help-0

[wheat prawn]

oh

[glossy current]

No

[wheat prawn]

so x = 4?

[glossy current]

there are 2 solutions

4 is one of them

[lethal ore]

$x^2-4x=0$\
$x(x-4)=0$\
$x=0\ text{or}\ x=4$\

[ocean seal]

my name is jeff

[alpine sable]

can someone help?

[stark blade]

how do i find the range of f
f(x) = x^3

I heard since its a cubic, x can be all real values thus y can too

written like this

[craggy bluff]

hey guys can anyone help?

ok wait thanksss

#4 & 9 I'm really debating on #4 if it's either C or D and on #9 I'm confuse as it didn't go as I expected to be when I was solving it

huhu desperate help

oh noh thats not an exam nor a contest

AHAHA that's just a small assessment way past the due date

#4 really debating if it's either C or D tho

[modern aurora]

I STILL NEED HELP

[tacit girder]

To go to school in the morning, I first walk to the garden shed at 6km/h to collect my bicycle. I then cycle to school at 15 km/h. The total journey normally takes 18.5 minutes. One day, I am late and I run to the shed at 18km/h and cycle at 27km/h. The journey takes me 10 min 10 s. How far is it from my house to the garden shed?

Please help

yeah basically

i need to know how long is the "6kmph" and "18kmph" part in that

[tacit girder]

length*

like distance

letv??

this question falls under simultaneous equations

and it gives us formula actually distance = speed x time

[naive lion]

What does it mean to be linear in paramater vs linear in variable?

[deft dagger]

uh i'm pretty new to math, what is the F mean in calc | intergration

also if I have:

f (2x^2/3) + (7x^2/2) - 15

Why is it not like the following

f (2x^2/3) + (7x^2/2) - (15x^2/2)

It is instead
f (2x^2/3) + (7x^2/2) - (15x)

[tender geyser]

if i understood you correctly then F is the function you get after integrating f (if you take derivatives the chain would be like this: F(x) -> f(x) -> f'(x) -> f''(x) -> ...)

alos 15x^2/2 and 15x are the same

2/2 = 1
x^2/2 = x^1 = x

[harsh swallow]

F is the integrated function

if you are given f

and are told to integrate

you will have F as the answer

[edgy delta]

hey everyone, how would I show that this function is injective?

[vale wigeon]

it may help to rewrite its formula a little bit before applying the definition of an injective function

(3x+1)/(5x+2) = 3/5 - 1/(25x+10)

[edgy delta]

and from there what exactly do you do to prove injectivity?

[vale wigeon]

apply the definition of injectivity

[calm grove]

Check if f(x1) = f(x2) then whether or not x1=x2
Or if f(x1)≠f(x2) then whether or not x1≠x2
Or just do the horizontal line test my making the graph of f(x)

[alpine sable]

Simple Question:
What we get as a result if we
1/2 - 3/4

I get "-1/4", but is this correct fraction? How can I rewrite this?

[peak gorge]

Can anyone explain to me how to calculate 52C5 and when would I use it

[vale wigeon]

what do you mean by "correct fraction"? is there something about -1/4 that makes it illegal?

[alpine sable]

No, I think it's correct, negative sign confused me a little )

[minor heath]

basically use the formula for nCr for combinations

$nCr=\frac{n!}{r!(n-r)!}$

[ocean seal]

G3oG0dly

[peak gorge]

So when would I use this formula?

[bold token]

If you wanna count how many combinations there are

[minor heath]

everytime you are asked to know how many ways you can pick a set from a bigger group

[peak gorge]

Ohhhhhh

[minor heath]

for this case, you can use 52C5 to count how many ways you can pick 5 cards from a deck of cards

[peak gorge]

Yeah that’s why the guy answering what the odds of a royal flush are used 52C5 to explain why he was doing

[bold token]

quick question can you do 52C52 right?

[minor heath]

lol

[bold token]

xD Ik

[peak gorge]

It’s like 2.3 million I believe?

I think

[bold token]

52C52 is just 52!

[minor heath]

what no its 1

[bold token]

oh

oh mb

combinations, got it

[minor heath]

$2598960=\frac{52!}{5!47!}$

[ocean seal]

G3oG0dly

[peak gorge]

Close enough

[minor heath]

about 2.6 mil yea

hopefully it answers your question

[peak gorge]

It truly did

Thank you

[minor heath]

no problem

[alpine sable]

can I ask here?

[minor heath]

yea you're available to ask now

[peak gorge]

Ye I’m all finished

[alpine sable]

I'm using Python's numpy library to sample from random distributions. I'm trying to sample from distributions with a specific min, max, mean, SD

How would I do that?

If I sample from any of the distributions in numpy, values fall outside the range that I want

[peak gorge]

I’m not that sure you will get a response in this server, but I do know of an awesome coding server that will most definitely give you your answer. https://discord.gg/code

[alpine sable]

thank you

[sand notch]

how the hell do i solve this? i substitute u = 1-x² and then solve for x, but how does it work ? sqrt on both sides??

[glass lichen]

$u=1-x^2\to\dd{u}=-2x\dd{x} \ \frac{-\dd{u}}{2}=x\dd{x}$

[ocean seal]

moshill1

[glass lichen]

You dont have to solve for x in this question

[sand notch]

why this du = -2x dx step, where does this come from

[sand notch]

why not

[glass lichen]

differentiated both sides of the u-sub

[sand notch]

every example online did this

first substitute , then solve for x, then derivate

[quaint trout]

When you replace x as the variable of integration with u, you have to multiply by du/dx. Intuitively, you can think of you need to replace the dx in the integral with du and du = (du/dx) dx

[sand notch]

i dont think i get it. when you for example substitute u = sqrt(1+x), you solve for x first. (example 2:) if you substitute u = 2x, you solve for x first too, why not here?

[quaint trout]

Give an example

Of what you mean by solving for x

[quaint trout]

If you mean, you need to find an expression for x in terms of u so that you can replace all the x's in the integral, then sure you can do that

But it's not necessary in this case, since you will replace the 1-x^2 with u directly, and the x in denominator will disappear when you replace dx with du

But you can do it

It's not wrong

[sand notch]

so you never have to solve for x ?

[quaint trout]

I didn't say that

I said it's not necessary here

But you can do whatever you like

[sand notch]

i really dont get the point when to do it and when not

[quaint trout]

You can do it here

[sand notch]

also where do all the du / dx come from, it appears later after solving for x and derivate

and not right after substitution

[quaint trout]

You need to replace dx with du in the integral, that's where the du/dx comes in

You can do it anyway you like. So if you want to solve for x, you can.

It's not wrong.

[sand notch]

but its complicated

this cant be right?

[rigid smelt]

you should have just found dx in terms of du and x

in this case where u= 1- x^2, dx = -1/(2x) du

and then substitute that into your integral, you will see that something cancels out nicely

[sand notch]

where do you get that dx = -1/(2x) du from

[rigid smelt]

so u = 1 - x^2

hence du = (1-x^2)' dx

or more well written it should be du/dx = (1-x^2)'

[grand kelp]

There you get that du/dx = -2x

Therefore du = -2x dx

[sand notch]

so, I dont really see a goal here by just having all these dx / du / u's here. what am i suppose to do with these

[grand kelp]

So what you're essetially doing is finding the integral $\int{\frac{-1}{2\sqrt{u}}}du$

[rigid smelt]

just sub it back into the integral

[ocean seal]

NickPro

[rigid smelt]

so where ever you see 1-x^2, you replace with a u

where ever you see a dx, you replace with -du/(2x)

[grand kelp]

Well we have an x dx in the numerator already

So we can replace that directly with a -du/2

[sand notch]

what is the formula to always get dx ?

[rigid smelt]

sure works too

[sand notch]

du / (u)' = dx ?

[rigid smelt]

theres none

you just have to judge it like a variable

[grand kelp]

Yes, by definition

[rigid smelt]

but its not really a variable

[grand kelp]

It's a change to a variable

[sand notch]

so u' = du / dx

i never wrote derivatives like this, now it seems I have to know it lol

so you always have to calculate dx, du, u and (u)' before you proceed?

[rigid smelt]

Well i mean its not a rule, its just that its necessary to make the problem easier

Technically u-sub is just to make the thing looks cleaner and easier to integrate

So when you subbed u into the expression, you would want to change the variable of integration too

Or else you would be integrating some expression of u with respect to x where u is a function of x

Which is just so so much complicated

[sand notch]

so yes

weird how it isnt written in any examples online

[rigid smelt]

Hmm could you link some of those examples?

[sand notch]

they are in german

[rigid smelt]

Do they have the work written out?

[sand notch]

https://www.mathebibel.de/integration-durch-substitution

[rigid smelt]

Ahh ok

So what they intend to say is that

They want x to be a function of u

So that they could find what dx is

And then sub that into their integral

At the same time

They can also sub the function of u into every place that has an x

Its quite the same like what we did here

[mild marten]

Let me know when I may ask a question next please

[sand notch]

ok, but once it's like x^2 it doesnt seem to work anymore

so I guess I just calc u, du , dx , u' every time

i guess im done

[rigid smelt]

Idk, but im much more familiar with the method i wrote out

If they dont force you to use their method, then you should use the u sub

Its a bit more straight-forward to me

Ig

[mild marten]

A given triangle with an unknown length has an opposite angle of 135. The other two sides have length 2.75. find unknown length

[rigid smelt]

Use cosine rule

[grand kelp]

Are you familiar with the law of cosines?

It's fine if you aren't, we can find the answer without it

@mild marten

[grim sedge]

Find the position to term rule for 12, 14, 16, 18, ....

help?

[mild marten]

I think it is cos adjacent over hypoteneuse

[grim sedge]

here are the choices too
2n+10
12n+2
10n+ 12
2n+12

[grand kelp]

That's not what we need

Okay

[grim sedge]

explain not awner

[grand kelp]

2n + 10 works

Look, we start with n = 1

[grim sedge]

great

man

i said explain

[grand kelp]

I sent too fast, but I will explain

[grim sedge]

ooooh ok

i understood how u got it

im good

thanks!

[grand kelp]

np

@mild marten Okay, then we'll use the Pythagorean theorem to find the answer

[mild marten]

I did the cos thing, and got 5.08
I think it is right

[grim sedge]

oh now it wants the oppisite?

5n – 3

2, 7, 12, 17
5, 10, 15, 20
2, 5, 8, 11
12, 17, 20, 23

[grand kelp]

Just plug in n = 1 and n =2 and look where it coincides

[grim sedge]

NVM

i found it

2,7

i understand

2 , 7 12 17?

correct?

i did the method correctly it has to be nvm thanks

[grand kelp]

It is, yeah

[small token]

Hi, I've got a quick question

It says that BC is 4cm, however, there's two lines connecting B and C.

So, which one is the one mentioned in the question, the 4cm one?
And how can I know which one is which in the future?

[grand kelp]

BC is a line segment, not an arc

4 cm is the straight line between B and C

If they wanted to tell you the length of the arc, they would specifically add this is an arc

@small token In general, if you have an expression like BC = 4 cm, it is a straight line segment unless you are told otherwise

[small token]

Alright thanks.

[fair saffron]

Could it be specified this way?

[grand kelp]

It could, yeah

Or simply "arc BC"

[small token]

Eh but then the question a below is just AD, but since the diagram only shows one line on it I guess that automatically means the arc

Thanks for the help Nick

[alpine sable]

can someone help me with a physics question?

my answer was 300 but its wrong

<@&286206848099549185> sorry for pinging

[glass lichen]

find the acceleration of the wagon, then apply newton's 2nd law

[alpine sable]

oh is it 75? @glass lichen

[glass lichen]

should be

[alpine sable]

thank u @glass lichen

[oak wigeon]

I need help

[sage dune]

how do I solve this?

[pliant ocean]

@sage dune which angle is the 45 degree angle?

[sage dune]

i think its the arc

[alpine sable]

Use Papa Pythagoras Theorem@sage dune

Construct the radius to the point of chords

[alpine sable]

i think its 2

[pliant ocean]

@sage dune I got 6.36 so the answer is A

[sage dune]

can you show me how you did it? @pliant ocean

[pliant ocean]

Ok wait a sec

@sage dune

[alpine sable]

pin me if you get this...im lost

[pliant ocean]

@alpine sable thiss a generalised version of the same question u asked. Hope it helps.

https://www.toppr.com/ask/question/a-2n-digit-number-starts-with-2-and-all-its-digits-are-primethen-the/

[alpine sable]

oooo

thanks a lot

wow this site is great

[pliant ocean]

Yup I luv it. I use it alot

[tender portal]

Just need something cleared up

X(t) is the inverse of f(t) graph right

[alpine sable]

Yes

[tender portal]

In this instance

[alpine sable]

Do you know the differential calculus

[tender portal]

So the particle is always speeding up

Yes im taking it rn

[alpine sable]

Do you know the derivative of tan inverse of t

[tender portal]

If it was f(t) the particle would be slowing down right

Yeah its 1/1+x^2

[alpine sable]

Yup. So the derivative of x(t), which gives us the speed is 1/1+t^2

And it's always positive

[tender portal]

Yep

[alpine sable]

So the particle would head in same direction

[tender portal]

But for part b

[alpine sable]

For that you need the sign of acceleration

[tender portal]

Its speeding up because its x(t) right

[alpine sable]

That's not very accurate.. you have the velocity function. How will you get the acceleration

[tender portal]

But when you plug t into the derivative equation of tan it shows that its slowing down in the x direction while maintaining a constant acceleration in the y direction which would cause it to speed up

[alpine sable]

First of all, there is no acceleration in y

Secondly, when you find acceleration by derivative of velocity, you will find it to be always negative. Hence particle is slowing down

You can alternatively do this by plotting the tan inverse graph. The slope is velocity. As you move in positive x direction, you will see that slope decreases. So particle slows down

[tender portal]

Its slowing down in regard to the x axis

But speeding up in regard to the y axis?

[alpine sable]

It's a one dimensional motion

Nothing happening in y

[tender portal]

Oh so only x direction

[alpine sable]

Yes

[tender portal]

I think thats where im getting tripped up

Ty I couldnt wrap my mind around that

How would you find the limiting position then

[alpine sable]

Do you know the graph of tan inverse of x

[tender portal]

Oh its 0

[alpine sable]

No

It's zero at t = 0

[tender portal]

Doesnt i get closer to 0 as t increases

[alpine sable]

No

[tender portal]

And no i dont know the graph

Oh nvm it get closer to 1

[alpine sable]

No

See tanx approaches infinity at π/2

[tender portal]

Isnt that for f(t)

[alpine sable]

So the inverse approaches π/2 at infinity

[alpine sable]

Yes this is tan inverse of t

[tender portal]

Ah okay

So the graph would be

In relation to x

[alpine sable]

Hm this is the graph of tan x

For inverse of a function, you flip the graph about the line y= x

[tender portal]

Yeah but the inverse of an inverse is the original right

[alpine sable]

Hm

[tender portal]

Cuz we have tan inverse

But its also in relation to x

So it gets inverted again

[sudden torrent]

MB

[sand notch]

how is sin(x) strictly monotonically growing on -pi/2 to pi/2 when it's actually getting smaller after x= 0 ?

no, my professor said its completly increasing

is this again some bullshit attribute of integrals or somehting?

[alpine sable]

Yo what is 0.57 as a fraction

[alpine sable]

Ok sorry it's true

[alpine sable]

My man this is the graph of effin cosx

[sand notch]

so what

[floral fjord]

?

[alpine sable]

Sine x is increasing from -π/2 to π/2

[sand notch]

no, you can see the y values decrease after x=0

[alpine sable]

1. channel occupied
2. don't multipost

[sand notch]

how is this increasing when its getting down

[alpine sable]

Take a look at graph of sine x and then recheck

[alpine sable]

This is not sine x

[sand notch]

ah so the drawn graph is not sin x

[alpine sable]

This is sine x

[sand notch]

ah thanks

[alpine sable]

👍

[vast drum]

the world's busiest pedestrian crossing is in Tokyo. In one day, a total of 1,250,000 people cross the street at this pedestrian crossing. How many people cross the street on average per minute? Please help me with this question and please explain to me.

[alpine sable]

How many hours are there in a day

[vast drum]

24

[alpine sable]

How many minutes in an hour

[vast drum]

60

[alpine sable]

So how many minutes in a day

[vast drum]

1440

[alpine sable]

Yup

[vast drum]

so?

[alpine sable]

Now if 1250000 cross in 1440 minute

[vast drum]

1,250,000/ 1440

[alpine sable]

How many cross in 1 min

[vast drum]

?

[alpine sable]

Yup

[vast drum]

thanks

[alpine sable]

👍

[vast drum]

❤️

[silk terrace]

Does anyone know if a complex sequence |a_n| converges to 0 implies that a_n converges to 0?

[muted raft]

That should be true?

I think it should.

[silk terrace]

I am having difficulties finding if it is true and if so a website with some proof of it.

[muted raft]

I assume the proof would use the triangular inequality I guess.

[silk terrace]

Hmm. Still unsure of the result as if a complex sequence |a_n| converges to 0 implies that a_n converges to 0 could be generalized to converges but I am certain that isn't true.

[alpine sable]

Somebody help me with this

[muted raft]

channel busy

move on

[alpine sable]

Oh my bad

Nobody was chatting so I thought it was open

[silk terrace]

And the contrapositive would also be true, no? Which I am pretty sure is not true.

[muted raft]

Do you have a counter example for it?

[alpine sable]

Any calc genuiuses here? Need help clutching my calc class

Calc 3

[muted raft]

Channel is again, busy.

[glass lichen]

try posting the question in an unused channel instead of asking to ask

[silk terrace]

No, unfortunately not on the spot. But still would like to know if the specific result if a complex sequence |a_n| converges to 0 implies that a_n converges to 0. That would mean the modulus of the sequence (Informal explanation I know) would converge to 0 and thus wouldn't that mean that the sequence has to converge if the complex modulus gets closer and closer to 0?

[muted raft]

I guess this might be useful to you?: https://math.stackexchange.com/questions/1934616/why-this-proof-of-absolute-convergence-implies-convergence-works-for-comple/1934692

[silk terrace]

But absolute convergence is for series and not sequences from my understanding?

[alpine sable]

Can someone help me with #1 and #3?

,rotate

[alpine sable]

#1 first subtract 7 from both sides

7- 19?

[muted raft]

Yeah I haven't found much convincing proofs either.

The closest one I have found upon searching is: https://people.maths.ox.ac.uk/flynn/genus2/AnI0506/analysisI-wk4.pdf

But it still is not exactly what you needed...

[alpine sable]

hi

[silk terrace]

I found this: https://calclab.math.tamu.edu/~sivan/math407_05a/S13.pdf - Check theorem 1.3.5. Doesn't that proof it for (iii)

|z|=|0|=0

[muted raft]

yeah that actually looks good

and it uses triangular inequality as well.

[silk terrace]

But the way it is written I do not see the way of implication or if it is a bi implication

Since my case is if a complex sequence |a_n| converges to 0 implies that a_n converges to 0 this could be problematic.

[bronze elbow]

its a simple question but i forgot the order

on how its suppose to be in

[polar whale]

Place those two triangles such that their sides match and they coincidence

Then u get the order

[sick radish]

Can you tell me when you done

Cause I got some questions

[polar whale]

Done what?

[sick radish]

Done helping

[polar whale]

Answer will be the fourth option. Observe the diagram carefully and you'll get it👍

[polar whale]

Ok shoot

[bronze elbow]

k ty

[polar whale]

What questions?

@sick radish

[sick radish]

Ok

I think it’s proportional

Nvm

I think I got it it’s non proportional

[polar whale]

Sry I can't see the image for some reason

My internet is troubling me

I think

[sick radish]

Can you help me out with this

[alpine sable]

Can someone help me with point 3?

[alpine sable]

what don't you get

[sick radish]

The first question

[alpine sable]

ok but know what proportionality

is

[sick radish]

Nah

Kinda

Ok I forgot

[alpine sable]

ok well no 1.

4 types of proportionality

Direct Proportion.
Inverse Proportion.
Compound Proportion.
Continued Proportion.

[sick radish]

Ok

[alpine sable]

no 2. if the graph goes through (0, 0) then then x and y are proportional

[sick radish]

Ok

[alpine sable]

Plus it even says

there is a proportional relationship

[sick radish]

Ok

[alpine sable]

between the time and distance

so I don't get what you don't get

[sick radish]

I understand

Can you tell me where do you see where it says proportional

[alpine sable]

$y\propto{x}\implies{y}=kx$ where $k$ is a constant.

[sick radish]

Ok

[ocean seal]

Several people are

[sick radish]

Thank you

[alpine sable]

This is directly proportional

[sick radish]

Idk understand when it says x- axis represent in the blue

[alpine sable]

wdym you "idk understand"

also whatchu askin

I don't get it

oh

right

What it represents

So obviously the x and y axis must represent a quantity

in this case

the x represents time (in hrs) and y represents distance (in miles)

[sick radish]

Oh ok

[hexed barn]

Am I understanding this right: for every element in Qv apply the function on the right and create a set based on the results?

[vestal hollow]

How did they get a radius of convergence of 1/2?

I'm getting 2

After ratio test and limits and bla bla, you end up with |2x-3| < 1

Which implies x < 2

If you divide everything by 2 instead, you get |x - 3/2| < 1/2

But if you add the 3/2 you still get x < 2

[wet fulcrum]

can someone help

[vestal hollow]

Oghhh I didn't set down a lower bound ok

[frigid elm]

Can anyone explain the integration steps between the second and the third line here?

[alpine sable]

is this correct?

0 divided by a number should be 0 right

[cold urchin]

what a weird q

yes x = 0

unless im missing smth

[dull solar]

Can someone help with trig question please

[alpine sable]

that would mean both intercepts are at the origin right

[cold urchin]

yes

y = (2/3) x and y = -5x

no constant c

[solemn lily]

Hello, how to explicit this function f(x)= {x}*(1-{x})

and domain is [0,3]

{x} is fractional part of x

[alpine sable]

idk how this could even work

[warped badge]

Can someone help me to solve this

I need to determine the stationary points (x and y coordinates)

[warped badge]

Can you show me the steps?

[crimson void]

Is this in anyway correct, sorta trying it but im kinda confused lol

top is q bottom is my answer

[alpine sable]

Adam can you help me with this

[crimson void]

if you read your choices and go over which answer shows each possible outcome then you should find the answer quite easily

Is this in anyway correct, sorta trying it but im kinda confused lol
https://cdn.discordapp.com/attachments/490557019623915520/841739335409598474/unknown.png
top is q bottom is my answer

[glass lichen]

4sin(20)-3cos(40) is a constant. . .

[wet fulcrum]

can someone help

[fickle bridge]

can someone help me

its a pyfagorom question

im kinda stuck on on

[analog locust]

how does this work?

[buoyant edge]

@fickle bridge just ask your quesiton

[fickle bridge]

i literally asked if someone can help

[buoyant edge]

thats not the question

[crimson void]

Ask your question lol

[analog locust]

im confused at the (1/2)e^-2t + 1/4e^-2t part

[crimson void]

if only we had a magic ball to rub

[fickle bridge]

ok

[buoyant edge]

@analog locust they integrated the second term on the right by parts

[analog locust]

@buoyant edge any advice on how it works?

[buoyant edge]

integration by parts?

[analog locust]

im a bit confused

yep

[buoyant edge]

it's essentially the integration analog of the product rule

[analog locust]

should I watch Essence of Calculus by 3blue1brown?

[buoyant edge]

I've never watched that so I cant recommend it myself

[analog locust]

@buoyant edge umm... easier explaination or example?

[fickle bridge]

helo

me

plz

[buoyant edge]

@fickle bridge now im not helping you at all

[fickle bridge]

why

[buoyant edge]

im clearly trying to help @analog locust

[crimson void]

take a look at rules of Pythagoras that will help, but just dont be like that lol

Its disrectspectfull

[fickle bridge]

ok thanks

[wet fulcrum]

can u send the figure

[fickle bridge]

ok

[karmic willow]

A bowl consists of a chocolate bar, a gum ball, a sucker, a candy necklace and a lollipop. How many ways can you select at least one candy?
Im having trouble understanding how I would get this answer would anyone be able to help

[fickle bridge]

sandwitch

[wet fulcrum]

basic pythagoras

wait

[frank epoch]

5 inch

[analog locust]

is integration by part the same thing as product rule?

que?

[fickle bridge]

ok thanks

[buoyant edge]

It's the inverse of the product rule since you're integrating and not differentiating

[wet fulcrum]

its 2 * root 13 my friend

[analog locust]

ooooooooooh

@buoyant edge would there be like a resource you can recommend to learn calculus holisticly?

I mean derivation and integrals*

[buoyant edge]

Paul's Online Math Notes

[analog locust]

im supposed to do ODE and I have zero idea on how to do it

[buoyant edge]

High School/College style notes; very accessible

[wet fulcrum]

can someone help after youre done with your current question

[analog locust]

thank you!!!

[wet fulcrum]

hello

[crimson void]

Hey can anyone give me some direction on how to approach this question still bit stuck

differentiating

[buoyant edge]

@crimson void The expression for y is a constant

so differentiation with respect to any variable is 0

[real fractal]

Is H a group?

[crimson void]

thank you Chris 🙂

[fair juniper]

Need help answer?

[real fractal]

Sorry I didn't realise someone is askinf

[fair juniper]

help pls

[alpine sable]

no

[analog locust]

WHAT

@buoyant edge did I understood a concept wrong?

integral(x*cosx) dx is not integral(x) dx * integral(cosx) dx?

O_O

[buoyant edge]

No, it is not.

[analog locust]

I feel so dumb...

[buoyant edge]

Don't worry, I should've been more careful with my words

Integration by parts is like the product rule in that you use it to evaluate integrals of products

much like how you use the produce rule to evaluate derivatives of products

[analog locust]

can't you use it the same way as product rule?

[buoyant edge]

However, they are not the same result

Even the product rule is NOT that (fg)' = (f')(g')

[analog locust]

like... integral(x cosx dx) = integral (x dx) * cos x + integral(cosx dx) * x?

(fg)' = (f')(g) + (f)(g') right?

[buoyant edge]

Integration by parts yields that $\int{udv} = uv - \int{vdu}$

[ocean seal]

Chris24

[analog locust]

holy crap im confused

do I really need to read 600 pages of calculus to understand ODE???

btw can anybody explain this to me too?

e^2ln|t| = e^2 * e^ln|t|

[buoyant edge]

$e^{ln(t)} = t$

[ocean seal]

Chris24

[analog locust]

log e on both side means

2*t

why is it t^2?

instead of 2*t

[buoyant edge]

If you take ln of both sides

on left side you get 2ln(t)

and on right side you get 2ln(t)

[analog locust]

?

I don't get it

[buoyant edge]

Which part do you not understand

[analog locust]

the 3 lines you just said

which "sides"

_

?*

[buoyant edge]

of the equation, i mean

[analog locust]

of which equation?

[buoyant edge]

The one you just posted

[analog locust]

so like

shouldn't it be 2*t?

instead of t^2?

ln(e^2) = 2

[buoyant edge]

On the right side of the equation?

I'm not sure what youre asking

[analog locust]

im confused

how did e^2ln|t| = t^2

not 2*t

[buoyant edge]

Ok

[analog locust]

since based on the rule it becomes e^2 * e^ln|t|

[buoyant edge]

That is not true

[analog locust]

oh?

[buoyant edge]

$e^2*e^{ln(t)} \neq e^{2ln(t)}$

[ocean seal]

Chris24

[analog locust]

wait its not?

[buoyant edge]

$e^2*e^{ln(t)} = e^{2+ln(t)}$

[ocean seal]

Chris24

[analog locust]

I thought e^2 * e^2 = e^4

OHHH

okay I was dumb :

^^;

how does it work then if its a multiplication?

[real kindle]

can someone help me with my math pls

[analog locust]

im so sorry for all of the dumb questions btw!

[buoyant edge]

@real kindle just ask your question

They're not dumb questions

[real kindle]

its not that type of question

[buoyant edge]

It's important that you understand fundamentals

[real kindle]

its data displays

[analog locust]

I really don't know how to learn the fundamentals

and I have only 10 weeks until my exam 😦

[buoyant edge]

Maybe look into an algebra textbook? There are plenty of good ones

You don't have to learn every single page of a textbook

[real kindle]

can i send a pic of question

[buoyant edge]

Just reference it when you need

Yes you can send a picture

[analog locust]

ohhh okay!

so that's how you learn the fundamentals

[buoyant edge]

Obviously practice can help a ton

as in doing practice questions

[analog locust]

would it be wise

to go straight to practice questions

and try to iterate the process?

[buoyant edge]

without learning the content first?

[analog locust]

yeah

[buoyant edge]

I would say that that is not too wise.

You'll get lost and discouraged.

[analog locust]

and try learning the content by going through it

[buoyant edge]

Well, possibly.

[analog locust]

as in, looking at the content only when you're stuck

[buoyant edge]

I would not suggest that

[pallid void]

does anyone know how to do inverse and direct and explain it to me

[analog locust]

okay...

[pallid void]

dm

[buoyant edge]

The content is important

[real kindle]

??

[pallid void]

you talking to me?

[buoyant edge]

Especially as you approach more complicated branches of mathematics

[pallid void]

chris could you help me

[buoyant edge]

hold on im helping someone else

[pallid void]

ok take your time

[buoyant edge]

@real kindle are you having problems interpreting the graph?

[real kindle]

yes

[buoyant edge]

@pallid void inverse and direct what?

[loud cobalt]

Yes, it's 90%.

[real kindle]

thx

[pallid void]

c varies inversely as the square of h and directly as n. If c = 1 when h = 12 and n = 25, find h when c = 4.84 and n = 4. i need you to explain it to me dont just tell me the answer @buoyant edge

[real kindle]

can a bot answer my question??

[pallid void]

no.

[real kindle]

ohhh

[loud cobalt]

No, it's a graph, if it were to be a problem that could be copy and pasted probably.

[real kindle]

ok

[buoyant edge]

@pallid void Direct variation means that your output value changes in the same direction as your input

[buoyant edge]

So for a generic output variable y and input variable x, direct variation means that $y=kx$

[ocean seal]

Chris24

[buoyant edge]

where k is some constant

[pallid void]

c varies inversely as the square of h and directly as n. If c = 1 when h = 12 and n = 25, find h when c = 4.84 and n = 4.

thats the problem

[buoyant edge]

I know im explaining what direct and inverse variation are to you.

Then you can answer the question yourself

[pallid void]

ok could you tell me how to set it up>

[native temple]

So can a explicit definition be derived from a recursive one?

to make my assignments easier

?

[buoyant edge]

@native temple its sometimes possible

[pallid void]

@buoyant edge

[buoyant edge]

@pallid void chill out

c varies inversely with the square of h

What does that mean to you

[pallid void]

idk what that means thats why im here

if i knew how to do it i wouldnt be here

[analog locust]

@buoyant edge what is the step again?

sorry I was taking a short break due to headache

[native temple]

OH

[loud cobalt]

Bar graph

[buoyant edge]

Inverse variation means that your output variable changes in the opposite "direction" of your input variable

Once again, generally, inverse variation looks like $y=\frac{k}{x}$

[ocean seal]

Chris24

[real kindle]

thx

[pallid void]

c varies inversely as the square of h and directly as n. If c = 1 when h = 12 and n = 25, find h when c = 4.84 and n = 4. i need you to explain it to me dont just tell me the answer

[buoyant edge]

My guy stop reposting the question

I need you to work with me here

[buoyant edge]

@analog locust $e^{2ln(t)} = e^{(ln(t))^{2}}$

[west ember]

Can some one help me with my homework

[analog locust]

does it also work the other way around?

e^2^ln(t)?

[ocean seal]

Chris24

[buoyant edge]

Yeah that also works

[analog locust]

so... upper exponents are exchangable?

3^2^4 = 3^4^2?

[gray gorge]

... no

[buoyant edge]

no

[analog locust]

I feel.... extremely dumb with my lack of basics

....

[gray gorge]

$e^{2\ln(t)}\ne e^{\ln^2(t)}$

[ocean seal]

~(aki R / I) / (J / I ra)

[gray gorge]

Rather, $e^{2\ln(t)}=e^{\ln(t^2)}$

[ocean seal]

~(aki R / I) / (J / I ra)

[buoyant edge]

Yes he's right

[analog locust]

O_O

[glossy current]

This is not entirely true

[buoyant edge]

My bad!

[analog locust]

how does that work?

is that some kind of rule?

[glossy current]

$\ln(t^2)=2ln|t|$

[ocean seal]

Darkness

[quasi scarab]

??

[analog locust]

???? wait whaaat

wtf

[knotty sleet]

Cause domain of ln is >0

[quasi scarab]

u dont need the | |

[gray gorge]

But I make the assumption that only t > 0 is permitted

yeah

[analog locust]

domain???

im

super confused

[gray gorge]

Take it easy Ken

There are good resources out there that teach you the basics about logarithms

[knotty sleet]

It's the same idea as e.g. saying cosx=sqrt (1-sin^2x)

[glossy current]

or ∫ 1/x dx

[knotty sleet]

Which isn't quite true because you need a modulus as well

[winged ledge]

does anyone know how to do it

[analog locust]

actually

why does integral(2/x) dx = e^2x?

[glossy current]

what

[gray gorge]

That's not true

,w int 2/x dx

[ocean seal]

Results provided by WolframAlpha

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

Requested by Rijinaru#5601

[analog locust]

oh wait

[glossy current]

it is 2ln|x|

+C ofc

[knotty sleet]

Lol

[glossy current]

Or piss your teacher off with -C

[knotty sleet]

😂

[naive belfry]

Z = sin^-1(sin(60)*11.5/13.8) afaik

[muted raft]

+C -C doesnt matter

[gray gorge]

tfw wolframalpha doesn't write absolute value for the log

[knotty sleet]

Woosh

[glossy current]

Blame them

😔

[alpine sable]

💀

[analog locust]

....what is the C in integral? 😮

[alpine sable]

That just looks unnerving

[gray gorge]

An arbitrary constant

[alpine sable]

Plus any constant

[analog locust]

and why is it 2logx?

I know integral (1/x) dx = log x

is there any rule?

[glossy current]

Factorize 2 out

[analog locust]

lets say integral (cosx/x) dx

how do I evaluate it?

,w int cosx/x dx

[ocean seal]

Results provided by WolframAlpha

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

Requested by Kenspectacle#9152

[knotty sleet]

Ken you should probably take it a step at a time to get the basics down, then stuff will all make sense🙂

[gray gorge]

Ken, are you following a calculus course atm?

[alpine sable]

Try u substitution

[glossy current]

Not possible with fundamental

[analog locust]

what is u subtitution?

[pallid void]

c varies inversely as the square of h and directly as n. If c = 1 when h = 12 and n = 25, find h when c = 4.84 and n = 4

[analog locust]

@knotty sleet I have only until Friday to understand all this + a bit of initial value problem in ODE 😦

[glossy current]

Channel in use

[gray gorge]

You're asking all kinds of questions that are discussed in any calc 1 course

[alpine sable]

Yea this integral, and another one sin x/x and literally hundreds of others, aren’t solvable in exact closed form they’re only solvable in numerical form

[glossy current]

sin(x²)

e^u/u

[analog locust]

you mean in definite integral? @alpine sable

[knotty sleet]

Oof😥

[alpine sable]

Just remember that you can move a constant through an integral and also through a derivative

[analog locust]

@gray gorge im doing an ODE course atm

:(((

[gray gorge]

... I think you might be a bit late on recapping everything then

[glossy current]

bruh take calculus slowly or you don't understand anything

[alpine sable]

Yea. If you integrate sin x/x you need to provide limits in order to get an actual answer in numerical form

[analog locust]

I still have 10 weeks until the exam

so I can go through it

[glossy current]

Yes

[gray gorge]

10 weeks is enough time to take a course in calc

[glossy current]

If you focus in math

[gray gorge]

I encourage you to do that

[alpine sable]

10 weeks bruh you only need like 4 weeks to get through all of calc 1 2 3

That is, of course if you study 12 hours a day

[glossy current]

There is 6 hours 100 integral video if you want to learn skill lol

[alpine sable]

Which I recommend doing cos corona

[gray gorge]

[alpine sable]

We have nothing better to do so might as well

[analog locust]

@alpine sable I am, and I can't

[glossy current]

asian: are you challenge me

[knotty sleet]

Or watch MIT integration bee

[analog locust]

I need to study computer vision, management of scientific data, and parallel computing

and also web dev for my work

reeeeeeeeeeeeee

[glossy current]

Wut

[alpine sable]

I recommend just getting a calculus book, locking yourself in your room and plowing through everything

[gray gorge]

Then why are you following a course on ODEs

[knotty sleet]

Sounds like a lot

[analog locust]

because... I overestimated myself

:DDDD

[alpine sable]

Also there’s this book, called almost impossible integrals. Highly recommend it

[analog locust]

and im a master student, who didn't do a bachelor technically

[alpine sable]

You can do anything! You just have to work hard

Like crazy hard tho

[gray gorge]

Have you ever heard of Inside Interesting Integrals?

[knotty sleet]

Personally I don't like integrals all that much

[analog locust]

thanks people!!!

[alpine sable]

No can’t say I have

[gray gorge]

good luck Ken

[knotty sleet]

Yh yh

[alpine sable]

Good luck🦔

[knotty sleet]

👍 👍

[gray gorge]

If you like cool integrals, it's a recommendation

[alpine sable]

Sure I’ll check it out

[gray gorge]

And I'll check out the title you mentioned

Haven't heard of it before

[alpine sable]

Are any of you interested in olympiads?

Like the IMO and stuff

[glossy current]

Speaking of integral, $\int_{2}^{4} \qty(\frac{\sqrt x}{\sqrt(6-x)+\sqrt x}) dx $

oof

How to write two range a and b

[alpine sable]

No idea

💀

[glossy current]

Lol it deleted

$\int_{2}^{4} \qty(\frac{\sqrt x}{\sqrt{6-x}+\sqrt x} dx)$

[ocean seal]

Darkness

[alpine sable]

Texit is drunk

[glossy current]

Some Indian say they can do this mentally

How :thinking:

[alpine sable]

Maybe rationalise this first

[muted raft]

I am assuming it is this trick:

[alpine sable]

They can’t. I’m indian and Indians love to show off

[glossy current]

O

[alpine sable]

Assuming of course, they’re not applying any tricks

If they do have any tricks then maybe

[glossy current]

The only thing I can tell you now. Stay safe mate

[muted raft]

$\int_{a}^{b} \frac{f(x)}{f(a+b-x) + f(x)},dx = \frac{b-a}{2}$

[ocean seal]

zslya

[alpine sable]

If I die I die

[alpine sable]

Ohh yea this is called king’s trick or something

[glossy current]

o

[gray gorge]

[alpine sable]

They use it mainly for that exam that you must’ve heard of. JEE?

[glossy current]

Why sometimes TeXit wrote it in light mode

[muted raft]

I have configured it to put it on light mode.

[glossy current]

Damn without knowing these tricks, it'd be painful to solve by hands

[alpine sable]

Yo YouTube channels that are great for learning integration are flammable maths and let’s solve math problems
If i remember correctly the second channel actually used this trick in one of his videos

And also another one which is checking if the function if odd so that way you can slay some monster integrals

[glossy current]

odd/even trick is well known enough ig

It is even written in my book

[alpine sable]

Which book do u use?

[glossy current]

local textbook

[alpine sable]

Ahh I see

I would study from spivak but it’s too expensive

[glossy current]

But that trick is something ig

Not many people know

[gray gorge]

@alpine sable so I'm checking out the book you mentioned and this is what I found in the foreword...

[alpine sable]

My calculus skills are pretty rusty tho

[alpine sable]

It even mentions the book you named

[gray gorge]

Yes, apparently the author of the book I mentioned wrote the foreword to the book you mentioned

[alpine sable]

u sure we aren’t talking abt the same book?

[gray gorge]

No, I can confirm that they're different books

[alpine sable]

Soooo anyways uh whatre ur education levels everyone?

[gray gorge]

PhD

[alpine sable]

💀BRUH

[glossy current]

O

Too far from me

[muted raft]

Wow on which subject?

[glossy current]

Guess I can ask one question then

[alpine sable]

I’m inclined to believe....maths

[gray gorge]

Efficient data-driven surrogate modelling and continuous black box optimization

[glossy current]

Smh

[muted raft]

Yeah but which field o fmath?

[alpine sable]

option a innit

[gray gorge]

or uh, machine learning, as some ppl call it

[muted raft]

Ah I see.

[alpine sable]

That even sounds difficult

[upper spruce]

I need help

No one helping

[glossy current]

try to put 2, 3, 4 to each option and see

[real kindle]

someone help

[glossy current]

I mean it's how you do multiple choice question lol
Surely a

[upper spruce]

Hey anyone there ?

[alpine sable]

Try to see from the definition of arithmetic progression which general form matches that one

[alpine sable]

What is a point? Try to see for yourself

[glossy current]

The second one is geometric progression right

[alpine sable]

Yea

Third one is a hybrid

Fourth one is just 💀

[real kindle]

i got the last one

[glossy current]

Last one is vectors

[real kindle]

huh

[alpine sable]

It’s A cos points are projections on a plane with no dimensions yk

[real kindle]

i dont get it

[glossy current]

Definition of point is?

you should relook at the definition of a point

I'mma flood this chat with

[ocean seal]

Darkness

[glossy current]

🗿

[alpine sable]

Imma try to do this In my head

Gigachad

Yea no I can’t💀

[glossy current]

There are 4 options btw

[alpine sable]

👁👁

[pseudo steeple]

Confusion

[glossy current]

Actually 6 options

A. 4950
B. 2505
C. 5000
D. 2500
E. 5100
F. 5050

[low night]

why doesnt that equation work for 10

[alpine sable]

So first of all you have all the x that are actually square numbers

So that would become 0

That’s 10 right there

[velvet pelican]

It's either B or D nvm

[gray gorge]

because that formula is for a geometric sum, and the question features a sum that's not geometric

[low night]

is there a formula for that type ?

[alpine sable]

For n^2 it’s n(n+1)(2n+1)/6 if I’m not wrong

[glossy current]

I can try to rewrite it with
$(x-1^2)(x-2^2)(x-3^2)....(x-100^2)≤0$

[pseudo steeple]

..…

Kool

[gray gorge]

There exists generalized formulas, but they're usually not taught in most elementary courses https://en.wikipedia.org/wiki/Faulhaber's_formula

[ocean seal]

Darkness

[alpine sable]

Yea and get a 100 degree polynomial but now what?

[low night]

oh okay thank you

[glossy current]

looks cuter than the big Pi then

[glossy current]

Nu I was rewrote it with other form

[alpine sable]

You just have to see which integers minus a square number, is negative and filter out the values that give odd number of negative ones

You could brute force it

But let’s look for a pretty solution

[gray gorge]

To me, the answer seems to be equal to the amount of integers between $(2k-1)^2$ and $(2k)^2$ for $k=1,\ldots,50$

[ocean seal]

~(aki R / I) / (J / I ra)

[velvet pelican]

Yes, that's what I got too

[alpine sable]

Ight good luck to y’all imma head out to sleep🌸gnnnn

[velvet pelican]

comes out to 5050, I think

gn

[gray gorge]

interesting

[alpine sable]

No no but only even factor terms must start getting negative right? That’s how you get odd number of -1s isn’t it?

[gray gorge]

I get 5100

[alpine sable]

For example if you have 64 and 49, any integer between these minus 8^2 would be negative but between 64 and the next thing, when it becomes negative the whole thing comes out positive

Yk? I’m sorry if I don’t make sense lmao I’m rlly sleepy

U need to start getting them negative starting from x-4 so you have 1 2 and 3. But this doesn’t work for x-9 cos we need all terms up till here to be positive so numbers will be 9,10...all the way to 16 now we’re missing 4,5,6,7,8

Am I making sense

Why isn’t anybody saying anything💀

[velvet pelican]

You get this

the even numbers squared - odd numbers squared

[alpine sable]

Oh yea💀💀bruh

Didn’t see that

Pls😭my one brain cell is dying

[velvet pelican]

I think that already includes the endpoints, so its just a sum from n=1 to 50 of 4n-1

= 5050

[gray gorge]

Any integer $x$ between (and including) $(2k-1)^2$ and $(2k)^2$ for $k=1,\ldots,50$ makes $(x-1^2)(x-2^2)(x-3^2)....(x-100^2)$ have $2k-1$ non-negative factors, namely those of $1^2,2^2,3^2,\ldots,(2k-1)^2$, which means that the remaining $100-(2k-1)=101-2k$ factors are odd. $101-2k$ is always an odd number, so the resulting product of factors will be non-positive. On the other hand, if the greatest square number below $x$ is the square of an even number - not equal to $x$ - you will have an even number of negative factors, rendering the product positive

[ocean seal]

~(aki R / I) / (J / I ra)

[nocturne burrow]

Need help

[gray gorge]

It doesn't though, you have to add the extra 1 in your sum

[gray gorge]

You'll subtract the lower bound of (2k-1)^2 accidentally if you do this

[nocturne burrow]

I need help plz

[gray gorge]

[velvet pelican]

oh yes, that makes sense

i was thinking it kept the upper boind

but forgot about the lower one

[nocturne burrow]

What is this shape

[manic quail]

Looks like a trapezoid.

[nocturne burrow]

What about this one

[manic quail]

Same thing.

Just turned around.

[sullen sigil]

what math class usually introduces fourier series?

[nocturne burrow]

How

[latent reef]

Can I have someone to walk through this problem with me ? It's very confusing

[gilded lake]

Trapezoids have one pair of parallel sides that are different lengths. So anything matching that description is a trapezoid

[calm scaffold]

Hey can someone help me with orbit integers I need 40 a min and 100 percent but I can’t get it

[native temple]

How to make this an explicit function

*explicit definition

[gilded lake]

Every term is the previous divided by two, so its going to be a geometric function with a common ratio of 1/2. To get f(0), you need to do the common ratio in reverse so 64*2=128.
Gives you f(x)=128(1/2)^x

Like that

[hot fox]

omg

so hard

[timid wedge]

Hi does anyone know what this is lol

I have a final tmrw he taught it today but didn’t say what this is called so I can’t YouTube

:(

@ if u know pls 🙏🏻

[jade birch]

Grid polynomial multiplication @timid wedge

[timid wedge]

Ty sm

[cinder cloud]

https://www.statsdirect.com/help/regression_and_correlation/simple_linear.htm#:~:text=Pearson's product moment correlation coefficient,regression of Y on x.&text=Thus 1-r² %3D s²xY %2F s²Y.

[thin salmon]

does anyone know how to find the measure of VY?

[limpid spade]

what do u have to use? trigonometry or Pythagoras?