help-23

[knotty viper]

Okay, thank you. I get it 🙂

[safe radish]

@knotty viper Has your question been resolved?

[lean otter]

.close

[safe radish]

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[tawny thorn]

11)b pls

[tawny thorn]

I got this and got 22 but the answer is 21

Can anyone confirm pls

[safe radish]

@tawny thorn Has your question been resolved?

[tawny thorn]

No

<@&286206848099549185>

[lean otter]

are we looking for the variable n in this case?

[tawny thorn]

Yup

I already solved as I showed but the answer is 21

So idk

[safe radish]

@tawny thorn Has your question been resolved?

[tawny thorn]

<@&286206848099549185>

Pls help with question above

[quasi bison]

,w 2000 * (1.06^n - 1)/0.06 > 80000

[flat frigate]

Results provided by WolframAlpha

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

Requested by Ann#0413

[quasi bison]

and the answer they give is 21 payments?

,calc 2000 * (1.06^21 - 1)/0.06

[flat frigate]

Result:

79985.453351521

[quasi bison]

21 payments would come just short of 80k

[tawny thorn]

Exactly ahaha

So 22 is correct right? @quasi bison

[quasi bison]

seems so.

[tawny thorn]

And also for the first question I got 16 but answer is 18

[quasi bison]

i have this feeling that some silly off-by-one bullshit is waiting for us around the corner

[tawny thorn]

😂

hopefully not

u are sure that we are right, right? @quasi bison

Just to make sure I’m not doing anything wrong

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@tawny thorn Has your question been resolved?

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[gloomy thicket]

Im not sure they derived this equation for linear interpolation

[safe radish]

@gloomy thicket Has your question been resolved?

[prisma siren]

we want a straight line between all pairs of points

between $(x_i,y_i)$ and $(x_(i+1),y_(i+1))$ the slope is $ \dfrac{y_(i+1)-y_i}{x_(i+1)-x_i}$

[flat frigate]

Grubinski

[gloomy thicket]

right yeah

they are generating the line based on the interpolation of the axis

[prisma siren]

now we need to find the vertical and horizontal offset

basically it's the same exercice as finding the equation of the line going through to points

[gloomy thicket]

yeahh

uh i dont get the formulae they have though

t in this case is $\frac{x -x_i}{x_{i+1} - x_i}$

[flat frigate]

shriller44

[gloomy thicket]

from this formulae

but like i dont see how they got this t value what does it even mean

like the bottom part is just the difference between any 2 x values right

and its creating a fraction based on x - the initial value

what does x represent though

[prisma siren]

do you get the formula (1-t)A + tB ?

[gloomy thicket]

well yeah its just some scale of how much to use A and B to generate a new point

(1-t)A + tB, so if t = 0.5 its the same value of each

1/2A + 1/2B

[prisma siren]

yes

[gloomy thicket]

i dont see how the other one makes any sense though

so its a function f(x) = y basically

y is the output point we are interpolating the height of okay

based on the fractional distance between 2 values of x or sumn

okay so $(y_{i+1} - y_i)$ is the distance between 2 y vaues

[flat frigate]

shriller44

[gloomy thicket]

so its starting at the initial y coordinate and scaling the distance to the next y coordinate based on the change in x factor

so its like edging up y by a equivalent factor that x changes on the same scale

thats my understanding atm

like if x moves 30% we move the y value up 30% too by multiplying the distance to the new point by 0.3

[prisma siren]

basically the first one gives you a parameterized description of a line where t is a sort of slider, the second one gives you y as a function of x

but the two are equivalent

[gloomy thicket]

yeah it does make more sense now acc i can see that

yeah so t is just how far we haved on x

over the total distance on x

and we plug this scale into ys output

[prisma siren]

yes

[gloomy thicket]

to create the line

fair that makes sense cheers

.close

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[fierce stirrup]

Hi, I have a set X which contains the element 0 and Y which contains the element 1, f : X -> Y maps 0 to 1. If I have another function say g, and now I have sets X which contains the element 0 and set Y which contains the elements 1 and 2, is f: X -> Y the same function or not (both functions map 0 to 1, but the sets are different)?

[safe radish]

@fierce stirrup Has your question been resolved?

[steel stag]

the answer actually depends on the field of math you're working in, but usually yeah it's called the same function

what you're doing is changing the codomain (the set of outputs the function might have) but keeping the range (outputs it does have) the same

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[slim portal]

got a question about what i do here

about the (2x - 1)

[steel stag]

what is the question asking you to do?

[slim portal]

write it as an algebraic sum as simple as possible

[steel stag]

like expanding this polynomial?

[slim portal]

not sure

the answer is 8x^2 + 8x - 6

how do i get that

[steel stag]

ah yeah it's asking to expand it

so to multiply those parentheses things you add all the pairs

like 2x*2x + 2x*-1 + 3*2x + 3*-1

that's 4x^2 - 2x + 6x - 3 = 4x^2+4x-3

but there was a 2 in front of all of this, so just multiply every number by 2 to get the answer

[slim portal]

alr

4x^2 - 2x + 6x - 3

how does the 2x + 6x turn into a 4x?

[steel stag]

it's a -2 and a 6

[slim portal]

oh

[steel stag]

always put the minus sign with the number

[slim portal]

-2 + 6 would be -4x

oh

alr thanks

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[cerulean sparrow]

https://i.imgur.com/vUedVIa.png

[cerulean sparrow]

How did they get 2.6360 for Q4?

1- z score of inf + z score of a = .62

1-z score of inf-.62 = (a-mu)/std
(1-zscore of inf-.62)* std + mu= a

How do they solve for zscore of -inf?

[steel stag]

I think you're overcomplicating it

P(-inf to a) = c to the z-score can be found by the inverse norm formula

https://www.wolframalpha.com/input/?i=inv+norm+of+0.62

tells me the z-score of a is 0.7324

oops I typod' let me fix

ok my bad I took the wrong approach

so erf() gives you the area between -z and z

but we're told -inf to z is 0.62

that means z to inf is 0.38, so we can subtract that 0.38 tail to get the middle area we want

0.62 - 0.38 = 0.24, and that gives the answer they have

[cerulean sparrow]

what is erf()?

also how did you get a from .24?

[cerulean sparrow]

also i dont understand why this is subtracted T.T

[steel stag]

yeah sorry I'm all over the place uh

you just look up the inverse of 0.62 and that's the z-score

[cerulean sparrow]

with the z score, how do you get a?
z= (a-mu )/ std?

[steel stag]

here we go https://www.wolframalpha.com/input/?i=invnorm(0.62)

this gives a z-score of 0.305, and 2.3+1.1*0.305=2.636

[cerulean sparrow]

Ohh I just realized wolfram gave x-values for that input and Probability values for the other site here

Thanks again

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[opal surge]

How would I apply trig substitution on this?
$$\sqrt{(9-4x^{2})^{3}}$$
$$\sqrt{a^{2}-x^{2}} \to x=asin\theta$$

[flat frigate]

RESIDGE

[dim kiln]

could x/2 = 3 sin theta work?

wait no, 2x = 3 sin theta

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[limpid lichen]

for this double integral

[limpid lichen]

is this the right region of integration?

[tame raft]

looks good

[limpid lichen]

why is this different then?

[tame raft]

in that case you'd be integrating the lower triangle, it looks like

wait

yeah

so the bounds for the interior integral should be x/3 to 1

if you see what i mean

[limpid lichen]

oh

i get that but wouldn't the lower triangle have the same area?

[tame raft]

it has the same area but the function inside will have different values

it's like

integrating x^2 from 0 to 1

vs integating x^2 from 1 to 2

intervals are the same length, but the values of f(x) are different

[limpid lichen]

ohh right

aight ty

.close

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[scarlet sage]

i need help with this question

[scarlet sage]

this is my working out so far

the website said im wrong

and it does not tell u thr right answer

so

idk what i did rong

[safe radish]

@scarlet sage Has your question been resolved?

[dim kiln]

Check your midpoint

[scarlet sage]

yes

but idk how to find it

i just tried some stuff

obviously i was wrong

[dim kiln]

How did you find that point?

[scarlet sage]

so like

between the two points

i checked the diff of y and x

so e.g

diff in y between poiints it

10

mid would beb 5

[dim kiln]

Yup, the midpoint is 5 units from the x coordinate of each end point

[scarlet sage]

ohhhh right

[dim kiln]

How ever that is not 5

[scarlet sage]

i need to add 5 to the y coordinate of a point

[blazing fiber]

and now you need a slope which is 90° from the original line and goes through the middle point

[dim kiln]

Well depends on which point you use

[scarlet sage]

does it?

if its -1 i add 5

if its 9 i -5

[dim kiln]

Yup

[scarlet sage]

yesyes

so if my mid point is right my equation will b right then?

[dim kiln]

That should fix it

[scarlet sage]

right

[dim kiln]

I think

[scarlet sage]

thank you

yeah

im pretty sure my gradient is correct

[dim kiln]

👍

[scarlet sage]

thank you

.close

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[kind beacon]

how does this factor out to 1/2(x+2) ?

[kind beacon]

,rotate

[kind beacon]

question e btw

[safe radish]

@kind beacon Has your question been resolved?

[dim kiln]

What’s the question prompt?

[kind beacon]

@dim kiln mapping notation

[dim kiln]

I can’t see how that would simplify to 1/2(x+2)

The only thing I can think of is factoring out the 2

Such that it becomes 2(2^(1/2x) - 1)

[kind beacon]

i don’t know either

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[zinc copper]

so do i just send a picture of my math problem here or just type it?

[tame raft]

whichever is easier to work with

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[lean otter]

I have a question about binomial and monomial math stuff

[lean otter]

Like this for example

Theres 4 letters

but its still a binomial right?

because the negative seperates them

[lean otter]

yep

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[opaque geyser]

Hello, i am not sure how to solve for x and y using this, idk how to show my work

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@opaque geyser Has your question been resolved?

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@opaque geyser Has your question been resolved?

[inland ivy]

Just break it down into pieces

Find out what you can know using pythagorean theorem and repeat

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[safe radish]

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[jaunty heath]

Middle q

Wrong one

[safe radish]

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[jaunty heath]

My calc Says 1/10 for some reason

[deft pivot]

because your calc did 1*(1/5) instead of 1+(1/5)

[jaunty heath]

So my answer is right then ?

[deft pivot]

of course

[jaunty heath]

Ok thank you, have a great day

How do I open this channel for others to use

[deft pivot]

.close ig

[jaunty heath]

.close

[deft pivot]

its already closed

[jaunty heath]

Ah ok

Ill delete my thing

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[glacial peak]

could anyone help me with question 8?

[left igloo]

just use similar triangles

1.8/2=x/8

[glacial peak]

ohhh, mkmk

I did that in an incorrect way

.close

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[random oar]

can someone help me with this problem too?

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[marsh walrus]

,w graph ( ( 1/(sqrt(7+x) ) - .25)/(x-9) from 7 to 11

[flat frigate]

Results provided by WolframAlpha

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

Requested by jan Niku#2119

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[azure wadi]

?

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[lean otter]

You use herons formula

[azure wadi]

i got it alr

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[burnt spire]

how does one prove that line segment FE is congruent to itself?

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[hazy wasp]

<@&286206848099549185>

What do you notice about the graphs of quadratic functions whose equations are of the form 𝑦 = (𝑥−ℎ)^2

[sand kestrel]

this is not how you're supposed to use this ping

stop

[hazy wasp]

ok sorry

[sand kestrel]

see #❓how-to-get-help

[hazy wasp]

okk this is the first time that i read it

sorrry

[burnt spire]

.close

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[real fiber]

.close

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[mortal plover]

yep

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@lean otter Has your question been resolved?

[mortal plover]

yes very good

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[serene remnant]

hi can someone show me how to do this step wise

[torpid oxide]

repeated differentiation!

[serene remnant]

do i have to use the product formula

[torpid oxide]

ya

[serene remnant]

okay thanks

[torpid oxide]

$\dv{x} e^{ax} f(x) = e^{ax}(af(x)+f'(x))$

[flat frigate]

Ryuzaki

[serene remnant]

oh okay

[safe radish]

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[high sedge]

Donnie is saving up money for a down payment on a motorcycle. He currently has $4086, but knows he can get a loan at a lower interest rate if he can put down $4962. If he invests the $4086 in an account that earns 5.9% annually, compounded monthly, how long will it take Donnie to accumulate the $4962? Round your answer to two decimal places, if necessary.

[high sedge]

<@&286206848099549185>

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@high sedge Has your question been resolved?

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[lean otter]

i got x^2-2x-2 = 0

but apparently c is not -2

here's my working out (ill type it)

x^2-x+2x^2+4x-1x-2 = 2(x^2+2x)

x^2-x+2x^2+4x-1x-2 -2x^2 - 4x

0 = x^2 - 2x - 2

[rain hare]

help pls

[lean otter]

This channel is occupied, press the 'MATH HELP (AVAILABLE)' section to find available channels for assistance.

help-3, help-25 and help-20 is available, quickly get it if you can

[swift oxide]

c = -2 is correct

[lean otter]

oh, i think it was a mistype

thank you

.close

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[golden lark]

right, so I solved the problem and got the answer wrong. I'm having a hard time understanding why I should use cos here?

[steel stag]

you'll use vcos for the horizontal speed and vsin for the vertical speed

[golden lark]

but aren't I finding height above release point here? why would I need horizontal speed?

[steel stag]

it's a 2 part solution, you don't have enough info for the vertical path, so you need to look at the horizontal part first to get the time to hit the wall

so like first you solve v=d/t in the horizontal to find t

then you use y=vt+1/2at^2 in the vertical to get y

[golden lark]

ah, alright. I'll give it a shot

for the second part, do I need to use vsint?

like y=vsint+1/2at^2

[steel stag]

right

vcos in horizontal vsin in vertical

[golden lark]

cool, I got it! Thank you so much

.close

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[lyric fog]

can someone help me out with this question please?

I don't know how to approach it

[safe radish]

@lyric fog Has your question been resolved?

[lyric fog]

<@&286206848099549185>

[flint ledge]

@lyric fog do you know inverse function notation?

do you know what that expression on there means

[lyric fog]

ummm

somewhat

not extremely well

f^-1(x) is finding x at y

instead of y at x

[flint ledge]

kinda

so first you need to find the inverse function

do you known how you would do that

[lyric fog]

umm

hmm

[flint ledge]

switch the place of x and y

remember f(x) = y

[lyric fog]

yea

then

solve for y

?

[flint ledge]

so we do x = 2y+cos(y), and solve for y

[lyric fog]

yea

[flint ledge]

ok to be fair

i don’t know how you would do that here

lol

[lyric fog]

LOL

uhh

hmm

let me use

handy dandy

calculator

to see how it would be done

uhh

idk

calculator not giving me a proper answer

[flint ledge]

we might have to do this a different way

let’s try an easier function for example

f(x) = x^3, f^-1(x) = x^(1/3)

[lyric fog]

yea

[flint ledge]

so if we put for example 2 in f(x), it gives us 8

[lyric fog]

yea and if 2 goes in inverse it would be whatever 2^1/3 is

[flint ledge]

and if we put 8 in f^-1, we get 2

[lyric fog]

ye

[flint ledge]

i’m trying to find a way to get what f^-1(1) is

for the original function

[lyric fog]

yea

[flint ledge]

without actually inverting it

[lyric fog]

of this function?

[flint ledge]

yes

so i think we would just do 1 = 2x+cosx

maybe

[lyric fog]

would it be something like this?

[flint ledge]

ugh they used an identity probably

[lyric fog]

yea kinda gross

[flint ledge]

oh wow i actually did it right kinda

[lyric fog]

pretty much yea

[flint ledge]

well apparently this is at least possible

[lyric fog]

yea

but i dont really get

how to get past this point

x = sin^2 x/2

[flint ledge]

we can’t even square root both sides

because we’d have like 4 possibilities

sin could be negative

[lyric fog]

yea

[flint ledge]

x could be negative, both could be negative or neither of them could be

wait actually no

we only have to consider sin being negative

[lyric fog]

since x doesnt have neg sign?

[flint ledge]

i honestly have no clue what to do

x isn’t squared

[lyric fog]

oh ye

so it cant be neg x

[pastel nymph]

sin(x/2)=sqrt((1-cosx)/2))

[flint ledge]

the solution is probably obvious but i don’t see it lol

[pastel nymph]

sin^2(x/2)=(1-cosx)/2

[flint ledge]

that identity was already used but in reverse

scroll up a bit

[lyric fog]

hmm

idk at all for this 1

[flint ledge]

same

[lyric fog]

you wanna help with this one instead ?

i can deal with the other one later too

I don't know how to approach this either

[flint ledge]

you know implicit differentiation right

[lyric fog]

somewhat

[flint ledge]

basically we assume y is an unknown function of x

if you have something like y^2 you would interpret that as g(f(x)) with f(x) = y and g(x) = x^2

to differentiate something like y^2 we would use the chain rule, dy/dx = (dy/du)(du/dx)

actually since we’re talking about y we should probably so something like y^2 = v

so dv/dx = (dv/du)(du/dx), with u = y and v = u^2

i might have gotten off topic

i just wanted to make sure you understood implicit differentiation properly

[lyric fog]

yea i get it a bit

[flint ledge]

anyways, to the problem

implicit differentiation is basically differentiate with respect to y and multiply by dy/dx

[lyric fog]

yea

[flint ledge]

so d/dx y^2 = 2y*dy/dx

so just differentiate both sides with respect to x, and solve for dy/dx

if will be in terms of x and y

not just x

[lyric fog]

i see

so like

[flint ledge]

afterwards substitute in x = -5 and y = 5

[lyric fog]

like this?

[flint ledge]

on the second term you need to do product rule

the first term is right though

and the last term is wrong too

[lyric fog]

hmm

[flint ledge]

wait why is there dx/dy

y is a function of x, x isn’t a function of y

[lyric fog]

wait its dy/dx

right

mb

idk how to do second or third temr

[flint ledge]

ok

so the second term you need to use product rule

d/dx (5x) * y + 5x*dy/dx

as you can see, you basically didn’t need to do anything with y

[lyric fog]

oh

i see

[lyric fog]

like this then?

@flint ledge

or is it like this

[flint ledge]

the dy/dx shouldn’t be squared

[lyric fog]

but it was 3y^2?

[flint ledge]

yes

[lyric fog]

it just deletes the square?

[flint ledge]

ok i can go through the process really quick

[lyric fog]

when you said plug in -5 and 5 how do I do that btw?

since there's d/dx and dy/dx everywhere

[flint ledge]

if you want to do it by the definition, we do dv/dx = (dv/du)(du/dx) with u = y, and v = 3u^2

literally plug in x = -5 and y = 5

so with what i just sent, the answer would be 6u*dy/dx, or 6y*dy/dx

or just remember to differentiate with respect to y and multiply by dy/dx

although you should remember both

[lyric fog]

wait im a little confused

[flint ledge]

also i just saw this, but it’s not 5x*d/dx

it’s d/dx (5x)

the other way doesn’t really make sense

[lyric fog]

right

[flint ledge]

ok what’s confusing you

[lyric fog]

ok can we start over a bit

where do I go from here

what is my next step

[flint ledge]

i don’t know where you got the 9y

the last term is 6y*dy/dx

also take d/dx (5x) and turn it to 5

[lyric fog]

right it was 3*2 i did 3^2 for some reason

[flint ledge]

take out the 3 before the dy/dx

and it will be right

[lyric fog]

like this?

[flint ledge]

ok

yeah

[lyric fog]

ok

[flint ledge]

so just solve for dy/dx

group all the terms being multiplied by dy/dx together on one side

[lyric fog]

i may have rearranged wrong

[flint ledge]

instead, you should add 6y*dy/dx to both sides

actually that works i think

let me check

[lyric fog]

does it work?

[flint ledge]

sorry i’m helping two people right now and i’m trying to multitask

[lyric fog]

oh ok

[flint ledge]

no it doesn’t

i don’t know why you divided by 5y

[lyric fog]

in here it was -5*-y-5x(dy/dx)

so i wanted to isolate -5x(dy/dx)

what should it be instead?

[flint ledge]

so we have 27x^2-5y-(5x*dy/dx)-(6y*dy/dx) = 0

[lyric fog]

yea

oh

i see

like this

then divide by -5x - 6y?

[flint ledge]

personally i would add or subtract the dy/dx terms on both sides but that works

no not yet

well yes but let me show you

[lyric fog]

ok

[flint ledge]

we can turn the lhs into (dy/dx)(-5x-6y)

which you probably knew actually

so yes

now you have what dy/dx is

so substitute in the x and y values

and you’re done

[lyric fog]

just to confirm

i plug in x and y to this?

[flint ledge]

yes

[lyric fog]

i got 130

[flint ledge]

lots of slope

[lyric fog]

seems like a massive number for a slope

ill check if it's right

it was

nice

!

ty for the help

this question is going to haunt me tho

[flint ledge]

same lol

maybe, just maybe, you could switch x and y

then take the derivative

using implicit differentiation

[lyric fog]

it makes my head hurt too much

[flint ledge]

for some reason i didn’t realize what value satisfies cos(x) = 0

[safe radish]

@lyric fog Has your question been resolved?

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[safe radish]

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[last escarp]

how do you solve this question

[lean otter]

what do you do when you have a negative in the exponent

[pulsar condor]

you have a tab with the answer it looks like.

[last escarp]

nope

i just need help

with that question

[last escarp]

4 x 2 so

[lean otter]

i think its just the search. probably didn't yield anything good

[last escarp]

4^-8?

[lean otter]

no i meant the negative

[pulsar condor]

searching 4^-2 does in fact give the answer

[last escarp]

no.

how?

[lean otter]

oh in bing

should've tried that first

[last escarp]

0.0625

[lean otter]

yes that's the answer

[last escarp]

i dont get how 5^0 = 1

[lean otter]

anything to the 0th power is 1

[last escarp]

i mean 5 x 1 = 5

lol

[pulsar condor]

yeah, and nowhere is 5*1 present

[lean otter]

that's not what exponents do

[flint ledge]

5^1 = 5^2/5, 5^0 = 5^1/5 = 5/5 = 1

[last escarp]

._.

[lean otter]

5^1 means 1 times 5

5^2 means 1 times 5 times 5

5^3 means 1 times 5 times 5 times 5

[worthy hemlock]

What's 5^0 mean?

[lean otter]

oh sorry i forgot the 1

[last escarp]

sorry if im annoying

idk how to do this

question B

[pulsar condor]

"assessment"

[last escarp]

yes

[lean otter]

we can't help with exams, tests, or any of the sort

[last escarp]

oh alr

can u explain me that one question doe

;~;

[ancient escarp]

you were just told you can't cheat then you ask to cheat again lmao

[last escarp]

oh ok

alr sorry, forgot it's a rule.

does homework still count?

[flint ledge]

homework is ok

[last escarp]

alr

ty for helping anyways

have a good day

.close

[safe radish]

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[teal reef]

Can anyone help me with this? https://cdn.discordapp.com/attachments/460248794223869962/907105133102514246/unknown.png

[teal reef]

oh wait

.close

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[hollow path]

woudln't there be no approximations because the vector is ortho. to the span? i feel like i'm missing something crazy obvious here

[safe radish]

@hollow path Has your question been resolved?

[steel stag]

you still just project it on the (1,-1) line (example image below)

here it's just 0,0

[hollow path]

i'm trying to work through the calc with the p norm, but i wanted to see if i understood intuitively what i'm being asked.
so the answer is the 0 vector here?

[steel stag]

umm p=1 is the special case I think

"all the best approximations" implies sometimes there are multiple that are just as close

[hollow path]

so my intuition is misapplied here? there actually are approximations?

[steel stag]

yeah there always is

best approximation is defined as the distance being as small as can be

think of the vector as a point and the span as a line

you just want the closest point on the line

do you know what p=1 is intuitively?

here's the picture of your problem

[hollow path]

so i'm trying to plug the p norm into this:
v=(1,-1)
u=(1,1)
u*,v lie on V=span{v}

| |u-v| |p^2=| |u-u * | |p^2+| | u*-v| |p^2

is this the right way to go about this?

sorry tv

[steel stag]

that's true but I'm unsure how easy it is to work with

[hollow path]

| |u-tv| |p^2=| |u-u * | |p^2+| | u*-tv| |p^2

where t is a complex scalar.

ok so what would be a better approach here?

[steel stag]

I thought it was just the projection of u onto line v

oh that probably doesn't work for p!=2, yeah try your equation

[hollow path]

wlp i'm getting something that looks like this

( | 1-t|^p + |1+t|^p)^2/p = ( |1-u* _1)^p + |1-u* _2)^p)^2/p + ( |u* _1-t|^p + |u* _2+t|^p)^2/p

that's u* sub 1, and u* sub 2
i hope that parses well

i don't really know what to do wit this, is this even the right direction ?

[steel stag]

I'm not sure what the sub 1 and sub 2 mean, but from here you need to minimize the right hand side

[hollow path]

cool, working on that

sub1 sub2 being the 1st and 2nd elements of the vector u*

u* is on V so i'm plugging u* =t* (1,-1)
and seeing where that takes me

[steel stag]

gotcha

[hollow path]

well that brings me to
( | 1-t|^p + |1+t|^p)^2/p = ( |1-t* |)^p + | 1-t* |)^p)^2/p + ( 2|t-t* |^p)^2/p

i don't see what else i can do with this.

i would expect to show that this equality only holds for t* = 0
but that doesn't seem to be happening

[steel stag]

I'm not sure what t and t* are but it holds for t=t*=0 right?

[hollow path]

t is the variable scalar that spans V=t(1,-1)
t* is the constant scalar of the orthogonal projection of u on V ( u* = t*=(1,-1) being the projection)

unless i utterly misunderstood what is supposed to happen here i need to find the t* values that produce the orthogonal projection, ie, those that uphold this equality.

does this all check out?

[steel stag]

I'm not sure why the t is there, I'd imagine you'd have 1 variable and need to set the derivative to 0

not sure if there's like a theorem in lecture that gives another approach to this question, because solving this for all p seems really rough

[hollow path]

oh wait it's actually quite possible,
the ortho projection equality holds for any vector v in the span right? i can just set a t

i'm gonna try to just set t=1 see if it gets less ugly,
you're right i think, i was solving for the entire span instead of a vector.

[steel stag]

yeah just pick a t

[hollow path]

well it simplified....weirdly

( | 1-t|^p + |1+t|^p)^2/p = ( |1-t* |)^p + | 1-t* |)^p)^2/p + ( 2|t-t* |^p)^2/p
setting t=1 RHS just becomes 4

so now it's:

4=( |1-t* |^p + | 1-t* |^p)^2/p + 2|1-t* |^2

by now i'm just feeling like i have something fundamentally incorrect in my approach or in the mechanics of my application.

[steel stag]

ooo now we have t*=0 holds

[hollow path]

do we?
isn't this an inequality now for t=0?
4=(1+1)^2/p+4
4^1/p=0

[steel stag]

um I read the last term as 2 * |1-0|^2 so it's 2 not 4

[hollow path]

yeah soz i was bound to lose a parenthesis at some point...
anyway can you see anything in particular i fucked up here?

[steel stag]

hm right now t*=2 works too so something's probably off

I believe the answer is meant to be 0,0 for p>1 and set of values for p=1

[hollow path]

0,0 makes sense to me but then wth happened here?
did i make a mistake opening the sums in the p norm? or is this more fundamental

[steel stag]

what do you mean by opening the sums?

maybe someone in #advanced-analysis knows a theorem that makes this way simpler (#get-advanced-access)

[hollow path]

well i was given this as an exercise in my orthonormal systems course.
based on that i think it shouldn't be something super esoteric

this is just a part of a 5 part problem in an exercise with 11 problems.
so i feel like i should have gotten this figured out by now without something too fancy

hell i'mma go sleep it off and trying again tomorrow

thanks for playing m8!

.close

[steel stag]

.close

[safe radish]

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[orchid kite]

Question with logarithims:
A population of wolves decreases by 2% each year. At the present time, there are 8,000 wolves. How long, to the nearest year, will it take for the population to become 500 wolves?

what would the rate be?

[orchid kite]

i know it's 0.02 but is it -0.02

[safe radish]

@orchid kite Has your question been resolved?

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[fast steppe]

eq of tan line at x=3?

of g/f

[safe radish]

@fast steppe Has your question been resolved?

[fast steppe]

no

[ancient escarp]

what info do you need for a tangent line?

[fast steppe]

slope\

points

[safe radish]

@fast steppe Has your question been resolved?

[safe radish]

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[spice imp]

Can I get help with b. of this problem?

[spice imp]

and can you tell me the formulas for those if I need to know them

[safe radish]

@spice imp Has your question been resolved?

[serene ledge]

Look for this 3 concepts, Expected value of a random variable, Variance of a random variable , Standard deviation of a random variable

[merry swift]

find the pmf of Y and use the standard formulas for mean sd and variance

[serene ledge]

also, your random variable is discrete, that may help you too

[safe radish]

@spice imp Has your question been resolved?

[spice imp]

how do i find the pmf of Y? @merry swift

[merry swift]

P(X=x)=p(x).
P(Y=y)=P(2X-3=y)=P(X=(y+3)/2)=p((y+3)/2)

[spice imp]

im lost

this is the hardest math class ive taken idk whats going on honestly

[pastel verge]

Do you know formula for E(X)?

[spice imp]

E(X) = the sum of xp(x) right

[pastel verge]

Yes

[spice imp]

is E(X) used in this problem?

[pastel verge]

So what is E(Y)

[spice imp]

yp(y)

but dont i need the probability of Y to do that?

[pastel verge]

Ye

[spice imp]

but i dont see where I'd get the p(y) from

[pastel verge]

What do you think about E(2X-3)

[pastel verge]

If this isn't working for you see the question in table

I mean table in question

Make one more row for Y

Then just comput Y for given values of X

[spice imp]

what are you trying to get at with E(Y)

what is E(Y) giving me in terms of the three things i need to solve for

[pastel verge]

If you make a table of Y then you will get values -3 , -1 , 1 , 3 , 5 and corresponding p will be 0.1 , 0.3 , 0.3 , 0.2 , 0.1

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[spice imp]

I solved it

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[shell oyster]

Question:Find R

[old pelican]

did you by any chance rotate the pic after taking it?

[quasi bison]

have you made any progress so far?

[shell oyster]

Yes

I can't :d

[quasi bison]

may i suggest drawing radii from the center to each of the three points you've marked?

[shell oyster]

Yes i did that but

[quasi bison]

also maybe give them some names

also if you did that they why didn't you show it

do you expect us to magically know what you have and haven't done?

[shell oyster]

I did but i can't see

Wait

Are you here?

[quasi bison]

can you give some names to your points

[shell oyster]

Okay

[quasi bison]

i want to point something out in your diagram but i can't do so without names

also brb

[shell oyster]

What is "brb" ?

[old pelican]

be right back

[shell oyster]

Okay ty

[quasi bison]

okay, i'm back.

can you send your diagram with all relevant points named?

[quasi bison]

alright

OBAC is a rectangle.

[old pelican]

which segment has the length of 12? and 8?

[quasi bison]

AB and AX respectively, where X is the intersection of segment AC with the circle

[shell oyster]

Al is 8

[shell oyster]

Okay

[quasi bison]

that message wasn't addressed to you.

[shell oyster]

:dd

[quasi bison]

the one that was addressed to you was this:

OBAC is a rectangle.

this alone is enough to get the radius.

[shell oyster]

Oh okay rectangle is paralelogram with 90° right?

Thank youu ❤

[quasi bison]

yes...

[shell oyster]

.close

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[kind bay]

Need help on this, I thought answer was D. Can anyone explain this to me.

[quasi bison]

how did you get D?

[kind bay]

sorry not d

I got c - 9 x 12 x 14

as i thought area is 9 x12

then you have to multiply that by length which is 14

[old pelican]

the area is actually half height * (sum of the two parallel side)

[kind bay]

dont get it

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[waxen oak]

In Graph theory, what exactly is a clique? I dont understand the difference between a clique and a complete graph
Seems to me its the same thing

[quasi bison]

a clique of size n is a K_n subgraph in your graph

[waxen oak]

Oh ok so its just a way of making it clearer, since saying a subgraph is a complete graph is weird, ty!

Also kudos on this new helpsystem really cool

.close

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[fresh crypt]

The volume of a rectangular prism is 252 cm^3. If its width is 5 cm less than its length and its height is 2 cm less than its length, what are the dimensions of the prism?

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[fresh crypt]

.reopen

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✅

[fresh crypt]

The volume of a rectangular prism is 252 cm^3. If its width is 5 cm less than its length and its height is 2 cm less than its length, what are the dimensions of the prism?

[safe radish]

@fresh crypt Has your question been resolved?

[fresh crypt]

Please help

[frosty kestrel]

what have you tried?

[fresh crypt]

i have tried dividing 252 by 3

[quasi bison]

and what do you think that should give you?

[old pelican]

How do you find the volume of the prism?

[lean otter]

V=b*h

[old pelican]

expand that b

[lean otter]

What do you mean ?

[old pelican]

V = abc

or V = width * length * height

see what I did there?

[lean otter]

Isn't it the same thing ?

[old pelican]

yes

I'm hinting the way to solve the problem

[lean otter]

Did you get the answer ?

[frosty kestrel]

why do this?

volume = lwh

you were given that volume = 252 cm^3, and that:
▪︎w = l - 5
▪︎h = l - 2

@fresh crypt

[lean otter]

Can we give the whole answer ?

You know what it's fine , let them find the answer

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@fresh crypt Has your question been resolved?

[fresh crypt]

back, just cooked

So what i should do is find the length

[old pelican]

plug w and h into this: volume = lwh

[fresh crypt]

im confused in finding the length

[old pelican]

volume = width * length * height
volume = (length - 5) * length * (length - 2)

[fresh crypt]

i multiply -5 and -2?

[old pelican]

?

253 = x(x-5)(x-2)

[fresh crypt]

alright now i get it

thanks @old pelican jesus christ

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[flint ledge]

1/x = x^(-1)

a*ln(b) = ln(b^a)

log identities

a = -1, b = 1/x

yes i know

ok

so we have 1/x = x^(-1)

do you understand that

[robust lotus]

1/x is basically x^(-1). so 1/3 is 3^(-1). get it?

a*ln(b) = ln(b^a)

remember that your a is (-1)

ur b is x

[analog acorn]

Yes. $1/x=x^{-1}\Rightarrow -\ln(1/x)=-\ln(x^{-1})$ and now by this ln-rule $-\ln(x^{-1})=+\ln(x)$ because $(-1)\cdot(-1)=+1$.

[flat frigate]

daniele_danielo

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[neon elbow]

Helppp plsss

[flint ledge]

@neon elbow perpendicular lines have reciprocal negative slope

so if the slope of one line was a, the slope of a line perpendicular the the first line would have a slope of -1/a

[neon elbow]

yes but they r asking me to write the equation

[flint ledge]

solve for y

[neon elbow]

and that will give me my y intercept?

[flint ledge]

just solve for y, plug in negative reciprocal slope, and see what value you have to add to both sides to get the point (3,0)

so 3x = 6+5y, 3x-6 = 5y, y = (3/5)x-(6/5)

what would the equation be for a line perpendicular to this?

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[neon elbow]

uhhh

-11/5?

[flint ledge]

-5/3

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[pale ether]

P wave arrived 100 seconds faster than S wave

[pale ether]

There is technically a formula given but it gives no information on derivation and I can't figure it out either

[the formula]

figured out

.close

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[rapid wren]

;-; my apologies, I believe I'm a new member of the server but can I request a bit of assistance?

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[dim kiln]

What have you tried?

[gloomy peak]

?

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[undone osprey]

This a proof that if a function is differentiable near c and that that f'(c) does not equal to zero then f(c) is not a local extremum .

I am trying to understand the epsilon delta part of the proof but am struggling

[undone osprey]

I don't know why epsilon has to be L/2

i don't understand why f'(c) must be equal to f(x)-f(c)/x-c

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[low coral]

I guess this would be geometry related, but if I was gonna use a random number generator to get random values between certain numbers in order to create a cone that goes out from a center point, what bounding values for the RNG would I use and why? I don't have much experience so having as much detail as possible would be extremely useful

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@low coral Has your question been resolved?

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[low coral]

I've come up with a very hacky solution specific to my application, it should work for now.

.close

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[lean otter]

How do i stop innatention errors? Im already slow enough as it is and cant afford to loose more time. But i keeps messing up the - and + and forget do add the right numbers for powers

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[feral narwhal]

9*3^(x+1) = 3^(2x^2-4x)

[feral narwhal]

Solving for value/values of x

What steps should I take?

[marsh walrus]

looks like logs?

what have you tried

[marsh walrus]

youll want to use logs, i think theres easier ways and hard ways, if you have tried something and got stuck its a bit easier to move forward

[feral narwhal]

Haven't been taught logs, this whole concept is new

don't really understand it

[marsh walrus]

logs undo exponents

kind of like division undoes multiplication

just the notation is a little different

so if you had something like uhh

[flat frigate]

jan Niku

[marsh walrus]

@feral narwhal maybe this is a helpful hint?

[feral narwhal]

Hm

Okay I'll see if I can find some videos and try a few simpler questions

thanks

.close

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[marsh walrus]

feel free to open again and ping if u have questions

logs are complicated

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[silver axle]

<@&286206848099549185>

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[steel stag]

@silver axle square all the numbers you see on the screen, and see which ones add to each other (a^2+b^2=c^2)

[silver axle]

Ohh

But none of them add to 17

[steel stag]

2sqrt(2) ->8 and 3->9 do

[silver axle]

Wait what’s the difference when there’s a 2 behind the square root and when there isn’t

[steel stag]

sqrt(2) is smaller

when you're squaring that, do them separately

2->4
sqrt(2)->2