help-26

[rigid ivy]

any complex number?

[late crypt]

Its either that or its (i-1) im not too sure with the exercise context but if arg (i-1)^25=arg(i-1) than thats that

[rigid ivy]

Can you show the original question?

[molten vine]

arg(z^25)=25×arg(z)

I think

[late crypt]

True

[molten vine]

Write (1-i) in exponential form

[late crypt]

What

[thorny flame]

Adam Chebil

[molten vine]

I meant i-1 sorry

[thorny flame]

Adam Chebil

Adam Chebil

Adam Chebil

[late crypt]

Yea

With this its not thr same

[molten vine]

wdym?

[late crypt]

It asks if the args are the same

[thorny flame]

Adam Chebil

[late crypt]

Huh

[molten vine]

u don't know that?

[late crypt]

Thats when u have sqrt

[molten vine]

sqrt where ?

[late crypt]

That formula is used if you have sqrt

[molten vine]

sqrt(z)?

[late crypt]

Y

[thorny flame]

Adam Chebil

$z=|z|e^{i\theta}=|z|(cos(\theta)+isin(\theta)) \\ \theta = arg(z)$

[molten vine]

the values of cos and sin don't change if you add +2kπ

[late crypt]

Sure

But do they change if I x25

[molten vine]

not necessarily

[late crypt]

Why

[molten vine]

they never change actually

[thorny flame]

Adam Chebil

Adam Chebil

[molten vine]

only the modulus change

but in ur case it's z^25

not 25z so u're not multiplying z

[late crypt]

I know

U do |z|^25 and 25xø

[molten vine]

ø = arg(z)?

[late crypt]

Y

[molten vine]

yeah multiply ø by 25 and then find out the principal measure of 25ø

and then comapare it with arg(z) to see if they're the same or not

[late crypt]

And does that make the arg change for 1-i

[molten vine]

no

do it and u'll see

[late crypt]

25x3/4pi

[molten vine]

ye

[late crypt]

75/4pi

[molten vine]

correct, but that's not the principle measure of the angle (argument)

[late crypt]

?

[molten vine]

u agree that we can add 2kπ and that doesn't change the value of 25z right ?

[late crypt]

Yes

[thorny flame]

Adam Chebil

Adam Chebil

[late crypt]

What is 2x-9pi

[molten vine]

i added 2kpi where k is an integer (in this case -9)

[late crypt]

So arg z^x = arg z

[molten vine]

in order to compare 2 angles (in trigonometry) u have to find out the principal measure of the angle which means u have to add 2kπ so that the angle is in ]-π , π ]

[molten vine]

not in general

[late crypt]

Ok

[molten vine]

in this case it happens to be the same

[late crypt]

Ok

In another way if you semplify z^25

It results -2^25 i

[molten vine]

wdym?

[late crypt]

You just calculate

Z^25

[molten vine]

what's -2^25 i

[late crypt]

=-2i

The resut

Result

-2^25i=z^25

[molten vine]

no?

z^25 is NOT equal to z

arg(z^25)=arg(z)

[late crypt]

I know im saying you just calculate (i-1)^25

[molten vine]

yeah

[late crypt]

Not using trig

Thats using trig

[thorny flame]

Adam Chebil

[late crypt]

Isnt it e^25iargz

[molten vine]

we said that arg(z^25)=arg(z) so to find out the value of z^25 u just have to calculate |z|^25

[late crypt]

Ah nvmnvm

[molten vine]

to find out the value of any complex number u just need to find out the value of arg(z) and |z|

[late crypt]

Thx

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[manic jungle]

Hello I am in desperate need of help for next complex numbers equeations.

[manic jungle]

can anyone solve these?

Using a paper or any kind of explaining steps would be so helpful.

[drifting swift]

these can be solved in a similar manner to real equations actually

the only thing that's different is the presence of i and the fact that division is now kind of a hassle

but other than that, the algebra is just like if you were working in the real numbers (for the most part)

[manic jungle]

I get the concept but I can't just picture how I exactly should I do it.

Really giving me a screenshot of those 3 would really make my day easier

[lyric lynx]

Yeah just solve it like you would solve smth like (1+5x)/(4x-1) = 40

[manic jungle]

I am literally about to get panic attack because I can't figure this shit out

[lyric lynx]

mathway

[manic jungle]

It cant solve it

Thats the thing

[lyric lynx]

Oh

Uhh

Wolfram alpha

[manic jungle]

I wouldn't come here and bother anyone if any of these apps could actually do it

[drifting swift]

uhh

[lyric lynx]

Oh ok

[manic jungle]

They just cant solve it I've tried

[drifting swift]

take a break

but also lets try actually

,w (1 + 3iz)/(z + 2i) = 7+3i

[thorny flame]

Results provided by WolframAlpha

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Requested by ann_dec

[drifting swift]

solves it just fine lmao

[manic jungle]

how

it didnt give me that I literally typed the same thing

[drifting swift]

strange

what did it give you?

time out?

[manic jungle]

I've tried this one as well

It can't solve it

[manic jungle]

Just gives me random numbers

[drifting swift]

i think if you're going into panic attacks it's best to first calm yourself down as best you can

and only then come back

[manic jungle]

the thing Is

Nothing gives me the correct answer

and it makes me go crazy

[manic jungle]

could you try typing this in wolfram?

[lyric lynx]

,w (-4+4*i)^2021

[manic jungle]

yeah it doesnt work

[lyric lynx]

???????????????

[manic jungle]

this is the answer

[gusty ginkgo]

its correct

[manic jungle]

rephrased otherwised I guess

[thorny flame]

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Requested by aol_real

[lyric lynx]

Aaaaaaaa

Crazy numbers

[manic jungle]

I know

[manic jungle]

I dont understand how they solved it this way

Its so confusing like I dont get it

[gusty ginkgo]

there is a pattern if u observe

try by observation

[lyric lynx]

-4+4i = 4(i-1)

[gusty ginkgo]

*= 4^2021 (i-1)^2021

[lyric lynx]

Yeah that

[manic jungle]

I still don't understand sadly

I get the -4+4i=4*(i-1)

[manic jungle]

but how does it get to 2^5052

[gusty ginkgo]

u can find in every 5th power the 1st square is repeating

[lyric lynx]

A typo

?

[manic jungle]

My english isn't that got let me translate that rq

You mean like i^1 and that or?

[gusty ginkgo]

i'll send a pic

[manic jungle]

Oh please 🙏

[gusty ginkgo]

It got 4 time in 2nd term

u can see that

[manic jungle]

yeah I see what you mean

but I still dont understand how it gets to 2^5052

[gusty ginkgo]

are u crazy

calm down mate

4^2021

4=2^2

2^(2^2021)=2^4042

then there is the repeating 4's are each 5th term

[manic jungle]

I am sorry I am just dumb for math

[gusty ginkgo]

no bro, its just how much u invest time

[manic jungle]

that probably as well

I got the exam in one month we just started doing this so I guesss I am panicking

I'll start practicing tomorrow slowly

[gusty ginkgo]

dont panick

else u will leave inte like me in exams

😂

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[tardy bramble]

is this possible ? the app i try using for it tells me they can't solve it yet

[knotty ledge]

what exactly are you asking is possible or not

this is part of the riemann zeta function fyi

[tardy bramble]

what is that

[knotty ledge]

a famous function

[tardy bramble]

ohhh i see

my friend asked me to solve this

he trolled me

ty btw

[winged moat]

Well

Not sure how one'd "solve" this

[tardy bramble]

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[frail python]

Hey how do I solve these

[frail python]

I'm lost, I have a quiz Tommorow on this, can someone help

[lyric lynx]

1st is a quadratic

[frail python]

How do I do it

[lyric lynx]

quadratic formula

[frail python]

Yeah but how do I start😭

[lyric lynx]

6*cos²x - 5*cos x - 4 = 0

[frail python]

Ok

I will try that

[gusty ginkgo]

cosx as t

[lyric lynx]

|t|<=1

[frail python]

Is this right?

[lyric lynx]

yes

[frail python]

Ok ty

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[raven plank]

Considering this system and A the set of real pairs (x,y) find S

[raven plank]

the (x,y) pairs that I got are (3,1) and (1,2)

so S should be 15

but the correct answer is 125/4

[opal vault]

can you show your work?

[raven plank]

y^2-3x+3=1
y^2-3x+2=0
(y-2)(y-1)=0

y1=2 x1=5-4=1

[opal vault]

do we always have y^2-3y+3 = 1?

you're tempted to say that if x^b = x^c => b=c, but is that true for any real number x?

[raven plank]

not for 1 or 0

right?

[opal vault]

yes, and for other values too, which ones?

negative x doesn't work either

(-1)^2 = 1^2 and yet -1 not = 1

[raven plank]

oh right since quadratic is always positive

so I should try to solve this in a different way

[opal vault]

not in a different way, just complete your analysis

you found that if x non-negative, not 0 and not 1, then y = ... and those work

now solve for x= 0 and x =1 and check if you get valid solutions

and finally, recall that if x is negative and x^a = 1, then a = 0 or (x = -1 and a is an even integer)

[opal vault]

rest assured, this might seem like a lot of cases, but as soon as x = -1, you get by the second equation y= ...

[raven plank]

i just solved it thanks for the explanation

[opal vault]

So all solutions should be :
||x < 0: (-1,3)
x = 0: (0,2.5)
x = 1: (1,2)
Otherwise: (3,1)||

[raven plank]

thanks

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[half pike]

how do i find a perpendicular line segment

@craggy haven hi! if you arent busy, could you help me like last time? also so sorry for tagging

[craggy haven]

hi sorry i'm at work

[half pike]

oh ok no worries

[half pike]

do i have to write y=2x+a random number to find a slope then just find a perpendicular line?

[raven plank]

the product of slopes of 2 perpendicular lines is -1

[half pike]

why?

can u show me how u do these questions?

[raven plank]

thats just the way it is

i dont know how to prove it

but that is a general rule

[half pike]

can u teach me the rule then?

[raven plank]

.

and for parallel lines the slopes are the same

m1=m2

where m1 is the slope of the first line and m2 the slope of the second one

[half pike]

and perpendicular is m1 = the reciprocal?

like does that make sense

like if m1 is 2/3

m2 could be 3/2?

[raven plank]

-3/2

[half pike]

ohhh

[half pike]

is that it?

[raven plank]

yes

[half pike]

okk tyy

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[half pike]

.reopen

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✅

[half pike]

hey i have a question

if m1 = 0.6 and m2 = 3/5

they are the same line so does that count as parallel

[hallow depot]

are m1 and m1 the slope coefficient ?

[half pike]

?

they have the same y intercept if thats what u mean

[glossy fable]

I mean, it does seem that way

[half pike]

can someone help with quesiton 3?

@craggy haven sorry i just have a quick question! if y = -5 in y = mx+b form, what is y = -5 in standard form? is it 0x+y+5=0? just reply, if you can, in a check mark or an X

tysm

[craggy haven]

yes or just y + 5 = 0

[half pike]

okk

[half pike]

could the slope be 0 then?

or is it undefinied

@craggy haven sorry for the tag again

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[west wagon]

need help

[west wagon]

for the f=O(g) im not sure whether to disregard nlogn + 2 or not since what we want is the dominant term right?(for the left hand side)

<@&286206848099549185>

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[lucid moat]

How does this explanation sound?

Am I missing something?

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[wooden widget]

pls

[neon iron]

find the extreme points (maxima and minima)

and see what is happening in between points

[wooden widget]

ik the derivative is 6x^2 - 36x + 54 and i found the critical points

and i got the repeated root at x = 3

but i keep doing it wrong

[neon iron]

can you send me wqhat work u did?

[wooden widget]

yea one sec pls

[neon iron]

k

[wooden widget]

i used 2 and 4 as my test

[neon iron]

i think your answer is write you jsut typed it in wrong

instead of (-inf,3), (3, inf) do (-inf, inf) because it still counts as increasing when x=3 because thats a single point

and instead of DNE use the null set symbol it told you to if needed

was just a format issue

[wooden widget]

okok

oh

it was right

bruh

that took me 4 hours

thank u

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[valid sedge]

Hi I need help solving this word problem “Newton's Law of Gravitation says that two objects with masses m₁ and m₂ attract each other with a force F that is jointly proportional to their masses and inversely proportional to the square of the distance r between the objects. Newton discovered the constant of proportionality is 6.67 x 10^-11

In a small laboratory experiment, two 700 kg masses are separated by 0.2 meters. What would the gravitational force between the objects be? Round your answer to 6 decimal places.

Force = [Mathematical expression input field] Newtons”

[regal isle]

F = Gm1m2/(r^2)

So now plug in the numbers

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[neon iron]

$If \begin{vmatrix} a&b \ c&d \end{vmatrix} = -2$ find $\begin{vmatrix} 3c-d & 6a-2b \ 2d & 4b \end{vmatrix}$

[thorny flame]

Derivative

[neon iron]

so what it tried to do is get rid of the d and b at the bottom row so I do 2R_1 + R2

to get

$\begin{vmatrix} 3c-d & 6a-2b \ 6c & 12a \end{vmatrix}$

[thorny flame]

Derivative

[neon iron]

now, I dont really know what to do but i pulled out a 6 in R2

so i get $6\begin{vmatrix} 3c-d & 6a-2b \ c & 2a \end{vmatrix}$

[thorny flame]

Derivative

[regal isle]

Just write the right hand side into an equation

[neon iron]

i thought I needed to try to get this into the LHS

[regal isle]

Nope

Just write it into an equation

[neon iron]

so a = 3c-d

b = 6a-2b

c = 2d

d = 4b

?

[regal isle]

The RHS into an equation

I gtg, I have smth to do. GL

[neon iron]

$\begin{vmatrix} 3c-d & 6a-2b \ 2d & 4b \end{vmatrix} = -2$

[thorny flame]

Derivative

[neon iron]

i do this

[neon iron]

ok np

solved it

thanks

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[edgy terrace]

Sketch the triangle, and then solve the triangle using the Law of Cosines. a=65 c=50 angle C =52

[neon iron]

ok

what is the law of cosines

ping me when you get back

[edgy terrace]

@neon iron a formula to find the side lengths

When I put it the sides and angles on a triangle calculator it gives me no solution

[neon iron]

is it 52 degrees bruh

@edgy terrace

its gonna think u meant 52

instead of 52 degrees

52 is like equal to 5000 degrees

lol

[edgy terrace]

correct but it say's no solution

[neon iron]

yea there isnt

you will see why if you try to draw it

and use the cos law

[edgy terrace]

Alr thankyou

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[orchid sonnet]

i dont get this question

\

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[uncut agate]

Hello, I need to do this but it is not clear to me how the integration limits work.

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[ornate magnet]

7j+6≡4(mod5)

[ornate magnet]

7j ≡ -2 (mod 5)
7j ≡ 28 (mod 5)
j≡4 mod 5

Is there a faster way to do this

?

[cursive thorn]

You could have also noticed that 7j = 2j, and immediately divided by 2 in the first equation, but that doesn't really make it shorter to write down

First equation would have been 2j = -2 in that case

[ornate magnet]

Ok thanks

x ≡ 2 (mod 3) and x≡3 mod5

I learned how to solve this

But is therea better way?

My way is x =5k+3
5k+3≡ 2 mod 3
k ≡1 mod 3
k= 3m+1
x= 15l +8

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[neon iron]

can someone help me find out whether this function is continuous or not? what would the general approach be to find that out for functions with multiple variables?

[valid marsh]

the function is continuous if it is a composition of continuous functions

be aware of the domain

[valid marsh]

Generally, the approach is to see if the function is a composition of continuous functions

[neon iron]

I see

so |x| is continuous iirc?

[valid marsh]

Yes, you can also see this by looking at its graph: you can draw it without lifting your pen/pencil

[neon iron]

exactly

I wasn't sure but continuity and differentiability is not the same thing

[valid marsh]

Yes, you can see this with |x| as well

[neon iron]

yes it is not differentiable

so the argument goes:

|x| is cont.,|y| is continuous ==> |xy| is continuous. Then |xy| is continuous, 1 is continuous ==> |xy| + 1 is continuous(sum of continuous functions is continuous)

oh and of course ln(x) is continuous

and what we derived before is continuous so the composition of both is continuous

How is this helpful to my question man?

[valid marsh]

For the first statement, be careful

Be aware of the domain

[neon iron]

hmm I mean the domain is R right?

[valid marsh]

Yes

I’m not even sure how to prove the first statement, but after that it’s right

[valid marsh]

yep

[neon iron]

it is trivial that

https://tenor.com/view/kappa-gif-4908381

[valid marsh]

or you could just start with “|xy| is continuous” and hope your teacher accepts

[neon iron]

Nyeeh I'll say |x| is continuous with domain R as well as |y|

and if he cries nyeeh it's not graded anyway

[pseudo jetty]

products of continuous functions are continuous

[neon iron]

true

[pseudo jetty]

and your domain is R^2

since f is a R^2 -> R function

but xy is a polynomial, and all polynomials are continuous

[neon iron]

you're right

thank you very much

.close

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[pseudo jetty]

note that this is when you're away from 0

but |xy| + 1 is certainly away from 0

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[amber yacht]

hey anyone know if three vertical lines represents similarity in triangles or not?

[amber yacht]

i cant find it anywhere on the internet but i think ive been taught that three vertical lines are similarity and three horizontal are congruent

im talking about this symbol: |||

[drifting swift]

looks like a strange symbol

can you show the entire problem

maybe context can help figure out what it means

[topaz sinew]

@amber yacht Has your question been resolved?

[restive inlet]

yes, some places use 3vertical for similarity of triangles

[amber yacht]

its not a context related thing, i mean as in general

[amber yacht]

right ty i thought so but i got taught that a few years ago

anyways just needed that confirmation ty

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[willow quarry]

How to express XOR using only NOT and IMPLIES?

[drifting swift]

can you express AND and OR using those only?

[willow quarry]

not sure how I'd start going about that

[drifting swift]

!occupied

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[drifting swift]

@timid prawn this channel is occupied, please move.

[drifting swift]

do you know how to express IMPLIES in terms of OR and NOT?

[willow quarry]

Not too sure, I only have the truth table written out atm

[drifting swift]

A -> B = (not A) or B

this? no?

[willow quarry]

ah

yes

[drifting swift]

yeah

you can make that into an expression for or in terms of implies and not

[willow quarry]

hmm

I've written out XOR in terms of NOT and OR from a previous part of the question

does that help

[drifting swift]

it does actually

cause then you can take that expression and replace all "p or q" by "not p -> q"

[willow quarry]

ahh

atm I have NOT(NOT X OR Y) OR NOT(NOT Y OR X)

so doing that I'd have

NOT(X -> Y) OR NOT(Y -> X)?

[drifting swift]

you need to replace the middle or as well

[willow quarry]

ah

(X->Y) -> NOT(Y->X)?

[willow quarry]

I've written out a truth table for this and I think I get the same output as XOR

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[timber mirage]

could anyone give me a hint for how i would do c? i did i and ii alr

[timber mirage]

for the norms i got sqrt(pi)

[drifting swift]

do you know how to prove that an orthogonal set of nonzero vectors is LI

[timber mirage]

I'm not sure if i have a full working proof of that, but right i'm aware that for a set of functions {f1,f2,...} to be linearly independent, i'd need to have c1f1 + c2f2 + ... cnfn = 0 which is only satisfied by c1 = c2 = ... cn = 0

I basically tried assuming LD and then used orthogonality

[drifting swift]

no need to assume LD

[timber mirage]

But the terms weren't canceling out after i integrated over 0 to 2pi

[timber mirage]

o

[drifting swift]

you do not need to integrate anything.

you have already done all the integration you need.

[timber mirage]

Ah maybe i'm overthinking this

[timber mirage]

let me try to use ideas from this to show iii

and i'll get back if i'm stuck

[drifting swift]

you definitely are

[timber mirage]

ahhh okay i think i figured it out nkw

thanks ann

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[neon iron]

how do i correctly apply AM GM inequality in this problem

<@&286206848099549185>

heyy

someone??

[mellow shard]

i can help

[neon iron]

wait a se

sec

[mellow shard]

Have you tried the square root? little hint;)

[neon iron]

someone ?

[neon iron]

what square root

and why

[mellow shard]

wait english isnt my first language

[neon iron]

same

[neon iron]

ohh 💀

[mellow shard]

ok

[neon iron]

can u redirect me to someone?

[neon iron]

use basic proportionality theorem maybe

[neon iron]

hmm

[mellow shard]

so you have to do a cross product and normaly you have seen somthing to change the DO with. but this is to the power of 2 so you have to take the square root of that

[neon iron]

i dont understand

[mellow shard]

Try bending your head and squinting your eyes a bit that usualy helps for me

[neon iron]

what

lol

<@&286206848099549185>

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

@neon iron Has your question been resolved?

[pulsar sun]

2 ig, when a=b=x=y

lemme check tho

[neon iron]

i did not ask for ans

i have it

just hint me

[pulsar sun]

hmm

factorize x^2y^2

ah crap

its opposite

nvm

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

@neon iron Has your question been resolved?

[wet herald]

Is there more to the question? Perhaps some constraint? I don't see how a minimum value can exist. Under the assignment,

$a = b = \frac{1}{\sqrt{2}n}$ and $x = y = n$, the function has the value $\frac{1}{n^4}$. As $n \rightarrow \infty$ this obviously approaches 0 but will never reach 0. So 0 is the infinum but not a minimum.

[thorny flame]

chencking

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[versed widget]

where is the mistake

[acoustic pecan]

come on, its not that hard my friend

[keen venture]

#❓how-to-get-help

There's pictures

[versed widget]

now

the book says a = e+1 and b = -e

how

[versed widget]

oh yh

a*b

[keen venture]

Basic algebraic mistake here

[versed widget]

nvm wait

no

ill fix it 1 sec

a/e^-3

[keen venture]

Yes that's true

It doesn't simplify very well

[versed widget]

but that doesnt rly give me anything or?

[keen venture]

Are you allowed to use the Wronskian for this? You'd have a much easier time

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@versed widget Has your question been resolved?

[versed widget]

what is that?

please eborate though

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[violet current]

Can someone help me find the correct answer?

[violet current]

Ain’t sure about this one

And plz I want an explanation

In how to find the correct answer

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[obsidian shard]

.close

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[violet current]

.reopen

Cuz I guessed

Can u help?

I had lack of time

Uhhhhhh

and it’s?

y= fx

Tbh idk 😭

I’m asking

I just need the answer of this question plz, what is it

I’m done with school

This is for university acceptance test in math

That’s the only question idk

Can u give me the answer plz

Ok, sure

But do u on know the answer?

Which option? Is it the highlighted ones?

Or first

Or third

Or last

😭

I read

Bro thx for helping me, but I need the correct answer option for this question, IT IS THE ONLY VERSION IN THE TEST

which option plzzzzzzzzz

[violet current]

1,2,3,4?

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[violet current]

@sage siren ??? 😭 which option bro

[violet current]

U can’t be serious 😔

Atleast give me the answer

[hollow drum]

We aren't here to give out answers

[supple sun]

Why would the two be right ?

[digital river]

!nosols

[topaz sinew]

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.

[supple sun]

?

Not giving sols doesn’t mean no help

[violet current]

Ok can u tell me the answer WITH EXPLAINATION, but I don’t have time to study, my test is after 30 mins 😭

HELP

[supple sun]

!nosols again

[topaz sinew]

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.

[violet current]

Oh

Okay

What should I do to find the answer

[supple sun]

First, why did you pick 2 ?

[violet current]

I guessed anything tbh, I had lack of time

😅

I feel it’s 1

Am I right?

[supple sun]

"I feel" is not a proof

[violet current]

Ok

What should I do

My test is in 20 mins

[supple sun]

Study ? What do you know about integral what do they represent ?

[violet current]

Well it’s a university acceptance test which comes with random stuff, and I never studied precalc at school so that’s why idk anything about this question

Can u atleast tell me the steps to solve this question

[supple sun]

In the question you’re doing the sum of what ?

[violet current]

Sum of area of rectangle as mentioned

[supple sun]

Ok, from what point to what point ?

[violet current]

uhhhhh, x1 to xn?

[supple sun]

Look at the x-axis

[violet current]

Uhhhh, 0 to b?

Or x1 to b?

[supple sun]

0 to b

[violet current]

Great!

Now what’s next

[supple sun]

What would represent the sum of areas ?

[violet current]

Well, for a rectangle, we add all sides?

[supple sun]

No like if I have a square of area 6 and another square of area 4 what would I get if I add the area of the two squares

[violet current]

10

24? If we multiply

[supple sun]

What would that be ?

It would be the area of a bigger square

[violet current]

Oh

Yes right

[supple sun]

Pythagorean theorem

[violet current]

Yeah ik it’s rule

Ok what’s next?

[supple sun]

Look up the definition of an integral

[violet current]

Okay

[supple sun]

What is it ?

[violet current]

So the since the definition states integral 0 to x, in the question it would represent as 0 to b

Right?

[supple sun]

Yes but what is an integral ?

[violet current]

It’s the sum of continuous analog, and sometimes represented as integral a to b y1-y2

But in my question

I can understand that the answer is 4 right?

[supple sun]

Yes

[violet current]

Tysm bro u really helped me fr

Now imma go prepare for my test

Thx a lot again

[supple sun]

👍

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[hollow dew]

Given the points A(0, 0), B(6, 3) and C(1.5, 0.75), find the ratio that point C partitioned segment AB, can someone help me solve this. Pretty sure the answer is 3:1, but idk how to solve.

[topaz sinew]

@hollow dew Has your question been resolved?

[neon iron]

Using standard inequalities

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@hollow dew Has your question been resolved?

[hollow dew]

<@&286206848099549185>

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[ashen osprey]

I forgot how to do log eq from table

[ashen osprey]

how do I do this again?

ik how to get -10

everythign else idk

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[solemn rampart]

i need help findnig the variance

[mint violet]

you can use E(X^2)-(E(X))^2

[solemn rampart]

is that correct?

[mint violet]

yeah

yes

[solemn rampart]

alright tysm

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[raw pewter]

could u guys help me to transform P into Q with the operation (2nd pic),please? i got stuck

[neon iron]

uh is that what the question is asking you to do, because when i reduce both P and Q i get completely different matrices

,w -2(2,0,4,-6) + (4,3,2,-5)

[thorny flame]

Results provided by WolframAlpha

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

Requested by 0izne

[raw pewter]

exactly, the question used to asked to transform the matrices with gauss jordan

[neon iron]

!xy

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[neon iron]

I got 108.165

The answer is 32.1

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[mild hearth]

ah, no the area of the sector isn't (1.2pi/2pi) * pi r^2

it's just (1.2/2pi) * pi r^2

[neon iron]

ahhh i see thanks

.solved

.cose

.close

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[wraith acorn]

can anyone explain how the parts in red came to be?

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[wraith acorn]

<@&286206848099549185>

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[wooden tide]

id love some help with this

[coarse tusk]

are you familiar with derivatives?

[wooden tide]

i am

teh derivative should equal 0

ive figured out that much

[coarse tusk]

indeed

[wooden tide]

past that not a clue how to actually accomplish it

[coarse tusk]

can you take the derivative of v(t)?

[wooden tide]

tke^t-1-8te^-2t-1

i was trying to replace e^t or smtn with x

and get x equal to something

but i couldnt make it wqork

wait until theres a channel free in available and then send ur q

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[hybrid halo]

oh boi whoever reads this poem, may god be with you

[hybrid halo]

Hey, Im a university student and currently studying computer science. I already passed my linear algebra course and am up for Analysis. I have realized, that I´ve AAAActually been struggling with a lot of fundamentals in the past year and realized that my intuition and feeling for math and abstractness is pretty off. But i´d like to change that, soooo I was just wondering if someone has some ressources that gets me going in my understanding of math and that may even refresh fundementals, which ive been lacking?

AND OFC I knoow that its a proccess that doesn´t happen over night. But starting in the third semester I realized that my lack of abstract thinking rather tends to be a sort of weight to my group members, which i so far have only been able to balance with an imense ammount of invested time in situational issues, rather than into my overall understanding.

iin short

are there sites for foundations and getting a better math feeling

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[balmy orchid]

how do I do this?

.clos

.close

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[whole nacelle]

how to do?

[raven sparrow]

I feel like it's quite easy to see what the antiderivative will be since you clearly have x/sqrt(1-x^4) that is almost the derivative of arcsin(x^2)

I'd say let u=arcsin(x^2) and go from there.

[whole nacelle]

okay

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[restive inlet]

!status

[topaz sinew]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[neon iron]

1

[restive inlet]

do you know binomial theorem

[neon iron]

yes

what does it mean by constant term in the expansion?

do i just expand the bracket?

[neon iron]

hi?

[restive inlet]

did you already do the first part of the question?

[neon iron]

wdym first part?

theres only one question

[restive inlet]

this is a two part question,
first part being to show the value of a = 3/2
second part to find the constant term of ...

[neon iron]

yh its just shown as 3/2.. so that means i dont need to find for value a

i dont get the question

what dose that mean by finding the constant term

[restive inlet]

e.g a simpler question would befind the constant term in
(x+5)(x-8)

find the term that doesn't have any x in it

[neon iron]

so -5 and +8?

[restive inlet]

no

what's the constant in the expansion, expand it out if you feel the need

[neon iron]

I literally dont get what it meant by constant term...

[restive inlet]

if you were to expand out and simplify, what's the term that doesn't have x in it

[neon iron]

ohh

it would be 2^8 + 1 ?

[restive inlet]

where's that coming from

[neon iron]

constant means a value that has no x

right?

so i only need to calculate 2, and 1

[restive inlet]

no

[neon iron]

for this one, it would be -40

[restive inlet]

consider partially expanding your expression
$$=\gray{1}(2 + ax)^8 +\frac{1}{x^4}(2 + ax)^8$$

[thorny flame]

ℝαμΩℕωⅤ

[neon iron]

yh

[restive inlet]

determine the constant from each term

[neon iron]

ok so for the first one

2^8 = 256

for the second one, theres no constant as every term is multiplied by 1/x^4

[restive inlet]

no

[neon iron]

oh wait

wait

when the inside brack has x^4

they cancel out and gives the constant

[restive inlet]

yes

[neon iron]

so if i use the bionomeal expansion

8C4 * a^4x^4 * 2*4

i get

5670x^4

cuz a = 3/2

so they cancel out, and that makes the constant term = 5670

[neon iron]

am i right?

[thorny flame]

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

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

[restive inlet]

for the second term yes

and the overall constant will be the sum of
256 and 5670

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

thanks it helped me a lot

👍

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[kind cloud]

Not sure where this goes

I'm not a math major

I have a system with 4 ODEs
I noticed A and B are just dependent on eachother so I solved those with Eigenvalues and Eigenvectors

C and D are tied to B and C
I can't figure out how I can get C and D from here

I tried Eigenvalues for 4 of them at once, didn't work, the values changed?
I tried to do laplace, something went wrong, couldn't get C still even tho I have B

All systems are time dependent
I do have a B function equation

How can I find C and D?

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@kind cloud Has your question been resolved?

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[dry kettle]

I'm trying to solve the ODE $\mathbf{x}' = A(t) \mathbf{x} + \mathbf{g}(t)$ where $A(t) = \begin{bmatrix} 0 & t\ 0 & 1 \end{bmatrix}$ and $\mathbf{g}(t) \equiv \mathbf{0}$. I believe I'm supposed to use a matrix exponential to solve it, but I think I

[thorny flame]

NcMobbets

[dry kettle]

'm stuck somewhere.

[thorny flame]

NcMobbets

[dry kettle]

According to W|A the solution is $\mathbf{x} = \begin{bmatrix} c_{1} e^{t} (t-1) + c_{2}\ c_{1} e^{t} \end{bmatrix}$ but I don't know how it got there

[thorny flame]

NcMobbets

[dry kettle]

I know there's something to do with the matrices not commuting but to be honest I'm just stuck

wait im sorry I re-read the rules and realized this is for pre-uni questions but this is a uni level question, my bad first time asking for help

.close

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[wintry oar]

Need help

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[past plinth]

Derivative of h(x) = x sinx cosx

[past plinth]

i know im supposed to do the product rule but idk what to do with that x in the front

[half edge]

Triple product rule

[radiant tapir]

it just extends

[half edge]

Or u can make it 1/2 * x * sin(2x)

But honestly I’d just do triple product lol

Why chain if u don’t need to chain

[past plinth]

where did the 1/2 come from

[half edge]

sin(2x) = 2sinxcosx

[past plinth]

ohh

[half edge]

So 2sinxcosx * x * 1/2 = xsinxcosx

[past plinth]

whats triple product rule

[radiant tapir]

Like this

how the product rule is something like f'g + f'g, you'd just extend it: f'gh + fg'h + fgh'

[past plinth]

ohhh okay

[radiant tapir]

how's it going?

[past plinth]

ok so i got:

is that it

[half edge]

Ye

U can do a bit of double angle simplification but other than that ur good

[past plinth]

ah alr thank you guys

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[half edge]

xcos(2x) + 0.5sin(2x)

In case u werent wondering

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[iron estuary]

Hey, need help with number 6

[iron estuary]

Specifically proving that the second interval does not meet the MVT

[broken niche]

What is -1^(2/3)

Nvm

I am ceo of illiteracy

[iron estuary]

You good lol

[broken niche]

Ok I think you put x^1/3 instead if x^-1/3 accidentally

[iron estuary]

O my goodness you’re right

My baaad

It’s late lol

Thanks

.close

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[neon iron]

Hi there could someone please check my answers thanks, just some simple year 9 math.

[lusty pelican]

All looks good besides #41. While your process is right, the answer looks like 89 not 39

[neon iron]

Thanks

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[winged brook]

According to the data in the diagram, find the areas of increase and decrease in each of the diagrams

I forgot how to do this ^

[spare monolith]

What does it mean when a function increases and decreases?

[winged brook]

from what I understand its what's above X

[spare monolith]

Increase means that in the interval, the y-value gets bigger and bigger. Vice versa, decrease means that the y-value get smaller and smaller.

[winged brook]

so like this

[spare monolith]

Yeah, the interval [-7, -2] do indeed is increasing. Remember to include the end values.

[wet sun]

but at the points -7 and -2 the derivative is zero right?

is that still counted as increaasing?

[winged brook]

I think if it reaches 0 then it isn't increasing and isn't decreasing

[spare monolith]

But the y values are still bigger.

[drifting swift]

all those ineqs should be nonstrict but this is kind of a fine technical detail.

[winged brook]

is the answer any X ?

for when it's increasing

[spare monolith]

Sure do.

[winged brook]

but is it also increasing to the left?

or its decreasing

[spare monolith]

The whole is increasing.

[drifting swift]

does it go up or down as you scan left to right

[winged brook]

oh yea it goes up

what about (0,0)

maybe x can't equal 0?

[drifting swift]

the derivative is 0 there but nonetheless the function is increasing everywhere.

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[flint steeple]

How to solve this one step by step?

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[flint steeple]

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[potent nova]

If f(xy) = f(x)+f(y), for all x, y ≠0, prove that f(1) = f(-1) = 0.

[potent nova]

I don't understand how two variables in a function work and how to deal with them

[flat kindle]

for these types of questions you usually try different values of x and y and see what happens

what values x,y gives f(1) and f(-1)?

[potent nova]

1

-1

Respectively

[ruby tree]

What does that mean "for all x, y + 0"?

[potent nova]

Oh I meant ≠ 0