help-0

[cinder wedge]

the inequality

🙂

I will use the AM-GM

pleas don't help me more, I mean for the question pleas because I want to solve this

please don't get me wrong 😄

[feral wind]

i feel dumb asking this, but, is this right?

or is it x^(2/3)

[spring harbor]

It is right

[cinder wedge]

yes it is

[feral wind]

then i think the author made a mistake here, right?

i made my u = 1 -5t so, du/dt = -5 which mates dt = -du/5

so, i just have to calculate the antiderivative of -(u)^(-3) * (1/5)

which should be (-1/10)(u^(-2)) + c right?

where did he even get that (2/3) exponent?

[vale wigeon]

$\frac{1}{\sqrt[3]{u}} = u^{-1/3} \neq u^{-3}$

[ocean seal]

Ann

[feral wind]

oh, got it

i got it right now, thanks

[alpine sable]

is this homework or exam? @outer pewter

[outer pewter]

homework

@alpine sable

[alpine sable]

ok

[vale wigeon]

@outer pewter what's giving you trouble here?

..........

they disappeared

[rigid smelt]

what have you tried?

[alpine sable]

puting it on desmos lol

[rigid smelt]

sure its a way to do it

[alpine sable]

but idk how to convert it

[vale wigeon]

part i or part ii?

[alpine sable]

1

[vale wigeon]

have you tried doing some algebra to this equation

[vale wigeon]

such as dividing both sides by cos(2x) to get tan(2x) + 3 = 0

[alpine sable]

idk how to get the 0 value

it says 0.946

[alpine sable]

???

[vale wigeon]

dividing both sides by cos(2x) in sin(2x) + 3cos(2x) = 0 gives you tan(2x) + 3 = 0

[alpine sable]

because tanx = sinx /cosx

right?

correct

[vale wigeon]

yes, so what was the "???" about

[alpine sable]

idk what you meant

now what do i do?

[vale wigeon]

i meant exactly what i said

[alpine sable]

to solve it

[vale wigeon]

tan(2x) + 3 = 0

[alpine sable]

yes

[vale wigeon]

try doing more algebra to it

and don't overthink it

[alpine sable]

$\frac{2\tan \left(x\right)}{1-\tan ^2\left(x\right)}%=$

??

[vale wigeon]

overcomplicated

there is no need to apply the double angle identity here

[alpine sable]

what other algebra can i do to it then?

[vale wigeon]

what about subtracting something from both sides

[alpine sable]

oh ok

[alpine sable]

tan(2x) = -3

[vale wigeon]

okay great

you're one step closer

[alpine sable]

now...?

[vale wigeon]

have you solved trig equations of the form tan(θ) = c before?

[alpine sable]

no

[vale wigeon]

bruh what

[alpine sable]

idk

[vale wigeon]

how much trig do you know

have you heard of the unit circle

[alpine sable]

um....

yes

[vale wigeon]

or inverse trigonometric functions

[alpine sable]

ik the unit circle

[vale wigeon]

arctan, to be more specific

[alpine sable]

ok

so tan^-1?

$tan^-1$

[vale wigeon]

it's $\tan^{-1}$ if you wanted to type it up with texit

[ocean seal]

Ann

[vale wigeon]

but yes that is what i am talking about

[alpine sable]

so i can work it out on calculator?

[alpine sable]

ty

[vale wigeon]

...

well i expected you to write down 2x = arctan(-3) + 180n but i don't think i'm gonna get that from you any time soon

[alpine sable]

so im not done?

[vale wigeon]

of course you're not done

[alpine sable]

oopsw

[alpine sable]

2x = arctan(-3) + 180n

i do that?

[vale wigeon]

do you understand why i had you go from tan(2x)=-3 to that

[alpine sable]

no

[vale wigeon]

do you know what arctan is

no, you are forgetting the +180n

[alpine sable]

its tan^-1

right

just inverse tan

[vale wigeon]

there is an important caveat

no, this is wrong still

(180n)/2 is not 180

tan is periodic and so does not have a true inverse

arctan(t) is the angle between -90° and +90° whose tangent is t

[alpine sable]

$x = arctan(-3)/2 + 180n/2$

ok ill just stop

[vale wigeon]

to solve the equation tan(θ)=c you must account for the fact that tan is periodic and its period is 180°

hence the +180n

[alpine sable]

ik it's 180 (idk how to get the degrees)

sign

[vale wigeon]

"it"...

[alpine sable]

"it"

???

[vale wigeon]

i'm unhappy with your wording of "it's 180"

but i don't have the energy to comment on it in more detail

[alpine sable]

what do i do now

[vale wigeon]

divide both sides by 2

get x = -arctan(3)/2 + 90n

work out which integer values of n yield a solution between 0 and 360°

[alpine sable]

$x = -arctan(3)/2 + 90n$

[ocean seal]

Science

[alpine sable]

sorry still dont understand

[vale wigeon]

yeah cause you're in dire need of an algebra review tbh

[alpine sable]

[vale wigeon]

you could not even work out how to get from tan(2x)+3=0 to tan(2x)=-3 before i pointed it out to you

so rn it's a bit of a "run before you crawl" situation if i attempt to walk you through the rest of the solution

[alpine sable]

i just didnt know what you meant

[alpine sable]

||ill TRY to follow along||

ok then

[outer pewter]

where to start 😭 like what to do

[eternal mantle]

18 dollars per hour times 8 hours

+0.15 times price of first item

+0.15 times price of second item

until the last item

[outer pewter]

ur a life saver

[vale wigeon]

...pluto, with all due respect, how come you just disappeared for almost an hour?

also, you could just calculate the total sales made by gwen and multiply that by 0.15

and get the total amount she made in commissions

it might save you a few key- or penstrokes

@outer pewter?

[eternal mantle]

yes that is a better explanation

[outer pewter]

i was just busy doing some stuff 😭 but tysm i rlly needed help

[vale wigeon]

you could have said "brb" or something along those lines.

[analog locust]

guys, what does P^2 here means?

tried googling it, didn't get any answer unfortunately

[outer pewter]

i know but i just left that's all

[alpine sable]

is this how you do nth integrals

[analog locust]

what does this mean? ._.

[glacial quartz]

....

[eternal mantle]

12

[glacial quartz]

TY

[alpine sable]

did you understand why it is 12?

[glacial quartz]

Nope

[eternal mantle]

it is a parallelogram

[alpine sable]

notice how AD and BC are parallel to each other?

[eternal mantle]

they also both have one arrow on them and that's a hint from whoever made the picture

that they are the same length

[sturdy valley]

heyy I have something i dont understand

you have to find "k" but I can't find a mathode to do that...

[neon burrow]

It's simple. You can compare the coefficients of the terms to find it's value

[minor aspen]

Hello! Shouldn't there be "1" instead of the circled "t" here?

Or am I overlooking something somehow

[indigo jetty]

should be a 1

[torn rose]

hi, how would you derive 2^x

[terse nova]

Do you know the derivative of $e^{kx}$?

[ocean seal]

AoiKunie

[terse nova]

Where k is any constant

[eternal mantle]

^

[torn rose]

ok that makes sense ty

is it possible to dervive loge(2)?

or you just leave it in that form

[pliant estuary]

Generally you can say that $\dv{x}a^x$ is $a^xln(a)$

[ocean seal]

marejak023

[torn rose]

👍

[lucid tendon]

Hi, would you use a change of variables for this integral?

or some goniometric substitution in the first variable?

[nimble meteor]

extremely confused

[glass lichen]

That's a constant

[nimble meteor]

tried using dimensional analysis and I went like this🤮

[glass lichen]

Just convert m^3 to km^3 and mm^3

[nimble meteor]

ohhh wait

I'm stupid

dang

that's why

I just realize

d

I just assumed that it was in km instead of 2 being mm🤦‍♂️

[alpine sable]

bruh, just write it in once sentence please xd

[nimble meteor]

thanks @glass lichen

[nimble meteor]

ok lol

[woven sphinx]

dont think there is a closed form; look up incomplete integrals of the first kind

[ivory otter]

Hey

dont really get this question

prove sin x = cos(90-x)

[terse nova]

They want you to show that sin x = cos(90-x) for all values of x

[burnt meadow]

How would u integrate this?

[ivory otter]

so do i just plug in random values

[woven sphinx]

no

[ivory otter]

for x

[terse nova]

No, there are infinitely many values to test

[woven sphinx]

wrt x?

[lucid tendon]

thank you!

[terse nova]

Have you defined sin and cos for angles greater than 90 degrees?

[ivory otter]

no

[terse nova]

Ah ok

[burnt meadow]

huh?

[woven sphinx]

how are you defining sin and cos? using SOHCAHTOA?

[terse nova]

Try drawing a triangle then, with some angle x

[ivory otter]

ye

[terse nova]

A right angled triangle

[ivory otter]

ok

[burnt meadow]

wdym

[dapper thistle]

Easy q to test memory

[terse nova]

Then see if you can find where the angle 90-x is

[woven sphinx]

are you finding $\int6e\sqrt{e^x}dx$

[ocean seal]

A Fellow Human

[burnt meadow]

yes

[lucid tendon]

@woven sphinx sorry that you are working on two questions at once haha, great tip about the elliptic integral; do you know how I should extend this to the two-variable situation?

[dapper thistle]

👁

[ivory otter]

@terse nova

[terse nova]

Looks good, say that the rightmost angle is x

Then what is the angle in the top?

[ivory otter]

right most angle ?

oh

[terse nova]

Could also be a good idea to name your sides something

Like a,b,c

[ivory otter]

i mean it would be

[dapper thistle]

🙈🙉

[ivory otter]

(90 - x )/ 2

[terse nova]

Not quite

[ivory otter]

hmm

[terse nova]

Remember all angles should add up to 180

[ivory otter]

ye

[terse nova]

So far you got 90 and x

[ivory otter]

90 - x

[terse nova]

Yeah exactly

[ivory otter]

but that would give me 90

[terse nova]

No, you got the right angle too

[ivory otter]

ahhhhhhhhhhhhhhhhhhhhhh yes yes

i see what you mean

damn i was a bit confused

[terse nova]

Now, what is sin x?

[ivory otter]

but how does that tell me that sin x = cos(90 - x) ?

[terse nova]

It's probably a good idea to update your picture with the new angles, and names for the sides of the triangle

[ivory otter]

ok

[terse nova]

That's the corners, you want the sides

[ivory otter]

aha

[terse nova]

Also don't forget the angles, x and 90-x

[ivory otter]

ok

[terse nova]

Neat

So what is sin x in this picture?

[ivory otter]

sin x = o/h

[terse nova]

That would be cos x

o is the side closest to the angle x

[ivory otter]

SOH = sinus, Opposite, Hypotenus?

[terse nova]

Yeah exactly

So what side is opposite to the angle x?

[ivory otter]

a

[terse nova]

Yep

[ivory otter]

aaaah

so that means

sin x = a/h

[terse nova]

Yeah exactly

[ivory otter]

aha

[terse nova]

And cos (90-x)?

[ivory otter]

Cos(90-x) = a/h

has to be

because O for cos(90 - x) is the opposite

[terse nova]

Yea

[ivory otter]

so it was correct?

[terse nova]

Yeah, so sin x = a/h

And cos(90-x)=a/h

So they are the same

[ivory otter]

ooooooooooooooooooohhhh

ok now i get it

that was good

and clear

[terse nova]

So we never specified what x was

So it works for any x

[ivory otter]

we can get x?

[terse nova]

(As long as it is less than 90 degrees and greater than 0)

[ivory otter]

aha i see

[terse nova]

No, the point is that the proof works for any x

[ivory otter]

aha ok

[terse nova]

Drawing triangles like this is a good tool to prove these trigonometric equalities

[ivory otter]

ye it was very clear

thank you @terse nova

[terse nova]

np

[woven sphinx]

apologies for not answering; you should move sin(y) out of the first integral and factor out the 4 in the square root, then apply the special function. not sure what to do after tho tbh

[ocean seal]

A Fellow Human

[glass lichen]

why did you feel the need to answer a question already dealt with..?

[burnt meadow]

uhh both answers are different

so um

[ivory otter]

anyone knows what this means

<CBA angeled triangle

[rigid smelt]

angeled?

[ivory otter]

triangle

[rigid smelt]

what does "angeled" supposed to imply?

[ivory otter]

idk

wait it doesnt say that

it says this

<CBA = 90 d

[rigid smelt]

it meant a right triangle

at B

probably

if that d meant degree

[ivory otter]

ye

[glass lichen]

answer is $12e\cdot e^{\frac{x}{2}}+C$

[ocean seal]

Mosh

[burnt meadow]

ah oke ty

[ivory otter]

@rigid smelt like this?

[rigid smelt]

yes and dont ping me for unnecessary reason

[ivory otter]

ok sorry

[alpine sable]

sorry to ask but

(?x4)-4=20

what is the missing number?

[glass lichen]

so solving 4x-4=20?

[vale wigeon]

do you know any algebra?

[alpine sable]

yeah

x is the missing number

[vale wigeon]

then you're being asked to solve the equation $4x - 4 = 20$ for $x$

[ocean seal]

Ann

[vale wigeon]

are you able to do that?

[alpine sable]

ayooo what

im a child not a mathematician i am not good at algebra

sorry if im being rude to you

[vale wigeon]

i specifically asked you whether you knew any algebra, and you appeared to answer yes

[alpine sable]

i meant kinda

im sorry

[vale wigeon]

okay, so are you familiar with common algebraic techniques like "adding __ to both sides" or "multiplying both sides by __"?

[alpine sable]

i know basic algebra

but only x that it

[vale wigeon]

...?

okay so how about i give you a simpler equation just to get a feel for what you do and don't know

[alpine sable]

yes please i appreciate that

[vale wigeon]

$z + 11 = 32$, solve for $z$

[ocean seal]

Ann

[alpine sable]

21?

but i can tell you how i got that

[vale wigeon]

yes, i am very interested in how you got that.

sure as hell hope it was not trial and error

[alpine sable]

it wasnt sir

[vale wigeon]

don't call me sir.

[alpine sable]

what happened is that

i thought of the 11 timestable

and

i thought of 11x11

[vale wigeon]

11 times table???

[alpine sable]

yes

[vale wigeon]

weird

you overcomplicated it way too much already

what happened to like... subtracting 11 from both sides, to get z = 32 - 11

[alpine sable]

i meant 11+11

my apologies

i thought of both numbers

and it gave me 22

then i added 22+10

and it gave me that

but then

i was wrong

so i did 11+10

which gave me 21

[vale wigeon]

your answer of z = 21 is correct, you're just taking a way overcomplicated route to get it

[alpine sable]

which is the easiest route

[vale wigeon]

this equation can literally be solved in one step

which i already said before but i will repeat myself

[alpine sable]

yes

[vale wigeon]

subtract 11 from both sides

z = 32 - 11

that's it

[alpine sable]

ohhhhhhhhh

dang

sorry

i now understand a;gebra

*algebra

[vale wigeon]

really now

i don't think it'd be accurate to say you "understand algebra" when you struggled on a one-step equation just now

don't take it personally

[alpine sable]

oh ok 😦

thank you for the help

[vale wigeon]

i did nothing worth thanking for

[scarlet thunder]

I’m guessing they’ve just been introduced to algebra or smth?

[alpine sable]

it was great talking to you have a lovely day

bye

[torn rose]

anyone know how to solve this

https://media.discordapp.net/attachments/423244559682764800/853613850788102144/unknown.png

this was my previous working to the other questions https://cdn.discordapp.com/attachments/423244559682764800/853615296774537246/image0.jpg

[scarlet thunder]

Well…. This seems very suspicious

[torn rose]

its an exam practice

[glass lichen]

it says 2018... it's clearly a previous exam

[gray isle]

for 1 stationary point, you'd only want 1 real solution to p'(x) = 0

[tawny lion]

teachers reuse exams

mine has went as far as using ib past papers

[glass lichen]

they wont use the same questions.. if they actively gave the previous questions as practice

[tawny lion]

i'm speaking just from personal experience

[gray isle]

they sometimes do, but the image indicates its at least not live

[tawny lion]

also what the fuck ios mathmeth

mathematical methods ?

pretty sure thats an ib course

or at least was before they split it into aa and ai

[glass lichen]

math methods is a uni physics course... also what does that have to do with helping?

[torn rose]

sooo umm, how do you find for one stationary point

[tawny lion]

no, it's not a uni physics course

search it up

let me correct myself, it can be a uni physics course, I mean that it was an IB course

the two are not mutually exclusive

[gray isle]

for 1 stationary point, you'd only want 1 real solution to p'(x) = 0

x = 1 is clearly real

so you'd want your other 2 solutions to be 1 if possible, or complex

[torn rose]

was is meant by complex

what*

[gray isle]

in this context, I'm referring to roots that will involve imaginary numbers

arent real

[torn rose]

why would that matter whether its real or complex number ,isn't just asking for one stationary point? I am bit confused

[lean gust]

how calculed the derivative of the integrate (sin t)/t dt from t=x to 2x

[gray isle]

for 1 stationary point, you'd only want 1 real solution to p'(x) = 0

if there are multiple distinct real solutions to that, you'd get more that 1 stationary point

[torn rose]

right

[gray isle]

so you only want one solution

and since x=1 is clearly a real solution, you'd want x=1 to be your only real solution

[torn rose]

this was the answer

[glass lichen]

yeah, if 1-a is negative, then you get 1 real solution and 2 complex solutions

which is inline with what Ram said

[cinder wedge]

Hello can someone tell me how can I continue ?

ab+ac+bc≥ 2ab√ac + abc√ab

I should to prove this?

If I divide both sides with 2ab and abc is this right

pleas help

[lean gust]

how calculed the derivative of the integrate (sin t)/t dt from t=x to 2x

???

[glass lichen]

FTC

and integral is the noun, not integrate

[glossy oxide]

Ion think that's allowed

[glass lichen]

you cant cheat. .

[glossy oxide]

A triangle has ratios a:b;c:r=3:4:5:u where r is the radius of inscribed circle and u is real,radius of circumscribed circle R is 5.What type of triangle is it and find the area of the max sized rectangle whoose one side is on the largest side of triangle.

I cant seem to figure out the last part

The triangle is a right angle and the sides are 6 8 and 10 but cant figure out the rectangle part

[uncut cosmos]

Man joined server just to cheat

cheap

[glossy oxide]

So aint nobody got any hints on how to continue this

[tall kayak]

anyoone????

[oak chasm]

@alpine sable Sorry, channel is busy.

@tall kayak Can you reduce it to a smaller problem?

[glossy oxide]

Didnt help

Anything i found was talking about calculus

[alpine sable]

hey ~ have you tried drawing the shapes?

visualising the problem is key

[glossy oxide]

Ofcorse i tried that i've been sitting looking at it for an hour drawing lines and nothing works

[alpine sable]

could you share your progress so i can see where you're at? 🥰

[oak chasm]

@glossy oxide If all else fails, there are some formulas here: https://opencurriculum.org/5492/circumscribed-and-inscribed-circles/.

[glossy oxide]

Idk i feel like none of the formulas connect the area of the rectangle to the triangle

Here is my work and i got stuck trying to connect the area of the rectangle with the triangle

[oak chasm]

@glossy oxide The main triangle and the three triangles formed by the rectangle should be all similar.

Subtract the area of the three smaller triangles from the larger triangle to get the rectangle's area.

Consider also a rectangle with one vertex as the right angle in the triangle.

[glossy oxide]

I think i figured it out

I managed to get that
P=10EF-EF^2 *3/4

Where ef is a side of the rectangle

Now i just need to find when P is max

[marble seal]

hello

anyone here?

[cursive bolt]

Hello

[marble seal]

can i get some help 🙂

[cursive bolt]

For

?

[marble seal]

here can i know what's going on

like why it become 7/3 not -7/3

and the lim part i didn't get it

[pearl marlin]

For limit part you can use l'hospital rule

[marble seal]

can u tell me limits rules plz

@dusk gazelle u 2

[bold breach]

a-b/√a+√b

[marble seal]

limit rule?

[dusk gazelle]

nah

[autumn plank]

can anyone explain how tos olve

[marble seal]

[polar whale]

We have to find the value of X?

[autumn plank]

yeah

[light nova]

what is primitives in integral calculus?

[glass lichen]

anti derivative

[light nova]

whats that

[autumn plank]

anyone

[tired elbow]

@autumn plank hi

Would you like to find the value of x?

[outer elm]

damn im trying to solve it its p hard

@tired elbow yeah x

you can open the left part using the identity sin(a+b) = sinacosb + cosasinb

[autumn plank]

@tired elbow yes

[light nova]

I opened it

But couldnt solve it

Microsoft math calc couldnt solve either

Wtf

[outer elm]

bruh

[autumn plank]

yeah I think they forgot to put a 2 before the sin(2x)cos(2x)

[tired elbow]

Give me a minute

[outer elm]

how would a 2 make this solvable man

[autumn plank]

double angle formula

[outer elm]

you can still do it

you just divide by 2

[autumn plank]

but then its unsolvable

since the left side is now 1/2

or 1/2sin(4x)

[outer elm]

no

once you open the left side itll be divided by 2

so its good

cuz then you can multiply the entire equation by 2

[autumn plank]

could you write it out

[outer elm]

yea

sin(x)/2 + cos(x)*sqrt(3)/2 = sin(4x)/ 2

you see?

you just multiply everything by 2

[glacial hedge]

@autumn plank your missing something very obvious

you can simplify the right side

[outer elm]

oh wait

youre right

adding a 2 would solve it

[autumn plank]

huh

can u just add a 2

[glacial hedge]

you can make it

1/2 * sin(4x)

[autumn plank]

1/2*sin(4x) is unsolvable

[glacial hedge]

wait

what class did this problem come from

@autumn plank

[autumn plank]

what do you mean

[glacial hedge]

what math class are you in

[autumn plank]

no clue I'm not american I dont know how the systems works

probably 11th

or 12th

[glacial hedge]

i mean what are you learning in math class

do you know calclulus?

[outer elm]

im pretty sure this shit is unsolvable

[autumn plank]

yeah probaly

[outer elm]

unless youre a genius

[autumn plank]

I think they just forgot a 2

[glacial hedge]

yeah

xD

@autumn plank the answers are ummm.....

[outer elm]

lmfao

theres surely a mistake in the question

[mellow frigate]

can anyone please help with the last part

[tired elbow]

@mellow frigate sorry, I am rusty at that topic

[mellow frigate]

oh no prob

[mossy berry]

$$P(\max{(X, Y)} = 1) = P(\max{(X, Y)} \le 1) - P(\max{(X, Y)} < 1)$$

[ocean seal]

ImperfeKt

[mossy berry]

Is it correct?

[mossy berry]

mean is n * p and variance is n * p * q

where q = 1 - p

[mellow frigate]

aah i get it, thanks mate

[alpine sable]

is this right?

[worldly gulch]

Guys what's 63 x 48

I'm not trolling

[alpine sable]

Why

[mossy berry]

coefficient of variance is (mean/Standard Deviation)

[alpine sable]

@mossy berryis this right?

[mellow frigate]

@mossy berry can you tell why you are multiplying n*p for mean?

[alpine sable]

LOL

[worldly gulch]

Shit wrong pic

My bad

[alpine sable]

@worldly gulch?

[worldly gulch]

I wanted to sent it in a diff server

[alpine sable]

why

[glass lichen]

<@&268886789983436800>

[mossy berry]

It's derived from mgf of binomial distribution.
first derivative of mgf gives mean.
Second derivative gies standard deviation.

[mellow frigate]

aaah got it thanks mate

[mossy berry]

Introduction to Mathematical Stats, by Hogg and Craig is a nice place to start if you are interested in derivation of these formulas.

[mossy berry]

the first one seems right. Sorry I dont have time for second one, Gotta go

[tall sage]

anyone know what this is

[tawny lion]

It's geometric series

S(infinity) = u1(1-r^n)/1-r

[tall sage]

so it would be..

162/486=r?

[tawny lion]

u1/1-r I mean

[tall sage]

how would I find r

[tawny lion]

Yes

[tall sage]

oh

[tawny lion]

Correct

[tall sage]

so then that's 0.333333333

u1 is 486

then what

[tawny lion]

486/1-1/3

[tall sage]

485.7

[tawny lion]

I got 729

Its 486/(1-1/3)

Not 486/1 - 1/3

[tall sage]

oh wait I got 694.3

oh

[tawny lion]

Idk i just used some website

[tall sage]

wait ye

oh

my calc says 729

[tawny lion]

Just do like 50 of these problems for sums, terms and all that other shit

You will remember the formulas in 1 day

[tall sage]

alr

[tawny lion]

Its 4 formulas

[tall sage]

do I use the formulas for this?

[tawny lion]

Divide 1 by 0.181818181818

[tall sage]

5.5

that's not the formula doe

[tawny lion]

So 2/11

[gray isle]

let your original number be x
consider doing some thing(s) to get numbers with the same thing after the decimal point

[tawny lion]

(69 * 11 + 2 )/11

[gray isle]

subtract the relevant equations to get rid of the repeating decimals

then solve for x to get your fraction

simplify as needed

[tardy robin]

Hey, is my understanding correct that $\oint_{circle} z^{-1} dz$ is only $2\pi i$ if $0$ is in the domain for the function, here $z^{-1}$?
If $0$ is not in the domain, the contour will just be $0$, right?

[ocean seal]

Kaishin

[alpine sable]

is this biased?

[tardy robin]

Oh, that is of course, if the domain is some other place - not that 0 is taken out as a single point.

E.g. if the circle is of radius 1 centeret at 2

[winter rock]

Hi how to simplify sqrt(9/2) please?

[subtle mantle]

look 👁️ for 4️⃣ things 🔢 you ☝️ can move 👈 out of the sqrt 🟦

for example 👐 how can you write 9 as a product of two numbers

[winter rock]

3×3

[subtle mantle]

yup, so what's the sqrt of 3 times 3?

or 3 squared in other words

[winter rock]

I found the answer thanks!

Thx !!

[magic kettle]

can someone help me get the answers for these please?

[winter rock]

@magic kettle wtfff

[magic kettle]

what? @winter rock

[magic kettle]

i have no clue man

[winter rock]

How old r u?

[strong furnace]

the thing in bracket is not a_n-1 its a_(n-1)

[winter rock]

what does _ means?

Wait I try do it again

[strong furnace]

subscript

standard notation for sequences indexed by natural numbers

[winter rock]

I'm 16 is it normal I don't understand what u're saying?

[strong furnace]

idk

[sterile beacon]

A train with the total mass of 260 tonne accelerate on a straight distance.
In the moment the velocity is 36km/h the locomotive develop the effect 650 kW. The resistance against the movement is 0.5% of the train's weight.

a How big pull force does the locomotive have and how large acceleration in the moment that the velocity is 36km/h.

b How does the acceleration change if the locomotive develop the same effect a while.

[winter rock]

Can u wrote that 4 me pls?

[vague coral]

yes and no

[winter rock]

@strong furnace

[strong furnace]

introductory calculus (limits) generally introduces sequence in high school syllabus

but I am not so sure since I self studied most of it

[winter rock]

Owwww I'm from Belgium I speak good English but math terms ☠

[vague coral]

You can speak french ?

[winter rock]

Yeah

And ndls and Arabic 😭

@vague coral u speak French?

[vague coral]

Grossomodo, il/elle te demande si tu comprends les notations des suites numériques

[tardy robin]

<@&286206848099549185>

For the question from before.

[winter rock]

A non jsp ce que c'est

[vague coral]

du genre $a_i$ avec i un entier naturel

[ocean seal]

Herels

[winter rock]

Non du tt

[vague coral]

chaud

[winter rock]

C'est quoi?

Jamais entendu de ma vie

[tardy robin]

Anyone?

[vague coral]

Une suite numérique est une application définie de $\mathbb{N}$ vers $\mathbb{R}$

[ocean seal]

Herels

[sterile beacon]

I second that pls help with my question

[vague coral]

En gros les nombres de N sont les nombres qui indexent la suite

[winter rock]

🤨

[vague coral]

On les appelle les rangs de la suite

mec, revise ton cours, j'essaie d'expliquer comme je peux

[winter rock]

je te jure on a jamais vu ca haha

Tu sais pas utiliser des termes plus simple stp

[vague coral]

Bah, pourquoi tu fais un exo porté sur ca ?

[winter rock]

Non je fais pas un exo sur ca

Ya qlqn qui en a posté un

[vague coral]

bah tout ce que je dis, c'est la version la plus simple

[winter rock]

Ducoup j'essaye de faire le sien

C'est de quel niveau ca?

[vague coral]

mini première

[winter rock]

Ca va j'ai une excuse haha

[vague coral]

donc ta jamais vu

[winter rock]

Oui x)

Mais j'vais regarder une video d'ivan monka

[sterile beacon]

Buenos espanol lingo

[vague coral]

te fais pas chier, ta pas besoin d'apprendre ca maintenant

[sterile beacon]

Por favor ingles

[ionic jewel]

i can almost read this conversation without speaking french

[strong furnace]

we forgot about the guy

who had asked the sequence problem

[vague coral]

oh my bad

[tardy robin]

nvm mine

[strong furnace]

maybe an early university channel can help you with contour integral?

[tardy robin]

I got help from the complex variable channel

[sterile beacon]

A train with the total mass of 260 tonne accelerate on a straight distance.
In the moment the velocity is 36km/h the locomotive develop the effect 650 kW. The resistance against the movement is 0.5% of the train's weight.

a How big pull force does the locomotive have and how large acceleration in the moment that the velocity is 36km/h.

b How does the acceleration change if the locomotive develop the same effect a while.

[winter rock]

@sterile beacon is that physic?

[sterile beacon]

is math...

@winter rock

[winter rock]

It looks like physic

[sterile beacon]

Alleged physic...

Even if it was true, physic uses math so it doesn't matter even if it was true.

[glass lichen]

you can do physics problems in a math class...

[winter rock]

Yeah but for physic we have to learn formules I mean

[sterile beacon]

I know that already

Thank youfsfosjfhniohnifgsjoifhbsfgbsuiowsfgsafgs

fssf

s

[winter rock]

😭

I wanna help u but tell me wich grades are u

[strong furnace]

P=(F.v) you are supposed to use this for both parts

[sterile beacon]

Effect is work / time though

[strong furnace]

Effect is power from what I understand and the way it is defined is dW/dt as you say you can use the definition of W and come up with this on your own*

[alpine sable]

v(t=0) = 0 ?

[sterile beacon]

Work is force times distance

divided by time

force times velocity

of course

now i feel stupid

[winter rock]

Hi

What did I did wrong

[alpine sable]

apply Newton's 2nd law:
F = m*a
F := sum of all forces. Pull force:= Fp. Resistance := Fr
then:

Fp - Fr = ma
Fp - (0.005 * m * g) = ma
Fp - (0.005 * m * g) = m* ( (v1 - v0) / (t1-t0) )
Fp - (0.005 * m * g) = m* (10 [m/s]/ (t1 - t0) )

[sterile beacon]

the picture is rotated sideways

[sterile beacon]

hey thanks pal

[winter rock]

I can not send it from another sideways

[strong furnace]

this is not a correct solution as there are many assumptions and you ignore the information provided by power at the given instance :/

[alpine sable]

F = P / v
F =650 [kW] / 10 [m/s] = 65 kN
(at conctant speed, meaning pull Force = resistance)

[harsh bone]

any one here speaks french

that could help

[restive heron]

i speak french but idk if i could help

ask ur question

[harsh bone]

its like a project and theres a part i do not undestand

[restive heron]

send a picture here

[harsh bone]

i have to make a parc

[restive heron]

not sure what do u mean by that

[harsh bone]

look

[alpine sable]

I think I got it

a)
P = (Fp - Fr) * v
Fp = (P/v) + Fr
Fp = ( 650 kW / 10 m/s ) + 0.005 * 260000 kg * 9.81 m/s²
Fp = 77'753 N

(not sure)

so Fp > Fr for acceleration a > 0

[jovial adder]

<@&286206848099549185> Hey quick question: What approach would I use to solve this problem? What I did: Agumented vector u and Matrix A and then did the rref form to get what I put in the answer box. However this was wrong as noted by the picture? Any idea what I did wrong? See picture below?: // Also I when solving my matrix I have determined that the system is indeed consistent if it helps

[tardy robin]

Please help

Anyone

In question room 7

[scarlet barn]

hey, anyone knows anything about big bang? any information it´s important. I´m from NASA and we are looking for evidences that Putin it´s an ET.

[clever locust]

<@&268886789983436800> obvious troll

[sly mantle]

@scarlet barn don't shitpost

[oak chasm]

@hybrid pike That's five rectangles. You can see the height of the top four rectangles. What are the widths of the top four rectangles?

[hybrid pike]

36?

[oak chasm]

No, they'll have different widths.

What's the width of the top left rectangle?

[hybrid pike]

7?

[oak chasm]

Right.

What's the width of the next rectangle?

[glossy ravine]

J

[alpine sable]

Hi, Can anyone help me?

[oak chasm]

@alpine sable See the rules and tips for getting help in #❓how-to-get-help.

[oak chasm]

@alpine sable OK, which of those would you like help with?

[alpine sable]

With the figures

[oak chasm]

Are you finding area or what?

[alpine sable]

Yh, the area

[oak chasm]

OK, so the top left is a rectangle and a semicircle?

[alpine sable]

Yes

[oak chasm]

OK, so what's the radius of the semicircle?

[alpine sable]

The diameter is 2 so the radius is 1

[hybrid pike]

9?

[oak chasm]

@alpine sable So, where in the height of 4 does the semicircle stop and the rectangle begin?

[alpine sable]

the 4 starts at the base and ends at the end of the semicircle

Here is a clearer picture

[oak chasm]

@alpine sable Right. Where the semicircle and rectangle meet, how far up the height of 4 is that?

@hybrid pike No, the ? here:

[hybrid pike]

12

[oak chasm]

What's the width of the third rectangle on the top?

[hybrid pike]

7

[oak chasm]

What's the width of the fourth rectangle on the top?

[hybrid pike]

12

[oak chasm]

What's the area formula of a rectangle?

[alpine sable]

4 covers the entire figure

[hybrid pike]

38

[oak chasm]

@alpine sable Right. I know that. I'm asking you to separate the semicircle and the rectangle. How much of the 4 height goes into the semicircle? How much of it goes into the rectangle?

@hybrid pike No, the area formula.

Not the width of a particular rectangle.

[hybrid pike]

A=LW

[alpine sable]

that is, I subtract the radius of the circle from the height of the rectangle?

then it would be 2 of base and 3 of height

[ocean seal]

Chai T. Rex

[oak chasm]

@alpine sable What are the red and blue question marks filled in with?

[hybrid pike]

426

[oak chasm]

Right, so the areas of the five rectangles added together is 426, so that's the whole area.

[alpine sable]

I don't know

[oak chasm]

OK, the blue is the radius of the semicircle, right?

[alpine sable]

yes

[oak chasm]

OK, so fill in the blue question mark with 1.

Fill in the red question mark with what's left of the total 4 height.

[fierce geode]

hi

[hybrid pike]

Is that the answer?

[oak chasm]

@hybrid pike It is.

@alpine sable What do you get for the red height?

[oak chasm]

@hybrid pike You have two triangles and three rectangles.

What are the area formulas for triangle and rectangle?

[hybrid pike]

Is the answer 646.68?

[alpine sable]

2?

[oak chasm]

@alpine sable No, the full height is 4. You take away 1 for the semicircle.

You have 3 left for the rectangle.

So, the red height is 3.

Does that make sense?

[alpine sable]

Aaah, yes, so I find the area of the rectangle and the circle and then add it all up?

[oak chasm]

@sudden coral Sorry, channel is busy.

@alpine sable Yes, but the area of the semicircle, not the full circle. Other than that, exactly.

[alpine sable]

I will look for the area of the circle with the radius of 1, right?

and after I have that result, I add it to the area of the rectangle, right?

[oak chasm]

Almost.

You look for the area of the semicircle with radius 1. What's the circle area formula?

[alpine sable]

p x r2

[oak chasm]

Sorry for the delay. Yes, that's the answer.

[hybrid pike]

ok

[ocean seal]

Chai T. Rex

[oak chasm]

@alpine sable You only want to get half the area of a circle because it's a semicircle.

@hybrid pike That's six rectangles. Use the same idea.

[alpine sable]

then after I make the area with the radius of 1, I divide it by two?

[oak chasm]

Yes, that's right.

Then add it to the full rectangle area.

[alpine sable]

Ok, I will do it and show you, thank you very much.

[oak chasm]

@alpine sable No problem.

[hybrid pike]

3820.2?

Is that the answer?

[oak chasm]

,w volume of cylinder with radius 8 meters with height 19 meters

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

@hybrid pike Yes ^

[steep steeple]

is any1 able to solve this proble, im a bit stuck

[hybrid pike]

565.5

[oak chasm]

@steep steeple Sorry, channel is busy.

@hybrid pike If you just want to check your answer, use this link and edit the values (make sure to use the proper units): https://www.wolframalpha.com/input/?i=volume+of+cylinder+with+radius+8+meters+with+height+19+meters

[hybrid pike]

ok

@oak chasm, so is it right?

[oak chasm]

Well, what I'm saying is that that site will tell you if you're right or not.

I can't do that any better than the site.

[hybrid pike]

That's cheating '

i got it right

@oak chasm

oh no

[placid zinc]

"To the nearest tenth" there should be a decimal

[hybrid pike]

oh

[oak chasm]

Yeah, circular things' area or volume tends to have pi in it.

[candid ridge]

please help!

[placid zinc]

,w 5π(20/2)^2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Kaynex#7520

[oak chasm]

@candid ridge Sorry, channel is busy.

[candid ridge]

its okay!

[placid zinc]

Yeah you just rounded a decimal too many

[plucky crow]

,w ellipse with foci (2,4) and (8,4) and minor axis = 4

[ocean seal]

Results provided by WolframAlpha

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

Requested by Syphax#3869

[hybrid pike]

I'm honestly stuck

[oak chasm]

@hybrid pike Do you know which place is the tenths place?

[hybrid pike]

Yeah

0.(THIS)

[oak chasm]

OK, your answer should stop with the tenths place as the last digit.

[placid zinc]

See this picture

[oak chasm]

That's what rounding to the tenths place means.

So, 1571 stops at the units place.

[alpine sable]

@oak chasm

Like this?

[hybrid pike]

So, 1570.8?

[oak chasm]

@hybrid pike 1570.x with some digit for x should be your answer.

Right!

[hybrid pike]

nice

882.5?

[oak chasm]

@alpine sable Do they say to round?

[placid zinc]

Give it a shot haha. You get two attempts

[alpine sable]

In the first, the 7.6 then divide it by two?

[oak chasm]

No, I mean, do the instructions say to round or do they want an exact answer?

[alpine sable]

An exact answer, but if I can round it I do

[oak chasm]

If they want an exact answer, you shouldn't round.

[alpine sable]

Like, if the answer for example is 7.27, I can round to 7.3, no?

[hybrid pike]

I got it right

3163.4?

[alpine sable]

The first is 6+1/2+pi : 2 right?

is this right?

[ocean seal]

Chai T. Rex

[oak chasm]

@alpine sable ^

@alpine sable Sorry, channel is busy.

[lean gust]

comment prouve que la somme de (-1)^k /k+1 allant de 0 a n
est egale ln (2) +(-1) ^n * integrale de t^n+1/1+t dt de 0 a 1

[oak chasm]

@lean gust Sorry, channel is busy.

[alpine sable]

is correct?

[ocean seal]

Chai T. Rex

[alpine sable]

and, the rest is correct same?

[oak chasm]

Yes, in the work I showed.

[hybrid pike]

@oak chasm Is this right?

[alpine sable]

Thanks u, can you help me with the last 2?

[oak chasm]

@alpine sable So, that's the exact answer. If you round it, it's no longer exact, so if they want an exact answer, that's what they want.

[alpine sable]

Ok, I understand, thank you

https://cdn.discordapp.com/attachments/490557019623915520/853753041915740200/20210613_233804.jpg

[oak chasm]

@alpine sable The second one is wrong. When you subtract the area of the circle from the square, you have four equivalent areas like the shaded area.

So, you should divide by 4, not 3.

Also, you shouldn't round if they want exact answers.

[steep steeple]

thanks, i got that too

[alpine sable]

do I have to subtract 3?

9/3?

[oak chasm]

What do you mean by subtracting three?

[alpine sable]

I mean, I don't understand what you said

[oak chasm]

You get the area of the four outer parts by subtracting the area of the circle from the area of the square, right?

[alpine sable]

Here, no?

[oak chasm]

That's your entire work. Where in there are you talking about?

[alpine sable]

Here

[oak chasm]

I still don't see you subtracting 3.

[alpine sable]

I made the area of the circle, the radius is 1.5 then I made the area of the square, with those two results the rest, no?

[oak chasm]

Yes.

[ocean seal]

Chai T. Rex

[oak chasm]

How many corner parts are there?

[alpine sable]

4, but I just have to find the area of one

[oak chasm]

Right, so you divide by 4 to get that.

[ocean seal]

Chai T. Rex

[alpine sable]

I wouldn't have to divide by 3 so that there was only one left?

[oak chasm]

You have four parts, right?

[alpine sable]

Yes

[oak chasm]

You want one of them, right?

[alpine sable]

Yes

[ocean seal]

Chai T. Rex

[oak chasm]

Like if you have a quarter of a pie, that's not 1/3 of the pie.

[alpine sable]

Aaah, ok, So that's why, the result of the two, I divide it by 4?

[hybrid pike]

@oak chasm It's right

[oak chasm]

The result of which two?

[alpine sable]

Of the two areas I got

[alpine sable]

Like this

[ocean seal]

Chai T. Rex

[oak chasm]

That's what you multiply it by.

[alpine sable]

Ok, I understand

[oak chasm]

OK, now simplify that.

[alpine sable]

The result is 0,48

Right?

[oak chasm]

No, you said they wanted exact results.

If they want exact results, never round.

[alpine sable]

Then 0.5?

[oak chasm]

No, that's not the exact result either.

[ocean seal]

Chai T. Rex

[oak chasm]

Separate into two fractions. What do you get?

[alpine sable]

0.4828541324

[oak chasm]

No.

That's rounded.

Please stop doing that.

I've repeatedly told you that if they want exact answers not to round.

[alpine sable]

It is that before I had been taught that for example with that result, in this case 0.48, I could round it to 0.5

[sage jacinth]

you need to give an exact answer

higher level math doesn't like decimals

[oak chasm]

@alpine sable If they want an exact answer, you can't round.

You said they want an exact answer.

Unless they want a rounded answer, don't round.

[alpine sable]

And how do I get the exact answer?

[sage jacinth]

give it in fraction form

[ocean seal]

Chai T. Rex

[oak chasm]

Separate the main fraction into two fractions.

[alpine sable]

9/1 - 9/4 pi / 4

Like this?

[sage jacinth]

maybe this will help

[oak chasm]

@alpine sable Almost, except the 9 is also divided by 4.

[ocean seal]

(バカ) baka

[alpine sable]

Ok, So the answer is 9/4 - 9/4 pi/4?

[oak chasm]

No.

[sage jacinth]

sure, but thats not simplified

[oak chasm]

The second term can be simplified a little.

[ocean seal]

Chai T. Rex

[alpine sable]

9/16pi

[oak chasm]

Right!

That's the exact answer.

Oh, sorry.

[ocean seal]

Chai T. Rex

[oak chasm]

There.

[alpine sable]

Thank you very much, and thank you for your patience 😅

[oak chasm]

No problem.

Exact answers are nice once you get used to them.

[alpine sable]

And with the other two that were in front, is there a problem?

[alpine sable]

I get it, is that sometimes with mathematics I get very confused

[oak chasm]

Yeah, it takes some getting used to if you've always done rounded stuff before.

The third one is wrong. It's not a rectangle, but you used the rectangle area formula.

[alpine sable]

But if the sides are different, isn't it a rectangle?

[oak chasm]

The opposite sides have to be the same.

So, the top and bottom have to be the same.

The right and left have to be the same.

Here, neither of those are true.

The left side is 5, the right side is 2.

[alpine sable]

Sum up all the heights that are on the right and that sum gave me 5, and the base is 2

[oak chasm]

The top is sqrt(5). The bottom is 2sqrt(2).