help-17

[slate island]

did my professor make a grammar mistake or is this correct?

[slate island]

"In other words the negation of the original statement is false. Hence the original statement is true"

nvm read this wrong

.close

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[viscid egret]

What does the Sigma denote? why does the mark scheme not write Sigma abc?

[onyx sparrow]

Sum of the values

[heavy yoke]

$\sum$ means sum. so in this case $\sum \alpha \beta$ probably means "sum of all products of two roots", taking $\alpha$ and $\beta$ to represent any of the two roots

[twin meteor]

cloud

[heavy yoke]

which is really just a more compact notation for the sums on the question statement

[viscid egret]

ah so they aren't specific to the alpha and beta mentioned in the question?

just any of alpha, beta or gamma?

[heavy yoke]

yes, i think that's what they're going for

[viscid egret]

but the thing is, the way I solved this question was by summing ab, ag and bg

so how does summing ab correspond to that?

[heavy yoke]

alpha and beta in the sum notation just means two different roots. so [ \sum \alpha \beta = \sum (\text{a root})(\text{a different root}) = \alpha \beta + \alpha \gamma + \beta\gamma ]

[twin meteor]

cloud

[viscid egret]

ahhh thank you

but what does that mean in ii)?

(sum of any root)^2 = sum of any root^2 +2(sum of any 2 roots)?

[heavy yoke]

yes. so we can write that out more explicitly as [ (\alpha + \beta + \gamma)^2 = (\alpha^2 + \beta^2 + \gamma^2) + 2(\alpha \beta + \beta \gamma + \gamma \alpha) ]

[twin meteor]

cloud

[viscid egret]

ah so the bit straight after the equals sign was sum of all of any of the roots squared

[vocal sleet]

@viscid egret Has your question been resolved?

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[strange zodiac]

what's wrong with my work?

[bitter pilot]

I think sqrt(c) is the magnitude of the gradient, because dividing by it seems to me we are normalizing the vectors

[vast shale]

yo i remember this from yesterday

[strange zodiac]

yes

i fell asleep lol

[wraith python]

c looks like it is too high.

[vast shale]

we already tried a=10, b=-10 and c=2 but it marks incorrect

[vocal sleet]

@strange zodiac Has your question been resolved?

[strange zodiac]

<@&286206848099549185>

i can confirm c = 8

but idk about a and b

[vast shale]

oh

i see what the problem is doing

they didnt simplify the sqrt

bruh

[strange zodiac]

what's our next steps

so a = 20 and b = -20

?

[vast shale]

redo everything without using sqrt(8) = 2sqrt(2)

i think so

[strange zodiac]

i got it, thanks!

[vast shale]

was it correct?

[strange zodiac]

i appreciate your help

yup

[vast shale]

i mean technically there are multiple solutions 😭

[strange zodiac]

.close

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[vast shale]

because the fraction can be reduced

but still

[strange zodiac]

right

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[foggy void]

i need help with d) when n is odd, what happens to a) b) and c), i've done everything else

[foggy void]

<@&286206848099549185>

[vocal sleet]

@foggy void Has your question been resolved?

[vocal sleet]

@foggy void Has your question been resolved?

[foggy void]

anyone?

[half imp]

is there something particular you're getting stuck on?

[vocal sleet]

@foggy void Has your question been resolved?

[vast shale]

is it $A_{ij}=(-1)^{i+j}?$

wow there is latex

[twin meteor]

villegas

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[velvet cove]

What are the dimensions of the rectangular box, open at the top, which has maximum volume when the surface area is 48?

[velvet cove]

i have to use lagrange multipliers

[ionic panther]

Yeah u do

Also use the reflexive property to help with that

It makes it so much easier

[lime gorge]

Show ur work

[ionic panther]

Wouldn’t the reflexive property would be better in this situation?

[velvet cove]

Look

[vast shale]

multiply both sides in each equation by x,y,z in that order

huh nevermind

ignore this

[lime gorge]

First component of ur constraint’s gradient vector is off

Wait Nvmnd

[velvet cove]

idk how to proceed from k=x-z

[lime gorge]

$xyz = kx(y + 2z) \newline xyz = ky(x+2z) \newline xyz = kz(2y+2x) \newline xy + 2yz + 2xz = 48$

[vast shale]

ok yes do what i said

[lime gorge]

So we have a system of 4 eqns and 4 variables

[vast shale]

. should remove a bunch of terms\

[velvet cove]

bruh moment

so much busy work lol

[velvet cove]

so like they would all have xyz

[lime gorge]

Yea I recommend doing this

[vast shale]

yes

then u equate the first and the second, the second and the third, and the first and the third

1,2 1,3 2,3 all combinations i think i dun remember

[velvet cove]

should i leave this unexpanded

oh wait

ok

$0=k[x(y+2z)-y(x+2z)]$

[twin meteor]

Jash

[velvet cove]

0=k(2xz-2yz)=2kxz-2kyz=0

x-y=0

x=y?

$0=k[y(x+2z)-z(2y+2x)]$

[twin meteor]

Jash

[lime gorge]

Yea that seems right

[velvet cove]

$0=xy-2yz$

[twin meteor]

Jash

[velvet cove]

x=2z

[lime gorge]

No

[vast shale]

oh yes i think u did the same

heres an example with 1 and 2 at least (i will not see ur simplifcation tho):
$kx(y+2z)=ky(x+2z) \implies xy+2z = yx + 2yz \implies 2=2y$

[lime gorge]

It should be xy - 2xz = 0 @velvet cove

[velvet cove]

oh ye

y=2z

[lime gorge]

x = y
y = 2z

Now just use ur constraint ig

x^2 + 2y(y/2) + 2x(y/2) = 48

x^2 + y^2 + xy = 48

3x^2 = 48

X = 4

Y = 4

Z =2

Is that what u got @velvet cove

[velvet cove]

hold on im still doing it

i got

$z=\pm2$

[twin meteor]

Jash

[lime gorge]

Why pm

No neg lengths

[velvet cove]

$x=\pm4$ and $y=\pm4$

[twin meteor]

Jash

[velvet cove]

arent they just coordinates

like dont u do 4-(-4) to find the dimension

[lime gorge]

It says dimensions

Nah I don’t think so

Dimensions just means l,w,h

[velvet cove]

ohh ye when i set it up i didnt do l/2

[lime gorge]

At least that’s what I’ve always been taught

[velvet cove]

wow the equation ended up just being $4z^2+4z^2+4z^2=48$

[twin meteor]

Jash

[velvet cove]

having an easy solution of z=2

[lime gorge]

Yea that’s a common theme for LM problems

[velvet cove]

so did i do 23 wrong the same way

when i said 2 in front of everything

[lime gorge]

Yea I don’t think that’s right

That doesn’t really make sense

[velvet cove]

so is it just a/sqrt3 by b/sqrt3 by c/sqrt3

[lime gorge]

Try plugging them back in if u want

You’ll see it doesn’t work out

[lime gorge]

Assuming ur work is right yea

[velvet cove]

ye when u plug in this u get 1

which is the intended answer

[lime gorge]

Yea, try plugging in the answers with 2 in front

U won’t get 1

[velvet cove]

how do i do c btw

[lime gorge]

Idk what maximizer or minimized means

[velvet cove]

like does it have a global mins or maxes

[lime gorge]

Oh I got no clue, calc3 was a while back for me, iirc there was some test for that, but I don’t remember the name

[velvet cove]

for second derivative test we gotta use like hessian determinant

ty tho

.close

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[merry imp]

hi

[merry imp]

my last guy died on me

i dont understand how this stupid equation is factorized

[vast shale]

gang this has got to be a one line answer

[merry imp]

what are you even saying

just tell me how this thing is factorized

[vast shale]

4x(x^2-3) ???????

[merry imp]

yes

how did you do that

[outer panther]

magic

[merry imp]

the 12 had an x

[outer panther]

obviously

[merry imp]

the 12 had an x where did that x go

[vast shale]

to china

[outer panther]

distributive property!!!!!

HAHAHA

the exact same problem

was on that video's thumbnail

epic

[merry imp]

factorization is reverse simplification?

[outer panther]

🤯

[amber pecan]

Factor out 4X

[outer panther]

or reverse expanding out

[merry imp]

if factorization is gonna be reverse simplification,

then this will be equal to

[vast shale]

you can say that...

[merry imp]

4x(xpower2 - 3)

and then what

[outer panther]

ur done

https://www.youtube.com/watch?v=gw893STHN9w&ab_channel=MashupMath

watch that

[vast shale]

thats it :DD

[merry imp]

no this is just a smaller part of a big question

am supposed to end up with these

[vast shale]

what's the "small" question

[spiral turtle]

So you took the derivative

[outer panther]

do u know what to do with the factorized derivative 4x(x^2-3)

[merry imp]

i know the first point is (0,4)

THEN WHAT

[merry imp]

?

[outer panther]

do u know why the first point is (0,4)

[merry imp]

yes i did the y' then substituted x for 0

because y' is supposed to be 0 since the line is horizontal

[outer panther]

y'(0) gives you the slope of y at x = 0

which is one of the answers

but theres another

[outer panther]

yes

which means y'(x) = 0

not y'(0)

[merry imp]

well sure ok

[outer panther]

so

[merry imp]

thats how i found the x

[outer panther]

you set each factor of y' equal to zero

4x = 0

x^2-3 = 0

[outer panther]

2nd one is where this comes from

[merry imp]

what!!

[outer panther]

sometimes its useful to graph stuff

one sec

[merry imp]

the question doesnt require graphin this how our teacher solved it

[outer panther]

red is y blue is y'

yes but just to demonstrate this

it's useful to look at a graph

whenever y' = 0, you can see that the red graph has a slope of 0

[merry imp]

the graph is just gonna confuse me even more idek how u managed to drew that with the function i gave you

[outer panther]

(y' is blue)

[vast shale]

hahahahaha

[outer panther]

hmmm

lets look at a simpler example

[vast shale]

setting y' = 0 and solving for x gives u the x coordinates for the points where the slope of the tangent is 0. slope is 0 means line is horizontal

[outer panther]

when the derivative of y = x^2-12, y' = 2x is zero, the slope of y is zero

[merry imp]

its solving for y

[vast shale]

thats the function

[merry imp]

how is it solving for x if its y=

[vast shale]

we need to determine where the derivative of the function is equal to 0

what's the derivative?

[merry imp]

its 4xpower3 - 12x

[vast shale]

yep so we set the derivative to 0

meaning......

[merry imp]

the derivative is already set to 0 because the line is horizontal

we didnt set anything

we just substituted x for 0 to make it equal the horizontal line

wich is zero

[vast shale]

what is a derivative?

[merry imp]

i know the derivative rules

[vast shale]

not the rules

[merry imp]

the power rule chain rule product rule quotient rule

and some others

[vast shale]

like literally what is a derivative

[merry imp]

tell me

[vast shale]

its the derivative of the tangent line at any given point

[merry imp]

a derivative IS A DERIVATIVE?

come on

[outer panther]

slope^

[vast shale]

i meant gradient*

anyways

[merry imp]

am taking a calculus course

[vast shale]

the tangent line is horizontal means the gradient is equal to ...?

[merry imp]

i wont be needing to know any geometry stuff

[outer panther]

calculus is geometry under disguise

(among other annoying concepts like trig)

[vast shale]

i think you should be a math major

[merry imp]

what even is a gradient WHY ARE YOU GOING OFF TOPIC

[vast shale]

slope

😭

you have got to be trolling

[merry imp]

i already did trig differentiation it wasnt hard

[outer panther]

gradient = slope

[merry imp]

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line

[outer panther]

changes from country to country

or even state to state ig

[outer panther]

who

[vast shale]

kokolofo

[merry imp]

this is cool and everything but concerning the question i asked before

[outer panther]

i dont know enough undergrad math to understand that lol

[merry imp]

how do i find root 3 from this

[vast shale]

you set the derivative to 0

and solve for x

[merry imp]

the derivative is already 0

so theres that

[vast shale]

GIRL THE DERIVATIVE IS 4X^3-12X

[outer panther]

we already factorized this as 4x(x^2-3)

[vast shale]

ITS DIFFERENT AT DIFFERENT POINTS

[outer panther]

then set each factor equal to zero

[vast shale]

WE ARE FINDING THE POINTS WHERE ITS 0

[merry imp]

(4X^3-12X) = 0

[outer panther]

xd

[vast shale]

there you goooooooo

[merry imp]

yea and weres root 3

[vast shale]

solve it...

[outer panther]

set each factor = to zero

4x = 0

x^2 - 3 = 0

[merry imp]

4x(xpower2 -12x)

now what

[vast shale]

nuh uh

[outer panther]

bruh

[merry imp]

4x(xpower2 -3)

[vast shale]

yepp now = 0

[merry imp]

factor = x?

i already did that

[outer panther]

show me

[vast shale]

this is incredible

[merry imp]

how else would i have gotten that (0,4 ) is the first point?

[vast shale]

you made it up

find the values of x satisfying the equation
4x(x^2-3) = 0

[merry imp]

4x(xpower2 -3) also if i substitute x for 0 that means

[outer panther]

no

dont substitute x = 0

[merry imp]

4 multiplies x is zero then 0 times everything is 0

[outer panther]

right answer wrong reasoning

[merry imp]

you said make all the factors a zero

[vast shale]

😭 😭 😭 😭

[outer panther]

thats why ur not getting +-sqrt(3)

[vast shale]

save me donald trump

[outer panther]

that means y' = 0 not x = 0

i said make each factor = to zero

4x = 0

$x^2 - 3 = 0$

[twin meteor]

MWB117

[vast shale]

how do you solve

4x(x^2-3) = 0

[outer panther]

$x^2 = 3$

[twin meteor]

MWB117

[outer panther]

$x = +-sqrt(3)$

[twin meteor]

MWB117

[merry imp]

you made this its own equation?

[outer panther]

yes

you can do taht when solving for zeros of polynomials

if you ahve two factors

if one factor is zero

the whole equation is zero

factor * zero = zero

[vast shale]

a.b = 0 means a=0 or b=0 remember
our a is 4x our b is x^2-3

[merry imp]

so 4x(xpower2 -3 ) 4x is a factor and xpower2 -3 is also a factor

[vast shale]

there you go

[outer panther]

yes

u some algebramaxxing before u get further into calc

[merry imp]

so you ignore regular math rules and seperate whatever has a variable next to it

[vast shale]

😭

[outer panther]

this is a regular math rule

if a factor of a product is zero then the product is zero

factor a * factor b = product

if factor a or b is zero then the product is zero

[merry imp]

the factor of a product?

so what the factor equals?

[outer panther]

product is the result of multiplication of factors

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

[merry imp]

whats the product in my equation

[outer panther]

the product is 0

or should be

[merry imp]

the product is the result

[vast shale]

ok take a simple example
3x = 5
what is the value of x?

[outer panther]

you want it to be zero so that the slope is 0

[outer panther]

yes

[merry imp]

and if the whole equation has variables and it equals to zero , i can split the variables

since the variables will be multiplied by anumber

and the result will always be zero

4x=0 and xpower2-3 =0

but xpower2-3 doesnt equal to zero

[outer panther]

bro

im gonna crash out

[merry imp]

if it doesnt equal to zero thats the solution?

[vast shale]

hahahahahaha

he has had enough

[outer panther]

https://www.youtube.com/watch?v=qeByhTF8WEw

[vast shale]

we are finding values of 'x' for which it x^2 - 3 equals 0

[merry imp]

i know quadratic equations

[outer panther]

x^2 - 3 is a function itself

made up of a variable

it's not zero

we want it to be zero

[merry imp]

its only a function after factorization. wich means we made our own function

[outer panther]

by finding an x that makes x^2 - 3 = 0 true we find the zero of that function

[merry imp]

its supposed to be multiplied by 4x

but we split it right?

because of what i said earlier

[outer panther]

sure, both factors are functions

[merry imp]

if we have 4x(5x)=5

this doesnt mean 4x=5

and 5x=5

it does or it doesnt?

[outer panther]

by solving for each of those equations you just wrote

you find values of x that satisfy 4x(5x)=5

[merry imp]

yea but thats just forcing it

[vast shale]

nuh uh u cant do that

[outer panther]

uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

ok in this case you do have to multiply the factors out

ig

[merry imp]

how does that work in my original question

[outer panther]

it does trust

[merry imp]

so i reverse the factorization?

[outer panther]

you find a value x that makes each factor = to 0

[merry imp]

be serious please am very tired

will 4x(5x)=0?

[outer panther]

when x = ?

[merry imp]

be 4x=0 and 5x=0

[outer panther]

well

[merry imp]

in my question it ends up as root 3

[outer panther]

forget what i said about setting 4x and 5x = to anything

in this case you multiply it out

20x^2 = 0

this works for ur original question tho

[merry imp]

4x(xpower2 - 3)

you want me to bring it to what it was before factorization

so we basicly did nothing

[outer panther]

no

im saying with y = 5x(4x) you cant set each factor = to anything to solve for x until you multiply the factors

but

with 4x(x^2-3) you can

4x = 0

x = 0/4 = 0

x^2 - 3 = 0

x^2 = 3

[merry imp]

why are you dividing by 0

[outer panther]

x = +-sqrt(3)

i divided by 4

[merry imp]

zero cant be in division idk what that that has to do with this

anywyas

[outer panther]

are u trolling

how are you in calc'

[merry imp]

4x=0 wich means x is 0

[vast shale]

ay bro chill

[outer panther]

im genuinely surprised tho

[merry imp]

and xpower2 -3 is also = 0 right?

[outer panther]

yes we set it = to 0

[merry imp]

i finished limits, differentation and trig differentation

those werent difficult

[vast shale]

clearly did algebra during covid

[outer panther]

yes but ur algebra is a little weak

^

i'd recommend taking a college algebra course next semester or asap

at some community college

[merry imp]

4x=0 and xpower2 -3 is also = 0 this is because we found that x = 0 when we got the derivative the first time right?

[vast shale]

nope

[outer panther]

nnnnnnnnnnnnnnnnnnnnnnooooooooooooo

4x=0 xpower2-3 is also 0, this is because we want them to be zero

not because of anythign else

[merry imp]

is it a rule that i have to want them to be zero?

or is it because the question says horizontal line

[outer panther]

if the question was asking for the points at which the tangent lines had a slope of 2, we'd set these equal to two

4x = 2

xpower2-3 = 2

[outer panther]

not necessarily

it depends on the question

as i just said

[outer panther]

yes

[merry imp]

ok

and then from 4x(xpower2 - 3)

4x=0 and xpower2 -3 =0

[outer panther]

yes

from there you find the x values

and since its asking for points of y, not y', you'd do (0,y(0))

and (sqrt3,y(sqrt(3))

[merry imp]

we bring 3 to the other side so its xpower2 = 0+3

[outer panther]

and (-sqrt3,y(-sqrt(3))

[merry imp]

is this correct?

[outer panther]

thats how you solve for x yes

[merry imp]

so the answer is 3

now what

[outer panther]

hahaha

x^2

not x

and you're solving for x

not x^2

x^2 is 3

but x isn't

what do you do to undo the square

[vast shale]

bros been at it for 50 mins

what a legend

[outer panther]

its free karma for my next math test

[merry imp]

to undo the square we do root

[outer panther]

yes

so x=

[merry imp]

but that would be us just adding a root on our own

a root is power 1/2

how can i add a number out of nothing

[outer panther]

oasmdoadmgsdf

sqrt(x^2)

= x^(2)(1/2)

= x^1

= x

[merry imp]

in the end the solution we be root 3

[outer panther]

what u do to one side you do to the other

yes

butttt

[merry imp]

root 3 isnt square root its power 1/3

[outer panther]

?

[vast shale]

HAHAHAHAH

[outer panther]

no

[merry imp]

root 3

[outer panther]

well

first off stop saying root

[merry imp]

the root is power 1/2

[outer panther]

its square root

its square root of 3

[merry imp]

square root is power 1/2

[outer panther]

cube root is power 1/3

[merry imp]

yea and square root is power 1/2 not power 2

[outer panther]

and?

[merry imp]

so how can you just put power 2 to cancel the root just because you want to

[outer panther]

other way around

we put square root to cancel power 2

x^2 = 3

sqrt(x^2) = +-sqrt(3)

x = +-sqrt(3)

[outer panther]

5x = 3

[merry imp]

whenver you have s power 2 you can just add a square root to cancel it whenever you want?

[outer panther]

why would you divide by 5 just becaue you want to

well its because i want to solve for x

[outer panther]

thats how u solve quadratics

[merry imp]

am just confused how you added something that wasnt there

i know that if you divide to remove a number next to a variable, you have to divide everything in the function

[outer panther]

5x = 3

5x = 3

how do u solv ethat

you add a division by 5 that wasnt there before

it's just a tool you use to solve for x

[merry imp]

you divide the whole thing by 5

i know the division wasnt there but it doesnt matter because the whole equation is getting divided

in my cause am not seeing the whole equation get squared

your adding to a single number

[outer panther]

the same way, in $x^2 = 3$ the whole equation is getting square rooted

[twin meteor]

MWB117

[merry imp]

yea but thats because you already have x power 2

in my case we have x power 1/3

because its a square root

[outer panther]

in your case

[outer panther]

this is ur case

you have x power 2

not x power 1/3

(if thats what ur referring to)

[merry imp]

you wanted to root it, transforming it into x power 1/3

[outer panther]

if you square root the square of x, you get x

sqrt(x^2) = x (technically |x| but whatever)

[merry imp]

it still its original value because power 1/2 is less than power 2

[outer panther]

wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwhat

you multilpy 1/2 by 2

getting 1

x^1 = 1

[merry imp]

when have we ever done that multiplication

you rooted x power 2

[outer panther]

here

[merry imp]

so from x power 2 you turned it to x power 1/3

so i can just turn powers whenever i like?

[outer panther]

sqrt(x^2) = x^(2)(1/2)

any nth root is just exponentiation to the 1/n

[merry imp]

YEA BUT THE 2 CAME OUT OF NOWHERE

[outer panther]

cube root (x) = x^(1/3)

wdym bruh

what 2

[merry imp]

............

listen

x power 2 - 3 = 0

wich means x poser 2 = 0+3

x power 2 = 3

[outer panther]

100%

[merry imp]

so we root 3 and root x to get rid of the power

[outer panther]

we dont root 3

we square root

oh

i see what u mean

sorry yeah

we dont root x

we root x^2

[merry imp]

yea thats what i meant

[outer panther]

ok keep going

[merry imp]

root x power 2 =root 3

and the root removes the power

[outer panther]

nuh uh

did we not root 3?

[merry imp]

root x power 2 =root 3

[outer panther]

one more thing

when solving for quadratics and square rooting x^2 we do something else to the other side

[merry imp]

yea just like dividing when we divide everything

[outer panther]

remember from algebra?

its plus or minus

[merry imp]

in this case its plus

[outer panther]

or

which means both are valid solutions

of x^2-3

[merry imp]

root x power 2 = root 3

so x = root 3 because root 3 = root 3

[outer panther]

yes

but when solving for zeros of quadratics, its + or -

this is why

when you square the negative solution you get the same number as the square of the positive solution

[merry imp]

alright so when rooting everything in the equation to get rid of a power 2 the result is both minus and positive

[outer panther]

yes

also works with other even functions

x^4, x^6 etc

dont ever say that sqrt(x^2) = +-x

however counterintuitive it may seem after what i just showed you

but sqrt(x^2) = |x|

[merry imp]

in the end. are my points (0,4),(+root3,4),(-root3,4)?

[outer panther]

• or - is only a tool to find both solutions of a quadratic

[outer panther]

not quite

is y(sqrt3) = 4?

[merry imp]

is it??

[outer panther]

idk

lets took at the y

[merry imp]

y = 4 in the first point

[outer panther]

$y= x^4-6x^2+4$

[twin meteor]

MWB117

[outer panther]

plug in 0, sqrt(3), -sqrt(3)

those are your y values

[merry imp]

?

[vast shale]

girl u should marry him u wont find anyone as patient in ur life ever

[outer panther]

do x = 0, sqrt3, -sqrt3

[merry imp]

what are my y values

[outer panther]

idk

you tell me

[merry imp]

where do i plug thse in

if i replace the y it becomes a function

[outer panther]

x = sqrt3

x = -sqrt3

x= 0

[merry imp]

so i find the x

[outer panther]

you found the x

now you find the y

[merry imp]

and with the help of x i go back the original equation in the question

[outer panther]

yes

[merry imp]

and use that equation to find the y

[merry imp]

-5

[outer panther]

dont let the graph scare you

[merry imp]

WHAT IS THIS

[outer panther]

black graph is y

red graph is y'

do you see your points

those are your points

when the slope of y, the black line, is zero

notice how the red line touches x = zero at these values of x

[merry imp]

how is this supposed to help me understand this better. you got the points i made and dreaw a graph with them

[outer panther]

no

u cant graph a quartic with 3 points can you

[outer panther]

i just plugged in y and y' in the desmos grapher

[merry imp]

a quadratic is a drawing with 3 curves right?

ofc u need 6 points for it

[outer panther]

quarticccc

you need n points to graph a polynomial of degree n

uh

is that right

i think its n+1

cause of the term with no x

[faint quarry]

Bro what

[merry imp]

tractic

[vast shale]

he is lagging bro

[faint quarry]

How can u make a parabola with 2 points

[vast shale]

let him be

[faint quarry]

Or even 3

[outer panther]

yeah its n+1

[merry imp]

a drawing with 3 curves you need 6 points

[outer panther]

you can make a parabola with 3

[merry imp]

a drawing with 4 curves you need 8 points

i understand that

[outer panther]

wdym 3 curves???

[merry imp]

like 3 u turns

[faint quarry]

Don't worry about graphs

[outer panther]

graphs very important man

[faint quarry]

Fr I've never had to do anything beyond a fcking line XD

[vast shale]

nah man let him explain

he got this

[outer panther]

kokolofo is gonna crash out when they find out about mvt/rolfe's

[faint quarry]

Lil bit more and he'll be talking about Stoke's theorem or som

[outer panther]

understanding the graph of a function and its derivative is essential tho

[vast shale]

kokolofo u gotta get a bachelors in math

[outer panther]

it's important to avoid becoming mechanical in solving problems

[faint quarry]

And become a professor

Stg

[merry imp]

as long as i pass whatever math course i need to pass

[faint quarry]

You'd be great

[outer panther]

is this sarcasm?

[faint quarry]

No

Like actually u have too much patience

Ironically most professors don't XD

[outer panther]

kokolofo does?

[outer panther]

you'll struggle a lot more if you become mechanical imo

[vast shale]

kokolofo walking into office hrs and arguing with the professor for 3 hrs about the law of indices

[faint quarry]

Tbh the graph and sht is also somewhat personal

Som people just don't work like that XD

I hate graphs I just like numbers and letters

[outer panther]

kokolofo prolly gonna do slope fields at some point tho

and other concepts that require graphing

[faint quarry]

That's for ODEs tho

You'd have to be in STEM for that

[outer panther]

🤷

its in ap calc

[faint quarry]

Ah probably

Canadian here so I wouldn't know

[outer panther]

whats your opinion on drake

[merry imp]

ok listen i resolved it on my own and got the same answer

i just want to ask

[vast shale]

genius

right here

[merry imp]

when we split 4x=0 and xpowe2-3=0

[merry imp]

do i do this kind of splitting whenever i have a similar question?

[faint quarry]

Same reaction

[outer panther]

yes

dont do what i did tho

and split 4x(5x)

[outer panther]

whats your opinion on drake?

is he a good canadian

[faint quarry]

Just so u understand what you're doing that makes it simpler if it's easy to factorise cuz u won't be solving a quadratic

[faint quarry]

Couldn't care less ngl

[merry imp]

i think solving a quadratic is much easier than what i spend the past hour doing

[faint quarry]

Lmao

[merry imp]

anyways thanks am going to bed

[faint quarry]

Probably but he also tried to shove down your throat the graph thing XD

[merry imp]

u need any financial help dm

as a thank you

.close

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[torpid steppe]

Can someone please explain to me why on question 10, y=-1.8 and not 1.8?

[kind light]

well how did you get 1.8

[torpid steppe]

4y-3y+6 = 6y + 15
Y+6 = 6y+15
-5y = -9
5y =9
Y = 1.8

[kind light]

if you send +6 to the other side, what happens?

[torpid steppe]

-6

[kind light]

so 15-6

[torpid steppe]

Which is why I did 15-6=9 and y-6y = -5y

[kind light]

yes

-5y=9

[torpid steppe]

Ohhh thank you! I keep forgetting the -, probs need to make my handwriting bigger on those sections so I can see it!

Thanks!

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[kind light]

try writing on a bigger paper

little smudges or mismoves can cause confusion if its small

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[brittle vault]

Guys i need help

[glossy whale]

Wht

[jagged cargo]

..

[brittle vault]

Wait let me find the phot of it

[jagged cargo]

,rccw

[brittle vault]

What dows this mean

[arctic mantle]

!xy

[vocal sleet]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[brittle vault]

.close

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[jagged cargo]

wut

[arctic mantle]

he opened a new one

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[river kettle]

An investment of 4000 earns interest at a rate of r% p.a over a period of 1 year. How much more interest would the investment earn if the interest is compounded half yearly rather than yearly?

a) $10r^2
b) $r^2
c) $ r^2/10
d) $ r^2/100

[river kettle]

dont know where to begin

.close

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[tranquil dome]

@river kettle still need help with this question?

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[unkempt gate]

How to find all integers $n$ such that $n^4-3n^3-n^2+4n+1$ is a multiple of 7

[twin meteor]

babario

[tranquil dome]

calculate for each mod 7 from n 0 to 7 consecutively

[vocal sleet]

@unkempt gate Has your question been resolved?

[unkempt gate]

No way that includes everything

<@&286206848099549185>

[hybrid flicker]

it does

if n = 0 mod 7, then n^4 = 0^4 mod 7, etc...

you will cover all cases

and notice that if you replace n by n+(some multiple of 7)

you will have the same remainder mod 7

so all that's needed is to check numbers 0 through 6 (since 7 = 0 + 7)

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[woven meteor]

Given pyramid S.ABC with SA = right angle with (ABC), ABC is an equilateral triangle with side a, center G. Calculate the angle between the two vectors SG and AB, round the result to the nearest unit.

[warped prairie]

Say ABC lies in the XY plane

S is some point on the Z axis

A is the origin

Say B is (a,0,0) then C will be

a/2, root3 a/2

Center G, as in?

I assume centroid

Then it's a/2, one third √3a/2

Say S is on (0,0,s)

So SG is (a/2, √3a/6, -s)

And AB is (a,0,0)

Dot product is a²/2

Now find the norms of the two vectors

And use the definition of dot product

Answer will be in terms of s and a

[woven meteor]

😢

💀 how did u know all of this

[warped prairie]

Coordinate geometry

Did u understand

What I did

[woven meteor]

saying yes is a lie 💀

[warped prairie]

I basically plotted the pyramid

Onto the 3 dimensional coordinate system

Found the two vectors in Cartesian form

Found their dot product, their magnitudes, and then therefore the angle between them

The neat thing is that SA is right angles with the plane of the equilateral triangle

So it fits nicely on the Z axis if we put the triangle on the XY plane

[woven meteor]

alr

[warped prairie]

Sooo

U got it?

[woven meteor]

nah bro im trying to learn what u said

to understand it

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[fast warren]

cross product

can anyone tell me the last line why 2 unit vector multiply tgt = 1 unit vector

[warped prairie]

Well that's only true if the "multiplication" here is a cross product AND the two unit vectors are perpendicular to each other

[fast warren]

isnt cross product of 2 same vector =0

[warped prairie]

Yes if it's the same vector

It's another unit vectors ONLY if they are orthogonal to each other

And if it's parallel then it's the zero vector

[warped prairie]

Lambda here is a scalar right

[fast warren]

yes

so meaning this unit vector direction is a "new" unit vector direction

[warped prairie]

So where did u get two n hats here

[fast warren]

n hat = n /magnitude n

[warped prairie]

Dot product of two vectors always gives a scalar

[fast warren]

actually what does dot product mean

wait lemme draw

[warped prairie]

After u did the dot product with n, everything is a scalar

There is no vector anywhere here

a2 DOT n is also a scalar

[warped prairie]

Ur dividing the dot product with a scalar and using the properties of ordinary multiplication on jt

Understand that dot product is a special operation done on vectors

U can't treat it like ordinary multiplication of scalara

Scalars

[fast warren]

i searched google and everything all they kept saying is a.b is like how close a is going to b

like how does that makes sense

[warped prairie]

It's the length of projection of a on b

[warped prairie]

Here |a|cos theta is the dot product

[fast warren]

then why multiply with magnitdue of b

since a.b = abcos theta

[vast shale]

with that they mean the shadow that vector a casts in the direction of unitary vector b

[fast warren]

why does a.b=0 means perpendicular

[vast shale]

90 deg --> cos90 --> RHS is 0

[fast warren]

yea if i use formula

but the concept behind it

[vast shale]

there are multiple approaches to it

give me one sec

[fast warren]

wtf

[vast shale]

i tried to give u the reason without using the ugly formula

[fast warren]

is it this?

[vast shale]

no

without cosine

i used AB = a1b1 + a2b2 + a3b3 + ... as the definition for dot product

[fast warren]

im gonna watch more vids to understand

thx for help

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[raw lynx]

in this why were selective terms only expanded

Please 😭

[bronze osprey]

wdym?

ah cause you want $\sin^2 \theta \cos^2 x$ to cancel

[twin meteor]

south's secret twin brother

[bronze osprey]

rewriting every single bracket using the Pythagorean identity would be a huge mess

[raw lynx]

But how would i know 😭

I mean

[bronze osprey]

that's why you look at worked examples I guess

there's not really a way to know otherwise

[raw lynx]

Ok so i basically take into account that RHS part of my equation real part, has cos inverse and root of sin theta like that

i was just concerned that if there was any such specfic method that i was not aware of 💀😭

[raw lynx]

@bronze osprey sorry for bothering you again except for this, there's no such purpose right its just pure manipulation??

[bronze osprey]

yep

[raw lynx]

thanks

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[indigo olive]

can someone help

[indigo olive]

but asap

[oak magnet]

just send your problem

[oak magnet]

,rotate

[kind light]

test?

[indigo olive]

no

homework

[twin meteor]

Baby Einstein

[grand linden]

Is this the solution?

[finite mist]

Shouldn't we guild them through it and not give out the answer?

[indigo olive]

i dont think thats the right answer anyways

[finite mist]

Is "a" known? Like is it a value?

[oak magnet]

just isolate t with simple equation manipulation

[indigo olive]

look

theres this question thats similar

[grand linden]

Sure I did well

$a=\dfrac{27,t}{25}+1052$

[indigo olive]

but i solved it

[twin meteor]

Baby Einstein

[grand linden]

Is this the original equation?

[indigo olive]

this is a similar question and i solved it

[twin meteor]

Baby Einstein

[indigo olive]

i need to solve for t so it should be “t=the answer”

[grand linden]

I'm saying the initial text

[finite mist]

Then baby einstein kinda give u the answer lol

[grand linden]

a=1052+1.08t?

[finite mist]

Assume his manipulation is correct

[indigo olive]

yes

[grand linden]

Ok

[indigo olive]

and i should find “t”

[lethal heart]

Hi

Looks easy

[grand linden]

1.08 = 27/25

so rewrite it like this

[candid wraith]

system of equations using substitution method

[lethal heart]

$t=a\cdot\frac{25}{27}-\frac{26300}{27}$

[twin meteor]

Baby Einstein

Baby Einstein

$t=\dfrac{25\,a-26300}{27}$

[candid wraith]

3x -y=4
x=4y-17

[twin meteor]

crazytime

[lethal heart]

👍

[indigo olive]

never mind i solved it

look

[candid wraith]

help

[grand linden]

!occupied

[vocal sleet]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[grand linden]

@candid wraith This room is already occupied

[indigo olive]

ok thanks

[candid wraith]

oh

[indigo olive]

bye

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@indigo olive Has your question been resolved?

[candid wraith]

help

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[sage monolith]

The author is trying to formally calculate a lower bound on Pr(U | G & L & B). I'm having trouble following his formal derivation.

What assumptions is he using to calculate this lower bound?

[spiral turtle]

Frankly, it looks like a "rectal figure."

[sage monolith]

huh?

[spiral turtle]

He pulled it out of his ass

[sage monolith]

I'm asking about his formal derivation

Does it logically follow?

If you're here just to make rude, cheap zingers, then someone else can provide helpful input.

[spiral turtle]

Just busy, I'll circle back to this

[vocal sleet]

@sage monolith Has your question been resolved?

[vocal sleet]

@sage monolith Has your question been resolved?

[spiral turtle]

Specifically, the rectal figure I was referring to was 10^136

So definition of conditional probability is:

[
P(A \mid B) = \frac{P(AB)}{P(B)}
]

[twin meteor]

OmnipotentEntity

[spiral turtle]

For this example $G = \sum_i G_i$

[twin meteor]

OmnipotentEntity

[spiral turtle]

In other words, the assumption is the reasons are all mutually exclusive

We can rewrite the summation equation in terms of the definition to find:

\begin{align*}
P(U \mid GLB) &= \sum_i P(U \mid G_iLB) P(G_i \mid GLB) \
&= \sum_i \frac{P(UG_iLB)}{P(G_iLB)} \frac{P(G_iGLB)}{P(GLB)} \
&= \sum_i \frac{P(UG_iLB)}{P(G_iLB)} \frac{P(G_iLB)}{P(GLB)} \
&= \sum_i \frac{P(UG_iLB)}{P(GLB)} \
&= \frac1{P(GLB)} \sum_i P(UG_iLB) \
&= \frac{P(UGLB)}{P(GLB)}
\end{align*}

So the identity holds at least

But that being said

The way of choosing the priors of G_i is where ideology gets smuggled in

[uneven flicker]

smuggled lmao

[spiral turtle]

@sage monolith hope this helps

[twin meteor]

OmnipotentEntity

[spiral turtle]

Rereading it. If I follow the thrust of the argument, perhaps some previous probability calculation gave the 10^136 value. Or rather a 10^-136. And the author is using that result.

It would be far more interesting to analyze this claim, as it is likely to be incorrect.

[vocal sleet]

@sage monolith Has your question been resolved?

[sage monolith]

dope, will take a look

[sage monolith]

from what i found, he's deriving it like this.
Pr(U | GLB) = Pr(G1 | GLB) ≥ 1 / n
n < 10^136
=> Pr(U | GLB) > 1 / 10^136

[spiral turtle]

So something to keep in mind is that the G_i are mutually exclusive. Which means if a hypothetical God can act with more than one reason simultaneously, which seems like a reasonable thing, then each of the G_i is a member of the power set of possible motivations.

10^136 ≈ 2^452

So if there are only 452 possible motivations, then the size of G_i is comparable to 10^136 (because the size of a power set of a set with size d is 2^d)

But again 10^136 seems like an oddly specific number. And if it's not harkening back to a previous argument, it's probably a meaningless large number that the author pulled out of thin air to attempt to bamboozle his audience.

[sage monolith]

Eh no, that would be extremely uncharitable. The 10^136 figure is from a prior argument. It's the number he gets from calculating the probability of life-permitting fundamental-constants given a uniform distribution over the possible values the fundamental physical constants could take.

The surrounding context is not relevant to my question. However, if you are curious, you can skim here: https://philarchive.org/archive/BARARL-3

[spiral turtle]

@sage monolith did you still have a question?

It isn't clear to me if you do or not

[sage monolith]

Yes. My question is what assumptiosn the author is using to formally derive his estimate.

As far as I'm aware, we now know he's assuming the following:

[spiral turtle]

It's not clear to me from the text excerpt what B represents.

[sage monolith]

p(U | GLB) = p(U|G1LB)p(G1|GLB) + ∑n i=2 p(U|GiLB)p(Gi|GLB)
0 = ∑n i=2 p(U|GiLB)p(Gi|GLB)
p(U|G1LB) = 1
p(U | GLB) = p(G1|GLB) ≥ 1 / n
n < 10^136
=> Pr(U | GLB) > 1 / 10^136

Does that look correct to you?

(Sorry idk how to write latex.)