help-27

[polar flax]

mu(t) = Ce^2t

That is what you got

Nicee

[tall knoll]

nice indeed

[polar flax]

So do we plug this bck into ti

[tall knoll]

well now we've gone far past where your initial screenshot's instructions ended

so hopefully it continues to tell you what to do

[polar flax]

Yeah

it does

I feel like this textbook was missing a lot of stuff

Or I am just stupid

[tall knoll]

textbooks tend to be light on some of the intermediate steps, and often times your instructor will be more explicit

sometimes, hopefully

not always (many such cases)

[polar flax]

Unfortunately I have no instructor

Yeah sometimes instructors skip a lot of steps

But right now I am just trying to teach myself

[tall knoll]

well we've caught up with the end of the screenshot, so follow the rest and if there's any more issues then you know what to do

[polar flax]

Message here

I have gotten confused right afterwards

Sorry for any trouble

But I do not understand how they are able to assume that when multiplying by the integrating factor, that the equation becomes the derivative of 2 products

[tall knoll]

i'm not a huge fan of that language

we multiplied by the integrating factor initially because it made one side of the equation look like such a derivative

that's the underlying motivation for why we're doing this song and dance in the first place

[polar flax]

Okay

Oh yeah

I remember now

OH

Okay

Thank you

[tall knoll]

anything else causing you issues?

or does the rest follow?

[polar flax]

Ummm

The last step

I understand the idea

But how do they get 2e^2t +c

from 4e^2t

Wait

I think I get it

U-substitution

@tall knoll

Thank you SOO much for the help

[tall knoll]

[polar flax]

I am very grateful

Bye

[tall knoll]

gl

[polar flax]

How do I close the channel

[tall knoll]

type .close

[polar flax]

Okay

Thanks

.close

[devout snow]

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[devout snow]

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[restive river]

Can someone work through this question with me I am confused and don’t know where to begin?

[lusty sapphire]

What do you know about similar triangles?

[restive river]

Nothing really

Well it depends what you ask me

[lusty sapphire]

Do you know about ratios of corresponding sides?

[restive river]

No but I do now

Wait

I see

Those are two right triangles correct?

3 corresponds with Y and 7 corresponds with 7

I assume I have to cross multiply but I don’t know how to set this up

[devout snow]

@restive river Has your question been resolved?

[lusty sapphire]

correct

[restive river]

So how do I set up the equation to find the answer?

[lusty sapphire]

ML corresponds with NO, but KL corresponds with KN, not just LN as you thought

[restive river]

Oh okay

So

How do I plug the numbers in

Im supposed to cross multiply right?

[lusty sapphire]

Yeah that should work

[restive river]

How would you do it

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[spice agate]

The domain of the inverse trigonometric function arcsin(x) is:
Someone please answer

[rocky ice]

[-1, 1]

[lusty sapphire]

It's the range of sin x

[spice agate]

Ok

[lusty sapphire]

!noans

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[mystic scarab]

It's the definition

[spice agate]

Ok tq

[mystic scarab]

Otherwise the inverse wouldn't exist

[frozen stump]

Ooo

Remember sinx cannot be 0

[spice agate]

yeah

How to find sin 120

[solar goblet]

EXTREMELY LOUD INCORRECT BUZZER

[rocky ice]

draw a unit circle first

[spice agate]

Uhh ok

Yo continue

<@&286206848099549185>

[junior wyvern]

yes

[solar goblet]

whats there to continue?

do you know whats a unit circle is?

[junior wyvern]

Yes is do.

[junior wyvern]

The unit circle is a circle with a radius of 1 unit, centered at the origin (0,0) on the coordinate plane. It is an essential concept in trigonometry and calculus.

[mystic scarab]

Is this ChatGPT generated?

[spice agate]

Ok thanks

.close

[devout snow]

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[junior wyvern]

No it is not i hate when people say this.

[mystic scarab]

Alright, it seemed, although

[solar goblet]

i wasnt asking you

[junior wyvern]

Oh sorry.😔

[devout snow]

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[dire slate]

what is the difference between the mixed partial derivative, differential, and directional derivative?

[dire slate]

it all looks like the same thing

[devout snow]

@dire slate Has your question been resolved?

[devout snow]

@dire slate Has your question been resolved?

[dire slate]

<@&286206848099549185>

[orchid charm]

Mixed Partial Derivative: Measures the change of a function with respect to one variable after differentiating with respect to another variable.

Differential: Provides a linear approximation of the change in a function, giving a sense of the tangent plane in higher dimensions.

Directional Derivative: Measures the rate of change of a function in a specified direction, incorporating the gradient and a direction vector.

[dire slate]

Right, that just sounds like the same thing if youre looking at the same function

Obviously the results are different

But the idea sounds the same

Thats where my confusion is

[orchid charm]

it's all about differentiating
ofc it will sound the same

but they are used in different cases

[dire slate]

Right, so how are each ones idea unique? They all measure rate of change of a function through all the independent variables

[devout snow]

@dire slate Has your question been resolved?

[devout snow]

@dire slate Has your question been resolved?

[frozen stump]

Ah shit nvm i disnt read the question properly lmao aoz

[dire slate]

.Close

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[eternal vigil]

Ahaha,I need helps with my half sleep brain

[eternal vigil]

How do I evaluate log5 (1/125)

[near stone]

use log rules

,tex .log rules

[woven radish]

K²en [𝔸𝔨𝔦𝔯𝔞]

[near stone]

also get some sleep

don't push yourself too hard

[eternal vigil]

Im in class and going to be called up soon

.close

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[devout snow]

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[prime narwhal]

wait do i need to get y alone so i can have it in the correct form?

[slow vigil]

if you wanna get the slope, then no

cuz itll still be 4x
in the mx + c form

so you get the same slope

[devout snow]

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[idle tinsel]

how do i simplify this

[idle tinsel]

i think i simplified it correctly to this point

[small urchin]

On the left you can take the root of 64

[boreal lion]

Can't u just square both sides

[restive river]

true

square twice

[devout snow]

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[hexed ocean]

Can someone please help with question 2

[eager nova]

What have you tried?

[hexed ocean]

I don't even know where to start tbh

does uniform distribution mean the graph is straight

actually I get the uniform distribution part

idk how to find the pdf of y = x^2 though

[tribal pier]

First find the cdf

[hexed ocean]

in this case it is x/1

why is is < sqrt(x) and not < x

[raven leaf]

lol that is completely wrong

ignore that

P(X^2 < x^2) = x

[hexed ocean]

ok

[raven leaf]

P(Y<y)=√x

that's better

[hexed ocean]

do we integrate that

[raven leaf]

differentiate

[hexed ocean]

o

alr

1/2sqrt(x)

[raven leaf]

seems about right

[hexed ocean]

why is it P(X^2 < x^2)?

im not really familiar with how it works

[raven leaf]

Well P(X<x) = x was obtained by integrating y dy between 0 and x ya?

[hexed ocean]

this is for the cdf right

[raven leaf]

wdym?

[hexed ocean]

the P(X< x)

[raven leaf]

this is cdf yes

[hexed ocean]

alr

yea i get that part

[tribal pier]

Cdf of Y should be sqrt y

[raven leaf]

here yes i forgot to change the variable

[devout snow]

@hexed ocean Has your question been resolved?

[hexed ocean]

alr

yea i think I get it now

thanks for the help

.close

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[devout snow]

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[prime narwhal]

did i do b correctly?

[dense vortex]

if this were a question on a test, and I got to where you got, I would try to verify it

[prime narwhal]

im just not super confident on what the question even means so

[frosty cradle]

whatever equation you come up with, to check your work you can plug in the two points you were given

you should get an equality

[devout snow]

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[sullen karma]

Is this correct or do I flip the sign?

[exotic dagger]

that's correct, you only flip the sign when you multiplied or divided by a negative number

[sullen karma]

But isn’t -11 divided by 2

Negative

Oh wait

Is it bc we bring the 2 across

And that’s positive

And not the -11

[exotic dagger]

yes

"divided by"

like you said, you divided both sides by2 and 2 isn't a negative number

[sullen karma]

Is this one correct

[exotic dagger]

yes

[sullen karma]

I don’t understand what my teacher done on my book

She said to divide by -1 one or something I don’t get it

[exotic dagger]

idk what she's on about

[sullen karma]

Maybe because on the third line she thought the x was -x maybe?

[exotic dagger]

ah yh, your $\le$ 's bottom line may have looked like a minus sign

[woven radish]

lgkoo

[exotic dagger]

but honestly that just mean your teacher wasn't paying attention

[sullen karma]

But if the x was -x would u have to divide by 1?

[exotic dagger]

well suppose the inequality was $13 \le -x$

[woven radish]

lgkoo

[exotic dagger]

then to find for x

[sullen karma]

Then we divide by 1

[exotic dagger]

-1

[sullen karma]

Yes my bad

[exotic dagger]

yh, and here you would flip the sign

[sullen karma]

But would the 13 turn negative

And the x turn positive

[exotic dagger]

yes

[sullen karma]

Ohhh so to turn a negative variable positive u divide by -1 on both sides

[exotic dagger]

yes, or multiply by -1 on both sides

cuz multiplying by -1 is equivalent to dividing by -1

[sullen karma]

Ahhh

Wait when u divide by -1 do u have to flip the sign

Always?

Cause my classpad says the sign should be flipped

[winter torrent]

yes when you divide (or multiply) by a negative number you flip the inequality sign

[sullen karma]

Even if the variable is on the left side?

[winter torrent]

yep, no matter where the variable is

even if it's on both sides

[sullen karma]

Ah thanks guys, makes sense.

.close

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[devout snow]

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[neat widget]

points a ( 2,4 ) and b lie on the line x+2y=10 and the perpendicular bisector has equation 2x-y=5 find coordinates of B

[winter patrol]

!status

[devout snow]

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

[dense vortex]

is this all you were given for this question?

[neat widget]

Yeh i am not sure where to start or how to solve it

[dense vortex]

i'm not sure i understand what it means by perpendicular bisector. I have an idea but i would want to know for sure. Do you have any material that can educate me on that?

[neat widget]

I think itjust means the line thats perpendicular to x+2y=10 that cuts at the midpoint

so x+2y=10 gradient is -x/2 and 2x-y=5 gradient should be 2 then and midpoint is x1+x2/2 , y1+y2/2

[winter patrol]

first find the intersection point

that will be the midpoint of AB

then apply the midpoint formula

[neat widget]

How would i find the intersection point?

[winter patrol]

sub or elimination

[neat widget]

Oh of the lines x+2y=10 and2x-y=5?

[winter patrol]

yes

[neat widget]

hm i did that and then got 4,3 so then i did (let B be coordinates h,k) ( 4+h)/2=4 and then (2+k)/2=3 to find the coordinates is that what you mean?

[winter patrol]

yes

[neat widget]

Ok then i got (4,4) but the answer is (6,2)

[winter patrol]

one sec

you mixed up the x and y coordinates of A

[neat widget]

Oh woops lmao

thanks

.close

[devout snow]

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[devout snow]

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[signal lava]

!help

[devout snow]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[signal lava]

hello

is the answer

120a square root 7a

symbolab gave me different asnwer

they gave me this so idk

[tawdry torrent]

It is correct

[wooden veldt]

Remember when multiplying the order doesn't matter

[signal lava]

why did symbolab give me different answer

[wooden veldt]

So compare yours with symbolabs

[signal lava]

it looks different visually

so its the same thing

is what ur saying

but written differently

i see

how do u know

there multiplying

where is the multiplication symbol

[wooden veldt]

Yes bc symbolab is trying to get it to look like (numbers)*(stuff with a)

Generally putting things next to eachother (juxtaposition) denotes multiplying, but you have to use a bit of context too

[signal lava]

oh

[wooden veldt]

If there is ambiguity we use parentheses ()

[signal lava]

i know how to simplify square roots

but i dont really understand what im doing

like for example inside the square root there are gonna be some random numbers squared

why are you suppose to put those random numbers that were squared outside the square root

and when u do that u literally remove the squared term

so if it was 9^2 it would be 9 outside the square root

(x^2)^2 it would be * x^2 outside the parantheses

like why are u deleting these exponents and putting it on the outside lol

[woven radish]

faiyrose

[wooden veldt]

most of your confusions about roots would likely be cleared up by reminding yourself of the power laws and how they work

[full kayak]

Hello
I need help on something
How to differentiate an intergral function
For example

Gn(x)=Ingerale,xdt
What's dGn(x)/dx

[ashen fossil]

#❓how-to-get-help

[full kayak]

Thank you
Sorry im new

[ashen fossil]

np

[signal lava]

oh

hm

ok ill learn about the power laws

i forgot about them

[devout snow]

@signal lava Has your question been resolved?

[devout snow]

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[onyx loom]

How would i intergrate the (x+4/5)^0.5?

[pastel pasture]

substitute whatever is inside the square root

[onyx loom]

so the x+4/5?

[pastel pasture]

yeah

[onyx loom]

so i got 18[10/3 u^3/2] and i just sub in u

[pastel pasture]

or you could've changed the limits

but yeah

go back to x

[onyx loom]

oh ye i forgot to change limits

so i just sub in 41 & -4 into x+4/5 to get the limits in terms of u?

or do i not have to change the limits for this question?

[devout snow]

@onyx loom Has your question been resolved?

[onyx loom]

im at $\left[ 30 \left( \frac{{x+4}}{5} \right)^{\frac{3}{2}} \right]0^9 - \left[ \frac{x^2}{10} + \frac{4x}{5} \right]{-4}^{41}$

[woven radish]

morphine_addiction

[onyx loom]

@fervent swallow

ight

.close

[devout snow]

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[steep umbra]

@onyx loom next time try using $$\int y \frac{dx}{dt}$$

[woven radish]

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

[onyx loom]

.reopren

.reopen

[devout snow]

✅

[onyx loom]

by parts?

[steep umbra]

no the parametric integration formula

it's not actually in the textbook

but you can use in in the exam

[onyx loom]

how do you get to the formula, like i remeber there was a way to expain it but icr how

[steep umbra]

well normally if $y=f(x)$ you do $\int y ,dx = \int f(x) ,dx$

[woven radish]

mrlegohead

[steep umbra]

so if we have parametrics we do $\int y , dx = \int y \frac{dx}{dt} , dt$ (where $y$ and $\frac{dx}{dt}$ are functions of $t$)

and the $dt$s "cancel" (like in the chain rule)

[woven radish]

mrlegohead

[steep umbra]

you must remember to change the limits to $t$-values instead of $x$-values (the same as you would change $x$-values to $u$-values in a substitution)

[woven radish]

mrlegohead

[onyx loom]

so we say we are intergrating y in terms of x even tho y is in terms of t?

[steep umbra]

yes

[woven radish]

mrlegohead

[onyx loom]

ahh that makes sense now ty

[steep umbra]

np

[onyx loom]

.close

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[frail notch]

Hello
Anyone studying maths in highschool And Needs some help
Feel free to dm me

[devout snow]

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[zenith lion]

Hello

[zenith lion]

my problem is not very great, I just miss the conclusion

basically I have a function f(x) = x/(x+1)

for x > 0

How do I mathematically find out the highest value point of this function

where f(x) is the highest

[lost laurel]

know calculus ?

[zenith lion]

from a graph I can see that at 1 its the highest

yes

[lost laurel]

btw, this has an asympotote

[zenith lion]

i know thats my problem lol

can this even be proven

algebraically

or with calculus

[lost laurel]

you could prove that the slope is indeterminate as we approach -1

[zenith lion]

x has to be greater than 0

its positive area only

[lost laurel]

not area

use derivatives

[zenith lion]

derivative is 1/(x+1)²

but setting this equal to zero doesnt make sense

since at highest point you have 0 slope

[lost laurel]

find the slope at x=-1

[zenith lion]

its infinity

approaching

[lost laurel]

the "maxima" will be at the asymptote

because the function is now increasing infinitely fast

[zenith lion]

yes I know in the negative x values

For this example I have to assume x is greater than zero

[arctic field]

do you mean the least upper bound?

x/(x + 1) has no maximum for x>0

[zenith lion]

its a technical subject where I assume the ratio for 2 resistors, resistors cant be negative

[zenith lion]

yes

How do I mathematically find out that x is approaching 1 or cant be greater than 1

[arctic field]

,, \f x {x + 1} = 1 - \f 1 {x + 1}

[zenith lion]

(mathematically speaking also never will be 1)

[arctic field]

i think this makes it plainly obvious

[zenith lion]

ah shoot makes it 100 times more obvious

as x approaches infinity the fraction becomes 0 and 1 remains

thanks

.close

[devout snow]

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[arctic field]

the - sign gives the inequality

[devout snow]

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[cunning roost]

what do i do

[polar chasm]

You got 3 eqns, 4 unknowns

You can probably reduce it a bit

[cunning roost]

so how would i solve?

[polar chasm]

to get rid of few variables

having p and q as unknowns in one equation would be quite helpful

but not necessary

the other approach is just choosing some value of p and then solving for q

e.g. p = -1, p = 0 and p = 1. Then solve for q in each case and you'll get 3 solutions to your system of equations

[cunning roost]

ohhh ok

so like

0 = 4a - b

wait no

[polar chasm]

Why not?

[cunning roost]

cause how do you solve for q

[polar chasm]

0 = 4a - b
q = a + b
5 = 7a + 6b

3 equations 3 unknowns

[cunning roost]

oh

i can do this

b = 4a

then i do

q = a + 4a

q = 5a

[polar chasm]

(the other way to do it would be to start by reducing the system to only contain 1 equation of 2 variables)

^ this way is a bit faster if you're comfortable with algebra

[cunning roost]

so can you show me yoru steps

[polar chasm]

do I read the last equation correctly as 5 = 7a + 6b?

[cunning roost]

yes

[polar chasm]

alright, cool

[cunning roost]

wait whatt

how did you do that

[polar chasm]

okay ill do it in more detailed way

firstly we can eliminate b from all the equations

to eliminate it from the 1st equation, we can add 2nd equation to the first one

p = 4a - b
q = a + b

so p + q = (4a-b) + (a+b)

or p + q = 5a

so now we have:

p + q = 5a
q = a + b
5 = 7a + 6b

we can proceed by eliminating b from the 2nd equation

[cunning roost]

ohh

[polar chasm]

or 3rd actually, that will be a bit easier

we can rearrange the second to get b = q - a

by subtracting a from both sides

now plugging that onto the last equation gets us 5 = 7a + 6(q-a)

that's 5 = a + 6q

notice that now we have

p + q = 5a
5 = a + 6q

2 equations completely without b

now it's time to eliminate a

I'll leave this step for you

can you get one equation that contains only p and q and doesnt contain a and b?

[cunning roost]

so

a = -6q + 5

p + q = 5(-6q + 5)

p + q = -30q + 25

[polar chasm]

yeah

[cunning roost]

31q + p = 25

[polar chasm]

perfect

So in order for the vectors to be coplanar, this equation has to be satisfied

we could also rearrange it as p = 25 - 31q

now you can just take q = 0 and get solution p = 25 - 0

[cunning roost]

oh ok

[polar chasm]

q = 1 and get another solution

q = -1 and get last solution you need

[cunning roost]

p = 25

do yk what my teacher did here?

[polar chasm]

that's solution when q = 0, so (q, p) = (0, 25) is one possible solution

[cunning roost]

oh okok

[polar chasm]

Yeah, he did it the slow way

instead of reducing it to the equation 31q + p = 25, which gives a nice way to get as many solutions as you want, he just substituted some chosen number directly in

and he had to solve system of 3 equations each time

while all you need to do with the reduced form p = 25 - 31q is just choose some q and immidiately get solution for p

[cunning roost]

ohhok

tysm

ur the best

[polar chasm]

np

[cunning roost]

.;close

.close

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[vivid topaz]

need help

[vivid topaz]

A deck of 32 cards is dealt card by card. What is the probability for
that the twelfth card is the 9 of clubs?

for this

[sacred hound]

Ok, let's start from the simple question, if I have a deck with 32 card, what is the probability that my first card is 9 of clubs?

[vivid topaz]

1/32

[sacred hound]

Yes. Then, what is the probability that my second card is 9 of clubs knowing that my first card is not 9 of clubs?

[vivid topaz]

1/31 ?

[lethal cove]

what the sigma

[sacred hound]

now, the question is. If I ask you this question after knowing that the first card is not 9 of clubs and if I ask the question like, for every kind of shuffled deck of card, what is the probability that the twelfth card is the 9 of clubs? Will your answer change?

[vivid topaz]

1/21 ?

[sacred hound]

that is true if I know that all the previous one is not 9 of clubs.

but if you care about the twelve card in the deck only, the answer will be 1/32

[vivid topaz]

without taking the card 1 , 2 ,3 etc ?

[sacred hound]

it is more like the case where says you distribute the card to 32 people one by one, you are the twelfth person, you see other people have different cards but not 9 of clubs, your probability of getting 9 of clubs there is 1/21. However, if you are talking about all the kind of shuffled deck possible, the probability that the twelfth card is 9 of clubs is 1/32.

and from the problem, which scenario this fits in?

[vivid topaz]

when im the tweltfh person

[eager nova]

I recommend you to show the exact original problem, to avoid missreading

[sacred hound]

yeah, because it can be viewed in both way

[vivid topaz]

it is the exact original problem

[eager nova]

Because in what you wrote there are not people

[vivid topaz]

how it is 1/32

I dont understand

[eager nova]

If the problem is exactly as you wrote, then the probability is 1/32

[vivid topaz]

why is 1/32

[eager nova]

Imagine you have 2 cards

[sacred hound]

because the card is already shuffled

[eager nova]

Ace of diamons and King of diamonds

What is the probability that ace is the second card?

[vivid topaz]

1/2

[eager nova]

And first?

[vivid topaz]

1/2

[eager nova]

Now add a new card

Queen

[vivid topaz]

1/3

[eager nova]

Now make a deck of 10 cards

[vivid topaz]

1/10

[eager nova]

The idea explain itself

The probability that the card is in 12th position is the same that the card is the first

Or the 29th

[vivid topaz]

oh ok

there are 32 position so its 1/32 because he can be in every position

[eager nova]

Correct

[vivid topaz]

Ok thank you

i though it was 1/21 because 11 card was already given

[sacred hound]

that is true if you are in the scenario I described.

In this case, you only care about the card in the deck

[vivid topaz]

this one ?

[sacred hound]

yes. In that scenario, it is conditional probability

because you have the "prior" knowledge that the first 11 cards are not

[vivid topaz]

oh ok

[sacred hound]

from observing other people not getting 9 of clubs

[devout snow]

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[unborn atlas]

Question 109 im lost

[unborn atlas]

I determined that the area of the parabola will be $$\frac{2a^3}{3}$$ and that the area of the triangle will be $$a^3$$

Idk what to do from there

[woven radish]

Nathan

[safe jasper]

upon double checking your work those areas look correct to me

the question asks about the ratios of their areas

triangle area ratio to parabola area ratio is a^3 / (2a^3 / 3), right?

can you simplify that at all

and after simplifying it, you evaluate your limit as a tends to 0 (spoiler, your answer becomes independent of a)

[devout snow]

@unborn atlas Has your question been resolved?

[unborn atlas]

Won’t it be 3/2?

Because the book says 3/4

[safe jasper]

book might be wrong

looks like 3/2 to me

[unborn atlas]

It’s never wrong

Unless I just went about it wrong

What about the limit part

It’s just a constant 3/2

Why did it want me to take the limit as a goes to 0?

[safe jasper]

the question doesn't make much sense if you could just plug in a = 0, but i agree, it's sort of a dumb question if the ratio never changes

what book is this

because some are def prone to errors and there's no universe where this answer is anything other than 3/2

[unborn atlas]

Thomas’s calculus 14th edition

It’s like from 2015 I think it’s fairly new

[safe jasper]

other people online have reported errors in the book

you're right here

the only way the book is right is if they're looking at the ratio of only half the triangle to the parabola area but that doesn't make sense

[unborn atlas]

Yeah

Alright then I’ll just move on

Thanks

.close

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[shrewd helm]

Hello, I would like some help with solving a vector integral. I have tried it but i always get the wrong answer. I know there are "shortcuts" to solve the problem, but i would like to actually do the integral. I painted the problem in paint, so the following picture is my problem:

[shrewd helm]

So, there was a test before, where you are supposed to solve whether F is conservative, i think i solved that. And the "shortcut" is just to use that to get the answer to the integral, but I want to see if there is another way

[winter torrent]

there is yes

[shrewd helm]

I naively and blindly and stupidly just tried to bash in x=y^2 into F, to get H(y), and then try to do that, but i was just guessing

[winter torrent]

the normal approach is to parameterize the curve

so let t go from 0 to 1, and say (x,y) = (t, t²)

then your integral becomes

$\int_\kappa \vec F(\vec x) \dd{\vec x} = \int_0^1 \vec F(t) \cdot \dv{\vec x}{t}\dd{t}$

[woven radish]

hayley

[shrewd helm]

i am slightly confused by this. By setting x=t, shouldny y=sqrt(t)?

[winter torrent]

oh maybe

i wasn't fully paying attention

yeah let y = t though

so x = t²

[shrewd helm]

So, i tried something similay, by just putting in y^2 instead of x

[winter torrent]

should work as well

[shrewd helm]

but when i do the integral i get the wrong answer 😦

[winter torrent]

hmm what do you get, can you show work?

[shrewd helm]

i erased it, but gimme a min

okay here

I just did this "blindly", i think i may have missed a step?

Anyway, the correct answer to the integral should be -5/6

[winter torrent]

i can't quite see but did you do a dot product at some point?

i don't see one

[shrewd helm]

that seems like a good idea

let me try

no I did not

[acoustic helm]

I suggest you choose a new variable (not x or y) for your parametrisation

[winter torrent]

remember it's F dot dx

[acoustic helm]

Otherwise it’s easy to get lost

[devout snow]

@shrewd helm Has your question been resolved?

[acoustic helm]

@shrewd helm have you figured it out?

[shrewd helm]

i got the right answer, but i wanted to show you, so you can say if what i did was okay

so i amdrawing in paint

okay here is what i did

So, the thing i am wondering is about the dot procduct thing

[winter torrent]

use a different variable I'm begging u

[shrewd helm]

does that come from how the problem is specified in the first place? That you need to solve the integral of Fdx, where F and d(x) are vectors?

[winter torrent]

yes

[shrewd helm]

okay i try with a differnt one

[worn flame]

you could also just replace x by y^2 everywhere

then integrate each coordinate in dy from 0 to 1

[shrewd helm]

this is what i wanted to do, did i do it wrong?

btw here is it with y=t parametrization

is this an okay way to do it?

[acoustic helm]

Much better

[shrewd helm]

Great! But why is this better than with (y^2,y) ?

[acoustic helm]

Easier to back track when you make a mistake

[shrewd helm]

One last question, i know i need to examine and study this more, but I have a question about integral of vector stuff. My questions is in the following image:

I sort of already got this answer, but just asking again

[worn flame]

oh it's a dot

okk

[shrewd helm]

but is the thinking here that F is a vector, and dX is a vector too, so the integral FdX is dot product?

[worn flame]

yeah think of it like you're trying to go on a road

thats dx/dt is the direction of the road

and you're experiencing some force as you're travelling thats F

and theyre asking you the total force you experience

as you curve on the road

[calm venture]

I think this is just uhh

[worn flame]

if this intuition doesnt make sense

ignore it

[shrewd helm]

For now, I am not really interested in intuition, more about just doing problems. There is a lot i dont understand, but i will read more. I am just wondering in general, if I see a problem to solve that has an integral that looks like that, with F and dX, where both F and X in dX have vector symbol above them, it's always dot product?

[worn flame]

lol ok

[acoustic helm]

Integrating over a vector field requires a dot operation
Over a scalar field it does not

[shrewd helm]

part of my process okay 😦

[worn flame]

yeah so use equation of the curve (x,x^2) whose derivative is (1,2x)

with f(x,x^2)

so take the dot product with (1,2x)

and then integrate from x going from 0 to 1

[winter torrent]

the reason you need a dot product is mostly to control for how fast you're moving along the curve

[shrewd helm]

I think I am happy with this for now. Thank you Hayley, Shsgd and Tyler for the help!

.close

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[devout snow]

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[wooden cairn]

theres an extra condition that pi2 + pi4 = 1

shouldn't pi2 = 1/4 and pi4 = 3/4???

[devout snow]

@wooden cairn Has your question been resolved?

[wooden cairn]

<@&286206848099549185>

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[glad halo]

What part are you not getting?

[sleek yew]

i cant find the equations that i need to solve

ive been doing this assignment for an hour and its supposed to take like 15 minutes 😭

[foggy vault]

?

what equations??

[sleek yew]

like to solve for x or y

i need to find the equation

like y+5 = 180

[foggy vault]

you need the VALUE

[foggy vault]

???

[sleek yew]

just an example bro

[foggy vault]

i think it means y + 5 = angle EFD

2x = angle AFB

[glad halo]

AFC = afb+BFC
128 = 2x+ 90

[foggy vault]

just do 120 - 90 = 2x

then you can use verticle angles to know that 2x = y+5 and easily solve that

[sleek yew]

ohhhh

[glad halo]

And after finding x using vertical angle property 2x = y+5

[sleek yew]

the only angle translation i see is 5x+6y = 90

i dont know what i can translate here

[foggy vault]

well

technically this isnt correct since they dont provide you with the specific angle

[sleek yew]

5x+10x+90= 180?

[foggy vault]

you could say 6y + 5x = 90

[foggy vault]

mhm

[sleek yew]

yeah but u cant solve that

[foggy vault]

yeah

[foggy vault]

you can after you solve this

[sleek yew]

oh true

yeah cus theres no indicator that HL is 180 degrees

but thats the information i used to solve

[foggy vault]

mhm

[sleek yew]

i need help finding the equation for y

how?

[proud adder]

Vertically opposite angles

BGC AND EGD

[final torrent]

the line CE has an angle 180 deg. you can find CGD with 180 - 2x

so 180 - 2x + y - 15 = 180
y - 15 = 2x

[sleek yew]

.close

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[lucid mason]

exponential math problem

im assuming i need the formula

y=a(b)^x

but idk how to make the formula for this one

equation i mean

i wrote y = 900 (0.03)^6

but its not working

[lavish radish]

because that’s not what ur supposed to do

[lucid mason]

im asuming i need to the power of a fraction..

[lavish radish]

ur solving for how much money he needs to put away

[lucid mason]

um

well yeah ik that but idk what to do

lol

[lavish radish]

it’s a number above one

a fraction is exponential decay

[lavish radish]

ur solving for the principal amount

[lucid mason]

ok can u show me the correct equation then

[lavish radish]

900 = a(1.03)^x

[lucid mason]

om

[lavish radish]

ur solving for a that’s what the question is asking

[lucid mason]

bro

i need to go sleep

i know its 1.03

omg

[lavish radish]

it’s asking how much money needs to be in the account

[lucid mason]

why did i write 0.03

💀

(ive been studying math for like multiple hours now i think im going crazy)

ok ty

[lavish radish]

i would just sleep

[lavish radish]

no problem

[lucid mason]

oh well

.close

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[coarse stream]

Hello
When finding the linear independance and dependance, we can use the row echelon and the determinant method to find it. I can use either correct?

[scarlet oriole]

yes for square matrices

[devout snow]

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[rough remnant]

can someone help me on integral calculus?

i already got the no. 25

but my problem is no. 26

[granite arch]

you could take out y since its a constant

[rough remnant]

like this?

i always stuck on this

[granite arch]

i think i got smt like that

yeah

[rough remnant]

what's the next step?

[rough remnant]

@granite arch

[granite arch]

continue on ur last line

just multiply and add and minus

simplify the expression

[rough remnant]

is this right?

[rough remnant]

sorry but i dont know how to get into one of the choices here

@granite arch

[granite arch]

combine the -y^3 - y^3/2

[devout snow]

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[devout snow]

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[normal crest]

translation: prove thr binomial formula for any complex numbers a & b for n is a natural number.

[normal crest]

oh yeah uh

i just have no clue what this means lol

it might be the wording

i just dont know what the exercise wants me to do

[honest lake]

i'm not in the mood of doing a proof rn bc i've got an assignment due, but i'm assuming it's a proof by induction

[normal crest]

ah

ill check

@honest lake proof by induction is if its true for the first term and true for n+1 right

its just in france we call it proof by recurrance which seems to be the same thing but im just making sure

[honest lake]

yep, substitute for n, then k, then k+1

[devout snow]

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[woeful tundra]

hello, I'd like to confirm if what I did is correct and if I got the correct answer. Thank you!

[magic sun]

that's a looooooonnnnnngg answer haha

[thin inlet]

wait i'm pretty sure that would help actually haha

[magic sun]

like...how?

[thin inlet]

well, take ln() of the expression

take its derivative

[magic sun]

ohh

[thin inlet]

I'm saying you could simplfy the calculations by instead of finding f'(x) directly, find

$\f{d}{dx}\ln(f(x))$

[woven radish]

🫎MooseyMooseMooser 🫎

[thin inlet]

and then use the fact that $\f{d}{dx}\ln(f(x))=\f{f'(x)}{f(x)}$

[woven radish]

🫎MooseyMooseMooser 🫎

[woeful tundra]

I'm so sorry, I don't know how to use this method 😓😓

[thin inlet]

you know the chain rule and derivative of logarithms dont' you?

or have you not learned derivative of logarithms yet

[woeful tundra]

yes, we haven't learned about the derivatives of logarithms yet

[thin inlet]

damn

[woeful tundra]

my teacher only told us to use the product rule, quotient rule, and chain rule for this

[magic sun]

well, then use them for now

simplify your answer. multiply those constants.

[woeful tundra]

this is what I got when I multiplied the constants

[magic sun]

try putting them in one denominator

[woeful tundra]

actually, I'll try asking my classmates about it tomorrow instead. Thank you for the help though I really appreciate it!

.close

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[short hare]

A question abt the properties of limits

[short hare]

If we had limit z/x

Cant we say that z/x is z times 1/x

And thus

Lim z/x = lim z * lim 1/x?

[winter patrol]

applicable if the individual limits exist

[short hare]

You mean 1/x?

[winter patrol]

both

[short hare]

Ok just a second let me show u smth

In lim ((1+5x)^10 -1)/((1+7x)^8 -1)) as x approaches 0

Here we cant use the multiplication property bc the equation at the bottom (deno smth) doesnt exist

Like- its limit doesnt exist

Ok ok i understand… can you help me find the limit of that function tho? Without using l’hopitals or anything that needs integratin/derivation and such. Im new to limits so i only took certain ways to solve them. Like long divison and theory 4 for example

[restive river]

where does (x^n-a^n)/(x-a) approach as x approaches a

[short hare]

Is that a question or what do you mean

[restive river]

a question

[short hare]

K give me a sec

[short hare]

ah if you plug in x as A you get 0/0

[restive river]

yeah but what's the limit

[short hare]

I dont really know?

[restive river]

mmm

you said you know long division right

[short hare]

Wait a minute

Wait

Wait

Its

[restive river]

how about you divide x^n - a^n by x-a

[short hare]

N times a^(n-1)

Thats theory 4 yes i took that

[restive river]

how did you find out

[short hare]

Find out what exactly? The limit? Its bc the three requirments to use theory 4 is present so i used it

Negative in between

Same power for x and a at the bottom

Same power for x and a at the top

[restive river]

so you saw the requirements hold and thus used the result, do you know where did that result come from, why is it valid

[short hare]

Not really.

[restive river]

so do you want to know

[short hare]

Yes please

[restive river]

alright

since you know long division, how about you divide x^n - a^n by x-a

do a few steps and see what you get

[short hare]

Long divison taught me how to simplify smth like x^4-81 where i do some basic steps to simplify it ( i can show you in a stream or smth). But, it didnt teach me to simplify such… quantity? What im trying to say is, i cant simplify that with long divison that i was taught

If you wish

I can show you how i “long divide” quantites in a voice chat

[restive river]

oh alright

how about we talk in dm

[short hare]

Yes

Should i close this

[restive river]

yea

[short hare]

.close

[devout snow]

Channel closed

Closed by @short hare

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[restive river]

hi

[restive river]

why is zero considered a number , don't numbers have an innate value to them? zero adds nothing and substracts nothing

so why is it considered a number

this is a serious question so i hope i get an answer

[rigid pewter]

because 'nothing' is a useful thing to be able to represent, i guess?

also you could say 1 is useless because 1 times something is still the same something

[restive river]

but it has value

zero is like an empty space

of nothingness

logically it cannot exist

[rigid pewter]

numbers don't exist
you can't have π or e apples

[winter torrent]

it's a number because it's useful to treat it as one

[topaz axle]

whyis there a word for "nothing" in English?

[restive river]

define a number

[topaz axle]

maybe it's the influence of the English language on math

[restive river]

can be used in other contexts
ex : what did you want to tell me?
>nothing.

[topaz axle]

that's the same meaning

[restive river]

zero can't have multiple meanings

Define a number

[topaz axle]

define a word

[restive river]

how is that relevant

[topaz axle]

i explained why it happens

english speaking people introduced the number zero into math because they have a word for nothing

you disagreed but i don't understand

[restive river]

is this a historical fact?

[topaz axle]

it's a conjecture

[restive river]

so it's a guess

[topaz axle]

yes

[winter torrent]

zero mostly came from the east, Arabic I think

[restive river]

Zero has no innate value , special characteristics that distinguish it from every other number , it needs at least it's own field

if it's considered a number

[winter torrent]

sure it does

[topaz axle]

maybe arabic languages have a word for nothing

[restive river]

they do

im arab

[topaz axle]

so it's your fault

[winter torrent]

cipher used to mean zero a really long time ago

from صفر

[restive river]

yeah but cipher is a number not a word

cipher = zero

unless you agree zero = nothing

linguistically speaking

[winter torrent]

well I mean nowadays cipher is very much a word and does not mean zero

but also, three is a word

and so is seventeen

so is zero

not sure what your point is about zero not being a word

[restive river]

frownyfrog asked for the synonym of "nothing"

you gave the synonym of zero

i don't think they're the same thing

[topaz axle]

i never asked for any synonyms

what

[restive river]

.

[topaz axle]

that's not even a question

[restive river]

i explained that cipher means zero not nothing

anywho

good talk

[topaz axle]

arabs influenced math a great deal
arabs have a word that doesn't have value, logically it's like an empty space

they introduced that concept into math

[scarlet oriole]

I think it's pretty interesting that 0 times anything is itself

and of course it's the additive identity

numbers are just abstractions for our ideas of us counting things and so zero abstracts nothing?

[restive river]

zero is nto a number gg

[scarlet oriole]

sure, if you'd like that

[devout snow]

@restive river Has your question been resolved?

[restive river]

there was nothing to resolve

[winter torrent]

there was zero to resolve?

[devout snow]

Channel closed

Closed due to timeout

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[soft tree]

How can I make this game fair and express it using a free diagram?
The game is and fair ground game where every time you press a button a random coloured ball is chosen. There are 3 red, 3 green and 3 blue balls. You can win by pressing the button and getting all of the same colors or you can win by having different colours. But the thing is after you have chosen a ball it will not be placed back

[hybrid snow]

hi

[low coyote]

Put a gaij w to winining, then calculate the expectancy of winning. Since you always pay 5, you can subscract 5 at the end. The result must be 0

[devout snow]

@soft tree Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
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• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[restive river]

Is the transformation $\RRR$ linear?

[rose girder]

What's \RRR

[restive river]

the real part of a complex number z

i can provide context for info btw so this isnt an xy

[rose girder]

!xy

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[restive river]

ok

[rose girder]

!jk

R-linear as a function R^2 -> R, or C-linear as a function C -> C?

[restive river]

\let\0\cm
So I am meant to simplify [
S(t) = 19\6vt +4\dv[v]t-2\int_{-\infty}^t\6vt\dd t
]
where $\6vt = 55\6\cos{5t+44\degrees}$ and we assume the value of the integral at $t= - \infty$ is zero

\bigskip
Basically, my physics book does some seemingly cursed shit with this and i dont get this. Basically I want to \emph{properly} do this mathematically. So I will use the following:
\e{align*}{
\6vt = V_m\6\cos{\omega t + \varphi}&= \0\RRR{V_me^{j(\omega t + \varphi)}} \ &= \0\RRR{Ve^{j\omega t}}
}
where I assigned $V = V_me^{j\varphi}$. Anyways, subbing in to our above equation gets us [
19\0\RRR{Ve^{j\omega t}} + 4\7{\dv t}{\0\RRR{Ve^{j\omega t}}} - 2\int_{-\infty}^t \9{\0\RRR{Ve^{j\omega t}}}\dd t
]
but now i dont know how to deal with those $\RRR$'s

[rose girder]

yeah, i have seen the other two channels

[restive river]

LOL

but yeah like

[rose girder]

[restive river]

i dont understand what u mean by that

[rose girder]

There is a difference between R-linearity and C-linearity

[rose girder]

R-linear means that f(ax + by) = a f(x) + b f(y) for all real numbers a, b and vectors x, y