help-33

[hearty reef]

.close

[marsh citrus]

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[rugged cobalt]

what you tried?

!status

[marsh citrus]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[pulsar latch]

I have drew the the two graph for y=e^2x and x=5/2

thats all :(

[rugged cobalt]

the area under a curve from a to b is the integral

$\int_a^b f(x) dx$

[elfin berry]

Køter

[rugged cobalt]

first we know that the area we want is 5/2

[pulsar latch]

so b must be 5/2

[rugged cobalt]

no

the area is 5/2

so $\int_a^b f(x) dx=5/2$

[elfin berry]

Køter

[rugged cobalt]

a is x=0 (the y axis)

and b is our C

$\int_0^C e^{2x} dx=5/2$

[elfin berry]

Køter

[rugged cobalt]

in words this means. the area under the curve e^2x bounded by x=0 and x=C is 5/2

[pulsar latch]

ohh

[rugged cobalt]

make sense?

[pulsar latch]

yup

but how do we find c?

[rugged cobalt]

also keep in mind that we are not interested in $\int_C^0 e^{2x} dx=5/2$ becuase C is a positive numer

[elfin berry]

Køter

[rugged cobalt]

do you know how to find definite integrals?

F(b)-F(a)

where F(x) is the antiderivative

[pulsar latch]

in this case the antider= 2e^2x?

[rugged cobalt]

no thats the derivative

antiderivative is opposite

[pulsar latch]

idk how to integrate with exponential

but i do remember using some type of rule

[rugged cobalt]

if you can find the derivative

you just do the reverse

like what is the derivative of 1/2 * e^(2x)?

[pulsar latch]

e^2x/2 ?

[rugged cobalt]

yes the derivative of that

[pulsar latch]

e^2/4 ?

100% wrong

[rugged cobalt]

i think youre just confusing them

what you are doing is using the chain rule when finding a derivative

d/dx e^(2x) = d/dx 2x * e^(2x) = 2e^(2x)

[pulsar latch]

so using chain rule if wrong?

is it product rule?

[rugged cobalt]

nono im just saying what to do

so the derivative of e^(2x) is 2e^(2x)

which means the antiderivative of 2e^(2x) is e^(2x)

because they mean the opposite

[pulsar latch]

sorry, i just struggle very much ur great at explaining but i just sux at math

i understand wym now

[rugged cobalt]

ok, so antiderivative of e^(2x) is?

[pulsar latch]

1/2e^2x

[rugged cobalt]

yup

this would be also + constant

usually called C but its confusing cause its a different C from your problem

[pulsar latch]

1/2e^2x + C

[rugged cobalt]

1/2e^2x+C

no the dx dissappears with the integral

and in definite integral like ours

the C cancels

because we do F(b)-F(a)

$\int_C^0 e^{2x} dx=F(C)-F(0)=5/2$

[elfin berry]

Køter

[rugged cobalt]

$\int_0^C e^{2x} dx=F(C)-F(0)=1/2e^{2C}+K-(1/2e^{2(0)}+K)=1/2e^{2C}-1/2e^{2(0)}=5/2$

i called them K instead to not confuse you

with the C

adn you can see they cancel

so in definite integrals the +C always disappears aswell

K-K

[pulsar latch]

👍

[elfin berry]

Køter

[rugged cobalt]

and i plugged in C and 0

for F(x) which was our anti derivative

now its just an equation and you solve for C

[pulsar latch]

so 5/2+1/2e^2(0)=1/2e^2(C) ?

[rugged cobalt]

2C

and +1/2e^(2(0)) if you move it to the other side

cause its already negative

yes

just simplify and isolate C

[pulsar latch]

When they say C is a positive real constant do they mean C must be a real number?

[rugged cobalt]

yes

and positive

oh i turned the integrals the wrong way around here

$\int_0^C e^{2x} dx=F(C)-F(0)=1/2e^{2C}+K-(1/2e^{2(0)}+K)=1/2e^{2C}-1/2e^{2(0)}=5/2$

[elfin berry]

Køter

[rugged cobalt]

do you need help solving this equation? or are you still working on it

[pulsar latch]

I keep getting a decimal number. pls help

[rugged cobalt]

it is a decimal number

you multiply both sides by 2

5+e^0=e^(2C)

6=e^(2C)

and then take ln both sides

ln(6)=ln(e^(2C))

you know ln and e^ are inverses no?

so they cancel

ln(6)=2C

ln(6)/2=C

,calc log(6)/2

[elfin berry]

Result:

0.89587973461403

[pulsar latch]

oh this part is where I need to revise

[rugged cobalt]

hmm is like solving equations like

7^x=5

you take log with base 7 both sides

log_7(7^x)=log_7(5)

x=log_7(5)

they cancel

and log with base e is called ln

log_e(x)=ln(x)

[pulsar latch]

then is 1/x = In(x)

[rugged cobalt]

no

1/x is the derivative of ln(x)

ln(x) is a function

[pulsar latch]

thanks a lot, this will def help during trials

[rugged cobalt]

np you should revise logarithms though 💀

watch a youtube vid or smth

or if you dont really care about understanding

just remember that ln and e^ cancels eachother

so you can solve equations like e^x=15

[pulsar latch]

youtube vid might help a lot but sometimes u need help with that one specific ques but they dont have

Like this one and its even diff becuz our teacher dont give answers

But thank you for your help, and sry for taking up your time

.close

[marsh citrus]

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[gritty lintel]

How did the system get 12 here

[gritty lintel]

its not a test its practice i just wanna know it got 12

[vast shoal]

$\frac{x}{2} + y = 1$

[elfin berry]

ColdTee

[vast shoal]

Two intercept form

[gritty lintel]

Why =1

[vast shoal]

,w intercept form

[elfin berry]

Results provided by WolframAlpha

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Requested by ColdTee#6459

[vast shoal]

That's just how the equation is written

But if you want the derivation

You can search on google or try deriving it yourself as well

[marsh citrus]

@gritty lintel Has your question been resolved?

[gritty lintel]

How is this done

[median quiver]

can someone show me how to solve this on a calculator

[gritty lintel]

Dude

This is

My channel

[twilit grove]

read #❓how-to-get-help

[median quiver]

my bad

[twilit grove]

they give you the y-intercept and you're "told" the slope because it is parallel to the other line

[gritty lintel]

How did -16 become 11

[twilit grove]

it doesn't; -16 is the y-intercept for line R

[marsh citrus]

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[marsh citrus]

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[marsh citrus]

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[red pecan]

3rd line far right

i can see how this is useful for this type of problem

[marsh citrus]

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[buoyant scaffold]

I am attempting to find the local minimums of $f(x)=xsin(x), 0\leq x \leq 4\pi$, I don't really know how.

[elfin berry]

KooKoo

[marsh citrus]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[buoyant scaffold]

I have put it into online apps and gotten minimums at x=4.913,11.086. I don't care about the y values, but I would wish to express the x values in terms of something exact and not estimations

I do not know if this is possible, btw. It is entirely possible that it is not.

This is to demonstrate something in a grad school level paper so it is fairly high-powered

[runic temple]

derivatives

[buoyant scaffold]

yeah I have attemped to do that

you end up with $x= arccos(-\frac{sin(x)}{x})$

[elfin berry]

KooKoo

[buoyant scaffold]

and this seems very difficult to do

[runic temple]

!show

[marsh citrus]

Show your work, and if possible, explain where you are stuck.

[buoyant scaffold]

I just did

[runic temple]

show how you got there

[buoyant scaffold]

I cannot derive $x= arccos(-\frac{sin(x)}{x})$

[elfin berry]

KooKoo

[buoyant scaffold]

and this is pretty basic how I got here, I just took derivative, set it equal to 0, isolate x

[still temple]

,w sin(x)+xcos(x)=0

[elfin berry]

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Requested by Toby#2275

[buoyant scaffold]

yeah ik I want to make it exact

and not an estimation

[still temple]

if its grad level, you are probably allowed to do it numerically

[runic temple]

best i can get you is -x=tan(x)

[buoyant scaffold]

Yeah but how do we turn that into something exact

[buoyant scaffold]

It's for a paper I'm writing and I want it to be exact

[still temple]

what makes you think that that number is algebraic

[buoyant scaffold]

Wdym?

[still temple]

there's a nonzero chance that the solutions is transcendental

[runic temple]

whats the original problem you need it for?

[still temple]

just pick your favourite numerical method and roll with it

[buoyant scaffold]

d'Almabert proved this

It has to have some root

[still temple]

link doi

[buoyant scaffold]

This was written in like 1700

It's fundamental theorem

[runic temple]

fundamental theorem of what

[buoyant scaffold]

Algebra

But I realize that's for polynomials

Shit

I think it's fair to assume this isn't rational

[runic temple]

its possible it isnt even algebraic

[buoyant scaffold]

Wdym not algebraic?

There might be complex numbers involved but idc

[runic temple]

a solution to a finite degree polynomial

is called algebraic

[still temple]

solution doesnt look complex

[runic temple]

(more or less)

[buoyant scaffold]

Hm

Oh

Yeah haven't heard that notation before

[still temple]

https://en.wikipedia.org/wiki/Root-finding_algorithms

[still temple]

you probably have seen it, its a big part of the fundamental theorem of algebra

[buoyant scaffold]

Oh yeah root finding algorithms are different

How would I prove or disprove that it can be written as an exact number?

[still temple]

define 'exact'

I dont think proving something is rational is usually easy

similarly, algebraic

[runic temple]

what do you need this for anyway?

[still temple]

https://math.stackexchange.com/questions/442332/express-solutions-of-equation-tan-x-x-in-closed-form

[buoyant scaffold]

Basically I'm writing a paper referencing gradient descent

And I'm trying to use the function f(x)=xsin(x) to show an example of how gradient descent can become stuck at local minimas

[runic temple]

an estimate would work just fine then

it can be shown (visually, or with some epsilon-delta) that the point never gets closer to what you wantn

[buoyant scaffold]

ok

[marsh citrus]

@buoyant scaffold Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[marble glacier]

Any physicist in this discord?

[marble glacier]

https://gyazo.com/546e24247644c128d2ae2a3fc964ce7a

need help with this

A piece of magnetically permeable material is placed so that the point at which you have evaluated the magnitudes of both of the magnetic fields lies within it. If the relative magnetic permeability of the medium is 107.1, calculate new values for the two fields (express the magnetic flux density in mT):

we know https://cdn.discordapp.com/attachments/1100525243082231919/1100525357746094131/318024849333288960.png

and this

and mu_r = 107.1

[main idol]

#old-network for physics server

[marble glacier]

im aware

taking my chances in here too tho

[main idol]

almost none of your question has math in it

[marble glacier]

this is a very valid point

ill take it down in like 15 mins if no one answers

[still temple]

What are the values of the two magnetic fields that you calculated before the permeable material was added (the problem refers to those)?

[marble glacier]

so youre thinking its based on my previous questions

hm

https://gyazo.com/70f0ddd4e7f5a6281ed6af97a37eef2b

However

the bottom one is at twice the distance as the top one

If what your saying is true

this is possible

but why would it be 8 marks

[still temple]

For the first field, wouldn't the answer just be $$\left|\vec B_{1,\text{new}}\right| = \mu_0 \cdot 107.1 \cdot 98.90,\mathrm{Am}^{-1}$$

[marble glacier]

Yea

it'd be the same

https://gyazo.com/f05bd61d3fdfc28b0dd09697f9b0d697

I just wasnt too sure if thats how the question was intepreted

[still temple]

For the second field, it would be $$\left|\vec B_{2,\text{new}}\right| = 107.1 \cdot 10.36,\mathrm{\mu T}$$

[elfin berry]

Landau08

Landau08

[marble glacier]

That is correct yes

Ok just makign sure

thanks

.close

[marsh citrus]

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[trim lodge]

thanks ahead of time

[trim lodge]

find the general solution to the trig equation: (2cos theta-1)(tan theta + 1) =0

I just want another pair of eyes going through and making sure its all okay

[marsh citrus]

@trim lodge Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[wind mural]

Hello! I'd like help on a, c, and e. I don't know how to confront c and e due to the higher orders, and I would just like someone to look over my work for a since I'm getting an absolute value sign around the x that I feel like isn't supposed to be there.
Thanks!

[wind mural]

Heres my work:

[marsh citrus]

@wind mural Has your question been resolved?

[wind mural]

<@&286206848099549185> help pls

[marsh citrus]

@wind mural Has your question been resolved?

[marsh citrus]

@wind mural Has your question been resolved?

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[still temple]

confused what this proof is saying

[sterile vapor]

3.1415926535897

[marsh citrus]

@still temple Has your question been resolved?

[main idol]

Which part exactly

[still temple]

Need help walking through it

tbh

[marsh citrus]

@still temple Has your question been resolved?

[main idol]

Look just ask a question

Read one sentence at a time and ask when something doesn't make sense

[still temple]

So p_xy is the prob that theres a noninfinite hitting time

starting at x and ending at y

right?

[main idol]

There's nothing to explain

[main idol]

Is that defined in the text? Show its definition

[still temple]

it is

basically the total probability that it hits y again

so

$\rho_xy = \sum_{paths} P(path)$?

[elfin berry]

! matthewzz

[still temple]

also

Also im concerned between the difference in notation here

The book uses the period of a state, and $I_x$ interchangibly, but then talks about $I_n (n\in \mathbb{N})$ (eg: $I_0$), im confused what $I_x$ vs $I_n$ is?

[elfin berry]

! matthewzz

[still temple]

.close

[marsh citrus]

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[heavy phoenix]

hello, i'm not sure how to go about this

[heavy phoenix]

i understand i am to use an augmented matrix, but what entries do i use

[whole sleet]

Good question before anything, what is the dimension of the space? That is, how many basis members should we expect to find?

[heavy phoenix]

3

[whole sleet]

So R³ does have dimension 3, but we have 1 limiting equation on our space. So you'll actually get 3 - 1 = 2

[heavy phoenix]

where does the 1 come from?

[whole sleet]

1 limiting equation

If we had 2 equations, would be 3 - 2

[heavy phoenix]

is that the "x_1 - x_2 + 3x_3"?

[whole sleet]

One way to think of this - we should expect to describe a plane in 3-space. The equation of the plane is right there

Ye ye. x1 - x2 + 3x3 = 0 is our plane

[shadow ibex]

https://tenor.com/view/eating-popcorn-jonathan-larson-andrew-garfield-tick-tick-boom-watching-gif-24503735

[heavy phoenix]

i see

[whole sleet]

And our basis will be from members of that plane! We need 2 basis members to describe the 2D space

[heavy phoenix]

so (1 -1 3 | 0) are the entries for the matrix?

what 2d space?

😵‍💫

[shadow ibex]

X,Y coordinates

Flatland

[whole sleet]

Your 2D space! The one that will be your answer

[shadow ibex]

(For example)

[heavy phoenix]

ooh ok

matrices are 2d

okay

[whole sleet]

Planes are 2D

Matricies are numbers

[heavy phoenix]

but the vector space specified is 3. what's a plane?

[whole sleet]

So R³ does have dimension 3, but we have 1 limiting equation on our space. So you'll actually get 3 - 1 = 2

[shadow ibex]

Are you sure you are in a Are you in a Linear Algebra course?

[heavy phoenix]

indeed, i am

oh, cartesian

the cartesian plane?

[shadow ibex]

https://www.cliffsnotes.com/study-guides/geometry/fundamental-ideas/points-lines-and-planes

https://www.youtube.com/watch?v=MD1Ob370TIA

[heavy phoenix]

thanks. i have now watched up to the plane part

[heavy phoenix]

i think i'm getting bothered by the fact x1, x2 and x3 aren't numbers, like i'm used to

[whole sleet]

Is it easier to think of it as
x - y + 3z = 0?

Same idea. I'll use that for simplicity.

Anyway, we are done when we find two basis vectors. Let's do that!

These facts are true:
x = y - 3z
y = y
z = z

But that's the same as this vector equation:

(x) (1) (-3)
(y) = (1)y + ( 0)z
(z) (0) ( 1)

And hey, that's our space described as the span of two linearly independent vectors. A basis.

@heavy phoenix

[marsh citrus]

@heavy phoenix Has your question been resolved?

[heavy phoenix]

oh-

(x) (1) (-3) why 1? why not -1? y is originally negative

(1,1,0) and (-3,0,1)

this is what my friend has

[whole sleet]

Heyo sorry I got distracted

Glad to see that your friend and I agree

[heavy phoenix]

it's all good

[whole sleet]

-1 for y? Notice I rearranged the equation to get the result that I did. That might explain the sign flip

[heavy phoenix]

ok, i see that

but what about
y = y
z = z??

are you making y and z subjects? it doesn't seem so, so how

[whole sleet]

Basically, those two lines are obviously true

One way to describe this is by "creating free variables". Two basis members, two obvious lines

I let y and z be free. So they each get a line like that. x is then determined by y and z. So it gets the top line

Ultimately the goal was to write
x =
y =
z =

And include our one equation somewhere

@heavy phoenix

[heavy phoenix]

i'm here!

[whole sleet]

Sorry I keep disappearing haha

[heavy phoenix]

i'm trying to get as much help as i can, so ig i am too. it's no biggie

[marsh citrus]

@heavy phoenix Has your question been resolved?

[whole sleet]

What was your question?

I believe I answered above

[heavy phoenix]

i'll have another in a min. guess, i'll close this and open another chat when i'm ready

yh, you did. thank youuu

.close

[marsh citrus]

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[pulsar coral]

I’m trying to calculate pesticide effectiveness over time. Once a pesticide is applied, the pest population is halved after 2 days. After a week, the pesticide effectiveness goes to 0. The pest population is updated (pop = pop * some scaling factor) hourly. How would I go about figuring out that scaling factor? Mostly just looking for methods/buzzwords to look into, I’m working on a personal project so doing some independent math research would help me grow as a programmer.

[marsh citrus]

@pulsar coral Has your question been resolved?

[marsh citrus]

@pulsar coral Has your question been resolved?

[wild zodiac]

at a glance, looks like you could apply the half-life formulas to this? 'halving every interval' seems pretty reminiscent of this

you just would stop at t=7 days

[marsh citrus]

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[lost hound]

Can someone help explain these answers to me (basic statistics)

[lost hound]

<@&286206848099549185>

[marsh citrus]

@lost hound Has your question been resolved?

[marsh citrus]

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[wispy grotto]

I have no idea how to solve

[winter meteor]

do you not know how to integrate?

[wispy grotto]

Function is given for x

But what about du

[cobalt spindle]

use newton leibniz theorem

looks like this

so by doing this you can get the derivative of f(x)

so from there you can either kind of check by eye which graph suits more

or you can integrate it

[wispy grotto]

It's different!

[cobalt spindle]

where did you get this from

[cobalt spindle]

that last formula isnt even the same theorem
its just definite integration

newton leibniz theorem is for the case when the limits of the definite integration is a function itself

[marsh citrus]

@wispy grotto Has your question been resolved?

[marsh citrus]

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[wary bluff]

Do I have to transform tan^2020(x)?

to (sinx/cosx)^2020

[whole sleet]

It works out well if you do

[wary bluff]

and then cancel bottom (cos^2020(x)) with the one outside to be left with sin(x)^2020 * cos(x) dx ?

[whole sleet]

ye

[wary bluff]

but now

this is where im stuck

[winter meteor]

where

[whole sleet]

u = sin(x)

[wary bluff]

shit

shit

my dumass transformed sin^2020(x) to (1-(cos^2(x))^1010

[whole sleet]

Oof that's getting complicated

[wary bluff]

ye tysm idk why im being so slow rn

.close

[marsh citrus]

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[wary bluff]

.reopen

[marsh citrus]

✅

[wary bluff]

for this im guessin that I shound use the ratio test on (sin(1/3^n))

[whole sleet]

The (-2)ⁿ will ensure that the terms blow up

[wary bluff]

oh I thought that means alternating series

wait so how should I approach this one.

[whole sleet]

It is alternating, but you still need the limit to go to 0

Since that doesn't happen, divergent

[wary bluff]

wait huhh

how were u able to tell dat

dat fast

[whole sleet]

The terms explode

Kind of like adding 2 + 4 + 8... there's no way that converges

[wary bluff]

ye but I still dont get how this is similiar to that

like how does (-2)^n tell that

oh is it coz of the 2?

[whole sleet]

Yeah

,calc (-2)^10

[elfin berry]

Result:

1024

[whole sleet]

And the sin doesn't do anything to reduce these terms

[drifting nimbus]

but sin(1/3^n) ~ 3^-n when n -> infinity

so the ratio is actually 2/3

[whole sleet]

Fair point, didn't consider that. I lied right at you

[drifting nimbus]

$\lim_{n \to \infty } \left| \frac{\left( -2 \right)^{n+1}\sin{\frac{1}{3^{n+1}}}}{\left( -2 \right)^{n}\sin{\frac{1}{3^{n}}}} \right| = 2 \cdot\lim_{n \to \infty } \left| \frac{\sin{\frac{1}{3^{n+1}}}}{\sin{\frac{1}{3^{n}}}} \right| = 2 \cdot\lim_{n \to \infty } \left| \frac{\frac{1}{3^{n+1}}}{\frac{1}{3^{n}}} \right| = \frac{2}{3}$

[elfin berry]

Unaty498

[drifting nimbus]

so the ratio < 1

[marsh citrus]

@wary bluff Has your question been resolved?

[drifting nimbus]

because $\sin{x}\sim x$ (as $x \to 0$)

[elfin berry]

Unaty498

[wary bluff]

ooooo

so it converges

[drifting nimbus]

yep

[wary bluff]

tysm noted.

wait but

[drifting nimbus]

just remember that sin is a tricky bastard around 0

[wary bluff]

(-2)(-2)^n / (-2)^n. when u pulled out the -2

it turned poisitive

coz of the absolute?

[drifting nimbus]

yep

[wary bluff]

and brah I didnt know u can cancel

sin like that

[drifting nimbus]

|ab| = |a||b|

only around 0

like

[wary bluff]

oh wow

so lim n -> inf sin(1/n^2)/sin(1/n)

[drifting nimbus]

when the limit of the inner term is 0

[wary bluff]

i meant

1/n^2 for the top

would the sin cancel there

[drifting nimbus]

absolutely

[wary bluff]

wowwww

wb cos

[drifting nimbus]

for cos it's 1-x^2/2

for more info : https://en.wikipedia.org/wiki/Series_expansion

https://en.wikipedia.org/wiki/Asymptotic_analysis

[marsh citrus]

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[wary bluff]

thats insane

tysm

.close

[marsh citrus]

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[azure trench]

Part d isn’t clear to me straight away

[azure trench]

I understand u use part c but there’s a sign change no?

nvm

.close

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[unkempt sorrel]

.reopen

.open

. open

bruh

[unkempt sorrel]

can someone please explain me this it has never been done in my school.

[drifting nimbus]

sum of angles in a triangle is always 180°

[unkempt sorrel]

oh ye

x=20

.close

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[wary bluff]

would this just be

$\frac{1}{12} \int_{0}^{12} 10 + sin(\frac{t \pi}{12}) , dt$

[drifting nimbus]

i'd say from 0 to 12 (and divide by 12) but yeah

[elfin berry]

Calc II Victim

[wary bluff]

but this is confusing me

do I just

set the integral equal

to the orignal equation

and solve

[drifting nimbus]

yep

[wary bluff]

damn alr

ty

.close

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[azure trench]

How can I find area of R if I have points A and B

[leaden monolith]

Depends on what techniques you have

[merry pivot]

Distance formula from point A to B

[azure trench]

ur treating AB as the base?

[merry pivot]

👍

[azure trench]

yeah i got it

used that as part of it

thanks

.close

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[azure trench]

How can u do this with no points

[marsh citrus]

@azure trench Has your question been resolved?

[pliant maple]

you can use the definition of a tangent line to disprove this as a tangent line of a circle is always perpendicular to the radius

[marsh citrus]

@azure trench Has your question been resolved?

[azure trench]

They’ve said there’s a point B outside and this forms a right angled triangle

Don’t really see that uh

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[flat junco]

Linear programming problem

[flat junco]

Can someone help me with a constraints and objective function?
What I did up to now:

1. Assigned an orientation to each edge, because input graph is undirected.
2. I added constraints that for each vertex hold sum of incoming edges = sum of outcoming edges
3. for all edge values holds x >= 1 (from 1 <= d(x,0))
4. for all edge values holds r - 1 -x >= 0 (from r-1 >= d(x,0))

[marsh citrus]

@flat junco Has your question been resolved?

[flat junco]

<@&286206848099549185>

[marsh citrus]

@flat junco Has your question been resolved?

[marsh citrus]

@flat junco Has your question been resolved?

[marsh citrus]

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[muted crystal]

I really don't know what to do, ivee tried pythagoras theorem but I don't know what to sub into it

[still temple]

,rotate

[stark salmon]

The other two angles will be 45 degrees. So sin(45)= ac/ab=ac/sqrt50

[celest wyvern]

well pythagoras should work too

[muted crystal]

if you dont mind me asking how did you get the 45 degrees?

[celest wyvern]

have a known side and two X length sides then solve

[stark salmon]

Sum of angles= 180. In an isosceles triangle, two of the angles are identical. So 180=90+2x

[celest wyvern]

in a triangle when two sides have same length the opposite angles are also the same

because u can split them in two and then are symmetrical by nature so yeah..

[muted crystal]

oh okay thanks

[stark salmon]

And like shah says, pythagoras works as well. 50=a^2+b^2, where a=b. So 50=2a^2

[muted crystal]

i got 50 = 4050

i dont think thats right

[stark salmon]

50=2a^2, divide both sides by 2

25=a^2

[muted crystal]

so |bc| is equal to 25?

.close

[marsh citrus]

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[marsh citrus]

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[wraith agate]

For d) why is 0.9999=1 false

[lucid zenith]

how is it true

[celest wyvern]

multiply both by 10000

if u are willing to make that trade with me it might be right

u are probably confused with something like 0.9999999......

the dots at the end indicate an infinite sequence

that indeed is equal to 1

but 0.999999999999999999999

is not

this might help out

https://www.youtube.com/watch?v=-tlIPvK9gmM

[wraith agate]

Ahh okay yeah ty

.close

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[dawn sand]

General question

[dawn sand]

for a trigonometry problem, tanx/2 + cotx/2 = 2cscx, I see options for tan x/2 but I don't see options for cot x/2. Am I supposed to manipulate another problem to get to cot x/2?

$\tan x/2 + cot x/2 = 2cscx$

[elfin berry]

zesty&festyII

[bright jay]

What exactly do you mean by seeing options?

[dawn sand]

This is a proof, so I need to manipulate one side, so I chose the left side.

I can use the half angle formula for tan x/2, but I'm not seeing other identity or formula options for cot x/2

[bright jay]

Also is that tan(x/2) or (tan x)/2?

Same with cot

[dawn sand]

Yes the first one

tan (x/2)

I can never figure out how to get the texit to work

[bright jay]

You can change the terms of tan/cot into terms of sin/cos

[dawn sand]

Ok so I would want to change cot (x/2) to cosx/sinx but what do I do with the 2 in denominator?

[bright jay]

It just follows, like tan(x/2) = sin(x/2)/cos(x/2)

[dawn sand]

So then I'd want to do a half angle formula for cot = cos x/2 / sin x/2

[bright jay]

I haven't done it myself so not sure

[dawn sand]

gotcha, OK thank you.

[bright jay]

This was just a suggestion I had since most problems, you convert tan/cot to terms of sin/cos

[dawn sand]

Thank you, got it, that is actually helpful.

[marsh citrus]

@dawn sand Has your question been resolved?

[dawn sand]

.close

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[still temple]

if a function is differentiable, does that imply continuity? what about vice versa?

[knotty trellis]

yes, it implies. Vice versa isnt true

[still temple]

ty

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[marsh citrus]

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[ashen flicker]

do not understand the step

[full orchid]

n! is the same as n * (n-1)!, right?

[ashen flicker]

yes

[full orchid]

you can expand that out further to n*(n-1)*(n-2)*(n-3)!

at which point you can simplify

[ashen flicker]

oh

ty

thank you

.close

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[rotund walrus]

whats the lcd of x^2-2x-3, 3-x, x+1

[rotund walrus]

is it just all of them

nvm

.close

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[winter meteor]

How do i solve this??

[jovial star]

Just put it in tha calculator

[marsh citrus]

@winter meteor Has your question been resolved?

[winter meteor]

Is this true?

[fair fulcrum]

79 is prime

[winter meteor]

and?

[fair fulcrum]

are both sides divisible by 79

[winter meteor]

huh

what does 79 have to do with anything

idk

maybe?

no

yes

idk

maybe

[fair fulcrum]

bc the right, as it's 81*80*79*78... is definitely divisible by 79

[winter meteor]

Desmos says no

maybe desmos is bad

[fair fulcrum]

that's backwards

mod(81!, 79)

[winter meteor]

It's not backwards

Wolfgram says yes

[fair fulcrum]

^

[winter meteor]

oh wait it is backwards

wtf

huh

[fair fulcrum]

wha

[winter meteor]

何！！！！

[fair fulcrum]

mod(a, b) = a mod b

[winter meteor]

そうですね

[fair fulcrum]

ok

guess they figured it out

[jovial star]

Easier would be to count the number of times 5 apears in the factors
Its obviously different as soon as you start counting

[winter meteor]

I didn't

[fair fulcrum]

disagree on the easyness thing

[jovial star]

How is that no ?
Mod 79 means it is divisible

[jovial star]

It might be longer but more natural place to start

[fair fulcrum]

fair

[marsh citrus]

@winter meteor Has your question been resolved?

[marsh citrus]

@winter meteor Has your question been resolved?

[winter meteor]

.xclose

.close

[marsh citrus]

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[untold gust]

Idk how to solve thsi problem

<@&286206848099549185>

<@&286206848099549185> ???

[sharp lantern]

Do you know how to represent a complex number in polar form?

[untold gust]

<@&286206848099549185>?

[sharp lantern]

@untold gust ?

[untold gust]

oh yea i do

i do

[sharp lantern]

How?

[untold gust]

rcox(theta), rsin(theta)*i

[sharp lantern]

Is it the crt way?

What does that mean?

[sharp lantern]

It is coordinate or complex number?

@untold gust you ther?

[untold gust]

yea i am

it's the

or did u mean

e^theta*i?

[sharp lantern]

re^(therai)

Which is rcos theta+r sin theta *i

[sharp lantern]

But you put , instead of i here

[sharp lantern]

Whatever..do you know this form?

[untold gust]

yea

i do know this form

[sharp lantern]

You can represent any complex number with that form

What are "r" and "theta" here?

[untold gust]

i mean for what

v?

[sharp lantern]

In general

[untold gust]

for v, r = 3

5pi/12 would be theta

right?

[sharp lantern]

How?

[untold gust]

bro this is simple man

cus each line

is pi/12 right?

[sharp lantern]

Yep

[untold gust]

yea

ok

[sharp lantern]

Does it mean you got the answer?

[untold gust]

no

i already knew this

[sharp lantern]

So what's your doubt?

[untold gust]

i don't know what to do from here

[sharp lantern]

You know why is zbar right?

[untold gust]

conjugate

[sharp lantern]

Yeah so find it

And multiply it

[untold gust]

is that the best way?

i will get v, w, and z

can you tell me if they are right?

?

[sharp lantern]

Or you can find in general what is z×zbar .. then just put the appropriate value

[sharp lantern]

Okie

[untold gust]

ok so i got the values

v = 3(sqrt(6)-sqrt(2))/4 + i*3(sqrt(6)+sqrt(2))/4

w = -sqrt(2) + i*sqrt(2)

z = sqrt(2)+sqrt(6) + i*(sqrt(2)-sqrt(6))

are those right?

@sharp lantern

[sharp lantern]

how do you find cos(5pi/12) value?

[untold gust]

it is

(sqrt(6)-sqrt(2))/4

[sharp lantern]

I don't know the exact value .. but if that's what the value is then it is right

[untold gust]

yea i think that's it

[sharp lantern]

v= 3cos(3 pi/12)+i 3 sin(3pi/12)

[untold gust]

ummm

how

[sharp lantern]

w = 2 cos(9pi/12)+i 2 sin(9pi/12)

z = cos(-pi/12)+ i sin(-pi/12)

[sharp lantern]

you got this much right?

[untold gust]

i do'nt know where u got pi/4 from

[sharp lantern]

what pi/4?

[untold gust]

3pi/12

[sharp lantern]

sry it's 5pi/12

[untold gust]

yea

[sharp lantern]

you got that w and z too right?

[untold gust]

right yea

but z tho

like shouldn't it be 4*?

[sharp lantern]

oh man, i made lot of careless mistakes

[untold gust]

all good

[sharp lantern]

anyway. now find conjugate of each

[untold gust]

i mean

it's just making the coefficient of the i negative

[sharp lantern]

yep

or

find (x+iy)(x-iy)

[untold gust]

x^2+y^2

right?

[sharp lantern]

yeah so you don't need too much calculations

just put x and y

[untold gust]

ok

ok so v*conjugate v = 9

[sharp lantern]

btw how you get the values of cos and sin for that values?

[untold gust]

just plug them into a calculator

or google the exact value

and it tells u

[sharp lantern]

wait

[untold gust]

w*conjugate w = 4

z*zconjugate = 16

[sharp lantern]

yeah

[sharp lantern]

yep

[untold gust]

yea thank you

.close

[marsh citrus]

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[shell hill]

hello that's the graph of : -\frac{1}{2}x^{2}+3x-x\ln\left(x\right)+\left(\ln\left(x\right)\right)^{2}
and im trying to find the limits and derivative of f(e^-x) without any calculation

[shell hill]

any one to help...

[opaque yacht]

Uhh

I think its too early in the morning

xd

[shell hill]

yeah

[opaque yacht]

No one gonna be online

[shell hill]

the best time to do maths

[opaque yacht]

Yep

Lemme see

Lemme hop on computer one sec

[shell hill]

ok

[opaque yacht]

I can't find urs

oh eait

wait

nvm im here

k

only reason im up so early is cos i wanna do some maths lmao

before skool

[shell hill]

you got a test?.

[opaque yacht]

,w -\frac{1}{2}x^{2}+3x-x\ln\left(x\right)+\left(\ln\left(x\right)\right)^{2}

[still temple]

timezones:

[elfin berry]

Results provided by WolframAlpha

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

Requested by 🥶💀🍷cold??#1875

[opaque yacht]

no

[opaque yacht]

im in the uk

[still temple]

You are, yes

[opaque yacht]

this solves the indefinite integral

[shell hill]

and u?

[still temple]

💪🇫🇷🥖

[opaque yacht]

france?

lol

what abt rulzer

[shell hill]

algeria

[opaque yacht]

k

this is the inegral indefinitive

pretty sure

,w -\frac{1}{2}x^{2}+3x-x\ln\left(x\right)+\left(\ln\left(x\right)\right)^{2}

[elfin berry]

Results provided by WolframAlpha

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

Requested by 🥶💀🍷cold??#1875

[still temple]

Algeria? More like... More like...
I don't know, there isn't much to say about Algeria
Alright I'm done clogging up this channel, good luck with your integral!

[opaque yacht]

ok

@shell hill did i lose you?

oh nvm xd

[shell hill]

man ur from france u know where Algeria is

[shell hill]

no i'm here

[opaque yacht]

k

with the indefinitve integral

[still temple]

I do, there just aren't much jokes that can be made about the country

[opaque yacht]

algeria more like algi

ha ha ''ha''

yo did i kill the vibe?

man i dont know how to do this im only in yr 8

the best i can do is this:

,w -\frac{1}{2}x^{2}+3x-x\ln\left(x\right)+\left(\ln\left(x\right)\right)^{2}

[elfin berry]

Results provided by WolframAlpha

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

Requested by 🥶💀🍷cold??#1875

[shell hill]

not trying to find the integral

[opaque yacht]

ik

the derivative

im not sure im in yr 8

mabs labyrinth can help u

cya

[shell hill]

and just to tell you because of your country i have to learn a large book of history to pass my exam

[still temple]

$-\frac{1}{2}x^{2}+3x-x\ln\left(x\right)+\left(\ln\left(x\right)\right)^{2}$

[elfin berry]

Labyrinth

[shell hill]

yeah

[still temple]

No need to thank us

Just doing what we were born for

[opaque yacht]

lmao

[shell hill]

nonono

[still temple]

So you said you wanted to find the derivative of f(e^-x)

Therefore let's just plug that in and follow the basic rules of derivation

$-\frac{1}{2}\left(e^{-x}\right)^{2}+3e^{-x}-e^{-x}\ln\left(e^{-x}\right)+\left(\ln\left(e^{-x}\right)\right)^{2}$

[elfin berry]

Labyrinth

[shell hill]

yeah it's -e^-xf'(e^-x)

[still temple]

Oh right that works too

Then let's find f'

[shell hill]

but look you can't use the ...

without calculation...

[still temple]

So we have this, do you know how to find its derivative?

[shell hill]

i know

but you're not able to use it

just in the graph ..

[still temple]

...Why not?

[shell hill]

it's not me it's the problem

[still temple]

Did they explicitly tell you "You cannot use the derivative of the function"?

[shell hill]

yeah using it is calculating..

wait lemme show you some of the correction ..

[still temple]

What do they define as "calculation"

[shell hill]

finding the derivative manually

[stoic saddle]

is the original problem statement written in arabic or french

[shell hill]

arabic french untill the university

[still temple]

It seems that all they want is the sign of the derivative

[stoic saddle]

arabic french? is that like french written in the arabic alphabet?

or did you mean "arabic; [we get problems in] french until university"

[shell hill]

noo arabic is used in highschools french in universities

[shell hill]

btw you can do that

[shell hill]

yeah

any idea?

@still temple

@stoic saddle

[still temple]

Bro be enumerating his contacts

[shell hill]

man just help me solving this shit i wanna sleep

[still temple]

Me too but I just don't know how to do this

Come to think of it, why does everyone have the need to stay up late to do homework?

Why is it that schools literally kill if you don't do it?

Sleep is a thousand times more important and beneficial to you and your learning

[shell hill]

i wish that it was a homework i'm studying for a final exam that will determine the rest of my life soo ..

[still temple]

o shit

[shell hill]

and this problem is from a bac

[still temple]

I recommend you close this channel and open a new one entirely

@shell hill Ey?
Anyways I need to go

[shell hill]

Ok man bye et passez une bonne journée !!

[stoic saddle]

it's how the ruling class ensures that children grow up overworked so they don't ever know they are overworked and incite a revolution

[shell hill]

More like brainwashed..

Let's just try to solve my problem please... Forget brainwashing my brain is already washed....

[stoic saddle]

so you're given the graph of a function, y = f(x), and asked to describe the monotony of f(e^x) without calculating its derivative explicitly?

[shell hill]

what is monotony..

[stoic saddle]

where the function is increasing and where it is decreasing

[shell hill]

yeah

[stoic saddle]

uh huh

[shell hill]

yeah exactly

[stoic saddle]

and are you given the coordinates of the extreme points of f itself

[shell hill]

yes

[stoic saddle]

uh huh

well then, let g(x) = f(e^x), then you have g'(x) = e^x f'(e^x)

[shell hill]

yeah

then..

[long arch]

e^x =/= 0

[shell hill]

it's e^-x

[stoic saddle]

then g(x) := f(e^-x) thus g'(x) = -e^(-x) f'(e^-x)

the sign of g(x) is the opposite to that of f(e^-x)

[stoic saddle]

what are the coords of the extreme points of this?

[shell hill]

(0.5; 2.18) (2; 3.09)

[stoic saddle]

ah, their k is my g...

[shell hill]

yeah

[stoic saddle]

k

well in that case

we know f is decreasing from 0 to 1/2, increasing from 1/2 to 2, and decreasing again from 2 to +infty

[shell hill]

yes

derivative of f(x) is negative ]0;0.5], positive [0.5;2] and negative [2;+inf[

[shell hill]

so how do we get the monotony of k(x) from f'(x) that's the main goal

[stoic saddle]

this is how

[shell hill]

what about the x values

they should change

[shell hill]

look how they changed these x values

alpha is equal to 0.5

[stoic saddle]

why write alpha and not 1/2

[stoic saddle]

yeah of course they should

[shell hill]

cuz 0.5<alpha<0.6

[stoic saddle]

thought you said it was equal to 0.5?

e^-x in (0, 1/2) => e^x in (2, +infty) => x in (log(2), +infty)

[shell hill]

the same thing ;}

[stoic saddle]

??

alpha=0.5 and 0.5<alpha<0.6 are mutually exclusive statements

[shell hill]

yeah yeah

[shell hill]

i didn't got a thing..

[stoic saddle]

$e^{-x} < \frac12 \implies e^x > 2 \implies x > \ln(2)$

[elfin berry]

Ann

[shell hill]

like replacing x with e^-x

??

[shell hill]

yeah now i get it so -log(2)<x<-log(alpha)

$-\log\left(2\right)<x<-\log\left(\alpha\right)$

[elfin berry]

RulzerFly.

[shell hill]

like that @stoic saddle ?

btw i'm going to sleep now thank you so much @stoic saddle for help , and have a good day

[stoic saddle]

yes...

[marsh citrus]

@shell hill Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

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.

[rustic rain]

i don't understand a

why is it 10(2.3)

[drifting nimbus]

because length of arc = r × θ

[rustic rain]

what's the difference between q a and c

[green sky]

Is that so?

Theta in what?

[drifting nimbus]

the angle

[rustic rain]

isn't p=rθ

then why is q c plus

instead of multiply

[twilit grove]

for c you have to add the length of segment AB

[green sky]

I mean in degree or rad?