help-36

[serene rain]

and it has parabolas and stuff

[stone wagon]

C is the easiest to find: plug in x=0

the value you get for y is C

[serene rain]

alr lemme try solving these rq

alr so

remove the x^2 and 3x as they both end up to 0

and y = -4

so C

(0,-4)

now what if i rearrange the equation for x

since i know the value of Y

x^2 - 3x = 0

[stone wagon]

not sure what happened here

[serene rain]

so uh basically

moved the -4

became a +4

[stone wagon]

A and B are quadratic formula/whatever other way you solve quadratics

[serene rain]

ohh

i moved the 4 to the other side

and got rid of it

as y = -4

4 -4 = 0

should i bring the -4 from y over to make it 8?

then solve as you said quadratic form?

[stone wagon]

i have no clue what you are doing

you have that y=0 for A and B

so do x^2 + 3x - 4 = 0

and apply the quadratic to that

that's it

[serene rain]

oh

yeah mb my brain aint braining

lemme solve this rq quad form

-4 and 1

so

(sorry took a bit, got off track a bit)

so (-4,0) for A

and

(1,0) for B

[final saddle]

@serene rain Has your question been resolved?

[serene rain]

(-2/3,-4) is my answer

perpendicular means the slope changes so

y = -3x+1

plugged in first the x to solve for y

then vise versa

correct?

[final saddle]

@serene rain Has your question been resolved?

[pine forge]

yep

actually, solve for y in terms of x in the first equation. Plug into the second and solve for x. Once you have your x values you can solve for y

This is how you solve simultaneous equations

[serene rain]

Alright sounds good

not even joking i forgot how to do these bruv

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@serene rain Has your question been resolved?

[wary egret]

Which one

[final saddle]

@serene rain Has your question been resolved?

[ionic narwhal]

Which one

Cause you just factor and the multiply

I mean subtract

Like for a you can factor the denominator to (x+3)(x+2)

Theb multiply the right side by x + 3

And just x squared minus three subtracting x plus 3

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[flat ravine]

Are two lines/rays perpendicular when their orientation is a 90 degree difference from eachother

[flat ravine]

And do they have to form a vertex

[dense coral]

that is correct

[flat ravine]

Thanks

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[minor yoke]

Can someone explain how to solve this??

[minor yoke]

it says i have to write the slope intercept form of the equation of each line given the slope and y-intercept

[mellow axle]

y=mx + b is what slope intercept form is

where m is the slope and b is the y-intercept

[minor yoke]

Oh

wait

so its y=8/5x-5 ??

Yes

Ok tyy

.closwe

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[surreal kernel]

I know the statement is wrong, but i don't know how to justify it

[surreal kernel]

is because is addition and not multiplication, but i don't know if that is a good enough answer

[craggy plank]

Square both side

justified ✅

[surreal kernel]

thanks

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[manic echo]

how can i find the area of an elliptical sector

[tranquil pine]

yeah you can

is this the equation of ellipse ?

[manic echo]

can i parametrise the ellipse then express theta in terms of t?

[manic echo]

yeah

[tranquil pine]

equation of line or smth else ?

[tranquil pine]

which theta ?

[manic echo]

the angle from the x axis to the line that makes the sector?

https://math.stackexchange.com/questions/493104/evaluating-int-ab-frac12-r2-mathrm-d-theta-to-find-the-area-of-an-ellips

i think thats what they did

[tranquil pine]

pi*ab

i see

[manic echo]

?

[manic echo]

that is the area of a normal ellipse

[tranquil pine]

yeah i know that

yes you can try this

[manic echo]

actually i think its easier to express it as a polar equation

[tranquil pine]

since the equation are bad too,

[manic echo]

then integrate it using the angle as the bounds

[tranquil pine]

true

[manic echo]

ill try that

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[hallow night]

So I’m finding the axis of symmetry for f(X)=2x^2-4x and when I plug it in to the equation to make -4/2(2) I get -1. But I’m supposed to get positive 1 on the answer key. This happened for a different problem too I was doing. Am I doing something wrong?

[amber holly]

Yeah, you are supposed to flip the sign

For the record, the axis of symmetry of y = ax^2 + bx + c with a nonzero is x = -b/(2a)

[hallow night]

Ohh I see

Thx

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[warm python]

so I think I'm having trouble solving this assuming the field in R

*is

so {0} is an element of $R^2 \cap C^2$

[soft zealot]

ƒ(Why am. I here)=I don't Know

[warm python]

if $v,w \in C^2 \implies v,w \in R^2$

[soft zealot]

ƒ(Why am. I here)=I don't Know

[warm python]

so it's closed under addition

and multiplication too

am I doing something wrong

[tropic cosmos]

are you sure it is closed under scalar multiplication?

[warm python]

I think it is

[tropic cosmos]

Ok, if I have some scalar that is complex, will that change your answer?

[warm python]

no

[tropic cosmos]

why?

[warm python]

it will still belong to the space

but not the sub-space

the field I'm assuming is R though

so won't the scalar be from R

[tropic cosmos]

if the field is R then yes... but I would think the field here should be C

because we are talking about subspace of the C

[warm python]

oh

okay

if the field in C, then won't it still be closed

the element will still belong to $\C^2$

[soft zealot]

ƒ(Why am. I here)=lin-alg

[tropic cosmos]

no... because how can you get i(0,1) to be in R^2 (i.e., your R^2 would not be a vector space)

[warm python]

ooh

so it isn't a subspace

[tropic cosmos]

yes

[warm python]

I see, thanks

how do I determine the field

if it's not mentioned

[trail mango]

you cannot

[tropic cosmos]

depends...

it is just your assumption mostly

[warm python]

in that case. it's easier to work with a field on R IMO

gives a neater result too

[tropic cosmos]

true... but sometimes it is easier to work in C because to disprove something is easier than to prove something

[warm python]

ok, thanks

[warm python]

got it , thanks

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[warm python]

.reopen

[final saddle]

✅

[warm python]

I'm just working out the entirety of the exercies here, as I don't have a answer key

so {0} is an element as (0,0,0) satisfies the given conditions

[ocean lintel]

a.0) give a more direct closed form expression of that set
a.1) deduce whether it's a vector space

[warm python]

what?

sorry, I don't follow

[ocean lintel]

Simplify their definition

[warm python]

it's the set of vectors such that $a^3-b^3=0$

[soft zealot]

ƒ(Why am. I here)=lin-alg

[warm python]

for the field $\R$

[tiny gorge]

in the reals, a^3 = b^3 if and only if....?

[soft zealot]

ƒ(Why am. I here)=lin-alg

[warm python]

a=b

[tiny gorge]

yep

[warm python]

oh

so $a-b=0$ and $c-d=0$

[soft zealot]

ƒ(Why am. I here)=lin-alg

[warm python]

wait

no

let (a,b,c)= v

and (d,e,f)=u

then $(a+d,b+e,c+f)=v+u$

[tiny gorge]

i'm not sure what you're doing

basically (a) reduces to asking whether the set
{(a,b,c) such that a = b}
is a subspace

[soft zealot]

ƒ(Why am. I here)=lin-alg

[warm python]

checking closure under addition

[tiny gorge]

you have to use the condition

a=b and d=e

[warm python]

yeah, I will now

[tiny gorge]

ah ok

[warm python]

$(a+d,a+d,c+f)$

[soft zealot]

ƒ(Why am. I here)=lin-alg

[warm python]

which satisfies teh given condition

[tiny gorge]

yea

[warm python]

so it's closed under addition

[tiny gorge]

right

[warm python]

closure under multiplication can be shown similarly

so it's a subspace of $\R^3$

[soft zealot]

ƒ(Why am. I here)=lin-alg

[warm python]

(b) is slightly more tricky

as $a^3= b^3 \centernot a=b$

[tiny gorge]

yea just be sure to also check that it contains the origin (it does)

[warm python]

That's the first thing I did

[tiny gorge]

ah ok good

[soft zealot]

ƒ(Why am. I here)=lin-alg
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tiny gorge]

and yes for (b) the key is that a^3 = b^3 doesn't imply a = b, as you said

every nonzero complex number has three cube roots

[warm python]

yeah

which means that $a+d \neq b+e$

[soft zealot]

ƒ(Why am. I here)=lin-alg

[warm python]

necessarily

[tiny gorge]

right, you can find a simple example

[warm python]

say $\omega, \omega^2, 1$

[soft zealot]

ƒ(Why am. I here)=lin-alg

[warm python]

the cube roots of unity

[tiny gorge]

yeah

[warm python]

so it isn't a subspace

thanks

[tiny gorge]

sure

[warm python]

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[sonic crystal]

how do i do this?

[magic sparrow]

I would start by finding the path length difference between the two waves at R

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[ancient ginkgo]

are there any non-linear transformations that satisfy only additivity or only homogeneity?

[ancient ginkgo]

all non-linear transformations i can think of satisfy neither

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@ancient ginkgo Has your question been resolved?

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@ancient ginkgo Has your question been resolved?

[atomic moon]

found an article talking about this, hope it can help

[rain lichen]

$f(x, y) = (\sqrt[3]{x^3 + y^3}, \sqrt[3]{x^3 + y^3})$

[soft zealot]

risujemmaaja

[rain lichen]

i think this works for satisfying homogeneity but not additivity

[ancient ginkgo]

thank you!

[ancient ginkgo]

oh yea i just checked and it seems to work

thats crazy

thanks

[rain lichen]

np

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[smoky bane]

Hello
Would it be subtraction because I would be subtracting 8 from both sides when I solve the problem?

[forest garnet]

yeah

[smoky bane]

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[peak kernel]

how do i do this question? No linear combination of the three vectors in U make it = 0

[main prairie]

0,0,2

0,0,1

0,0,3

0,0,11111234556

[peak kernel]

?

[main prairie]

You need alpha,beta,gaama that makes equation 0 right

[peak kernel]

yes

none of those are correct

[main prairie]

1,0,0

2,0,0

[peak kernel]

oh wait

shit yeah im stupid

[main prairie]

120304958827171,0,0

Math is fun

[peak kernel]

lol

ty

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https://tenor.com/view/top-gun-burak-başdüzen-tayfun-yıldırım-gif-26946661

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[rocky drum]

how am i suppoed to find this

[clear moon]

RQS and 115 are adjacent angles on a line

so the angles are supplementary

[rocky drum]

mhm

so how do i get the answer

[clear moon]

do you know what supplementary angles are..

[rocky drum]

angles that add up to 180

yea

[clear moon]

do you still need to know how to get the answer?

[rocky drum]

so ur saying its 180?

[clear moon]

RQS and 115 are supplementary

you just told me what supplementary meant

[rocky drum]

so 65

[clear moon]

sounds like you can set up and equation to solve for RQS

yes

[rocky drum]

alr thanks

ur a big help

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[patent pike]

idk where to begin. please explain how you got the answer too

[patent pike]

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[rustic sinew]

Pythagorean theorem btw

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[chilly beacon]

they said b is wrong

[chilly beacon]

,rotate

[chilly beacon]

here is my work

idk if it will help

i just don’t know how to get to find b

[dire solar]

i think they are asking the value of f at the local maxima

basically, what is the maximum value this quadratic equation can take

[chilly beacon]

like the y value?

i did that thro chatgpt made sure it was right and got 7/4

but it still said it was wrong

but i just put 7/4

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[chilly beacon]

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[cosmic forge]

It probably wants a simplified answer.

[cosmic forge]

!nogpt

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[peak kernel]

Why is 8sinh(u) wrong?

[peak kernel]

it says the correct answers are 8cosh(u) and 8sec(theta) but why is 8sinh(u) incorrect?

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[fathom stream]

For conditional mean this is what I did:

[fathom stream]

P(X_1 = 1) = p(1, 1) + p(1, 2) = 3/18 + 5/18 = 8/18 = 4/9 right

and then

E[X_2 | X_1 = 1] = 1 * p(1, 1)/(4/9) + 2 * p(1, 2) / (4/9)

right?

which should = 13/8

but online someone posted this as the solution

what m I doing wrong

and for E[X_2 | X_1 = 2]

P(X_1 = 2) = p(2, 1) + p(2, 2) = 4/18 + 6/18 = 5/9

so

E[X_2 | X_1 = 2] = 1 * p(2, 1)/(5/9) + 2 * p(2, 2) / (5/9) = 8/5

and we can see that

E[X_2^2 | X_1 = 1] = 1 * p(1, 1)/(4/9) + 4 * p(1, 2) / (4/9) = 23/8

so var(X_2 | X_1 = 1) = 23/8 - (13/8)^2

[versed crater]

this is so

[fathom stream]

ngl I think the person who posted that solution online is trolling or something

it doesnt seem right

[versed crater]

ok let's see

find $\mathbb E[X_2 | X_1 \in {1, 2}]$

[soft zealot]

Frosst

[fathom stream]

wait shouldnt I find it for each? like

E[X_2 | X_1 = 1] and E[X_2 | X_1 = 2] seperately?

[versed crater]

yeah but if you think about it, the expectation of X_2 given X_1 is 1 or 2

clearly should depend on the probability that X_1 is 1 or is 2

[fathom stream]

mhm so will the formula be different thn what I did?

[versed crater]

cos if X_1 = 1 is very likely compared to 2, then the E[X_2|X_1 = 1] is "worth more"

it sounds like $\mathbb E[X_2 | X_1 \in {1, 2}] = P(X_1 = 1)\mathbb E[X_2|X_1 = 1] + P(X_1 = 2)\mathbb E[X_2|X_1 = 2]$

[soft zealot]

Frosst

[fathom stream]

[versed crater]

this sounds very reasonable to me i think

[fathom stream]

wait shit

I copy pasted

2 of the same ones

lemme redo

(4/9) * (1 * p(1, 1)/(4/9) + 2 * p(1, 2)/(4/9)) + (5/9) * (1 * p(2, 1)/(5/9) + 2 * p(2, 2)/(5/9)) = (4/9 * 13/8) + (5/9 * 8/5) = 1.611

[versed crater]

put ` and ` between your texts

looks like this

how are you getting 5/9

[fathom stream]

P(X_1 = 2) = p(2, 1) + p(2, 2) = 4/18 + 6/18 = 5/9

[versed crater]

that's right ok

[fathom stream]

all of it?

[versed crater]

just that part it's hard to read

[fathom stream]

are u getting the same answer as me

1.611

[versed crater]

my question is why does it just c ancel

[fathom stream]

what cancels

[versed crater]

ok but X_1 can only either be 1 or 2

that's the only things it can be

[fathom stream]

Im so confused rn

[versed crater]

think about htis

$\mathbb E[X_2|X_1 = {1, 2}]$

[soft zealot]

Frosst

[fathom stream]

right

[versed crater]

this is how much on average is X_2, given X_1 is either 1 or 2

but look at the support

X_1 can only ever be 1 or 2

[fathom stream]

right

Idgi

[versed crater]

so if i tell you X_1 is either 1 or 2

that's like saying nothing

[fathom stream]

should we have done it seperately?

[versed crater]

like imagine a coin is coloured red on heads and blue on tails

[fathom stream]

right

[versed crater]

and X_2 tells you the colour

and X_1 tells you if it's head or tails

we flip the coin

i tell you "the coin landed on either heads or tails"

well no shit sherlock

[fathom stream]

😭

[versed crater]

so X_1 really doesn't tell us anything at all

[fathom stream]

I think the question wanted me to find E[X_2 | X_1 = 1] and E[X_2 | X_1 = 2]

[versed crater]

that should be easy

but E[X_2| X_1 = {1, 2}] = E[X_2]

[fathom stream]

https://www.assignmentexpert.com/homework-answers/mathematics/statistics-and-probability/question-242557

came across another solution

[versed crater]

why the hell are there squares

[fathom stream]

I think they made a typo doe

should have been

3/18 and 5/18

right

[fathom stream]

wym

the table?

[fathom stream]

oh so they can find the variance later ig

[fathom stream]

thats what I was trynna do here

[versed crater]

oh variance

oh that makes sense

[fathom stream]

so I did it correctly?

earlier

[versed crater]

yeah

i think it's right

E[X_2] = 1*(1+2)/18 + 2*(1+4)/18 + 1*(2+2)/18 + 2*(2+4)/18 = 1.61

[fathom stream]

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[charred raven]

Need help with question b

Did this working but I think I went wrong somewhere

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[charred raven]

<@&286206848099549185>

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[jaunty sluice]

help

[violet stream]

did you use chain rule?

[jaunty sluice]

where

i dont think so

i dont know how to get vector u(t)

[violet stream]

you need to calculate the derivative of f(t)

[candid hull]

you don't need u(t) for all t

if they gave you u(3) and u'(3) it's cause they're enough to answer the problem

[jaunty sluice]

oh

[candid hull]

u(t) . v(t), how do you differentiate a dot product ?

[jaunty sluice]

am i able to do the derivative of vector u(3) dot the derivative of vector v(3)

[candid hull]

no

[jaunty sluice]

this?

[candid hull]

it works like the product rule

yes

[jaunty sluice]

so

[jaunty sluice]

i can still use u(3) and v(3) as long as i use this right

[candid hull]

sure

[jaunty sluice]

okay

[jaunty sluice]

i got 8t^3 + 7t -19

do i need to plug in 3 into those t variabkles?

im confused because i already used the u(3) and v(3) to differentiate

oh nvm

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[warm hemlock]

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[smoky bane]

Hello
How do I solve this? First step is to find X right?
I did 36x-1+134x=169 but that did not work..

[smoky bane]

And this is my weird drawing idk if it’s wrong 🥲

[supple copper]

what was your x value?

[smoky bane]

Like 0.97 or smt

[supple copper]

can you show your work?

[smoky bane]

Yes

Oh

Nvm hahah

I got

1

[supple copper]

[smoky bane]

Thxx

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[midnight warren]

how could I use a ti-84 plus CE to find one zero of this function: f(x)=5cosx+2/5x

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@midnight warren Has your question been resolved?

[dreamy iron]

put it in a graph and just go on calc - zeros

i have a ti 84 really old but thats what you do

you might need to adjust the scale

but thats just it

[midnight warren]

when I plug in 5cos(x)+(2/5)x it's giving me a straight line

my window is xmin=-20 xmax=20
ymin=-20
ymax=20

I know it's supposed to be a cos function so idk what I'm doing wrong

when I graph it in desmos it's just fine

[dreamy iron]

try

xmin = -6
xmax = 6
ymin = -8
ymax = 6

[midnight warren]

no change it's still linear for some reason

[dreamy iron]

how does it look in the calculator

[midnight warren]

similar to y/x

[dreamy iron]

are you sure you inputed everything correctly

[midnight warren]

trying to put a pic in here

I can't find this text channel on my phone for some reason??

[dreamy iron]

check if thats the right plot and everything

if everything fails try like restarting the calc

i gtg now tho

[midnight warren]

how do I check if that's the right plot?

I do not understand

[dreamy iron]

that calculator has 3 different plots

[midnight warren]

I see them at the top

[dreamy iron]

just check if all the other ones are empty

[midnight warren]

lol how?

[dreamy iron]

i gtg tho

[midnight warren]

ok

[dreamy iron]

good luck and im sorry

[midnight warren]

all good

🤦‍♂️ I was in degree mode

problem solved

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[fathom zinc]

what is the difference between n-dim real coordinate space and n-dim euclidian space? i want to be sure my notion is correct.

[blissful meadow]

I'll look it up again, but iirc Euclidean just presupposes the Euclidean dot product, whereas you can have spaces of R^n with other inner products defined

[hybrid heath]

Depends on how you define them

[fathom zinc]

i assume you are using the distinctly appearing terms "dot product" and "inner product" to coincide each other while denoting the same definition

thank you though

[blissful meadow]

I mean the dot product as the standard inner product

[fathom zinc]

so essentially; in 5 year old terms, you meant to say dot product twice in the sentence

[fathom zinc]

can you elaborate please?

im glad there is more than one person in this server.

[blissful meadow]

Sort of. Just that the Euclidean space has the specific inner product we usually call the "dot product", but you can have the same underlying vector space with a different inner product. But yeah, you can think of it as meaning other dot products.

[fathom zinc]

i see.

[fathom zinc]

and as an informal notion in differentiating the two, would it be that euclidian space denotes physical, "space"; and real coordinate space is a way of "graphing" to represent positions of vectors (n-tuple cartesian coordinates) on thet eucildian space?

[hybrid heath]

Euclidean space doesn't really denote physical space. We can use it to represent physical space in a non relativistic context, but that's not it's sole purpose

[final saddle]

@fathom zinc Has your question been resolved?

[blissful meadow]

That can work if it makes sense to you.

An inner product space is a vector space with a choice of an inner product, much like you choose the field over which your vector space is defined.
The Euclidean space is physical in origin, as it comes from Euclid's postulates, used to describe the only geometry that made sense at the time. That is, a geometry where we can measure angles and distances as we could in the physical world, so flat space without weird curvature.
In this sense, the Euclidean space is an inner product space where we chose the dot product (multiply corresponding coordinates together and add everything) for our inner product.

On the other hand, the space R^n is a bare vector space : we haven't made the choice of inner product yet, but it could be any, not only the dot product as you learned.

While saying that the real coordinate space is a way of graphing vectors of the Euclidean space isn't false per se, I do feel like it misplaces the reason. We can represent positions of vectors in Euclidean space as n-tuples because the Euclidean space is constructed from the vector space R^n, on which we added a notion of distance through the dot product.

[fathom zinc]

it would be extra helpful if you'd attach what your notion of the Euclidian space is, so I can have a reference!

[fathom zinc]

I see!

although it may make sense to me, I don't think it will work

given that there are opposing views of 'abstract' euclidian space

i seek a reliable definition.

[fathom zinc]

although I am familiar with the ambiguity of the terms regarding informality and formality

[hybrid heath]

Euclidean space is just $\bR^n$ with dot product as its inner product.

[soft zealot]

SWR

[fathom zinc]

okay, sure. Thank you!!

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[elfin quartz]

Can someone help me with part B? What do I say for it?

[violet stream]

draw all points on the graph

[elfin quartz]

Yeah I have

[violet stream]

do you see a correlation?

how strong it is? Are there outliers?

[elfin quartz]

Is there a right or wrong answer for these questions?

Like just by looking at it

Because in part d, it asked to calculate the correlation coefficient then compare the answer to part b

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[elfin quartz]

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[merry lodge]

how do i do any of this question

[merry lodge]

i only know how part A and its bc the rate < 1

other than that idk

[dusky lily]

ok so lets start with part (b)

when they say initial temperature

what does that suggest

[merry lodge]

temperature before it starts to decay

?

[dusky lily]

yes, and you know T is a function of time t

as time increases, the temperature decreases

as the value of t increases, the value of T decreases

but where does 't' start from

[merry lodge]

69 i think

[dusky lily]

nope t itself starts from 0

at the 0th second, just when the coffee has been served

then 1 second later, the temperature is lesser

a 1000 seconds later your coffee is even colder

[merry lodge]

so how do i do the rest of the question

[dusky lily]

well for (b) you calculate the value of T when t=0

"initially" means t=0

[merry lodge]

isnt the number before the 1/2 always the initial value tho

[dusky lily]

nope

the initial value is when t=0 (or whatever the variable in the function is)

T is the temperature as they say. T(t) means the temperature changes with time 't'.

thats how functions work

[merry lodge]

so answer to b is 90

[dusky lily]

yep

[merry lodge]

how do i graph this

[dusky lily]

now for graphing it
do you know what the graph of a^x looks like? (a being any number)

like the general shape of the graph

[merry lodge]

yea

[dusky lily]

yep. this is the case when a>1

so like 2^x
it will increase exponentially as x increases

but what if a<1

like it is in your case

(1/2)^x

or (1/2)^t whatever, variable doesnt matter

[merry lodge]

isnt it like thsi

[dusky lily]

yep perfect

now all you gotta do is add some details

such as where does the sketch of the function intercept the y-axis

(you calculated this in part (b) )

[merry lodge]

90

[dusky lily]

yep so when 't' is the 0th minute, the Temperature is 90 degrees

in other words

when x=0, y = 90

so you mark (0,90) on the point where the curve intercepts the y axis

[merry lodge]

ok but what else do i do

[dusky lily]

you also gotta make sure your curve isnt going to the left of the y-axis

since that would mean x<0

or time< 0

and time cant be negative

so instead of going all the way, your graph ends at x=0

[merry lodge]

ok but how do i graph the rest of it

[dusky lily]

you have a curve so far, you have the point where it intersects the y axis

and youve made sure time isnt going negative

thats your curve

if you want you can add one last detail:
as "t" keeps on increasing.. there will eventually be a time where t is so large that 69(1/2)^(t/30) will become so incredible small that your graph will turn into a straight line at y=21

[dusky lily]

as you can see here, at the end, the graph is almost a straight line

so you could draw out a dashed line indicating that at any point, the temperature of the coffee doesnt go below 21 degrees

thats the entire graph

you dont need to make the axis with 0, 50,100,200 etc as long as you mark (0,90) on the graph

and if needed, (0,21) indicating where the graph becomes a constant

[merry lodge]

is there not some table of values or something tha ti can follow

to graph itaccurately

[dusky lily]

you do that when you dont know what the shape of the graph looks like

but since you already know that

i mean you could use the table of values method if you want to make the "shape of the curve" pass through all points it should

[merry lodge]

is there a parent function table of values for exponential functions i can follow

[dusky lily]

you take different values of "t", and you find the corresponding value of "T" for that specific "t"
then you mark (t,T) on the graph

[dusky lily]

theres no universal table of values

you make the table of values

in this particular question, the table consists of some test values for t, and the corresponding values of T

[dusky lily]

you mark a couple sets of points (t,T) on the graph and connect them

but as i said, you dont need to do that if you mention (0,90) on the graph, and that y=21 is the least it goes by marking (0,21) on the graph as well

thats what brings the accuracy

[merry lodge]

ok

[dusky lily]

(d) should be pretty easy given what youve learnt so far

[merry lodge]

mb for not saying anything, it is easy

ty for the help

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[slate meteor]

I have to find the determinant of the second matrix. Given the result of the first matrix.

This has to be done by applying determinant properties.

But I don't know how to proceed any further.

[barren hound]

try expanding along the first column instead of the first row

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@slate meteor Has your question been resolved?

[slate meteor]

I did both

And by expanding the first column I got a determinant with 2 equal rows, so that's 0

[barren hound]

oh I see

so is your question how to take the determinant of a 2x2 matrix?

[slate meteor]

Not really, i just don't know how to proceed.

I need to get something out of the determinant of the 3x3 matrix that I can compare to the 2x2 matrix determinant.

I will try to expand the 2x2 matrix determinant and check if I can get smth

Ok, I believe now I can do something

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[slate meteor]

It seems correct to me, but I don't know since I don't have the correct answer to check.

.reopen

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✅

[slate meteor]

Well technically if I pick some N for the a,b,c,d I could check it by myself right?

mmm nope

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[slate meteor]

Yesn't

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[snow karma]

does it matter how i write the solutions?

[snow karma]

as in, for the case gama is not equal 0, not equal 1, can i just write

or can i also write a row of the solutions?

as in ${ (-3\gamma+2/\gamma, \gamma, \gamma) } $

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@snow karma Has your question been resolved?

[inland smelt]

the convention is to write it as a column vector. If you want to express it as a row vector you can use the transpose operation, like $$[-3\lambda + \frac{2}{\lambda} ;;;; \lambda ;;;; \lambda]^T$$

[soft zealot]

Crystopher

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[cobalt vigil]

property:
If two intersecting lines of a plane are parallel to another plane, then the planes are parallel.

[cobalt vigil]

I don't know when to use n , c or element of symbol

I mean I don't understand how to put the sentence (the property) in symbols

[forest ember]

What exactly is your question?

[cobalt vigil]

How do I see from the text I have to use these symbols?

[forest ember]

Do you know what the symbols mean?

[cobalt vigil]

yes n = intersection "not if its the right term" i dont speak english

c = subset

[forest ember]

Yeah, so you want to identify the variables of the property.
“Two intersecting lines of a plane”
Already you know you need to define 2 variables for the lines and a variable for the plane, the 2 lines must intersect and they lie in the plane (are a subset of the plane)

“parallel to another plane”
Now you also have another plane in play, and both lines are parallel to the new plane

[cobalt vigil]

Oh yea I see now thanks

but ive another question

whats the diffrences between c and E ?

you know the c with the stripe

I feel so dumb now ;-;

[forest ember]

$x \in V$ means a single element $x$ is a member of a set $V$

[soft zealot]

shsgd

[forest ember]

e.g. 1 € R, where R is the set if real numbers

[cobalt vigil]

so its like E is one part

and C is the full part of something?

[forest ember]

$y \subset V$ means a set of elements are members of a set $V$

[soft zealot]

shsgd

[forest ember]

e.g. {1,2,3} c R

[cobalt vigil]

aight

thanks

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[warm python]

find the direction cosines

[faint locust]

What do you mean by that?

[warm python]

what's your native language, maybe I can find the word in that language

[faint locust]

German

[warm python]

,w direction cosines

[soft zealot]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by physicsrocks

[warm python]

Richtungskosinus

[faint locust]

,w direction cosines in German

[warm python]

heard of this>

[faint locust]

What's that?

[warm python]

esssentially a way to describes slopes in $\R^3$

[soft zealot]

ƒ(Why am. I here)=I don't know

[warm python]

I'll send some resources

wait

[faint locust]

I think with describe the position it more means to talk about symmetries, if the origin is in included etc.

So this is symmetric to the x3-axis

[faint locust]

Also, it doesn't include the origin

It isn't symmetric to any coordinate plane or anything like that

[faint locust]

Well I don't think it asks us to calculate the direction cosines

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[faint locust]

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[waxen bobcat]

Huh?

Not understanding ur question

X-X-8

You get -8?

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[thick ravine]

How do I simplify this

[thick ravine]

Do i multiply by conjugate ?

.Close

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[snow karma]

how do I prove there exists 2 numbers a,b such that:
(2^a - 2^b) | 2017

I understand the Pigeonhole Principle, but i just don't know how to prove it

[snow karma]

the solution says I need to think that there is a finite amount of remainders for 2017 ({0,1,2,...,2016}), but I don't understand how to prove it

as in that necessarily there will be 2^a - 2^b | 2017 then

[royal schooner]

hm?

2017 is prime

[snow karma]

how do you that for sure?

[blissful condor]

2017 divides the other thing

[snow karma]

i didn't know it before looking at one of the solutions myself

[royal schooner]

so if 2^a - 2^b | 2017 either (a,b) = (1,0) or 2^a - 2^b = 2017

[royal schooner]

uh

[blissful condor]

are you sure you copied the problem right

[royal schooner]

i assume this is from some olympiad right

[snow karma]

yes

[snow karma]

from Linear Algebra 1 homework number 2

[royal schooner]

oh

[snow karma]

first question by the way (4 parter)

[royal schooner]

also since you just need to proof there exist a,b 2^a - 2^b | 2017 isnt puting (a,b) = (1,0) enough

[snow karma]

but that would be 1 | 2017?

[royal schooner]

what is 2^1 - 2^0

yes

[blissful condor]

that’s right, and it’s true

[royal schooner]

what do you think 1 | 2017 means

[snow karma]

yeah but it's not divisible by 2017

[blissful condor]

yeah the problem is written wrong

this is what i’m saying

[snow karma]

I don't follow

[blissful condor]

a|b means the opposite of what you think it means

[snow karma]

oh

I did write it wrong

"prove that 2 numbers a,b, makes:
a^2 - b^2 is divisible by 2017"

[snow karma]

didn't have much experience using it so I forgot it's opposite sides, sorry

[blissful condor]

it’s okay, it happens to the best of us

[royal schooner]

you want a^2 - b^2 = 2017k
=> (a+b)(a-b) = 2017k

can you find some a and b which make it possible

[snow karma]

no?

oh

[royal schooner]

you want a factor of 2017 on lhs

[snow karma]

a=+-b?

[royal schooner]

no

[snow karma]

then no

[royal schooner]

(2016,1) works for example

[snow karma]

how did you get there?

[royal schooner]

cos then a+b = 2017
(a+b)(a-b) = 2017*2015=2017k

[snow karma]

I see

good solution

[royal schooner]

since (a+b)(a-b) = 2017k if we can let either a+b or a-b = 2017m the 2017s cancel out

[snow karma]

but do you know how I could use the Pigeonwhole principle for this question instead?

[royal schooner]

uh no

hm maybe

[snow karma]

oh my bad, I meant:
2^a - 2^b

[royal schooner]

ah ..

[snow karma]

yeah

[snow karma]

this is what I had

it's a reasoning that there must be 2 numbers 2^a and 2^b exist that do make this possible to get 2016+1 or something similar

since that's their remainders

[fierce orchid]

a=b

[snow karma]

a

[fierce orchid]

for nontrivial cases

a=b+n*phi(2017)

[snow karma]

wow

[fierce orchid]

its easiest wiht just basic number theory

[snow karma]

i found a similiar question in some pdf

[fierce orchid]

let me try to find a pigeon hole solution

[snow karma]

wdym?

[snow karma]

heres one

i understand it now

[fierce orchid]

yeah makes sense

[snow karma]

yeah

ty so much mates

.close

[final saddle]

Channel closed

Closed by @snow karma

Use .reopen if this was a mistake.

[fierce orchid]

euler totient function

youll need it for olympiad

[snow karma]

i dont get it?

[fierce orchid]

get what

youll learn totient sooner or later

[snow karma]

i dont see the value in the theorem i mean

i see the see it, but i dont see an application like Pigeonwhole principle

[fierce orchid]

what?

[snow karma]

what is it used for?

[fierce orchid]

if i asked to you to find distinct (a,b) such that 2^a-2^b is a multiple of 2017, how woul dyou do it?

do you know modular arithmetic?

[snow karma]

like the solution did using Pigeonwhole principle

[snow karma]

no?

[fierce orchid]

you would have to try every 2^a from 0 to 2016

[snow karma]

oh to find

not prove existance

[fierce orchid]

yeah

ok youll learn it on your olympiad journey

once you start learning number theory

[snow karma]

will it be in Linear Algebra?

[fierce orchid]

no

well actually maybe

[snow karma]

do you know what year as a math major?

[fierce orchid]

but not classical linear algebra

oh are you doing this for olympiad or college?

im still a student idk

[snow karma]

college

[fierce orchid]

ohh

nvm then

[snow karma]

it's my homework

oh i see

[fierce orchid]

idk when ever you start number theory

[snow karma]

does it get easier to do proofs?

[fierce orchid]

wdym?

[snow karma]

we still are learning group theory in a parrelel course

[snow karma]

i mean im 3 weeks in and i have to look up proofs

for my homework

[fierce orchid]

if you practice proofs writing proofs will become easier ofc

[snow karma]

it's so weird because these are so hard

[snow karma]

but does it become normal?

or do you too need to look up solutions for homework problems?

[fierce orchid]

itll become normal

[snow karma]

okay

[snow karma]

well sorry for bothering you like that

[fierce orchid]

youre good

[snow karma]

ty for your help mate

[fierce orchid]

np

[snow karma]

.close

[final saddle]

Available help channel!

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Remember:
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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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[gentle zephyr]

find all $a \in \mathbb{R}$ such that $\\\sum_{n = 1}^{\infty} \frac{(1+a)^n}{n}(x-2)^n\\$ has radius of convergence equal to 2

[soft zealot]

938c2cc0dcc05f2b68c4287040cfcf71

[gentle zephyr]

bruh I was talking in other help channel because I thought it was mines

mine closed due to inactivity

basically after taking root test

I get this

but I think I made a mistake

or does that mean that

,, \lim_{n \to \infty} |1 + a| < \frac{1}{|x-2|}

[soft zealot]

938c2cc0dcc05f2b68c4287040cfcf71

[gentle zephyr]

?

im still confused

I dont get it

[final saddle]

@gentle zephyr Has your question been resolved?

[fallen vigil]

what about

R=1/|1+a|

[final saddle]

@gentle zephyr Has your question been resolved?

[uneven totem]

can u state the relation of n with the other vars?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[gilded flame]

I am stuck on this question, the answer I am getting is not even on the line. I can't figure out where I am going wrong.

[gilded flame]

@tired galleon are you still around to help? I know you said to use this formula

$$\mathcal{L} (x,y,\lambda) = f(x,y) + \lambda g(x,y)$$

[soft zealot]

TheDragonOfFlame

[gilded flame]

But it isn't in my textbook so I was trying to do it the way they do

But there shouldn't really be a z value, so I'm unsure what "f(x,y)" would even be?

Other than 0

[ivory vessel]

is lagrange required?

[ivory vessel]

this is called lagrange multiplier

bit of an overkill id say

[fathom walrus]

ur missing 2 nablas

[gilded flame]

Yes, it says to solve using lagrange multipliers

[ivory vessel]

hm, sure

[gilded flame]

That's just what the other guy sent, it isn't the formula I am using

I've been using $$\nabla f(x,y,\lambda) =\lambda \nabla g(x,y)$$

[soft zealot]

TheDragonOfFlame

[tired galleon]

Fairly sure in the first channel the original thing said the Q wanted him to use lagrange multiplier so I did lmao

[ivory vessel]

yeah in that case its fine

[gilded flame]

Right, sorry

Forgot to say

[tired galleon]

Must sleep as I have been in a plane for too many hours today to stay awake any longer, sorry But a comrade should get you to the answer

[gilded flame]

Why is g=0?

[fathom walrus]

set g(x,y) to 0, thats ur constraint

[gilded flame]

Wouldn't that be when they intersect?

Or wait what?

I thought g would have to refer to the point in some way

[fathom walrus]

this is just the general methodology for lagrange multipliers

[gilded flame]

But if g is zero isn't the gradient of g also 0?

Meaning that gives no information on the Lagrange multiplier?

[fathom walrus]

no

we set g = 0 as our constraint equation, let me link u a page that helped me when i learned this

[tiny gorge]

g is not identically zero
g=0 means you restrict yourself to the level set where g is zero

[fathom walrus]

https://openstax.org/books/calculus-volume-3/pages/4-8-lagrange-multipliers

[gilded flame]

Ohhh yeah I see

So the point where g=0

Ok yes

So, am I not doing that?

I thought I was kind of

Because g(x,y)=0 when x=4 and y=2

Oh but is it only true when I plug the points in?

[fathom walrus]

i didnt look at ur work

lemme see

honestly i cant really tell what ur doing on that page, it looks like u flip flopped f and g tho

[gilded flame]

Do I need to solve for the multiplier and then use that to find y in terms of x and x in terms of y and then plug that into g(x,y) to get the values of each that make g(x,y) = 0? That's what I did for previous questions

[gilded flame]

f(x,y) is the given equation and g(x,y) is the square of the distance between them

Oh but I am trying to maximize the distance not the given equation

True

[fathom walrus]

$f(x,y) = (x-4)^2 + (y-2)^2 \newline g(x,y) = y - 2x - 3$

[fathom walrus]

just start again with this and use this

[gilded flame]

So the line is the constraint, I was thinking backwards

Ok just to check the steps. I find the gradients, set them equal, solve for the Lagrange multiplier, find each variable in terms of the other, and then substitute them into the constraint formula g(x,y) to find the point?

[fathom walrus]

find gradients of f and g
multiply grad g by lambda
set vector components equal
solve for lambda in each equation
set both values of lambda equal
now u have 2 equations in terms of x and y, the one u just made, and the constraint g (set g equal to 0)

dude i gotta go outside, the sky is so nice, if u want i can check ur work later

just dm me or keep this channel open or smth

[gilded flame]

True 🥲 Gotta hate summer school

Thanks for helping

[fathom walrus]

np, lmk later if u need help

[gilded flame]

I think I can probably get it? I'm having a tough time really grasping this concept for some reason

.close

[final saddle]

Channel closed

Closed by @gilded flame

Use .reopen if this was a mistake.

[gilded flame]

.reopen

[final saddle]

✅

[fathom walrus]

bro i literally just got back

what did u end up getting

[gilded flame]

The same thing

I get the same equations for lamda still

[fathom walrus]

show me ur work

[fathom walrus]

ok so

[gilded flame]

Well the lamda equations are inverse, but the x and y relationship is the same