the vector we make from the partial derivatives are just parallel aren't they

?

[grand flare]

-131(x-7) + 124(y-8) - [z(x, y) - z(7, 8)] = 0?

[grand flare]

I dont think so....

[restive river]

.

y'all

[restive river]

I resubmitted this

and it said it was correct.

wtf is wrong with this platform. this is why I hate browser platforms for math
update: bruh it was yelling at me for an extra space I had in between????

[grand flare]

lmao

[restive river]

alright well

uh

thanks waqq

really appreciate it

.close

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[nova quail]

.reopen

test

[nova quail]

ok

[midnight dirge]

test

[nova quail]

I'm confused abt this

[midnight dirge]

🥣

[nova quail]

x+y=2

and the y

I have no literal idea

[midnight dirge]

same

[nova quail]

what

your a helper right?

[midnight dirge]

yea

[nova quail]

so can you please help me?

[midnight dirge]

but

i havent learnt the mind reading bit

[nova quail]

x+y=2
cant find the m
can't find the y either

????????

[midnight dirge]

lol

where did m come from

🥣

[nova quail]

slope

[arctic field]

gradient probably

[nova quail]

wait

is it y=-x+2

[midnight dirge]

lol

idek

what u r trying to do

[nova quail]

like I said

x+y=2

[midnight dirge]

r u trying to find eq of a line

[nova quail]

the y

[arctic field]

yes

[midnight dirge]

u just said

o well

at least

weve a mind reader here

so u good

[nova quail]

ok

thanks ig

I just answered my own help 😂

[midnight dirge]

np

[nova quail]

.close

[midnight dirge]

🥣

[devout snow]

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[restive river]

how do I find the slope for this equation

when reading through the example in order to the line equation I have to first find the damned slope which I have no idea how to find

as seen in the example it just randomly says a slope and then goes with the flow not explaining how it got it

and this is coming from the text book

<@&286206848099549185>

ok guys

well I guess im gonna struggle to hell

Given two points slope is m=(y2-y1)/(x2-x1)

yes

but what does that mean

I know what you mean hang on

Well it's a formula so you can just apply it

hang on

you can take (5,2) and (6,4) and you find the same equation

given in your problem

hang on

Im gonna get this question wrong so we can start over

y=mx+b

It means each time you add 1 to x you add m to y

With A a point of coordinates (x,y) , you can deduce B (x+1,y+m)

ok so heres the new one

ok so lets start from the beginning what am I looking for when they are asking me to...

wait let me put in the scatter plot

[restive river]

Can I do the same thing with

(2,14) and (2,8)

For this new equation?

what

where do you find those points

When they ask you to find the points on the graph

(2,2) (8,14) are in our table

You see the chart at the top

No no

That’s not what they want

Yeah

post the problem we'll see

They want the first two of the columns and they want the last two of the columns

lmao

You’re laughing

But that’s exactly what they did

That's (2,2) and (8,14)

Not (2,14) and (2,8) you just don't know how to read it

Oh

I’m tired

Honestly

Misread it

Ok ok

So what do I do now

Use formula and done

Formula?

[restive river]

.

We never found the slope

Oh

You should either know the formula or find it by hand

[restive river]

Do they want the y’s from here

[restive river]

from here