help-49

[dull ember]

how do i do that?

[astral garnet]

x^2 + 3x-4=0 ??

solve it

like a normal quadratic

[dull ember]

oh right

FUCK OH MY GOD

im done with this shit mate

[midnight plank]

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[shy ice]

How would I go to starting out with these questions? I am trying to simplify the expression for the 1st one and i get 2cos^2(theta) + i 2(2cos^2(theta)sin(theta)-sin(theta)), the 2nd one I dont know

[cedar kraken]

Ok 69 first

Do you recognize this construct?

$cos(2 \theta) + i sin(2 \theta)$

[grand pond]

Mutty

[shy ice]

$cis(2 \theta)$

[grand pond]

shark in a pool

[cedar kraken]

no

What I mean is this

$e^{i2 \theta}$

[grand pond]

Mutty

[cedar kraken]

Euler formula

[shy ice]

never learned abt that in the txtbook before

nope its not in the txtbook

[cedar kraken]

ok so

[astral garnet]

u dont need that

fomula

[cedar kraken]

Do you know what's the formula of the module of a complex number?

[astral garnet]

expand cos2theta and sin2theta

[cedar kraken]

No not that

If you have a complex number in the form A + iB

Module is

[astral garnet]

brother i aint the guy, im providing a solution that involves not using eulers forumula

[cedar kraken]

Scrap that, I found a better one

Take A = 1 + cos(2 theta) and B = sin(2 theta)

And do sqrt(A^2 + B^2)

[shy ice]

ok so

[astral garnet]

expanding first is easier

[shy ice]

$2cos^2(\theta)$

it's real part

[grand pond]

shark in a pool

[cedar kraken]

There is a simpler way

[astral garnet]

yep that is the real part

[shy ice]

imaginary is

$2(2cos^2(\theta)-1)(sin\theta)$

how did u get to that step?

[astral garnet]

imaginary is 2sincos i

[shy ice]

oh yea im dum

i added 2theta like a monkey

[astral garnet]

yeah now wwe can take the modulus

[shy ice]

$2sin(\theta)cos(\theta)$

[grand pond]

shark in a pool

[shy ice]

$sqrt((2cos^2(\theta))^2 + (2sin(\theta)cos(\theta))^2)$

oh modulus 💀

[foggy pawn]

that's your question?

[astral garnet]

lol

it should be a plus in the middle

[shy ice]

yea

[grand pond]

shark in a pool

[shy ice]

now perfect yay

[astral garnet]

right now expand out those squares

[shy ice]

ok and in brackets is 4cos^4(theta) + 4(sin^2(theta)cos^2(theta)

and now factor out 4cos^2theta

and i get 1 remaining

yay ty

[astral garnet]

all g

[shy ice]

so do i make theta 2x for the 2nd question

Re: cos^2(theta/2)
Im: 2sin(theta/2)cos(theta/2)

oh factor out cos(theta/2)

[cedar kraken]

you will get the same result but the argument of the cos is theta/2 this time

[shy ice]

ah makes sense

[astral garnet]

it wants the argument

[shy ice]

yea

$2cos^2(\theta/2) + i 2sin(\theta/2)cos(\theta/2)$

[grand pond]

shark in a pool

[astral garnet]

yeah

[shy ice]

can i factor out 2cos(theta/2)?

[astral garnet]

not yet

[shy ice]

ok

[astral garnet]

i'd first use the argument formula

[shy ice]

is it tan?

[astral garnet]

arctan(imaginary/real)

[shy ice]

$arctan((2sin(\theta/2)cos(\theta/2)/(2cos^2(\theta/2)))$

[astral garnet]

other way around

[shy ice]

oh yea mb im is y

[grand pond]

shark in a pool

[astral garnet]

yeah what can you do from here?

[shy ice]

factor that out

$arctan(tan(\theta/2))$

[astral garnet]

dont have to factor

[shy ice]

so the 2 cancel out

and leaves me with 2cos...

[astral garnet]

dont factor the cos theta/2

[shy ice]

thanks Galacy I probably wouldn't have thought abt the arctan

[astral garnet]

cancel them out

[shy ice]

oh so nothing

[grand pond]

shark in a pool

[astral garnet]

yep

[shy ice]

just theta/2

ah ty

[astral garnet]

yeah

[shy ice]

yay :D

[astral garnet]

good work

[shy ice]

ty for the help

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[astral garnet]

all g

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[static valley]

Need help understanding the solution

[cedar kraken]

At which step you are stuck at

[static valley]

part b

when they find BP does it matter which round you subtract the numbers

[cedar kraken]

yes because you are doing in both cases

P - position vector

first for A then for B

[static valley]

ok so for AP if I was to switch which way I subtract the numbers I would also swith them for BP ?

[cedar kraken]

the order in both A and B cases is P - position vector
A's P. Vector is given at step a

for B you have to use the generic formula, aka r

hence you get what's on the third row (vector with lambdas, before calculating BP)

[static valley]

yh makes sense

thank you for the help

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[cedar kraken]

yw

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@gritty solstice Has your question been resolved?

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[chrome wren]

what test can I use for this improper integral of type 2?

[chrome wren]

<@&286206848099549185>

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[left terrace]

can someone tell me what i did wrong

[gleaming latch]

show your work 😎

[left terrace]

Showing work for this problem would only slow the help down

[gleaming latch]

how can we tell you what you did wrong if you don't show how you got your answer

[left terrace]

because the answer is almost the same

[gleaming latch]

5/3 is in the interval of convergence but 7/3 is not i think you flipped those

7/3 yields 1/n+2 as your series which diverges

[left terrace]

yea that was the problem

[gleaming latch]

5/3 yields a series which converges in comparison to the alternating harmonic series

which converges

[left terrace]

@gleaming latch I appreciate the help

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[daring sluice]

Can someone help me with this one?

[sinful trout]

chain rule

[novel herald]

it's just ftoc and chain rule

let F be the primitive of f

[sinful trout]

primitive?

is that the term?

[novel herald]

antiderivative

[sinful trout]

i didn't know

huh

[novel herald]

apply ftoc, then differentiate and use chain rule to do so

[cobalt sigil]

@daring sluice bro use leibnitz

rule

There bro ?

Answer would be u'(x) * f(u(x))

[daring sluice]

waait

gonna check that

idk how it works, but thanks

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[lone yacht]

How does it go from step 2 to step 3

[tribal tartan]

combine like terms

-3-3 is -6, -3+3 is 0

[lone yacht]

Oh so that bracket it just useless

[tribal tartan]

well we essentially just used the associative property

where (a+b)+c=a+(b+c)

[lone yacht]

Yea the brackets kinda confused me

Idk why they are there

[tribal tartan]

just so it’s more clear

since you used the difference of two squares

[lone yacht]

Wait

So if it was like (2x-3)+3

U just add the 3’s

[tribal tartan]

yeah

[lone yacht]

U do that when the number is after the bracket

But if it was infront

U would multiply

Alr

It’s basically like an invisible 1 infront of the bracket

Right?

[tribal tartan]

yes exactly

[lone yacht]

Alr

[tribal tartan]

the parenthesis you mean

[lone yacht]

Thanks

Yea

[tribal tartan]

bracket is the one on the very outside

[lone yacht]

Alr

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[tidal wyvern]

Hi, can I have some help please

[tidal wyvern]

I'm supposed to finish this paper so I get a D instead of a G in my maths

[nova yoke]

G doesn't mean Great?

[tidal wyvern]

No...

There's a shit ton to cover because I have dyscalcula and I can't understand much with maths.

Sorry if they're blurry I have really shaky hands

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[tidal wyvern]

<@&286206848099549185>

[tidal token]

So we have 3 quarters of a circle and the hypotenuse of a right triangle

We know the radius is 6 so the diameter is twice that

Use the formula for circumference and multiply by 3/4

for the hypotenuse, we use pythagoras theorem as suggested, with a = b = 6

[tidal token]

this is all for this question

[tidal wyvern]

I don't understand

So i multiply 12 by pi?

[tidal wyvern]

Ysa I got it

[tidal token]

multiply 12 by pi, then multiply again by 3/4 to get the circumference of the three-quarter circle

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[onyx cloak]

two regular dice are thrown. one is blue and the other is red. the following events are determined by points scored. a- the dice showed the same number b- the sum of points is at least 10 c- the amount is an odd number d- the biggest number is 4 e- points on one dice are divisors (except for the number 1 and the number itself) of the points on the other dice. a) find the following probabilities: p(e) p(c and d) b) find two pairs of incompatible events c) how many pairs of incompatible events are there in total

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[last slate]

Hello ,
if we have vector like that
and we decompose it into y and x component and
x cancel out

will Yt = Y1+Y2 or Y1sin + Y2sin

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[left terrace]

if it was 200 force diognal right and left, then 200cos(theta) and -200cos(theta) would cancel out

then you would add 200sin(theta) + 200sin(theta)

[last slate]

So why here
he just add the two vectors of E without Finding Sin of them ?

[left terrace]

yup i thought your question was about mechanics but it is circuits. i dont have an answer to your question

ping helpers

[last slate]

@stiff heart

[twilit vector]

I think the soln is wrong

[last slate]

No True

it's official

[twilit vector]

It shoud be added by vector law of addition

2Esin(theta)

If it have been potential then it would be justifiable as its a scalar quantity but not electric field

[last slate]

idk

[twilit vector]

Have u calculated the value?

[last slate]

of what ?

[twilit vector]

I mean placed all their respective values and solved it

[last slate]

without using sin
= 1.5 x10^8

Using sin in this question is not possible since there's no given theta

[twilit vector]

U can use sin

Just a little geometry

[last slate]

ill try it

[twilit vector]

Its a right triangle use trigonometry to get the sin of theta

Spare my drawing btw

[last slate]

sin = 0.13

2Esin= 0.15x10^6

N/C

[twilit vector]

Pls check sin theta is coming 2/√5 ≈ 0.89

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[last slate]

🫠

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@last slate Has your question been resolved?

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[smoky brook]

I was doing an investigation question i cant get past this step in 3.c

[smoky brook]

<@&286206848099549185>

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[ruby imp]

Could someone explain or given an example of a sequence which makes this true?

[trail sphinx]

Have you seen dirichlet function ?

[ruby imp]

No

[trail sphinx]

you can check them out

for now, notice you if you can find two sequences that converges to pi, but their corresponding images sequences f(x_n) converges to two different limits, then we conclude f is not continuous at x= pi

did you get that?

[ruby imp]

Not really but kinda

[trail sphinx]

we say f is continuous at x=c, if there every sequence that converges to c, has it’s image sequence converge to f(c)

[ruby imp]

Ah ok

[trail sphinx]

by image sequence of (x_n), i mean, construct a sequence (f(x_n)) that is the function ouput for each terms in the orginal sequence

[ruby imp]

Yeah i got the image part

[trail sphinx]

alright

[ruby imp]

I dont think i really understand why this is though

[trail sphinx]

Let’s go through one example

consider f(x)= x^2

i want to check if f is continuous at x=2

consider approaching to 2 from the x axis through a sequence

(x_n)= (8,7,6,3,2,2,2.1,2.01,.2.001,…)

suppose sequence converges to 2 alr?

[ruby imp]

yeah

[trail sphinx]

i need, f(x_n)= ( f(8),f(7),f(3),..,f(2.01),f(2.001),…) converge to f(2)= 4

It should give you some intuition now

approach to x=c through a sequence in x axis

the corresponding sequence in y axis converges to f(c)

[ruby imp]

I think it makes more sense now yeah

[trail sphinx]

but the main thing is this should happen for every sequence

so really it’s not helpful to prove if a function is continuous

but it’s useful for determine discontinuity

Notice, to show f is not continuous at x=c, you need produce 2 sequences (x_n) and (y_n) such both converges to x=c but f(x_n) and f(y_n) converges to 2 different limits

[trail sphinx]

so here, take (x_n)= pi-1/n

notice (x_n) is only rational for every term

take (y_n)= pi- sqrt(2)/n

notice (y_n) is all irrationals

both of them converges to pi

but f(x_n) converges to 0 (because every term is rational) and
f(y_n) converges to 1 ( every term is irrational)

[ruby imp]

ah ok

Was struggling to come up with an example like that myself

Also, i had a look at dirichlet function. I wanted to ask how its different to thomae's function which I have seen?

[trail sphinx]

thomae function is continuous at every irrational point

dirchlet is nowhere continous ( or discontinous everywhere)

[ruby imp]

Why when i look up dirichlet function it looks the same as thomae's function

[trail sphinx]

look at the graph

[ruby imp]

I am, shouldn't the image of dirichlet function be {0,1}

[trail sphinx]

yes

[ruby imp]

Oh i found it now, for some reason theres lots of images of thomae's function when i looked it up

[trail sphinx]

I don’t have a zoomed one

you have it mapped otherway

both Q and I are dense in R, it should look same

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[ruby imp]

Can someone explain how the first implies the second 2

[ebon sable]

I think they used L'hopital's rule after dividing the whole equation by (2x+1)

[brazen palm]

I was thinking
lim (f(x)+g(x))=lim f(x) + lim g(x)

[ruby imp]

Yeah that makes sense now\

I just split it up and move the lim as x->inf of (2x+1) to the right

thanks

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[ebon sable]

but does that explain lim of f'(x)? or am i missing something? 🤔

[brazen palm]

oh, can we just differentiate the whole equation?

[ebon sable]

we sure can

isn't that equivalent of L'hopital there? 🤔

(no, im not a L'hopital basher)

[brazen palm]

no sure

[ebon sable]

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[smoky brook]

I was doing an investigation question i cant get past this step in 3.c

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[topaz wolf]

ok so

[topaz wolf]

i have a question that says

prove that for every complex number z (z!=-i) that makes this equation happen |z|=1 makes this: (the equation in the pic) and that this is a real number

on the left pic thats the solution

i didnt get at the end

how did that actually prove that the equation always gives real number if the condition happens

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[novel herald]

The expression is identically 0 which is real

[midnight plank]

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[topaz wolf]

ok but how did he get from 2i(|z|^2 -1)/(z+i)(z-i) to 0

[brazen palm]

is it because |z|=1
then |z|²-1=0?

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[devout cove]

i'm stuck at this systems of equations

[devout cove]

i tried substituting but it leads to nowhere

[solid hornet]

What are you substituting

[devout cove]

i substituted x into x^2 + y^2 = 34

[solid hornet]

How do you get that equation

[devout cove]

.

[solid hornet]

Oh

I mean in the beginning

What did you substitute to get that

[devout cove]

can you send me the picture?

i don't quite understand what you're talking about

[inner wolf]

Don't use substitution here

[devout cove]

that's the original problem

[devout cove]

what do i do then?

[inner wolf]

you can write first equation as (x²+y²)/xy = 34/15, you have x²+y² and you get xy using this

Then you can find out values of the expansion of (x+y)² and (x-y)²

once you have that you can add and subtract those 2 equations to find a and b

[devout cove]

it's not quite obvious to me, how do you rewrite the first equation as follows?

[solid hornet]

common denominator

[inner wolf]

Make the denominators same

[devout cove]

oh i see

alright i'll try, brb

[devout cove]

alright so here's the thing i don't get

[devout cove]

you can get 2 answers for x right

[inner wolf]

Yeah

[devout cove]

ok i got confused by wolfram's answers

1 sec

[inner wolf]

,w solve x/y + y/x = 34/15, x²+y²=34

[grand pond]

Results provided by WolframAlpha

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

Requested by ankitwa

[inner wolf]

Confirm your solutions from this and if u still have doubts show me work I'll help

[devout cove]

ok yea nevermind

how can it equal to 5 though?

isn't it 5 when the entire expression is squared?

like (-5)^2

i'm overthinking this

[devout cove]

ok yea i get it now

x^2 just means the entire thing squared right

[inner wolf]

This is wrong x²-25=0 will give u x²=25

[devout cove]

so it can be -5 and 5

[inner wolf]

Hence ±5

[devout cove]

yea i get it now

[inner wolf]

Kk

[devout cove]

thank you 👍

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[plucky thorn]

helo

[lethal path]

hi

[plucky thorn]

How do i find the length? ik this is an old question but yeah

[shrewd bronze]

the length of what?

[plucky thorn]

diameter

od is thrrr not enough information?

there-

[lethal path]

Nah there should be enough information

So you need to know your circle theorems

So $ED \cdot EC = EM \cdot EB$ if $M$ is where the line $EB$ cuts the circle

[grand pond]

south

[lethal path]

And can you set up an equation with the segments MF, FB, AF, and AC?

[plucky thorn]

Ahhh alright alright imma try it

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[tranquil wagon]

I just need a problem like this that already solved so i can study the work

[midnight plank]

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[carmine portal]

How do I find the Trigonometric Formula with only Hypotenuse = d, and Adjacent = 7?

[grand seal]

Sin(θ) = opp/ hyp, cos(Θ) = adj/hyp

But you better have a right triangle.

[unique stream]

yes :)

[midnight plank]

@carmine portal Has your question been resolved?

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[twilit field]

find the domain of $\sqrt{\frac{\log_{0.3}\left(x-1\right)}{x^2-2x-8}}$

[grand pond]

ƒ(Why am. I here)=I don't know

[twilit field]

so either both the denom and num have to be >0

or vice versa

considering the first case

$\frac{\log_{0.3}\left(x-1\right)}{\left(x-1\right)^2-3^2}\ge0$

[grand pond]

ƒ(Why am. I here)=I don't know

[twilit field]

let. x>4

that gives

$x-1\ge1$

[grand pond]

ƒ(Why am. I here)=I don't know

[twilit field]

or $x \geq4$

[grand pond]

ƒ(Why am. I here)=I don't know

[twilit field]

but that's wrong

why

,w domain of$\sqrt{\frac{\log_{0.3}\left(x-1\right)}{x^2-2x-8}}$

[grand pond]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by physicsrocks

[slow thorn]

or we can find the critical points of the functions in the numerator and denominator

numerator becomes 0 when x = 2

because log of 1

so its positive before x = 2

and negative after x = 2

[lapis dew]

one question

how did u got x>=4

[slow thorn]

wait good qn

[twilit field]

$x\geq2$

[grand pond]

ƒ(Why am. I here)=I don't know

[twilit field]

but I've established earlier that x is more than 4

[twilit field]

here

[slow thorn]

hmmhmmhm it should be\
$x \in (-2, 4)$

wait 1 min

ill recheck

[lapis dew]

I think the problem could be the 0.3

[slow thorn]

oh mb

[slow thorn]

0.3 is pretty trivial tbh

[lapis dew]

no wait

[slow thorn]

critical point for it is always 2

log_a(1) is always 0

regardless of base

[lapis dew]

$log_{0.3} (x-1)=ln(x-1)/ln(0.3)$ but $ln(0.3)$ is negative

[grand pond]

svc

[slow thorn]

so what?

sqrt(5)/-1 is valid

[lapis dew]

so it should be x-1<=0, not x-1>=0

[slow thorn]

oh

youre saying like that

[slow thorn]

thats impossible

[lapis dew]

it should be an 'and'

[slow thorn]

log cannot be taken for negative numbers

[slow thorn]

wdym and

anyways this is how both graphs would look like

critical points

[twilit field]

hmm

ok

[lapis dew]

i messed up, x -1 <= 1, not x-1 <= 0

[twilit field]

hmm

yeah, that makes sense

[lapis dew]

when you take the intersection of (inf, 2] and (4, inf), you get no solution when both are positive

so now you consider when both are negative, prob that gives the solution

[twilit field]

yeah, got ti

thanks!

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[twilit field]

$\sqrt{e^{\arccos\left(\log_4x^2\right)}}$ find the domain

[grand pond]

ƒ(Why am. I here)=I don't know

[twilit field]

would I be right to say it's $(1,infty)$

[grand pond]

ƒ(Why am. I here)=I don't know

[still nacelle]

but isn't the domain of arccos [-1,1]?

[twilit field]

oh yeah

right

so it's just {1}?

[still nacelle]

I think it will be ||[1/sqrt(2),2]||?

[twilit field]

huh

oh

it's a log

right

[lapis dew]

shouldn't it be -1 <= log_4 x^2 <= 1

[still nacelle]

yh

[lapis dew]

okay it is not

nevermind it is

im dum

[still nacelle]

okok

[twilit field]

yeah, got it

thanks !

[still nacelle]

np

[twilit field]

thanks

.done

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[twilit field]

.coose

[midnight plank]

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[twilit field]

$\left(\log_{10}\left(1-\log_{10}\left(x^2-5x\right)+16\right)\right)$

[grand pond]

ƒ(Why am. I here)=I don't know

[twilit field]

find the domain

I think

$0<\log_{10}\left(x^2-5x+16\right)<1$

[grand pond]

ƒ(Why am. I here)=I don't know

[twilit field]

is this right?

wait

$-\infty<\log_{10}\left(x^2-5x+16\right)<1$

[grand pond]

ƒ(Why am. I here)=I don't know

[sage helm]

your parenthesis are all over the place man

[sage helm]

but yeah

power 10 on all three sides

[twilit field]

thanks

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[cerulean geyser]

... self explanatory

how do i divide the shape though

[latent elk]

I dont think you should

This is surface area, not volume

By cutting it into smaller piece, it may cause confusion

[last slate]

just draw a bunch of lines such that u get a bunch of rectangles

[cerulean geyser]

yeah but theres no formula for a shae like that

[last slate]

to work with

[latent elk]

Use common sense

[cerulean geyser]

hahah...

wow thank u guys

[last slate]

something like this works for example

[cerulean geyser]

yeah thats what i did thoughh

i got either 74 or 118

...

[last slate]

so like uh i guess intuiting it out is probably best. Lets go through it. What is the surface area of the squares facing front?

[cerulean geyser]

3 for both

[last slate]

how so?

[cerulean geyser]

huh

isnt it 3*1?

[last slate]

they are both length 1, their area is 1 as well

[cerulean geyser]

but the height of it is 3 no?

[last slate]

oh yes my bad i didnt notice the 3

yeah so 6 in total

[cerulean geyser]

i feel u fr

yeahh

[last slate]

now the rectangles on the side ans bottom

[cerulean geyser]

and thenn for the sides, it's 12 each

[last slate]

of both things

[last slate]

yeah but u have to be careful bc

one of the sides

is like

not the same

[cerulean geyser]

there's those insides of the shape too

oh em gee

[last slate]

anyways the normal faces are what then

all

[cerulean geyser]

the sides are 12 each, the fronts are 3 each

[last slate]

yeah but in total i mean

[cerulean geyser]

oh

let me work it fr

[last slate]

u have how many of 12

[cerulean geyser]

2

the very top and very bottom are both 14 each

[cerulean geyser]

uhhhuhhhh

[last slate]

so all of the like wedges are what then

[cerulean geyser]

which wedge

[last slate]

this is kinda hard to describe/explain over text

uh

[cerulean geyser]

i feel u brah

[last slate]

maybe it's better to just like let u count how many of each face there are and just add them all up at the end

ok so

[cerulean geyser]

okkk so that and the other side of it is 12

[last slate]

yeah

[last slate]

so

face with 12: 2 of them

[cerulean geyser]

thats 3 each

[last slate]

yes

so

face with 12: 2 of them
face with 3: 2 of them

[cerulean geyser]

14 each (also for the bottom) because i used this

[cerulean geyser]

huhh whats this

[last slate]

yeah

[last slate]

its just the amount of faces

[cerulean geyser]

thats 3*3 so 9

[cerulean geyser]

ahhh got ittt

[last slate]

ye

[cerulean geyser]

that and another side of it, im assuming is 2*3, sooo theres 6 each

[last slate]

yeah

but now the back of the thing

[cerulean geyser]

and thennn the back

yeah

15

WOOOOOOO

ok

LETS GO

[last slate]

yeah sum all of them up noe ig

[cerulean geyser]

15+6+6+9+14+14+3+3+12+12

[last slate]

yeaaa

sounds right

[cerulean geyser]

94

WOOOOOOOOOOOOOOOOOOOOOO

[last slate]

AYEE

[cerulean geyser]

ITS IN THE CHOICESSSSS

FINALLY

THANK YOUUU

💪

[last slate]

LOL NO WORRIES !!

[cerulean geyser]

the other ones who helped me here sound so quiet 😭

thank u for matching the energyy

[last slate]

😭

[cerulean geyser]

OKK BYEE

[last slate]

it be like that 😔

BYE

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[deft flint]

how do I solve inequalities like this (no calculator/

[deft flint]

I know that k=-9/2 if I just make it an equation

[dreamy lichen]

That's when it equals 0

[deft flint]

yeah

so how do I do it when it's an inequality

[dreamy lichen]

so on one side of it, it might be greater than 0 and on the other it might be smaller, which is what we are looking for

but there is also one more "critical point"

and that is when the denominator is 0

Those are the only points where the expression can switch from being positive to being negative or vice versa

[deft flint]

if denominator is 0, isn't it undefined?

[dreamy lichen]

It indeed is

but it can switch at around that point from negative to positive

or vice verse

[deft flint]

ok

[dreamy lichen]

e.g. 5/-0.001 is something extremely negative

[deft flint]

is there a way to do this without a sign diagram

[dreamy lichen]

like -50000

[deft flint]

yeah, limits

[dreamy lichen]

and 5/0.00001 is something positive like 500000

[dreamy lichen]

It's actually the simplest thing you can do

examine the critical points, and quickly think at which intervals its gonna be positive and where its negative

[deft flint]

is graphing quicker if I have a calculator?

[dreamy lichen]

hmm

depends on experience ig

i can see the solution instantly just when i look at it

[deft flint]

how

[dreamy lichen]

in my head i work with the "sign diagram"

[deft flint]

wow

[dreamy lichen]

so let's look at the "critical points"

[deft flint]

I can do u sub in my head but not this

[dreamy lichen]

there are 2, k = -4.5 and k = 0

[deft flint]

ik how to do a sign diagram; i forgot how to find crit points

[dreamy lichen]

you know calculus?

[deft flint]

yeah

[dreamy lichen]

that will make it easier for you to do this

[deft flint]

ok

[dreamy lichen]

when k is large enough, the expression will be positive or negative?

[deft flint]

+ve

i think

[dreamy lichen]

indeed

there is nothing that can be negative

[deft flint]

yep

[dreamy lichen]

now at k=0, it must swithc

since the denominator will become negative

so some k<0, it must be negative

now the next critical point is -4.5

[deft flint]

alright

[dreamy lichen]

and at that point it will switch back to positive, because the numerator will become positive again too

[deft flint]

yes

[dreamy lichen]

so our solution is interval from -4.5 to 0

[deft flint]

oh that's smart

[dreamy lichen]

open interval, since it's strict inequality

[dreamy lichen]

btw watch out when there are squares

when there is e.g. k^2 in the denominator, it will not become negative

because even powers are always positive

[deft flint]

absolute values too

[dreamy lichen]

indeed

[deft flint]

what about square roots

[dreamy lichen]

sqrt x is undefined for x < 0

otherwise its positive

or rather non-negative

because its 0 at x = 0

$\frac{\left(x-1\right)\left(x-2\right)}{\left(x+3\right)^{2}\left(x-4\right)^{3}}<0$
Let's do e.g. this. So the critical points are x=-3, x=1, x=2, x=4. For large enough values of x, it will be positive. then at x=4, it will switch from positive to negative (because cube keeps the sign), and at x=2, it will go back to positive. So first solution interval is (2, 4). Then it will go back negative at x=1, but it will not go positive again at x=-3, because it's squared. So the other solution interval is (-infinity, 1)

[grand pond]

MethIsAlwaysRight

[dreamy lichen]

its just a matter of practise then

[deft flint]

this approach is what i was looking for

thanks

I'll practice from here

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[inland patio]

Consider the following proposition (absolute continuity of the integral):

[grand pond]

Philip

[inland patio]

Now consider the following example:

[grand pond]

Philip

[inland patio]

Can someone explain why does (1) not hold?

[visual tiger]

Because 1/x is not integrable

And no matter what delta you take, v((0,delta/2)) = +infinity

[inland patio]

ok, I think I understand what you are saying, but why does the author write nu(A)=0 if mu(A)=0, why is this relevant?

does this implication imply that nu(A) is small whenever mu(A) is?

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[terse burrow]

im having problems with the first one

<@&286206848099549185>

[midnight plank]

@terse burrow Has your question been resolved?

[midnight plank]

@terse burrow Has your question been resolved?

[midnight plank]

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[wicked mist]

i dont know why i get this message

im pretty sure i got the antiderivative correct

[hard ore]

None of your answers should have x in them

They should be real numbers

And for D it’s negative

[wicked mist]

i see

i dont need to add the x just the number in front of it

ty

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[kind sundial]

Conuses base radius is 5. The conus when spraed out is the second one and its also a sector the angle is 120 need the conuses surfice area

[wary thorn]

!xy

[midnight plank]

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.

[kind sundial]

well the problem is in a different language if you dont get anything please ask

[wary thorn]

You need the cones surface area?

[kind sundial]

yes

that the same conus btw

[flint axle]

Is the height of the cone given?

@kind sundial

[kind sundial]

nope

[flint axle]

I see

<@&286206848099549185>

Is that given?

[kind sundial]

no

if any of thoes where given it would be simple

@wary thorn got any ideas?

wait if i find the volume and -the base area would i be left with1/3 hight?

[flint axle]

Well assuming the lone i marked is 5 units in lentgh

We can find the area of the second part of the diagram

[kind sundial]

why is it 5?

[flint axle]

Because in the 1st part of the diagram radius is given 5

[kind sundial]

thats the base radius

thats 5

dude if you dont know please dont help

@wary thorn do you have any ideas please help need to do this fast

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[flint axle]

@kind sundial

I got it

[kind sundial]

how

[flint axle]

.reopen

Ok

So

[kind sundial]

.open

[flint axle]

Give me a sec

[kind sundial]

ok

[flint axle]

Lemme wrote it down

Ok so

In the first figure

The perimeter of the base circle is onvi 2pi×r

So the perimeter of base circle of first diagram is equal to the lenght of arc of the open conus

[flint axle]

Logically

So we can find the length of the radius of open cones by using the formula of the lenght of arc

[wary thorn]

!nosols

[midnight plank]

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.

[wary thorn]

Why the rush?

[flint axle]

And after we find the lenght of the radius of open conus we use that value in the formula 1/2×r²×angle

@kind sundial u understand?

[kind sundial]

i got to hand it in in 1h

[flint axle]

Did u follow?

[wary thorn]

Is it a test?

[kind sundial]

wait is the arc 10pi?

[kind sundial]

na just homework

[flint axle]

Yesss

It is 10pi

[kind sundial]

what formula is this?

[flint axle]

It is the formula to find area of a sector

The open conus is basically a sector

U get?

Ill try to be more concise

1. perimeter of base circle=lenght of arc of the cone
   2)we use that information to find the radius

[kind sundial]

sectors area is 25pi/3?

[flint axle]

Of the open cone

[flint axle]

Lemme do the calc

[kind sundial]

.reopen

[midnight plank]

✅

[flint axle]

The area of the open conus is basically the area of a sector

As the open conus is a sector

<@&286206848099549185> please verify my answer

<@&286206848099549185>

Lenght of arc formula is = r× angle

[kind sundial]

Area if the sector is 25pi/3

@wary thorn

Help us pls

[midnight plank]

@kind sundial Has your question been resolved?

[flint axle]

<@&286206848099549185>

[wary thorn]

Stop pinging helpers. This is not even your channel.

!15mins

[midnight plank]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[wary thorn]

!nosols

[midnight plank]

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.

[wary thorn]

I already warned you once @flint axle

Read the server rules in #rules

[wary thorn]

!noping

[midnight plank]

Please do not ping individual helpers unprompted.

[wary thorn]

Be patient and follow the rules or close the channel

[kind sundial]

its ok man you good @flint axle

.close

[midnight plank]

Channel closed

Closed by @kind sundial

Use .reopen if this was a mistake.

[flint axle]

Sorry i just was trying to help wont happen again

[midnight plank]

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[patent oyster]

Hello I need help with a CRT question

[dusky sphinx]

Chat I need help

[flint axle]

Use the formula to find the length of line when two points are given

When u have the lengths u will be able to clasify what sort of triangle it is

[dusky sphinx]

Give me answers chat

[flint axle]

Is this for homework?

!nosols

[midnight plank]

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.

[copper terrace]

it’s a quiz lol

[dusky sphinx]

YES

[flint axle]

!nosols

[midnight plank]

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.

[flint axle]

Plz read

[midnight plank]

@dusky sphinx Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

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Remember:
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[vapid token]

so, example I have a sphere at 5,5,5 with radius of 5, how can i find the radius if you look at like z=3?

[valid fiber]

What do you mean ?

[vapid token]

so at z=5 the radius is 5 because its the center, but if you look at like z=4, how can i tell the radius at that point?

idk if i make sense

like when account for the curve of the 3d sphere

[rose trout]

The sphere has equation (x-5)^2+(y-5)^5 + (z-5)^2 = 25.

What happens when you plug z=3 in there ?

[vapid token]

oh so you can just relace r^2 with 3?

[rose trout]

Well if you plug in 3 and bring the constant it gives to the other side, it yields

(x-5)^2 + (y-5)^2 = 21.

So what is the radius of that circle?

[vapid token]

sqrt(21)?

[rose trout]

Yes

[vapid token]

ive been overthinking this, so much

tyfr

[rose trout]

No worries

[vapid token]

.close

[midnight plank]

Channel closed

Closed by @vapid token

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[midnight plank]

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[tranquil turtle]

how do I simplify sin^3x/cos^2x to sinx?

[tranquil turtle]

or that's not possible

?

[dull yoke]

are you asking to put sin^3x/cos^2x in terms of sin(x), or saying that it simplifies to sin(x)?

[tranquil turtle]

the latter

[dull yoke]

hmm

,w ((sin(x))^3)/((cos(x))^2)

[grand pond]

Results provided by WolframAlpha

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

Requested by northsteve

[dull yoke]

@tranquil turtle it doesnt simplify to sin(X)

[tranquil turtle]

ah then I have a mistake, well this is the question. a) I modified the left side to:

(cosx) x (sinx^3x)/(cos^3x)
= sin^3x/cos^2x

but I wasn't able to simplify further, im not sure where's my mistake

[dull yoke]

sin^3x/cos^2x

ur not mistaken

try writing it as

sin * sin * sin / cos * cos

then make tan if u can

see what u get from there

[tranquil turtle]

alr

[tranquil turtle]

yeah I got the right side now

thanks for the tip

[dull yoke]

yea np

[tranquil turtle]

.close

[midnight plank]

Channel closed

Closed by @tranquil turtle

Use .reopen if this was a mistake.

[midnight plank]

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.

[last slate]

what does the 127 whole mean

[last slate]

like wdym wdym bruh

[wary thorn]

How old are you?

[last slate]

shush

[steel trout]

Lmao

[last slate]

what does 127 whole mean

[wary thorn]

127 is the whole number part of 127.368

[steel trout]

It’s means 127 before the point

[last slate]

incant imagine it

ik but i cant imagine it bruh

[nova yoke]

you don't have to imagine it

[last slate]

like is it the length of the circle

[nova yoke]

it is there before your eyes

[wary thorn]

What?

[nova yoke]

behold it

[wary thorn]

⁉️

[last slate]

ok wait

[wary thorn]

if I give you 1 and 1/2 apples

or 1.5 apples

equivalently

you have 1 whole apple

the rest is the decimal part

[nova yoke]

Austin might give 1 and 1/2 apples to okfine83 for various reasons, depending on the context of their interaction:

Sharing: Perhaps Austin has a surplus of apples and wants to share them with okfine83 as a gesture of kindness or friendship.

Fair Distribution: If Austin and okfine83 are dividing food or resources among themselves or a group, giving 1 and 1/2 apples could be a way to ensure an equitable distribution, especially if there are not enough whole apples to go around.

Specific Request: Maybe okfine83 asked for a certain amount of apples, and 1 and 1/2 apples is the quantity that satisfies their request.

Practical Considerations: It's possible that Austin has a reason for giving a specific quantity of apples, such as needing to use up a portion of a larger quantity before they spoil or are otherwise no longer usable.

Overall, the reason for giving 1 and 1/2 apples could vary depending on the circumstances and the dynamics between Austin and okfine83.

[last slate]

represent it by the black

[wary thorn]

the 127, is 127 of those circles completely filled in

[last slate]

label it

[steel trout]

Bruh just GPTed his response

[wary thorn]

do it yourself

[wary thorn]

im not ur math monkey

[last slate]

idk what u mean dawg

[wary thorn]

What is possibly confusing about what I said?

[last slate]

ohhhh

127 of those circles

[steel trout]

I would reread the rules about GPT btw

[wary thorn]

Don't tell my sir bungo what to do

[last slate]

so there are 127 of those circles?

oh yeaa

i forgot thx guys

brain fart shi

[nova yoke]

my sir was expounding on the 1 and 1/2 apples example, not clearing the doubter's doubt

[last slate]

rightt?

127 of those circles that are each 3/10?

[wary thorn]

It appears llspacebarll's comment about rereading the rules regarding GPT might have been misinterpreted by Austin as instructing Bungo directly. Austin playfully defends Bungo, suggesting that llspacebarll shouldn't tell Bungo what to do.

Meanwhile, 🤫 seems to have had an "aha" moment, understanding the concept of whole numbers and decimals through the example provided earlier. They express gratitude for the clarification and attribute their initial confusion to a "brain fart."

Bungo clarifies that their earlier comment about apples was simply expanding on the example given by Austin and not directly addressing the doubt expressed by the other member. This clarifies any potential misunderstanding and provides context for Bungo's previous comment.

[wary thorn]

no, that are each completely filled in

[nova yoke]

these blow-by-blows are compelling

i prefer them to the actual dialogue

[steel trout]

GENIUS