help-0

[slate jolt]

because for a flat surface theres no parralele force

well i replace 15 by 0

[supple fiber]

no i mean

but it just goes against trig

like

sin 15 = opp/hyp

and the hyp is the parallel component

so hyp sin 15 = opp

hyp = opp /sin 15

[slate jolt]

could you draw the right triangle you are using for this?

[supple fiber]

sure

[slate jolt]

well ok but the hypotenuse here is just a length in meter

not a vector force

[supple fiber]

yes but thats fine bc we can just multiply by the horizontal cector

but am i looking at the wrong triangle?

[slate jolt]

you are mixing things

one of your side is a vector

and the others are lengths

like how many meters is 50N?

if u are using trigonometry on vectors

[supple fiber]

wait how am i finding metres

[slate jolt]

all three of the side of your triangles should be vectors

[supple fiber]

okay

can u explain how to do it

to find both components of weight acting on the block

[slate jolt]

the parrallel and perpendicular components should add up to the total value roght?

since they are components

and by add up i mean vector addition

not adding thz lengths

in fact

they are the projection of the total vector

in the basis defined by the inclined plane

[supple fiber]

yea

[slate jolt]

so take the initial vector

and project it orthogonally onto the inclined plane

this will give you a right triangle

[supple fiber]

ty

[slate jolt]

draw the triangle and label the sides with the vector components

then you can do trig

[supple fiber]

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[autumn tartan]

what decides if its a bracket or parenthesis or one on each side?

[alpine sable]

open parenthesis = not included = open circle, square bracket = included = solid circle

[autumn tartan]

in the picture the circles are open

and they have bracket

[alpine sable]

meaning?

[autumn tartan]

it should be ( ) right.

[alpine sable]

sorry I meant parenthesis

I consider everything brackets open brackets square brackets squiggly brackets

[autumn tartan]

so why do they have square bracket for range?

because thats where the parabola(?) dips to?

[alpine sable]

Yep

the lowest point on the parabola is -4 on the y-range

[autumn tartan]

that makes more sense

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[zenith carbon]

Idk if I’ve done this right

Ik some of it is

[keen pasture]

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

[zenith carbon]

Oh right

Yes

Alright I’ve got it thanks

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[zenith carbon]

.reopen

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✅

[zenith carbon]

Actually I’m still stuck

Now what

Can’t really do anything

2x + 3 is on the same side

[slate jolt]

they still cancel out

[zenith carbon]

Is that legal?

[slate jolt]

(ab)/(cd) =(a/b)(c/d)

take your left fraction and divide it by 2x+3 then multply it by 2x+3

all in all youve done nothing

[zenith carbon]

So you can cancel on either end

No matter what placement

[slate jolt]

you can do multiplication and divisions in any order

so in your fraction

[zenith carbon]

If you do 2 / 5 and 5 / 2 it’s different

[slate jolt]

you can start by ( 2x+3)/(2x+3)

[zenith carbon]

Different answers

[slate jolt]

well because its not the same operation

what i meant is that

ab/c

=(a/c)*b

=a(b/c)

=(ab)/c

[zenith carbon]

Alright

2x . 2x - 3?

Should I do (4x + 3)(x - 3) instead

Ok I did this

<@&286206848099549185>

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[edgy cape]

How do I do (ii)

I have expanded (1-4x)^1/4 correctly: 1-x-(3/2)*x^2 -(7/2)*x^3

[alpine sable]

you mean you did a taylor approximation of $(1-4x) ^{\frac1{4}}$ ?

[ocean seal]

AimaneSN

[edgy cape]

i just expanded it with the (1+x)^n

binomial expansion

[alpine sable]

well n is an integer, not a fraction such as 1/4

[edgy cape]

taylor series stuff isn;t in my course

answer sheet says i am correct

[alpine sable]

yes, this looks very much like taylor expansion

[alpine sable]

there is no other way to expand this

[edgy cape]

ye and that's in a level further maths not maths. my use of the (1+x)^n expansion even if it technically isn't supposed to be used has always given me the correct answer so far

[alpine sable]

sounds like there is a generalized theorem of the binomial

yeah it's possible I think, but be careful anyways

not sure about what it says

[edgy cape]

I think I expanded (1+ax)(1+bx^2)^7 correctly: 1+ax +7bx +7ax^2 +21*b^2*x^4 +21*ab^3*x^5 +35*b^3*x^6 +35ab^4*x^7

but I am not sure what to do next

[alpine sable]

you don't need the whole expansion, just the term where the monomial is of degree 3

then take the other monomial of degree 3 from the expansion of (1-4x)1/4

[edgy cape]

just to be on the safe side if more x^3 values turn up

[alpine sable]

there is none here I can see

[edgy cape]

yes, did I do the expansion wrong?

[alpine sable]

the seventh power is on (1+bx^2) only, not on (1+ax)

so the expansion involves bx^2

which would be mutliplied by ax at some point

there has to be a power of 3

[edgy cape]

I know I first expaned (1+bx^2)^7 and then multiplied that with (1+ax)

[alpine sable]

the expansion of (1+bx^2)^7 involves bx^2

[edgy cape]

(1+bx^2)^7 = 1 +7bx +21b^*x^4 +35b^3*x^6

[alpine sable]

so you would have (1+ax)(....+ bx^2 +...)

ax * bx^2 = abx^3

[alpine sable]

how do you get 7bx ?

[edgy cape]

no idea i think i saw my first mstake

[alpine sable]

sounds like something is wrong

[edgy cape]

is it: 1+ 7bx^2

[alpine sable]

x here is equal to bx^2

n=7

[edgy cape]

and then (1+ 7bx^2) * (1+ax) = 1+ax+7bx^2+7abx^3

[alpine sable]

yes, that sounds correct

[edgy cape]

but then the statement in the question is a lie

the term of the lowest degree is ax

unless it means that ax = -7/2

[lone heart]

@edgy cape Has your question been resolved?

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[old rain]

hi guys what are the rules for carrying over greater than and smaller than?

[old rain]

-7 + x < 5 for example

does the < flip?

[mortal trellis]

addition and subtraction are always fine

multiplication and division with positive numbers is also fine

but if you multiply or divide by a negative number you need to flip the sign

[old rain]

ah that was it okay so if I were to divide both sides by lets say -3

or multiply

[mortal trellis]

then you need to flip < to >

[old rain]

okay thanks

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[spring kiln]

Hello. How can one efficiently calculate the cross correlation between two binary images?
I want to exploit the fact that all values are boolean, and avoiding using the FFT, and perhaps use the NTT.

[spring kiln]

I am trying to come up with an approximation of the cross correlation surface between two masks using NTT

any pointers to readings are greatly appreciated

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[alpine sable]

Hello!

[alpine sable]

Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?

Can anyone help me with this question?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

A friend needed help with it, sir.

Kindly solve it sir.

anyone?

[tacit arch]

@warm obsidian did you forget to log out of your alt

[alpine sable]

they are my friend sir

we both are seeking answer to it

i found the answer at reddit

https://www.reddit.com/r/puzzles/comments/uqrjwt/i_want_to_know_your_answers_and_opinions_on_this/

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[mortal harbor]

if kb^2 = a^2 why is k a factor of a

[mortal harbor]

its confusing to me for proof by contradiction

or is that a false statement?

[boreal drum]

think its false: take k=9, b=1, a=3. Then kb^2 = 9 = a^2 but k=9 is not a factor of a=3

[mortal harbor]

ahhh yes makes sense but then im confused

if i were to say prove sqrt 6 is irrational

what would i do

after this step

?

im assuming that you write a/b is the simplest integer ratio

[boreal drum]

I think this holds if you assume k is not divisible by any square numbers

eg k=6 works

[mortal harbor]

whys that?

[boreal drum]

not sure, but we can try to prove it?

[mortal harbor]

sure :)

i have 0 clue how to though LOL

[boreal drum]

i'd think in terms of prime factors of a^2

we know that they come in pairs becasue its a square

w8

[boreal drum]

I think the statement you want is "If kb^2=a^2 then k is not squarefree"

[mortal harbor]

i went onto maths stack exchange idk if this might help
i dont really understand the step past gcd

[boreal drum]

I think ive got it now

[boreal drum]

lets do this example. you have shown 6b^2=a^2 and you want a contradiction right. Count how many times 2 divides each side

we know 2 divides 6b^2 an odd number of times, but it divides a^2 an even number of times

hence, contradiction

and this works for any squarefree k (other than k=1)

[mortal harbor]

oooo

that makes sense

but then if for example we were doing sqrt 4

4b^2 = a^2

why cant we assume 4?

there shouldnt be a contradiction right?

[boreal drum]

well sqrt(4)=2, so there should not be a contradiction

[mortal harbor]

yeah so thats what confuses me 😢

[boreal drum]

what is confusing you? if you try to show that sqrt(4) is irrational its not gonna work right? becasue sqrt(4)=2 is not irrational

and the reason it doesnt work is becasue k=4 is not squarefree

[mortal harbor]

i dont know what to say this confusing me

https://math.stackexchange.com/questions/1748624/false-proof-that-sqrt4-is-irrational

its this thing

and i dont really understand the maths behind it

about square free etc

like i have no number theory under my belt

[boreal drum]

"Now $a^2$ must be divisible by $4$" is the part that doesnt work

[ocean seal]

Pishleback

[boreal drum]

for example 4*1=2^2 and 4 does not divide 2

[boreal drum]

square free means that it is not divisible by any square numbers

and that is useful because then you know that the highest power of any prime that divides it must be 1

[mortal harbor]

AHHH so 6 = 3 x 2

and the power of 3 and 2 are one?

[boreal drum]

yeeeee

[mortal harbor]

so now if you were to prove irrationality of sqrt 12 would you just do sqrt 4 x sqrt 3 = 2sqrt3

to make it square free?

[boreal drum]

👍 you got it

[mortal harbor]

AYYY

thanks man :)

appreciate it

[boreal drum]

np

[mortal harbor]

.close

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[vivid canopy]

I need help idk how to convert fractions to decimals to percents how do I do 99% to decimal and in fraction?? I need help with other ones too

[trail flicker]

99

fraction is 99/100

decimal is 0.99

99%=99/100

[vivid canopy]

What about —
6

6 repeating

[trail flicker]

?

type it normal

[vivid canopy]

?

Idk how

6……….

[trail flicker]

0.66666666?

[vivid canopy]

Yes

[trail flicker]

well

[vivid canopy]

0.66666666…..

[trail flicker]

0.6666666

is 66/100

so its 66%

[quartz oxide]

Wouldn’t you round that up tho?

[vivid canopy]

He did idk

[tight locust]

Not really

[trail flicker]

no because if you round it up

it goes 67%

[quartz oxide]

Ye

[trail flicker]

its not what it asked

[vivid canopy]

It’s 66%

[trail flicker]

he wants 0.66 to a percentage

[vivid canopy]

Its 6 repeating

[quartz oxide]

In the question it’s 99% (no decimals!!!) but this other one is 66.6666…% (non-terminating decimal

[vivid canopy]

It says round decimals to the neartest hundredth unless repeating

[trail flicker]

then elon mask is right

[quartz oxide]

Yeah so that makes 67%

[trail flicker]

yup

[quartz oxide]

Because .6666… rounds up

[vivid canopy]

It’s not

[trail flicker]

no

you dont round

because its repeating

[quartz oxide]

Oh wait

[trail flicker]

you have to leave it 66.6666666....

[quartz oxide]

Bruh

[vivid canopy]

Yes

[quartz oxide]

Yeah just write 66.6666….% xd

[vivid canopy]

66%

What do I do to 12/15 to a decimal then a percent

[trail flicker]

use calculator

[quartz oxide]

Is that allowed?

[vivid canopy]

Not this one

[vivid canopy]

Yes

[trail flicker]

you know long division?

[vivid canopy]

Yes

[trail flicker]

use long division

and you should get

uhmm should be 0.8

thats the decimal

[vivid canopy]

What about x

Multiply

[trail flicker]

multiply what?

[vivid canopy]

The fraction

[trail flicker]

you mean percentage?

its already in fraction

if you want its simplified you can write it as 4/5

[vivid canopy]

k illldo long didviosn

[trail flicker]

do you want it to be as a multiplication of fraction?

like (2x2x3)/(3*5)

[vivid canopy]

What

12/15 to a decimal

[trail flicker]

0.8

[vivid canopy]

0.80 is the same too right

[trail flicker]

yes

0.8000000000000000000 is the same

[vivid canopy]

K

[trail flicker]

doesnt matter how many 0's it has after

[vivid canopy]

How did you figure it out

[trail flicker]

figure out what?

[vivid canopy]

To a decimal

[trail flicker]

you make a long division

and the answer is the decimal

[vivid canopy]

What about x4

[trail flicker]

x4?

[vivid canopy]

Yes

[trail flicker]

what is that supposed to mean?

[vivid canopy]

It would be 80/100

???

[trail flicker]

the percentage

of 0.8?

oh

now i understand

yes

you can also do that

you can multiply it until it goes to 100 and divide it like that

you can multiply your denominator until its 100 then you divide it

works like that too

[vivid canopy]

How to simplify 12/15?

[trail flicker]

4/5

[vivid canopy]

What did you do

[trail flicker]

find the biggest number

that can divide bot

both*

and in this case its the number 3

12/3=4

15/3=5

[vivid canopy]

?

The same rows

In a multiplication chart

nvm

[trail flicker]

listen i have a tough time understanding some phrases because i study maths in a different language

but when you simplify a fraction

you find the biggest number that can divide both numerator and denominator

in this case

12/15 the biggest number that can divide 12 and 15 is 3

so you divide both of these numbers with 3

and the answer is 4/5

[vivid canopy]

I don’t understand

It’s ok let’s do long division

[trail flicker]

if you use long division

[vivid canopy]

Soo 1 into 1? Or 5 into 1

[trail flicker]

of 4/5

the answer is 0.8

the same answer is to 12/15

so 4/5=12/15

[vivid canopy]

Ik but

I want to divide 12 15

[trail flicker]

do you know

highest common factor?

[vivid canopy]

No

[trail flicker]

okay

highest common factor

is a number

that can divide 2 or more numbers

lets say you have 2 numbers

10 and 15

whats the biggest number that can divide both of them

[vivid canopy]

idk 5?

[trail flicker]

yes

now you have 12 and 15

whats the biggest number that can divide both?

[vivid canopy]

4

[trail flicker]

4 cant divide 15

[vivid canopy]

Why

[trail flicker]

technically it can but it leaves decimals

forgot to mention that

divide them perfectly with no decimals

what number can divide 12 and 15 and leave no decimals?

[vivid canopy]

I can’t divide with decimals?

[trail flicker]

you can

but to find the highest common factor

the number must divide both without leaving any decimals

[vivid canopy]

ok

[trail flicker]

with 10 and 15 the highest common factor is 5

because it leaves no decimals when you divide it with them

[vivid canopy]

Im using my multi chart

[trail flicker]

and its the highest number that can divide both

[vivid canopy]

3

[trail flicker]

yes

[vivid canopy]

😭

[trail flicker]

so you divide 12 and 15 with 3

[vivid canopy]

36891215 oh

[trail flicker]

so 12/15=4/5

[vivid canopy]

yes

[trail flicker]

thats how you get the simplified version of it

you just divide both with the highest common factor

[vivid canopy]

Then what do I multiply by to get 100 in the denominator

yea

Don’t answer that

What is 4/11 to a decimal

Mist

oh

pls help

@trail flicker I’m

[trail flicker]

bro im tryna sleep

use long division

[vivid canopy]

Idk how

[trail flicker]

the answer is the decimal form

you dont know how to division 11 from 4?

[vivid canopy]

1 in 4?

[trail flicker]

no

11 to 40

[vivid canopy]

Oh k

So 11 in 4?

[trail flicker]

40

11 cant go to 4

so you make 4 a 40

[vivid canopy]

How do I

[trail flicker]

may i ask

what grade are you in

[vivid canopy]

7 I’m 13

[trail flicker]

and you never learnt how to do long division with decimals?

[vivid canopy]

I did learned

Not this

[trail flicker]

4/11

let me

[vivid canopy]

What

4

[vivid canopy]

Sleep?

[trail flicker]

no

explain

[vivid canopy]

K I’m waiting

[trail flicker]

its 3 in the morning here

okay

[vivid canopy]

Ok

[trail flicker]

so when you want to divide

a number thats bigger

you want to divide 11 out of 4

[vivid canopy]

Yes

[trail flicker]

what you do in this case

[vivid canopy]

Write a 0

[trail flicker]

yes

11 goes to 4 0 times

so its 0,

[vivid canopy]

?

Oh ya

[trail flicker]

you multiply 4 with 10

and you have

40/11

and it goes 3 times and leaves 7

so you have 0.3

you multiply 7 with 10

70/11

it goes 6 times

0.36

and 4 remainder

[vivid canopy]

11x0 is 0 fhen 4 bring down 40 it is repeated

[trail flicker]

and it goes 0.36363636363636363636363636

yes

questions like these

can be easily answered on google

and they have good explainations

[vivid canopy]

wait

I keep getting 0 😔

[trail flicker]

how u get 0

bro im tired im really sorry

just use a calculator

[vivid canopy]

I’ll ask someone else it’s ok

.close

[lone heart]

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[bold mantle]

help pls

[bold mantle]

ty

[alpine sable]

this is only right for x in [0,1]

this is for x in [1,2]

this for x in [2,3]

this for x in [3,4]

[bold mantle]

ok

ty

can you help with this?

[alpine sable]

its gona look like this

[bold mantle]

ok

[alpine sable]

u need to find the reason

one sec

[alpine sable]

-35,5

[bold mantle]

for #16?

[alpine sable]

yes

[bold mantle]

those seem like coordinates though

[alpine sable]

remove 1,&

1,1

from each other

ul understand

[alpine sable]

start from 4,1 and remove 1,1

ull get 3

then 1,ç

1,9

[bold mantle]

so your finding the common differene first

[alpine sable]

then 0,8

yes

and ive done that 37 time

[bold mantle]

oh

[alpine sable]

i counted 4,1 as first step

[bold mantle]

well i believe there is a formula for it thoug

[alpine sable]

4,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1-1,1

[bold mantle]

arithmetic sequences

[alpine sable]

4,1-(1,1)x36

[alpine sable]

d=1,1

n=37

a=1 4,1

a37=4,1+(36*-1,1)

[bold mantle]

do u mean 4.1

or 4,1

out of curiosity

[alpine sable]

yes

[bold mantle]

ok

[alpine sable]

the formula

needs to know

where you start

and where you finish

it cant come up by that alone u need to provide

so

where it start where it finish

and the steps

its not the same if i jump one step instead of 2 steps

step here is 1,1

[bold mantle]

ok

[alpine sable]

but -1,1 not 1,1

caues the numbers keep getting smaller

4,1 to 3

4,1- 1,1=3

good night

[bold mantle]

ty

gn

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[blissful ether]

How do I set this up?

For the first equation do I just take the integral from 1 -> 3?

and second 4 -> 5

[stone pond]

Yes

[blissful ether]

Do I subtract one from the other?

[stone pond]

What do you mean?

So you know what the integral between 1 and 3 means?

[blissful ether]

yes

My point is I'd get 2 different numbers as a result since it's 2 equations

[stone pond]

You will indeed

[blissful ether]

That's why I asked if I subtract one from the other to get the difference

= area between them

[stone pond]

But those two equations just make up f

[blissful ether]

yes

[stone pond]

I think I see where you're getting confused

[blissful ether]

what do I do after getting the 2 numbers is where I get confused xD

[stone pond]

So your first number will be the area under f between 1 and 3

The second number will be the area under f between 3 and 5

[blissful ether]

oh duh

So I add them

[stone pond]

🙂

[blissful ether]

adding will give the full area under the curve right?

[stone pond]

Bingo

[blissful ether]

awesome!

Thanks 😄

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[dusk umbra]

anyone have any idea how this became a negative?

how we got r_i - r_j rather than a sum?

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[tacit arch]

Impossible to answer without context

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[merry python]

is 2sin^2x=6cos^2x = to pi/3,2pi/3,4pi/3, and 5pi/3 in (0,2pi)?

[placid zinc]

It's easy enough to check. Let's do π/3:
2(√3/2)² = 6(1/2)²
2(3/4) = 6(1/4)
That's correct, so π/3 is a solution

[merry python]

when you take the square root wouldnt you get 4 solutions?

<@&286206848099549185>

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[viscid rose]

hey quick question

[viscid rose]

if i take the integral test and my result of my integral is 0, does the series converge or diverge?

because the test has to be any positive finite number for it to converge?

[tight locust]

What series

There's a few conditions to be able to use the integral test in the first place

[viscid rose]

any series that satisfies the conditions

any positive series that decreases that is continous

im talking about in general

[tight locust]

For the integral test to be valid your function must be continuous, positive and decreasing

[viscid rose]

ik

but im saying

[tight locust]

So if the integral is 0

[viscid rose]

after i take the integral

[tight locust]

That either means your summand is 0

[viscid rose]

which means it converges

[tight locust]

Or that it is not valid

[viscid rose]

so which can it be?

converging or inconclusive

[tight locust]

Inconclusive

Because the integral test doesn't apply

Can you draw a positive decreasing function whose integral from 0 to inf is 0

[viscid rose]

oh cuz technically we have 0 area under the curve created by the series

and an infinite area means the series diverges

[viscid rose]

not that i can think of

it was just a question

[tight locust]

See, so integral test does not apply in that case

[viscid rose]

ok thanks

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[hallow coral]

Hello, I need help with this

x = ?

[hallow coral]

A) $\sqrt[81]{81}$
B) $\sqrt[80]{80}$
C) $\sqrt[50]{50}$
D) $\sqrt[70]{70}$
E) $\sqrt[40]{40}$

[ocean seal]

Yushu

[tight locust]

I'm assuming there have to be parantheses there

[hallow coral]

Nope

[tight locust]

Yeah you didn't write it correctly

(72+sqrt(x))^(72+sqrt(x))^(72+sqrt(x))

Is that what is meant?

[hallow coral]

No

[nocturne wave]

eh i would just sub all the answers

brutal

[tight locust]

So we have:
72 + sqrt(x)^(72 + sqrt(x)^(72+sqrt(x)))

?

[hallow coral]

Yeah

[tacit arch]

yea same

[nocturne wave]

pog

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[hallow coral]

<@&286206848099549185>

🥺

[nocturne wave]

are you allowed to sub

[lone heart]

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[old rain]

HI

How would I solve a linear system with greater than and smaller than

So for example
x1 + x2 + x3 > 5
x1 + x2 > 5
x1 + x3 > 5
x1 < -5

[olive oar]

x1 + x2 + x3 > 5
x1 < -5

x1 - x1 + x2 + x3 > 5 - (-5)

try from here

[old rain]

x2 + x3 > 10

[olive oar]

yea, this try to combine some of the other equations

it works a lot like a regular system (except you need an extra equation like the x1 < -5)

[old rain]

oh you trying to find a range where x is?

[olive oar]

yes

[old rain]

ah okay I was given a set of values x can be and brute-forced the solution but yeah you get no points for just the solution

[old rain]

Here you do assume x1 = -5

[olive oar]

no

im saying that if subtract x1 from the left

im subracting AT MOST -5 from the right

since x1 < -5

[old rain]

oh

so I did
x1 - x1 + x2 - x2 + x3 > 5 - (-5)
x3 > 10
x1 - x1 + x3 + x3 - x3 > 5 - (-5)
x2 > 10
x1 < -5

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[wild jolt]

My teacher said to do an early review about our next topic, but I don't know how to start this one

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[wild jolt]

<@&286206848099549185>

[naive valley]

what is f(x) on the interval of integration?

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[last sage]

I do not understand why my calculation is incorrect

[last sage]

The question was as follows: a circle with midpoint M(0,r) and a parabola with y = x² can intersect once or thrice.
For which r do these intersect three times

So I did:
c: x² + (y-r)² = r² and x² = r² - (y-r)²
f(x) = x² = y
therefore
y = r² - (y-r)²

But this does not work out

-y²+(2r-1)y = 0

And this does never have three solutions

[naive valley]

well y = 0 is one solution, and that gives you x = 0

the other possibility is y = 2r - 1

if you plug that into x^2 = y then you get x^2 = 2r - 1

[last sage]

The correct method was substitution btw

[naive valley]

and if 2r - 1 is positive then x^2 = 2r - 1 has two solutions

(both corresponding to the same y, but different x)

which is what you would expect geometrically

[last sage]

Yes it is positive

[naive valley]

well it's positive as long as r > 1/2

[last sage]

That is correct

[naive valley]

so isn't that the answer to the problem?

[last sage]

How did you get 1/2?

[naive valley]

you will have three solutions if and only if 2r - 1 is positive

which is true if and only if 2r > 1

which is true if and only if r > 1/2

[last sage]

I see, thank you

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[safe island]

what is happening in the 3rd line

[olive loom]

summation over i, j means u have sum all the combinations starting from
(1, 1), (1, 2), (1, 3), …, (1, n), (2, 1), (2, 2), … (2, n), … (3, n), till (n, n)

the third line simply breaks all these combinations of i, j in 3 terms

in the first term, they fixed x=k and then summed over j
so all the (k, 1), (k, 2), (k, 3), … (k, n)
except for j=k as they take it in the third term

similarly the second term for (1, k), (2, k), (3, k), … (n, k)
no i=k cuz its in the third term

and then finally the third term for solely (k, k)

[olive loom]

oh also where did the (1, 1) or (1, 2) etc terms went?
they become 0 cuz partial derivate wrt k

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[trim reef]

This is an integral question. I can clearly see I can do it with u-sub and get a nice answer. But, when I first tried it I went on a tangent and and tried to use trig sub with x=3tanu and went from there. I got something that seems like it works but I do not get the same answers when plugging in the limits to the u-sub and trig-sub evaluated versions. Is it possible that both answers are correct or did I do something wrong?

[trim reef]

x=3tanu => dx = sec^2u du

so can be rewritted as , 3tanu / 9tan^2u +9 * dx

= tanu/3(tan^2u+1) * sec^2u du

[uncut plank]

dx = 3sec²(u) du, not sec²(u) du

[trim reef]

ah

indeed

[wary stream]

If x = 3tan u and you plugged it in, wouldn't the numerator be 3 * 3tan u?

[trim reef]

Yeah, but I did some cancellations

retrying now

all just algebra mistakes :p thanks

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[limpid spade]

https://gyazo.com/2e404605bdfa4029aa96297f13fb4678 how did they solve for r_star

[remote heron]

is that equilibrium?

err

fixed

can you give any more context

[worn fox]

Just times everything by r^3

Then rearrange

[limpid spade]

distance r_star from origin when its a circular motion

[limpid spade]

lemme try

nice it worked

smart method will remember thx @worn fox

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[sand crown]

Hey guys im trying to do this question here. I have found the first partial derivatives and went to find the second derivatives and got 2 for w.r.t x and 24 w.r..t y but the solution says that the second derivatives at (0,0) is 0 so those terms are cancelled from the final solution but im not sure how theyre 0 if i got two numbers for them

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[thorny bough]

Given these:

Population size: 10000
Sample size: 500
Voting intentions: 42.24%

I need to calculate the proportion variance.
I found this formula online:

variance = (p(1 - p)) / n
where p is the success rate and n the sample size

but that gave me :
0.000487956
but I need to find
Variance: 0.000464

[thorny bough]

am i missing something ?

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@thorny bough Has your question been resolved?

[thorny bough]

<@&286206848099549185>

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@thorny bough Has your question been resolved?

[lone heart]

@thorny bough Has your question been resolved?

[thorny bough]

<@&286206848099549185>

[thorny bough]

<@&286206848099549185>

[tacit arch]

looks like you just have a rounding error

whatever answer/solution has a rounding error

[thorny bough]

Did you manage to get the calculation through good ?

cuz I'm using the highest precision settings

@tacit arch i even tried plugging it into other software

[tacit arch]

Then the answer has a rounding error

Or maybe you're supposed to use certain number of significant digits only

Follow whatever your instructor uses

[thorny bough]

How would you approach my problem from scratch

cuz I read the assignement and it doesn't have specifics but other students succeeded

[tacit arch]

show the original problem. screenshot or picture

[thorny bough]

for now I just want to get the variance

[tacit arch]

https://online.stat.psu.edu/stat415/lesson/6/6.3

[tacit arch]

you were calculating the wrong thing the whole time

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[open folio]

ADO and ABO are right angles because a tangent is perpendicular to the radius at that point, so DOB Has to be 360 - 40 - 180 = 140 because sum of angles in a quadrilateral ADOB is 360. Then by inscribed angle theorem angle BCD is 140/2 = 70 CBO is 90 - 75 because complementary angles (Since the tangent line). DOB and BOD add to 360, because they are central angles of a circle. 360 - 140 = 220. Now the angles in quadrilateral CBOD add to 360. 220 + 15 + 70 + ODC = 360.
ODC = 55 degrees?

.
.

Yes it is!! Honestly that felt too easy though

@abstract fractal I bet you have harder problems I could try

[abstract fractal]

Solve my parents marriage

[open folio]

42

Is the answer

[abstract fractal]

Thanks

[open folio]

Honestly pretty simple

Trivial

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[lone skiff]

hi guys help me to find the pattern of this

1 : (1)
2 : (2)
3 : (3)
4 : (4)
5 : (1)
6 : (2)
7 : (3)
8 : (4)
9 : (1)
10 : (2)
11 : (3)
12 : (4)
13 : (1)
14 : (2)
15 : (3)
16 : (4)
17 : (1)
18 : (2)
19 : (3)
20 : (4)
21 : (1)
22 : (2)
23 : (3)
24 : (4)
25 : (1)
26 : (2)
27 : (3)
28 : (4)
29 : (1)
30 : (2)```

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[lone skiff]

hi

help

don't close

.close

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[alpine sable]

<@&286206848099549185>

[tacit arch]

read

[supple tundra]

do u just want the answer or help solving it

[dawn birch]

y = mx + b

if slope is 3 what is m

[alpine sable]

Help solving it

Ofc I don’t want the answer 💀

This is y = mx+b , but once I plug in the equation I don’t know how to solve it

[dawn birch]

if slope is 3 what is m

[alpine sable]

1.5?

[dawn birch]

no

do you know what m and b stand for in y = mx + b

[alpine sable]

Y = 3(-2)+b

and then idk

[sweet chasm]

this is an x,y coordinate right

[dawn birch]

what does the m stand for

[sweet chasm]

that means when x = -2 y = -2

[clear stump]

You don't put -2 in the equation

so it's y=3x+b

now what would b be

[alpine sable]

Midpoint

[alpine sable]

O

[alpine sable]

Base? Idk

[dawn birch]

what—

[alpine sable]

Idek

[clear stump]

b is where the line cuts the y-axis

crosses

idk english

do you know how to solve it

Draw a picture and send it @alpine sable

[alpine sable]

No

[clear stump]

Draw a picture

@alpine sable you done?

[alpine sable]

A picture of what?

[clear stump]

The line

[alpine sable]

Ok

Uh I have no idea how the line is supposed to look like

[clear stump]

Do you know how to solve a slope

[alpine sable]

Nope

Forgot

[clear stump]

ok so the slope is $\frac{rise}{run}$

[ocean seal]

.,..

[clear stump]

now what divided by what is 3

@alpine sable you here?

Imma go sleep so you'll have to figure it out since you clearly don't care

[alpine sable]

Sorry I was doing something meanwhile trying to do my homework-

Like

3 divided by 1 is 3?

[clear stump]

yes

so you draw a line that passes through (-2, -2) witch goes up by 3 and across by 1

[alpine sable]

uh

Imma try

Kinda hard ngl

[clear stump]

huh

[alpine sable]

nvm

desmos hard to use

[wary stream]

https://www.youtube.com/watch?v=AqONrrPhJvk&ab_channel=BrianMcLogan

[clear stump]

that should teach you

ight imma go sleep

[alpine sable]

Done

I did it-

💀

[clear stump]

What did you get

[alpine sable]

nvm

I read it wrong

[clear stump]

Then you continue the line all the way through

[alpine sable]

O

All the way through where?

till the end or something

[clear stump]

atleast over the y axis

[alpine sable]

Ok

[clear stump]

so you get b

But you should probably calculate it

[wary stream]

You don't even need to graph it, you can if it helps. But it's not needed

Just watch that video

[alpine sable]

And I do rise over run?

[clear stump]

It is there

[alpine sable]

Oh

And I do rise over rin

Run or sum

[wary stream]

I suggestion still stands, watch that video

[alpine sable]

alright

gonna watch

the video

what if I don’t get it after watching it

[wary stream]

Then come back, simple as that

https://www.youtube.com/watch?v=REXFV61M37Q&ab_channel=BrianMcLogan

Here's another one

[lone heart]

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[lone heart]

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[spark pebble]

i dont understand what the last 4 mean

this is for triangle proofs

i understand the rest

but i dont understand the last 4

this is what i have so far

i dont know if im correct

[gray isle]

4 is incorrect

you haven't concluded congruent triangles yet so you cant use that justification

the justification for that is also a lot simpler than that

[spark pebble]

ohhh

cuz we havnet figured out if they are actually congruent

so i cant say that yet

so waht would it bee

im so confused

[gray isle]

try not to overthink this

[spark pebble]

oh

all right angles are congruent?

<@&286206848099549185>

[gray isle]

yes

[spark pebble]

alrr

so i dont understand how to do the next one

[spark pebble]

and i dont understand the meaning of the last 4

[young finch]

Is that upside t symbol perpendicular or bisect

[spark pebble]

perpecdicular

right?

[young finch]

would make the most sense

since a line containing a point can't be bisected by a line that contains one of it's endpoints

Idek why I asked that question its obvious

[spark pebble]

lol

[young finch]

Draw the figures out

to visualize it better

[spark pebble]

alrr

leme do that r

q

alr i drew itt

so how would I write

CPCTC?

because

now i kind of know that they are congruent

and parts of congruent triangles are congruent

right?

<@&286206848099549185>

[kind sierra]

Question? It doesn't show me in the pinned messages

[spark pebble]

yeah

i was gonna ask them another question

but they just ghosted me

💀

but yea

would I put congruent parts of congruent triangles are congruet?

for the 6th step?

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@spark pebble Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[wet beacon]

find the radius of the circle

a sphere is inscribed in a square pyramid

can anyone give me any hints

[lone heart]

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• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hardy gyro]

yo guy i need help

[young finch]

what

[hardy gyro]

c = 1

[wintry parcel]

c was the correct answer?

[hardy gyro]

yes

[wintry parcel]

ok u know why?

[hardy gyro]

nope

[wintry parcel]

read up ur lesson notes for improper integrals

[hardy gyro]

ok

[hardy gyro]

how would i find the antideriv of the intergrand tho?

[lone heart]

@hardy gyro Has your question been resolved?

[pure bolt]

through substitution

u=x-1