help-36

[final saddle]

@vernal pulsar Has your question been resolved?

[vernal pulsar]

<@&286206848099549185>

[celest crane]

This might help. From theta = 0 to pi,

[final saddle]

@vernal pulsar Has your question been resolved?

[vernal pulsar]

is this for q10 or q9

also for the volume to be negative the product of x,y,z must be negative, right?

[celest crane]

For Q10, and only z needs to be negative. The problem here is that the volume cancels out to zero from 0 to pi.

[final saddle]

@vernal pulsar Has your question been resolved?

[vernal pulsar]

ye that makes sense but why didn't that happen for q9 as well?

cuz even there you have parts of the graph that are below the xy plane and parts that are above

[final saddle]

@vernal pulsar Has your question been resolved?

[final saddle]

@vernal pulsar Has your question been resolved?

[final saddle]

@vernal pulsar Has your question been resolved?

[tranquil pine]

maybe ping the helpers atp 😭 😭

[vernal pulsar]

think i can only ping them once

[tranquil pine]

no, you can ping them once 15 minutes pass 😭

[tranquil pine]

#info message

[tranquil pine]

ohh I see your thinking, but you wait for 15 minutes and THEN ping the helpers and then wait for 15 minutes to ping it again.

I've pinged multiple times before with this system and I wasn't reported, I only got talked to when I pinged the helpers ping right when I made a help channel which we're not suppose to do

[vernal pulsar]

i see

<@&286206848099549185>

here's the question for reference

[vernal pulsar]

<@&286206848099549185>

[crimson gate]

isnt it for 9: $z^2-y^2+y^2+a^2 -2\cdot a\cdot y -a^2 = 0$

[soft zealot]

clonesolopros

[crimson gate]

$\implies z^2 = 2\cdot a\cdot y$

[soft zealot]

clonesolopros

[vernal pulsar]

ye that makes sense

but i was using polar coordinates which is why I have an integral in terms of r

[vernal pulsar]

.close

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[plucky orbit]

so first i assumed a(t)=c

then integrated to get v(t)=cx+d

i assumed it started at 27

so it would be v(t)=cx+27

then 54=4c+27-->c=6.75 but it said it was wrong

[robust mulch]

dumb units

[plucky orbit]

oh

[robust mulch]

it goes from mi/h to ft/s/s

[plucky orbit]

im dumb ty ty

[robust mulch]

the question is dumb

yw

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[rustic bough]

Prove this function always has positive correlation on R

[final saddle]

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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
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7. None of the above

[tiny gorge]

define correlation in this context

[rustic bough]

its always go up

like this

idk what word to describe in english

[tiny gorge]

positive derivative?

[rustic bough]

yes

prove it always increasing

[junior osprey]

so basically strictly increasing right?

[rustic bough]

yes

[junior osprey]

ok

differentitate the function

dy/dx=(m^2+1)(3x^2)+2(m+1)x+3

[rustic bough]

i kinda stuck after that

[junior osprey]

basically for a function to be strictly increasing, its derivative should always be positive

[junior osprey]

this has to always be positive

for a quadratic equation ax^2+bx+c=0 to always be positive, 2 conditions have to be satisfied

a>0

and b^2<4ac

here a=3m^2+3

which is positive

now just check if b^2<4ac

[rustic bough]

it does

which means

its strictly increasing

[junior osprey]

which means the quadratic is always positive

[junior osprey]

yes

[rustic bough]

ty

[junior osprey]

np

[rustic bough]

also

does the phrase "strictly increasing" commonly used in cases like this?

my country doesnt speak english so i want to know

[junior osprey]

its just something my teacher said so i believed him

[rustic bough]

lol so what do they commonly use

[junior osprey]

i mean you can just say "increasing" or "strictly increasing" and people will get what you mean

[rustic bough]

okay ty

[junior osprey]

now close the channel

[rustic bough]

.close

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[queen walrus]

<@&286206848099549185>

Guys the 7 th question please

[junior osprey]

multiply and divide by 1-x

[queen walrus]

M not able to do

[junior osprey]

ok lets go step by step

[queen walrus]

Okay

Nice pfp tho lol

[junior osprey]

first we multiply and divide by 1-x

let the denominator stay as it is

[queen walrus]

M not able to do the application of this

[junior osprey]

in numerator we get (1-x)(1+x)

which gives is 1-x^2

got this part?

[queen walrus]

Noo

[junior osprey]

can you multiply (1-x) and (1+x)?

[queen walrus]

Okay I'll show you

[warm python]

this channel is closed, please occupy a new channel

try #help-49

[queen walrus]

Wym

[queen walrus]

M not able to do

Tbh just confused

[warm python]

do you see this message, it means the channel is closed

[queen walrus]

Bruh it's maybe because she got the solution of her doubt I see that msg in every channel

[junior osprey]

its ok just ask in help 49

[warm python]

yes, and now this channel can be locked at any time

a bot does that work

[queen walrus]

I see

[queen walrus]

Okay

[final saddle]

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[rich jasper]

i need the equation

[vocal forge]

Piecewise function?

or Modulus or something?

[stable rose]

yeah i was gonna say it looks like a modulus graph

[rich jasper]

The following graph is the result of applying a sequence of transformations to the graph of one of the six basic functions. Identify the basic function and write an equation for the given graph. Identify the basic​ function:

thats all it tells me

[vocal forge]

ah then modulus it seems

[junior osprey]

|x+3|=y+3

[rich jasper]

it said incorrect ;/

[final saddle]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[junior osprey]

i was gonna explain bro chill

[rich jasper]

i gotta fill out y=

[junior osprey]

we can start by writing piecewise equations

[vocal forge]

transform that y=

[junior osprey]

first for x>=-3

we know line passes through (-3,-3) and (0,0)

[rich jasper]

yup

[junior osprey]

so we can write y=x

makes sense?

[rich jasper]

yeah

[junior osprey]

now for x<-3

we know line passes through (-3,-3) and (-4,-2)

slope is $\frac{-3+2}{-3+4}$

[soft zealot]

United states of uselessness

[junior osprey]

which gives -1

understood till here?

[rich jasper]

yeah

[junior osprey]

so equation is y-(-3)=(-1)(x-(-3))

y+3=-1(x+3)

which is x+y+6=0

but we have to enter answer in modulus

we know both lines pass through (-3,-3)

so i can write y=x as y+3=x+3

and x+y+6=0 as y+3=-x-3

y+3=|x+3| because when x>=-3 we get y+3=x+3 and when x<-3 we get y+3=-x-3

final answer is y=|x+3|-3

got it?

[rich jasper]

yeah thanks now i understand

[junior osprey]

np

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[rich jasper]

i need help with this

[vocal forge]

what did you try?

which basic functions does this refer to?

[rich jasper]

I’m not sure

[empty vigil]

Maybe y=x³ or something like that?

[empty vigil]

y=(x-3)³+1

[rich jasper]

that was correct thanks alot

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@rich jasper Has your question been resolved?

[rich jasper]

im having trouble with this question

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[mild sentinel]

i have found x and y coordinates im just not sure which method to use and why

[barren hound]

most students understand shell/washer better

[mild sentinel]

ok

which do i use

[sinful fox]

I would use washer personally

[mild sentinel]

why

[sinful fox]

Cuz ı like it?

[mild sentinel]

ok

then how do i proceed

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[tranquil pine]

Is this right?

[tranquil pine]

,rccw

[tranquil pine]

Thanks pun pun

LMAO

bro wait

💀

What makes you think d is correct option??

@tranquil pine

Oh you wrote something

What do you mean by rate of change of volume

In mathematical terms ?

[tranquil pine]

I changed my answer to D from E because whenever you get the derivative of a square root it becomes 1/2sqrt(x), but I might change it back to E because the derivative was already defined as the square root of the original function

Thougts?

I thought I cooked with D 😭

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[tranquil pine]

.close

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[zinc patrol]

Hallo

[zinc patrol]

Angle of elevation

70m tree 100m shadow

Is it tan theta = opp/adj
= 70/100

[tardy sigil]

Yep

[zinc patrol]

How do I write this out exactly

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[wintry kindle]

which tricks are there for computing eigenvalues?

[wintry kindle]

for instance, if a matrix is symmetrical, does that benefit determining the eigenvalues?

[sudden matrix]

are you talking numerically or by hand?

[wintry kindle]

by hand

e.g. some simpler case like this one

I could laplace expand, but the characteristic polynomial becomes difficult by hand

at least I don't see any good approach

[opal plinth]

I'm not confident in this area but for this matrix A, it's pretty easy to see that (A - 6I) (1,0,-1,0) = 0

You also have (A - 4I) (0,1,0,1) = 0

And then into the negative (A - 10I) and (A - 12I)

So it's 4,6,10,12

[wintry kindle]

ah I see, that's why they use the grid structure in some textbook samples

so the "intuitive guessing" approach is to select eigenvalues

such that we get linear dependence in columns

is what I'd presume you did

[opal plinth]

Pretty much

[wintry kindle]

hm kk thank thees

[opal plinth]

Not in all columns, just some

The others can just have a corresponding 0 in the eigenvector

[wintry kindle]

yea, any linear dependence in a subset would suffice

[opal plinth]

Right

[wintry kindle]

I also tried diagonalizing it but that just added extra steps :D

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[azure halo]

When I tried solving it did not work

[azure halo]

<@&286206848099549185>

[inland smelt]

What did you try?

[azure halo]

so

I subsittuted the valsues of x and y in 3x - y = 8

[inland smelt]

ok, what did you get from that?

[azure halo]

I got 3(2k-2) - k + 1 = 8

[stable dew]

You forgot that it is -1

[inland smelt]

which gave you k = 13/5 I guess

[azure halo]

how?

[azure halo]

yeah

[inland smelt]

well, it is as trollstar says, you forgot to apply distribution on +1 in k+1

[stable dew]

Ye

[azure halo]

oh

[stable dew]

You get k=15/5

So 3

[azure halo]

Oh yeah -1

ill try again

[azure halo]

yeah k =3

[stable dew]

Ok

[azure halo]

thx @inland smelt and @stable dew !

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[stable dew]

Yw

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[spring haven]

Isn’t this just the contrapositive

The second one

First one seems pretty obvious

[faint locust]

The contraposition of the first one, yeah. So they're equivalent. But I'm asking about what the premise and claim of the statement are

[spring haven]

The theorem itself states the second statement

I’m pretty sure

The first one is the contrapositive

[faint locust]

The course notes say that the second is the contraposition, so the first one is what it really says

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[sacred lynx]

Indian tea is 5/4 times more expensive than American tea. What proportion do we need to mix the indian and American teas so that we get a tea that is 6/5 more expensive than American

[lucid marsh]

What have you tried

[sacred lynx]

Well lets say

American tea is x

Indian woild be 5/4x

x+5/4x=6/5

Is that correct?

@lucid marsh

[weary spruce]

I think using a multi equation would make you understand better

[lucid marsh]

Yep

with 0<x<1

Wait no not quite

You missed a small part of the equation

[sacred lynx]

Mhh

What part?

@lucid marsh

[lucid marsh]

Think about it: you have x% american tea, then what percent indian tea do you have

[sacred lynx]

1.25x

Soo?

[lucid marsh]

what

You have 20% american tea. What percent indian tea

[weary spruce]

Pizza has 8 pieces. You take two, while Alex takes the rest. How many pieces Alex hold?

[sacred lynx]

6

[weary spruce]

Since your math question says that it's a mixture, it should be similar to the Pizza problem.
You took two, mean you hold 2/8 = 1/4 of the pizza, which is 25%, while Alex holds the rest, which is 6/8 = 3/4 = 75% of the pizza.

[sacred lynx]

Where are you going with this

[weary spruce]

So if you have x% of American tea, then the rest should be the Indian tea, and it'll be 100% - x%.

[sacred lynx]

Mhh yes

Soo whats next

[weary spruce]

I'm not gonna solve the whole thing for you.

[sacred lynx]

Well i need assistance

Guide me

[sacred lynx]

Is this equation good?

.close

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[grand wadi]

in a normal matrix, (AB)' = B' A' but is it also equal to A' B' ?

[warm python]

no, $(AB)^T= B^T A^T$

[soft zealot]

ƒ(Why am. I here)=I don't Know

[grand wadi]

aw man

so (AB)' isnt = A' B' by any chance

sad

why did these guys have to make it so weird aaaaaaaaaaaaaaaaaaaaaaaa

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[warm python]

You can prove it

[warm python]

I don't think so

[grand wadi]

thanks dude

[warm python]

,w is A^TB^T =(AB)^T

[grand wadi]

there could be exceptions tho 👽

[soft zealot]

Results provided by WolframAlpha

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

Requested by physicsrocks

[grand wadi]

not always

so there is a chance

[warm python]

when A=B both ways

[grand wadi]

damn i see

dude

how old ru

u seem pretty old

aaaaaaaa i might gtg now complete my assignment

thankusomuchhh girlieee/ dudeeeee<3333333

dont forget to hydrate 🙏

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[winged trail]

Why is this the answer for c?

Also yes, this is the correct answer, from the answer key

I just don't know why

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[winged trail]

<@&286206848099549185>

[winged trail]

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[rancid grove]

hi

[rancid grove]

i need help proving this identity

i tried by making cotx = 1/tanx

and then like multiplying it to be cosx/tanx

[undone nymph]

Try writing cotx as cosx/sinx

[tiny gorge]

when in doubt, convert everything to cos and sin

[rancid grove]

ok yeah that was my second try

(cosx/sinx)(cosx) + sinx

cos^2x / sinx + sinx

so now i am stuck on it rn

[blissful meadow]

Same denominator.

[rancid grove]

i tried converting cos^2x to 1 - sin^2x

[undone nymph]

No need

Jus make the same denominator

[rancid grove]

ok so cos^2x + sinx / sinx

[undone nymph]

Sin^2 x

[rancid grove]

where

[undone nymph]

In numerator

[rancid grove]

how

[undone nymph]

Cos^2 x /sinx + sinx

[rancid grove]

ok

[undone nymph]

So multiply second term with sinx to make same denominator

[rancid grove]

it's addition tho thats what i dont understand

[undone nymph]

Sinx = Sin^2 x/ sinx

[rancid grove]

oh get rid of the denominator?

wait nvm

is it ok if you can write it somehwere

i cannot visualize it

[rancid grove]

ok so you multiplied that sinx by sinx/sinx

wait if you do it to one side dont u needa do to another or something

[undone nymph]

Nope

There is no other side

[rancid grove]

only working on one side right

[undone nymph]

Sinx / sinx is basically 1

[rancid grove]

yes

[undone nymph]

So I'm multiplying it by 1 which doesn't make a difference

[undone nymph]

Yup

[rancid grove]

oh i see

since sinx is basically 1 * sinx

like that?

(sinx / sinx) * sinx

[undone nymph]

Yup

[rancid grove]

ok i see sin^2x / sinx

bro this feels like cheating

where the 1 come from

anyway

cos^2x + sin^2x / sinx

1/sinx

= csc

[undone nymph]

Yeahhh

[rancid grove]

can you confirm another way i tried

[undone nymph]

There's no point of bringing tan

U have to break it into sin/ Cos again anyway to reach cosec

[rancid grove]

besides the messy writing it can still be understood?

[bold gull]

like convert cot in form of cos/sin

[rancid grove]

(cos/sin)(cos) + sin = csc

sin [(cos/sin)(cos) + sin] = 1/sin(sin)

is working on both sides allowed

or no

[undone nymph]

Nope

They asked u to prove right

[rancid grove]

yes

[undone nymph]

If u work on both sides what r u trying to reach?

[rancid grove]

good point

ok i will just remember I can pull 1

[undone nymph]

Yup

[rancid grove]

ok thank you

[rancid grove]

do you know how to solve for ambiguous case

[undone nymph]

Wdym by ambiguous case

Post the prblm

[undone nymph]

The answer is none

[undone nymph]

Do you know sin rule ?

[rancid grove]

yes, i did

sin41/1.5 = sinB/2.8

i resulted in math error on calculator

i thought it was because i entered it wrong

so it means no triangle

[undone nymph]

What error

[rancid grove]

1.8369 = 1.5sinB

[undone nymph]

I don't think that's the reason tho

Yup

And (1.8369/ 1.5) >1

[rancid grove]

ye

how do you know what triangle to draw based on the lengths and angles it gives us

like how do I know if one is the hypotenuse or not

because if i draw the triangle wrong then it will affect my answer

[undone nymph]

Hypotenuse is the largest side

[rancid grove]

do i assume the given sides are not the hypotenuse?

[undone nymph]

Do u mean this problem?

[rancid grove]

because a = 1.5, b = 2.8 how do I know the third side is smaller or bigger

yes

[undone nymph]

Why r u drawing a triangle?

We jus concluded such triangle cannot exist

[rancid grove]

oh ok

and to solve it we just use sin law right

to figure it out?

[undone nymph]

Yup

Yup

[rancid grove]

what if it works tho

like lets say I got an 40

does that mean there could be potentially another angle

with an obtuse angle 140?

and to figure if that triangle exists I need to use the side length that we are given to solve for that triangle to confirm right?

[undone nymph]

if all 3 side lengths r given then u can use that sum of any 2 sides greater than third

[rancid grove]

ok

[final saddle]

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[fathom stream]

Could someone explain this

[fathom stream]

I dont get the solution

[loud sundial]

Which part

[fathom stream]

Honestly

all of it

the solution

I dont get it

Im so bad with php

[final saddle]

@fathom stream Has your question been resolved?

[hearty zephyr]

p_i is the partial sum of the number of games played. So if p_k - p_i = 14 then you're done because you found a sequence of consecutive days where 14 games were played.
to find this, they define q_i = p_i + 14 which is basically just rewriting our p_k above.
Then, since at least one game is played per day each p_i is different (because the partial sum added at least 1 to the previous p_i)
Then, since there are 30 days, there are 30 p_i and 30 q_i, so there are 60 numbers between the two lists.
However, p_i is at most 45 and each one is distinct, and so q_i is at most 59 and each one is distinct.
So we have 60 numbers, and at most 59 places to put them. By PHP, two numbers must be the same. Since each p_i distinct and each q_i is distinct it must be that one of the q_i is equal to one of the p_i.
That means that q_i = p_i + 14 = p_k and we have our sequential days of 14 games.

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[dense saddle]

help

[pale oracle]

Set up the inequality, then
Factor into sines and cosines

[dense saddle]

This right?

[pale oracle]

So far, yes

[dense saddle]

Then i got to here

[warm python]

when is sin(t)=1/2?

[dense saddle]

when t = pi/6?

[warm python]

yes

so you have sin(πx/4)<sin(p/6)

[dense saddle]

Ok i get that part

[warm python]

so this implies (πx)/4<π/6 ( As sin is increasing )

[dense saddle]

ok i think i got it

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[quartz spade]

I'm doing this problem, but I don't actually know how to do b

[quartz spade]

I think it's asking me what the limit of that is

[tiny gorge]

consider how |x_n| (the abs value) behaves as n->infty

[quartz spade]

Oh it's supposed to be the absolute value?

[tiny gorge]

no, but it will help to answer the question

[quartz spade]

It would be the same as a if you take the abs

[tiny gorge]

right, what was your answer for a?

[quartz spade]

Converges to 1

[tiny gorge]

right

now suppose n is quite large

so |x_n| is near 1

what does the (-1)^n contribute?

[quartz spade]

Right.

It makes it flop back and forth between 1 and -1, or keeps at 1 if abs value

[tiny gorge]

yea

it won't quite reach 1 and -1 exactly but it'll get closer and closer

[quartz spade]

Right

[tiny gorge]

alternating between values near 1 and values near -1

so what can you say about convergence or divergence

[quartz spade]

I guess it would converge

But there's no limit?

[tiny gorge]

to what?

[quartz spade]

If we're talking absolute value, to 1.

[tiny gorge]

no, convergence of the sequence itself

[quartz spade]

1 or -1

[tiny gorge]

as written (with no abs values)

a sequence can't converge to two things

[quartz spade]

Uh

So it doesn't?

[tiny gorge]

right

[quartz spade]

That's an option?

[tiny gorge]

does not converge = diverges

[quartz spade]

Oh

Fair enough

Do I have to list a value if it diverges?

[tiny gorge]

nope

just saying that it diverges is sufficient

[quartz spade]

So if I have a function that goes to infinity, it also diverges?

[tiny gorge]

sometimes people distinguish between divergence to infinty vs divergence due to oscillating around like this one

[quartz spade]

Does this look acceptable then?

[tiny gorge]

but divergence just means failure to converge for whatever reason

yep all 4 are good

[quartz spade]

And then adding sequences is similar?

[tiny gorge]

do you have an example?

[quartz spade]

Not really?

[tiny gorge]

ah yea this is something called the algebra of limits

[quartz spade]

Sounds fun

[tiny gorge]

basically if two sequences converge, then so does their sum or difference

[quartz spade]

Makes sense

[tiny gorge]

in your case for this problem you want to form the difference

because Y equals (X + Y) - X

[quartz spade]

Right

Do I have to use the definition of a limit?

[tiny gorge]

depends on whether you have that theorem available (" if two sequences converge, then so does their sum or difference")

if not then you should probably prove it first

[quartz spade]

$\forall\epsilon>0,\exists K\in\mathbb{N} s.t. \forall n, n\geq K, |x_n-x|<\epsilon$?

[soft zealot]

Narutoes

[tiny gorge]

yea

[quartz spade]

Let me look

[tiny gorge]

if you assume that holds for x_n and y_n

then prove that it holds for x_n + y_n

[quartz spade]

I wasn't in class yesterday because I had a concert.

[tiny gorge]

ah i see

i suspect you may have covered it since this problem is sort of a variation of that

[quartz spade]

Although this isn't yesterday's content.

This thing?

[tiny gorge]

yes!

you can use that

[quartz spade]

Oh yeah we definitely proved this in class already.

[tiny gorge]

cool

[quartz spade]

Can I say that X+Y is a convergent sequence, and X is a convergent sequence, so (X+Y)-X is also convergent?

[tiny gorge]

yep exactly

you're applying that theorem with (X+Y) and X in place of X and Y

slightly confusing due to the reuse of the same letters haha

[quartz spade]

So like that?

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[polar bloom]

So i basically found cos through sin^2 + cos^2 = 1 rule; then divided sin/cos and got square root of 2. However, the answer must be square root of 2 divided by 2

[inland smelt]

Would make sense since $\frac{\sin \theta}{\cos \theta}=\tan \theta \neq \tan \frac{\theta}{2}$

[soft zealot]

Crystopher

[polar bloom]

yeah right, then i divided tan(theta) by 2

is it correct?

[inland smelt]

Why divide it by 2? The angle is the one being halved, not the value of tan.

[polar bloom]

so that was my mistake. how do i find it for behalved angle?

$\tan \theta = \2*rootof2$

[soft zealot]

dchan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[inland smelt]

You can use tan double angle formula $$\tan 2\theta=\frac{2\tan\theta}{1-\tan^2\theta}$$
Or find some other way which may be more complicated.

[soft zealot]

Crystopher

[polar bloom]

so the only better way is to use this formula?

im going to try it now

[inland smelt]

At least that I can tell, the other way I can think of is somehow using the double angle formula for sin.

[polar bloom]

that way it becomes very messy, it transforms into quadratic equation and solving for the roots of equation becomes harder

so it gets this form after all: $$x^2 + 2x - 2\sqrt{2} = 0, where x = \tan \frac{\theta}{2}$$

[soft zealot]

dchan

[inland smelt]

I get $x^2+\frac{x}{\sqrt{2}}-1=0$

[soft zealot]

Crystopher

[polar bloom]

can u move on to webwhiteboard?

for just a minute, i will get it fast if i see how u do it

[polar bloom]

oh i have a mistake on my side, let me correct

yeah, now i have the same

so i got: $$ x1 = \frac {-\sqrt{2} + 3\sqrt{2}}{2} and x2 = \frac {-\sqrt{2} - 3\sqrt{2}}{2} $$

wait

[soft zealot]

dchan

[inland smelt]

Now you have to wonder, wich one of these is correct?

[polar bloom]

the one which is positive, right?

[inland smelt]

Yes, the motivation can be seen using the unit circle, which shows that both $\sin (\theta /2)$ and $\cos (\theta / 2)$ are both positive.

[soft zealot]

Crystopher

[polar bloom]

yeah, bcs both cos and sin of theta are already in positive quarter of a circle

but then if i take x1 its final result is $\sqrt{2}$ which was wrong

[soft zealot]

dchan

[polar bloom]

oh no my mistake

[polar bloom]

i divide it by 2 but should divide by 4

now its correct and i understood everything, thank u so much @inland smelt

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[pseudo kite]

how do i get the direction of a vector

[pseudo kite]

it says it's wrong

when i did the proper formula

ignore the context of the question

i know for a fact a_y and a_x are the components of the vector

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[jagged flare]

x,y,z are real positive numbers where xyz=1, x+1/y=2, y+1/z=3, find z+1/x

[junior osprey]

I got 7/5, can you confirm the answer?

[jagged flare]

its correct, howd you get that?

[junior osprey]

write y=3-1/z

from this we get y=(3z-1)/z

now take reciprocal on both sides

1/y=z/(3z-1)

from xyz=1, we get 1/y=xz

so xz=z/(3z-1)

we can cancel z on both sides because z can't be 0

therefore, x=1/(3z-1)

now put x and y values in terms of z in the equation x+1/y=2

which gives 1/(3z-1)+z/(3z-1)=2

now using algebra you can find z

use z and find x value

put the values in z+1/x

there you go

[jagged flare]

ok ty

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[olive dune]

if i have
f(y) $x^y + x^2 + 2^y$

[olive dune]

is everything 0 the answer?

[soft zealot]

Juan

[olive dune]

derivative

[spring haven]

!xy

[final saddle]

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.

[olive dune]

the problem is

$\ln^5(x^y + x^2 + 2^y)$

[soft zealot]

Juan

[olive dune]

at the moment i have

[spring haven]

What do you wish to do with this?

[olive dune]

im asking if derivating with respecting to y is everything 0 in the inside

[spring haven]

No, why would it be?

[olive dune]

because there is any y as numerator

only as exponent

[spring haven]

$\frac{\partial}{\partial{y}}(x^y)=0$ according to you?

[soft zealot]

kheerii

[olive dune]

exactly

[spring haven]

Why?

[olive dune]

yes exactly

i dont know

and i cant find videos about this

[spring haven]

Would you say $\frac{d}{dx}(a^x)=0$?

[soft zealot]

kheerii

[olive dune]

i know im not correctly

because i dont know

[spring haven]

^

[olive dune]

thanks

i think i wont further here

[spring haven]

What?

Did your question get answered?

[olive dune]

no, but i think you cant answer me neither

[spring haven]

Why not…?

[olive dune]

because i already told you i dont know

[spring haven]

I asked you what you think this is

[olive dune]

thats why i opened the thread

i dont know for me that's 0

but i know im wrong

[spring haven]

Okay, well that’s wrong

[olive dune]

i want to cry

[spring haven]

$\frac{d}{dx}(a^x)=a^x\ln a$

[soft zealot]

kheerii

[olive dune]

whaaaaaaaat

and the same for the 2?

[spring haven]

Yeah

[spring haven]

Can you do this now?

[hard musk]

How do u derive x^y 🤨

[spring haven]

Differentiate*

[spring haven]

Yes exactly

[olive dune]

this is the answer basing on what you said

thanks

[spring haven]

I assume you needed to find the partial derivative wrt y?

[olive dune]

what is wrt

[hard musk]

Derivative a^x is a^x ln(a) but it’s x^y

[olive dune]

[spring haven]

With respect to

[olive dune]

ohh

wow

yes

with respect to x too but i already do it because was easier

[spring haven]

They’re calculating the partial derivative with respect to y (I assume)

So the x is treated as a constant

[olive dune]

$yx^{y-1} + 2x$

[soft zealot]

Juan

[olive dune]

thats the answer respect to x

[hard musk]

Ya ok

[olive dune]

one question kheeril

are you right?

[hard musk]

I thought it’s with respect to x

[spring haven]

What?

[olive dune]

are you correct

sorry my english is not good

because hoffdog makes me think you were wrong

but aight

thanks guys

[spring haven]

Yes I definitely am

[hard musk]

?

[olive dune]

fuck, you guys are blessed borned in an english country

[hard musk]

Is it not with respect to x 😭

[olive dune]

xD

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[soft zealot]

dchan
Compile Error! Click the reaction for more information.
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[polar bloom]

i dont know if its useful but thats the only thing i could do here

[polar bloom]

$e^t \sin{x}$ is F(t), right?

[soft zealot]

dchan

[cold sable]

I feel like recognizing a pattern from here could help you a bit

[polar bloom]

oh u again 😊

[cold sable]

The formula in question being $f^{(-n)}(x)=\frac1{(n-1)!}\int_a^x(x-t)^{n-1}f(t)dt$

[soft zealot]

otheol

[cold sable]

Which just so happens to match your left-hand side when you let n = 2

[cold sable]

Hello there

This is slightly outside my range of knowledge

So I'm not sure I will be of complete help

[polar bloom]

at least u provided me a link that might help thank u

[cold sable]

If you let $n=2$, you get that $f^{(-2)}(x)=\frac1{(2-1)!}\int_a^x(x-t)^{2-1}f(t)dt=\frac1{1!}\int_a^x(x-t)^1f(t)dt=\int_a^x(x-t)f(t)dt$

[soft zealot]

otheol

[cold sable]

Which looks an awful lot like an expression in your equation

[polar bloom]

yeah right, then $f^{-2}x = (e^x - 1)\sin{x}$

[cold sable]

Yeah

So then you can solve for f(x)

And then f(0)

Without much trouble

[soft zealot]

dchan

[polar bloom]

yeah great, i will try now

[cold sable]

Have fun differentiating 🙂

[polar bloom]

wait, i had to differentiate??

[cold sable]

Yep

$f^{(-2)}(x)$ means the anti-derivative of the anti-derivative of $f(x)$ here

[soft zealot]

otheol

[polar bloom]

F(F(x)) ?

[cold sable]

$\iint f(x)$

[polar bloom]

wooah

[cold sable]

So differentiating twice would get you your f(x) here

[soft zealot]

otheol

[cold sable]

Deriving this thing twice would get you $\frac{d^2}{dx^2}\iint f(x)dx^2=\frac d{dx}\int f(x)dx=f(x)$

[soft zealot]

otheol

[polar bloom]

so it leaves me with the same f(x) ?

[spring haven]

it seems like you're overcomplicating this

[cold sable]

Yeah, deriving $(e^x-1)\sin x$ twice gives you $f(x)$

[soft zealot]

otheol

[cold sable]

You are probably right

[spring haven]

you can just use the extended Leibniz rule to differentiate the left side

$\frac{d}{dx}\int_{g(x)}^{h(x)} f(x, t) dt =f(x, h(x))\cdot\frac{dh}{dx}-f(x, g(x))\cdot\frac{dg}{dx}+\int_{g(x)}^{h(x)}\frac{\partial}{\partial{x}}f(x, t) dt$

[soft zealot]

kheerii

[cold sable]

That's quite a mouthful

[spring haven]

it's really quite simple once you start doing the differentiation

[cold sable]

Ah

I see

[polar bloom]

i dont 🙂 it seems quite tough
i will skip this task and go on for now, thanks @cold sable @spring haven

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[urban grove]

how do i do this :3

[opal plinth]

The limit exists when the function approaches the same value from both sides

The function is not continuous at some point if its value at that point is not the same as its limit (or if the limit doesn't exist)

[urban grove]

how do i do C ?

[opal plinth]

It's literally just B - A

[urban grove]

thanks :3

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[stable dew]

Can someone pls help me with question 4

[warm python]

can you find the current flowing though the circuit?

[stable dew]

well i think you use current=v/R

[warm python]

yes

[stable dew]

so you get current as 5

or do you use 25 ohm caus it also passes through the first resister

[warm python]

i=3/15

not 15/3

[stable dew]

oh

[warm python]

I think

[stable dew]

i used this logic
if it 3V drop in 15 ohm then it is 1V drop per 5 ohm

so for 10 ohm it drops by 2V

but is that even correct?

[warm python]

ah, that's right

I think

[stable dew]

ima look the question up on google and see if anything pops up

@warm python the answer is correct and the reasoning in kindof also correct

but this reasoning wont work in parralel since there current changes

[warm python]

yes

[stable dew]

ima practice some more electricity numericals for test

bye and thx

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[autumn carbon]

hello

[autumn carbon]

ok

one sec

for part c

why have they used 5.65 instead of 5.52?

[wanton pine]

arent u testing whether the mean diameter of all bolts is less thant 5.7?

i asume they used continuity correction too

[autumn carbon]

yeh

[wanton pine]

i cant be bothered to read it though so idk

[autumn carbon]

isnt that when you approximate

binomial distribution

ill wait for another person cuz im i heard from someone else that the MS is wrong

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@autumn carbon Has your question been resolved?

[final saddle]

@autumn carbon Has your question been resolved?

[autumn carbon]

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[carmine crow]

I’m trying to show that |Z|=|N|

By showing that there exists a function for from N to Z such that f is bijective

,rotate

[meager vault]

start by proving f is injective

you can do this using proof by cases

and the definition of a one-to-one function

this should be pretty straightforward since you have already constructed f(x)

[final saddle]

@carmine crow Has your question been resolved?

[carmine crow]

ok thanks

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[charred vine]

Hello i apologise if this is considered basic level math however i cannot understand the answer to part a. I know that the discriminant needs to be > 0 in order to have 2 real distinct roots but i dont understand further from that

[charred vine]

I have the answer available. If someone could explain what this means

[vast summit]

basically you just want to choose b in terms of a and c

so no matter what a and c are, you always guarantee discriminant is positive

[charred vine]

I see thankyou

So its just asking me to show that i can choose any value of b?

[vast summit]

no

it wants you to show that there exists such a value of b

[charred vine]

which satisfied the inequality?

satisfies*

[vast summit]

ye

[charred vine]

alright

[deft timber]

You need to show that [\exists b \in \mathbb{R} \ni b^2 > 4ac \quad \text{given} \quad a \neq 0 \text{ and } c \neq 0.] Try to set [b = \sqrt{4ac} + \epsilon \quad \text{for some} \quad \epsilon > 0.]

[soft zealot]

adzetto

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[mild portal]

the point of this paragraph is to show that a is a lower bound of B

what does the sentence “it follows that a <= x for every x in B” follow from?

[stoic falcon]

anything smaller than alpha cant be in B so alpha is <= all elements of B

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@mild portal Has your question been resolved?

[mild portal]

ah i see

it follows since its just the contrapositive of the previous sentence too

.close

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[cloud raft]

i dont understand the solution

[warm python]

they have re-arranged the equation

[cloud raft]

can u give the steps to reach that rearrangement?

[warm python]

ok

$kx=-12-5x^2$

yes?

[soft zealot]

ƒ(Why am. I here)=I don't Know

[cloud raft]

yes

[warm python]

so now divide both sides by x

[cloud raft]

ohh

the x^2 becomes x

and u get 12/x

am i correct?

yay

[cloud raft]

why is the underlined true

[warm python]

as k is an integer

x has to be an integer too

well, that's not strictly true

I'm not too sure actually

sorry

[cloud raft]

oh

[warm python]

let me think

just a minute

[cloud raft]

okay

[warm python]

can I see the OG problem ?

[warm python]

ok, so x HAS to be an integer

according to the question

[cloud raft]

yes

[warm python]

so the range of k is (-200,200) yes?

[cloud raft]

why -200

cant it be any number before 200?

[warm python]

200>|k|

[cloud raft]

im still confused about why its (-200,200)

[warm python]

modulus k <200

[cloud raft]

yes

[warm python]

so -200<k<200

[cloud raft]

sorry but i still dont get it

[warm python]

hmm

one minute

so what does |x| mean?

[cloud raft]

sqrt(x^2) ?

[warm python]

not really

what is $|x| \forall x \geq 0$

[soft zealot]

ƒ(Why am. I here)=I don't Know

[cloud raft]

i

i dont know what that upside down A symbol means

[cloud raft]

what does it mean

[warm python]

what is |x| for all x> 0

[cloud raft]

x

[cloud raft]

is it x?

[warm python]

yes

what about $\forall x <0$

[soft zealot]

ƒ(Why am. I here)=I don't Know

[cloud raft]

does that mean whats |x| for all x<0?

if it is, is the answer -x?

[warm python]

yes!

Ok, i have to go now , please ping helpers

sorry

[cloud raft]

oh okay

<@&286206848099549185>

[ember juniper]

Ello

@cloud raft

[cloud raft]

canu help me>

?

[cloud raft]

why is the underlined true

[ember juniper]

Just wait a sec

[cloud raft]

ok

[cloud raft]

im pretty sure that a second is over

.close

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[cloud raft]

(cuz gotta sleep)

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[viscid flicker]

g(x)=|f(x)| ; find the approximate value of g'(6)

[viscid flicker]

I tried 1/2 but it's wrong

[stuck mirage]

It cant be 1/2

Even visually

[viscid flicker]

My logic was go to where x is 6

y is 3 there

so rise over run

but that's not right

[viscid flicker]

so it would be a negative value

[stuck mirage]

As you can see, the tangent has negative slope

[viscid flicker]

ah ok

it looks like -3/2 a little

[stuck mirage]

Rise over run yes, but of whom

[viscid flicker]

should i try that

[viscid flicker]

slope of the tangent line

I got it thanks

.close

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[ruby shore]

what does failing to reject a null hypothesis imply?

[ruby shore]

that’s the question

i’m thinking that it implied there isn’t enough info to support an alternative hypothesis

does that sound right or am i missing something?

[frigid hawk]

it means that the data isn’t statistically significant

which means that the probability the sample matches the original assumption isn’t low enough

[ruby shore]

oh