help-0

[brisk oak]

and from here you can easily figure out the indefinite integral

[fair spindle]

Can you explain where that’s coming from

[brisk oak]

logarithm rules

this is still 2^x just rewritten so we have e as the base

because e^x is easier to integrate

[fair spindle]

Ok

I think the indefinite integral is 16 right

[brisk oak]

where did you get that from

[fair spindle]

e^(4ln(2)) - e^(0ln2)

Ah hold on

[brisk oak]

no you still have to integrate that

[fair spindle]

I meant 15

Oh nvm

[brisk oak]

you cant just plug in the values

[fair spindle]

Yeah I forgot

[brisk oak]

yes :p

the solution should be around 21.6

[fair spindle]

How would you solve it without using u-substitution

[brisk oak]

do you know the derivative of 2^x

?

[fair spindle]

(2^x) * ln2 right

[brisk oak]

you just need to apply the same principle in reverse here to find the antiderivative

[brisk oak]

yes

if you differentiate a certain function you get 2^x as the result

and we know that if we differentiate 2^x we get 2^x *ln(2)

so the solution must be 1/ln(2) *2^x

[fair spindle]

Oh ok

Thanks

[brisk oak]

this is a useful general rule to remember :)

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[versed knoll]

Learning bias-variance tradeoff in Machine Learning.

[versed knoll]

Here's a slide from my lecture.

Doesn't adding a "noisy variable" to Case I simply turn it into Multivariate Linear Regression?

Also, if we add a "noisy variable" but its Beta coefficient is 0, it's having no effect on the Simple Linear Regression, right?

But on the very next slide, my professor has included a graph that marks the bias of Beta as p increases... but isn't that just turning simple linear regression into multivariate linear regression?

And then, next slide, the increasing variance of Beta, with the number of added noisy variables... but I thought every added noisy variable had a Beta of 0?

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[fair musk]

Anyone have a mnemonic for euler's formula e^(it)=cost+isint?

[rare gale]

not really a mnemonic but just remember that in imaginary plane we use the horizontal (x-axis) for real component and vertical (y-axis) for imaginary component so it makes a lot of sense that the cos part is real (cos is x on the unit circle) and the sin part is imaginary (sin is y on the unit circle)

[fair musk]

wait what the hell this is actually crazy

i never thought of it that way😂

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[quick turret]

Someone able to help with this questions

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[wary inlet]

can anyone help me with this integral, my and my math friend were doing it for fun and got stuck because we both suck at integrals

[wary inlet]

Also could you explain it like you are talking to a 13yr old

[tall topaz]

exquisite handwriting

does that say 2xsin(2x^2)?

if so theres an obvious substitution here

[wary inlet]

yea

my bad it was microsoft paint

and on a trackpad or whatever they're called

[tall topaz]

Conveniently the derivative of x^2 is 2x

[wary inlet]

hmm

yes

ohhh

I see

that doesn't change much

from my POV

but it prob means a lot to you

Come back

@tall topaz

nooo

I'll just close

.close

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[unkempt vector]

https://gyazo.com/dfd5a9832883f06ac0ec26ac01e881f5

[unkempt vector]

hey can someone help me understand this

im confused on the third line on how they got (x^2+1)^2 to just x^2+1

oh wait

nvm

.close

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[void sedge]

Thus a multiset breaks one of the cardinal rules of sets, namely, elements are not repeated in sets;
they are either in the set or not in the set. The set {a,a,b} is the same as the set {a,b} but not so
for multisets.

What are the other "cardinal" rules of sets? I guess one is they must either belong to a set or not and the other that there is no repetition. Are there any other rules besides these two?

[mortal trellis]

well depends on how deep you wanna go

set theory can be a very complex topic

not caring about order or amount is the basic idea of sets. you only care about something being in the set or not. nothing else

[void sedge]

Okay

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[brazen heath]

hi can someone help me with these problems for calc 2? i solved it but i think i messed up somewhere along the way. i will attach screenshots

[left isle]

,rotate

[left isle]

for number 3, shouldnt n!/(n+1)! be 1/(n+1)?

you did it correctly in number 6

unless i missed something

[brazen heath]

sorry im lost for number 3

[left isle]

i mean it looks great besides that one little hiccup

[brazen heath]

can you write it down and show me where i messed up im sorry im a little lost

[left isle]

the part where you simplified everything and have arrows drawn to there corresponding values, 1, 8, n+1, -1

n+1 should be 1/n+1 since you simplified it from n!/(n+1)!

[brazen heath]

OHH

i see

[left isle]

yeee

[brazen heath]

but i got the problem wrong for that one

would it be conditionally convergent or absolutely convergent?

because i put conditionally convergent and got it wrong

and can you also help me with this problem? i got it wrong as well but i thought it was fully correct

hello???

.close

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[lone heart]

Please don't occupy multiple help channels.

[fickle sandal]

well, what is the key part of a linear function? if I know the different between the function at x=1 and x=2, what can I say about the difference between x=2 and x=3

[fast widget]

what does that even mean

[left isle]

if (x,y) is a linear function, shouldn't both x and y be increasing or decreasing steadily? like x is going up by 3 each time and y is going down by 1 each time

or something linear like that

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[lethal adder]

Hello I have weird question not even sure if it is math related but it seems like math. There are those 3×3, 4×4 sliding puzzles where you have tiles of image and one tile ussually bottom right is removed. But if I take this puzzle and just shuffle all tiles randomly with that same one removed can there be unsolvable situation?

[lethal adder]

Because if I start with full solved puzzle where all pieces are in right place then I move one by one I will make solvable solution because it went from solved to unsolved but I want to know aboug pure random shuffle

[weak bison]

Yea there are unsolvable combos

[worn fox]

think even about 2x2
1 3
2 _
is unsolvable

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[tribal haven]

not only is it possible the probability is exactly 1/2

some parity argument but i forgot about the general construct

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[narrow thistle]

it's probably wolframalpha just thinking that this is simpler than the "no radical in denominator" form

yeah that's likely
I'm not entirely sure how wolframalpha works but there may be a way to ask it to show equivalent expressions

it usually does that by default from my experience...
but still it wouldn't really be that useful compared to just calculating by hand

idk there's just limits to online tools ig lol

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[charred dock]

help 0 is good luck

so I used some stuff to get it to tan(x) = (1-tan^2(x) cos(x))

am I on the right track maybe

also got tan(x) = sqrt ((cosx - tanx)/2)

it is clean after 10 minutes idk what I'm doing

<@&286206848099549185>

take your time

hellooooo

😭

I can wait all day

please let me get a 70 percent on this don't get impatient

would it be evil to ping help again

I'm going on a walk

if anyone could at least give me some identities to start with

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@charred dock Has your question been resolved?

[charred dock]

I am falling asleep

I suppose the mathematicians have as well

Perhaps the C was not meant to be

[north perch]

U can write tan2x in terms of sin and cos and then solve

It's easy

Sin2x/cos2x=2cosx

Sin2x=2sinxcosx

Sinx=cos2x

Now it's doable

@charred dock

I only viewed this channel bc it was help 0

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[lethal salmon]

This looking right so far for finding zeros

[lethal salmon]

Is there a way to figure out the divisor quickly or just plugging it all in one by one is the fastest

But im also just not sure if these are the right values

[ocean whale]

The first one is suppose to be 1/2, not 2/1

[lethal salmon]

Ah my bad

[cerulean crescent]

Try to use the Cardano's Method

If you don't know it

then search about it

you'll learn something new on the way

[lethal salmon]

This?

Uhhh yea this is making me way more confused

[ocean whale]

If you can use a calculator, just plug in each one

[charred dock]

Tan 1/2 = 0

[lethal salmon]

Do i write 0x or just x or what

And also do i factor past this

[ocean whale]

You can write 0x or just leave it out since 0x is just 0

Just x means 1x

[ocean whale]

You can factor or use the quadratic formula

[lethal salmon]

So B value is 0

[ocean whale]

Yes

[ocean whale]

Looks good

[lethal salmon]

Says incorrect when i type it in

[ocean whale]

How are you typing it in?

The format might be wrong

[lethal salmon]

Maybe sqaure root of -13 comma square root of 13

[ocean whale]

One, you should separate that to be sqrt(13) and -sqrt(13)

And two, you forgot about the first root you have, when you did the division

The -7/2

[lethal salmon]

Oh

Yea im not sure how to format that in lol

[ocean whale]

You can type it just how it is

-7/2

[lethal salmon]

Like

As the answer

I mean the whole thing laid out

[ocean whale]

The question is asking for all the zeros, so you need to type in all of the zeros

[lethal salmon]

Which is just -7/2,sqrt13,sqrt-13?

[ocean whale]

It's -sqrt(13)

Not sqrt-13

Because sqrt-13 makes it look like sqrt(-13)

[lethal salmon]

How can sqrt on its own be negative?

[ocean whale]

It's just a value

Like -4

But this is -sqrt(13)

[lethal salmon]

Ah ok

Thanks a ton got it working 🙏

.close

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[lethal salmon]

Ah shoot wait lol

use complex zeros to factor f?

I thought i just factored it

.reopen

[lone heart]

✅

[lethal salmon]

@ocean whale

[ocean whale]

Just factor the question

[lethal salmon]

From the beginning

[ocean whale]

In the form of f(x) = (x - a)(x - b)(x - c), where a, b, c are the roots

[lethal salmon]

with -7/2 replacing x?

Uhhh

So f(x) = (x-sqrt13)(x+sqrt13)(x-7/2)

[ocean whale]

Almost, it should be x + 7/2 because it's (x - c) and c = -7/2 so (x - (-7/2)) which is then x + 7/2

[lethal salmon]

Ah right

Welp

Ok well thanks for the help

.close

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[noble bough]

On my homework for circular motion, I was asked to find the angle a pendulum makes with the vertical at its max height. I was able to do part A fine, but got the answer wrong while solving for part B. Could anyone help me get it right and understand my mistakes? The first image is the problem, and the image below it is my work

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[alpine sable]

what is the parametric equation of a line that is just on the y axis?

[alpine sable]

like z = 0, x=0 y = some number

but i dont know

z= 0, y = 0, x=0

[foggy current]

It's just (x, y, z) = (0, t, 0)

[alpine sable]

if we define x to be out of page, y to the right, z is up

ah ok

what's the starting point tho?

[foggy current]

Starting point?

[alpine sable]

like in the form $(x,y,z) = x_0 + tv$

[ocean seal]

Derivative

[alpine sable]

i think that's vector form

[foggy current]

Oh I was just going to mention that

So the starting point is the origin because the y-axis goes through it

[alpine sable]

(0,0,0) + t(0,1,0)

it's this?

[foggy current]

Yes

[alpine sable]

ok thanks

thank you very much

[foggy current]

x_0 can also be any point on the y-axis by the way

[alpine sable]

yes

i think the origin is simpler tho for calculation

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[waxen turtle]

My guess is 25 meters because it looks like it

Idk what to do

[echo socket]

Draw a line crossing the tree on the left and perpendicular to the side with length 25

You will get a right triangle whose legs are known and hypotenuse is what you are looking for

[pseudo ice]

Turns out you're lucky

[waxen turtle]

LOL

YES

IM 'him'

https://tenor.com/view/luke-skywalker-green-lightsaber-mandalorian-jedi-luke-gif-19627631

That's me

[pseudo ice]

Just escaped math jail today

Next time though, you gotta show proper reasoning

[waxen turtle]

I'm blessed to be in the waking presence of chartbit

[pseudo ice]

Awww

[pseudo ice]

Anyways idea is as per here

[waxen turtle]

Oh I see it

Meow

Anwyays ty

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[waxen turtle]

.reopen

[lone heart]

✅

[waxen turtle]

This is 4√3 right

[echo socket]

Yes

[waxen turtle]

So cool

I got 96💀

Oh

9.6

Didn't put the decimal

Idkk

Is it 9.6 someone plz checm

9.63

It says hundredth fr

[pseudo ice]

yep

[waxen turtle]

Yay

Ty

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[lost steppe]

please help me with these questions

[foggy pecan]

they are very nice to solve 🙂 but too much to do it here

[lost steppe]

can we work on it somewhere else?

[foggy pecan]

sure

[lost steppe]

nvm its okay i was able to get in contact with my teacher thank you so much though

..close

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[foggy pecan]

🙂

.close

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[cinder sundial]

I’m trying to prove that omegas are the solutions of the top equation

[tacit arch]

Do you know geometric sums

[lone heart]

@cinder sundial Has your question been resolved?

[cinder sundial]

yes i do

[tacit arch]

Use the formula on omega

[cinder sundial]

Wdym

The formula

[tacit arch]

What do you know about geometric sums

1+r+r^2 + ...+r^n = ?

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[delicate yacht]

solve for X^3=A,where X, A are 2x2 matrix

[delicate yacht]

$\begin{bmatrix}1 & 1\-1 & 1\end{bmatrix}$

[ocean seal]

vectori primi

[delicate yacht]

this is A

I ve tried using Cayley theorem, but i ve got
$$A^2-2A+2I_2=0$$

[ocean seal]

vectori primi

[delicate yacht]

the eigen values i ve got are
$$r_1=1+i$$
$$r_2=1-i$$

[ocean seal]

vectori primi

[delicate yacht]

I know
A=r1B+r2C
I ve tried using a notation X^3=Y
But it ended I would get A by solving for B, C in relation

$$A^n=r_1^nB+r_2^nC$$

[ocean seal]

vectori primi

[delicate yacht]

Y^n***

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[heady void]

what does it mean

[mortal trellis]

geometrically, all points (alpha,beta) which satisfy this are on a line. which means you can express beta in terms of alpha in some way

or equivalently, there is a certain equation which all those pairs (alpha,beta) solve

yes

[heady void]

oh alr

but are all three dots on the same line?

[mortal trellis]

not necessarily, no

make a sketch of the situation

[heady void]

ok

one sec

So something like this?

[mortal trellis]

yes

and now mark some possible points (alpha,beta) on this

(just eyeball it, dont make it precise)

[heady void]

yeah wait lemme make it more obvious

one sec

oh wait

If we connect the blue dots do we get the answer?

Since the points I drew were the x and y intercepts

[mortal trellis]

yes

[heady void]

oh

alr

[mortal trellis]

although thats just a sketch

and the actual intercepts arent exactly those points

[heady void]

yeah

so one sec

ok got it

.close

[lone heart]

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[digital mural]

How can I find dr/dt and r, someone told me to use similarity of triangles but I don’t know how

[digital mural]

.close

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[opaque heart]

Been a long time since I've done geometry, how would I find x?

[opaque heart]

I know it's something with sin, cos, or tan

[snow cobalt]

tan theta = adjacent/base

tan x = 1 mi/1.4 mi

[opaque heart]

lemme give that a try

uhh what

how do I get the x by itself (get rid of the tan)

[snow cobalt]

arctan

basically tan inverse

[opaque heart]

so

arctan(1/1.14) ?

[vapid shuttle]

Normally it’s stated as tan(theta) = opposite / adjacent

Referring to the side lengths

SOHCAHTOA

You might’ve learned

So yes here tan(x)=(1/1.4)

[vapid shuttle]

Yup

[snow cobalt]

yes so basically tan inverse of 5/7

[vapid shuttle]

And then from this, take tan inverse, sometimes called arctan

To find x

[opaque heart]

why 5/7?

[snow cobalt]

1/1.4 = 5/7

[vapid shuttle]

That’s just a simplified version

Because then you don’t have to deal with decimals in the fraction

But they’re the same

[opaque heart]

oh im dumb

so ~36 degrees

is arctan built into most calculators

[snow cobalt]

idts its exact 36 but something below that

[lone heart]

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[somber dew]

I got notes from a friend and I'm confused on where '22' came from at:

(4x - 22) = 90
Can't tell if it's a mistake or not, if that's how it's supposed to go, why and how?

[white pike]

I think it's a mistake

4X-12=90
4X=102
x=25.5

[somber dew]

so it's actually just a typo?

[somber dew]

okay actually, i just got an update there was a typo in the book and we weren't clarified about it until now, thanks for coming to help though

.close

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[ripe mulch]

can someone help simplify this

[ripe mulch]

do i factorise the 5k out

5k(k-1) / k^2 - 1

[limpid spade]

try factoring denominator too

[ripe mulch]

you cant

unless you're trying to do something like

-1(-k^2 + 1)

[limpid spade]

bring it in the form (k+-a)*(k+-b)

[rich lion]

yo everyone, is this correct? im new to this stuff

[limpid spade]

nah get your own channel blud dog

[lone heart]

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[vocal tapir]

I don't understand how this happens. Do I have to find the limit inside log first?

[vocal tapir]

idk why it's -1

[lone heart]

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[void nymph]

what

[lone heart]

@unborn verge Has your question been resolved?

[lone heart]

@unborn verge Has your question been resolved?

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@unborn verge Has your question been resolved?

[lone heart]

@unborn verge Has your question been resolved?

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@unborn verge Has your question been resolved?

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[polar spire]

How can one demonstrate using set theory element method that:

A ⊆ B ⇒ P(A) ⊆ P(B), where P represents the power set.

Here is my try: by hypothesis A ⊆ B. Now we can rewrite

A as A∈P(A) and B as B∈P(B)

A∈P(A) ⊆ B∈P(B)

x∈A∈P(A) ⊆ x∈B∈P(B)

x∈A∈P(A) ⇒ x∈B∈P(B)

x∈P(A) ⇒ x∈P(B)

P(A) ⊆ P(B), which is exactly the right side.

But we can't just say x is an element of a power set right?

[carmine reef]

no, you can't contract membership like that

0 is an element of {0}, and {0} is an element of {{0}}, but 0 is not an element of {{0}}

Instead, solve the problem by assuming something is an element of P(A) and proving it must be an element of P(B)

[placid zinc]

Note that "A ∈ P(A)" is not a set, and you can't have it be a subset

[carmine reef]

I am assuming they mean x is an element of A, and A is an element of P(A)

[lone heart]

@polar spire Has your question been resolved?

[polar spire]

well what do I do then

how can I represent sth with P(A) I tried finding a formal definition of it from which I can derive sth but couldnt find any formula

[lone heart]

@polar spire Has your question been resolved?

[sly mantle]

the others are saying that the language of the proof is very messed up. we do not abbreviate the statement A∈P(A) as A itself

in general to prove X is a subset of Y, we prove any element of X is an element of Y

in particular to prove P(A) is a subset of P(B), assume C is an element of P(A) then show C is an element of P(B)

[lone heart]

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[ruby ruin]

where does the n go?

[hushed locust]

|x/3e| don't depend on n, so take them out of the limit. now you have
(constant) * limit as n-> infinity |(n+1)/n|

[ruby ruin]

why doesnt it depend on n?

[hushed locust]

|x/3e| doesn't depend on n since 1/3e is a constant and x is not a function of n

[thick lynx]

[\lim_{n \to \infty} \Big|\frac{(n + 1)x}{3ne}\Big| = \lim_{n \to \infty} \Big|\frac{nx + x}{3ne}\Big| = \lim_{n \to \infty} \Big|\frac{x}{3e} + \frac{x}{3ne}\Big|].

The second summand goes to 0 as n goes to infinity

The first stays the same

(You could take it out of the limit)

[ruby ruin]

how does the n on the top gets taken out when you seperate it why is it not lim n-> infinity |nx/3ne +x/3e|

[thick lynx]

Yes, it is

But you can simplify the first

n and n cancel

[ruby ruin]

sorry can u further explain idk why im confused on something as simplification on this

[thick lynx]

Sure

[\lim_{n \to \infty} \Big|\frac{(n + 1)x}{3ne}\Big| = \lim_{n \to \infty} \Big|\frac{nx + x}{3ne}\Big| = \lim_{n \to \infty} \Big|\frac{nx}{3ne} + \frac{x}{3ne}\Big|] [= \lim_{n \to \infty} \Big|\frac{\cancel nx}{3\cancel ne} + \frac{x}{3ne}\Big| = = \lim_{n \to \infty} \Big|\frac{x}{3e} + \frac{x}{3ne}\Big|.]

[ruby ruin]

oh i see where i messed up i didnt put the demoninater to both have 3ne

ty alot

[thick lynx]

np

[ruby ruin]

!close

.close

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[wild agate]

Hello

[wild agate]

Can I get some help with this question

[lone heart]

@wild agate Has your question been resolved?

[wild agate]

hello?

[lament wyvern]

@wild agate well, what is the equation for finding the midpoint?

if you know your points are (bx, by) and (ax, ay)

[wild agate]

it doesnt show an equation, i need help im confused LOL

[lament wyvern]

what is halfway between - for example, 2 and 8

and then can you see how you find the halfway between a and b

and then from that, can you see how you'd find halfway between two 2D points

[wild agate]

would the midpoint be -1?

[lament wyvern]

for your original question? well, the midpoint is a point on the graph

so it'll be (x, y)

not just a number

[wild agate]

so the midpoint would be an equation?

[lament wyvern]

there is an equation to find the midpoint of some arbitrary A and B

but you know the points A and B

so you can find the exact midpoint

the midpoint is in the MIDDLE, so it must be in the MIDDLE of the x coordinates of the two and the MIDDLE of the y coordinates - right?

[wild agate]

so point b is -5 x axis and y axis 2, and point a is -4 y axis and 4 x axis

[wild agate]

right

so i have to find those to find the midpoint?

[lament wyvern]

yep!

you're looking for the middle between -5 and 4, and between 2 and -4

[wild agate]

ohhhhhhh

okayyy

i get it

so finding the middle for those id find the midpoint

[lament wyvern]

yep

[wild agate]

okay thank you

[wild agate]

to find the midpoint do i have to look in between these or both of them

[lament wyvern]

not sure what you mean

[wild agate]

im saying because you stated "you're looking for the middle between -5 and 4, and between 2 and -4" im asking if i have to look in the middle between those numbers or do i have to look in the middle between both of them seperately

[lament wyvern]

ah - you can do them separately

the midpoint will be at (middle of the 2 x vals, middle of the 2 y vals)

[wild agate]

ohhh okay

so would the mid point be just val or just one

[lament wyvern]

it would be a point. it would be e.g. (4, 5) or (6, -7) or something

[wild agate]

oh okay

thank you i get it

you can close it ty vm

[lament wyvern]

.close

[wild agate]

.close

[lament wyvern]

I think you need to do it 😛

[lone heart]

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[ruby ruin]

im a bit confused on where the -1^n is coming from when they integrate

[kind sparrow]

The series is alternating prior to integration

[ruby ruin]

how do you know or when to check to see if the series is alternating

[kind sparrow]

Do you know what alternating means

[ruby ruin]

yes its when it goes neg and pos

like -1 + 2 - 3 + 4

[kind sparrow]

Just look at it?

[ruby ruin]

this is the solution if i was doing it without looking at the solution i wouldnt be able to see the work showing its alternating

i could get up to the summation

[kind sparrow]

Then what's the problem

[ruby ruin]

the top part

[kind sparrow]

What is the top part, if you have the summation it's already clearly alternating

You either see it algebraically by rewriting (-x^2)^n = (-1)^n x^2n or you write out enough terms to convince yourself

[ruby ruin]

the part that doesnt say solution

but what im saying is do i have to do that for each time i get a summation

to check if its alternating

[kind sparrow]

Well, yes, but it's not a big deal.

[ruby ruin]

.close

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[wispy ether]

what is the answer

[wispy ether]

for

b)

[stark crater]

have u attempted it

!status

[lone heart]

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

[wispy ether]

yes i want to double check my answer

[stark crater]

Can u send work

[wispy ether]

I have no idea how to type it out here but i can tell you my answer

[stark crater]

You can just explain your process (or send a pic)

and your answer of course

[stark crater]

yeah that is correct

[wispy ether]

really?

but how come the acceleration is negative ?

[stark crater]

the velocity is negative

because its going down

[wispy ether]

hmmm okay thanks i appreciate it

.close

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[twin tapir]

i need desperate help with stuff to do with sine rule and cosine rule , (its for mathswatch homework)

[twin tapir]

<@&286206848099549185> i know it says toonly ping after 15 mins, but this is urgent 😭

[alpine sable]

Ok

i’m here

[twin tapir]

omg ty ily

ok so, this question

idk what im meant to use

[wild umbra]

cosine rule

also it doesnt matter if its urgent or not, u dont ping them unless its 15 m

[twin tapir]

all these rule thingies are so confusing to me

i dont understand any of it

[twin tapir]

sorry

[wild umbra]

do you know what cosine rule is

[alpine sable]

we can use laws of cosine

[twin tapir]

a^=b^+c^-2bccosA

[alpine sable]

raised to the what?

[twin tapir]

is the asnwer 26.2

[alpine sable]

good job !

[twin tapir]

i alsdo got a bit stuck on this one

is it cosine rule aswell?

i can never tell what rule im meant to use

is the answer 48.8

no it isnt

hmmm

oh wait

thats angle c

ok yeah its 93.2

could someone help with this

i dont understand any of it

<@&286206848099549185>

.close

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[wide onyx]

whats the

horizonatal

asymptote here

how do i figure it out

[toxic lion]

For which problem?

[wide onyx]

the c(t)

[toxic lion]

Can you take another picture sideways?

[wide onyx]

is this fine?

[toxic lion]

Yep

So. Do you understand what a function is?

[wide onyx]

wdym

[toxic lion]

Like.

f(x)

[wide onyx]

yea

[toxic lion]

It’s the same concept, just with different letters.

[wide onyx]

but where do i find the h.a here

[toxic lion]

Variables, rather than letters but I was trying to make it simple.

Well.

It depends on what you need to find.

[wide onyx]

usuallay i look at the degree of den and num of the rational function

and find it

[toxic lion]

I need to see the whole problem.

[wide onyx]

but i duno what to do here

,rotate 270

[toxic lion]

What level is this? Algebra 1 or 2?

[wide onyx]

hel

,rotate 270

[wide onyx]

this is advanced functions

grade 12

[toxic lion]

Erm.

Well.

I can’t say I know this with 100% certainty.

[slate vortex]

Basically try what it's asking you. What happens to c(t) as t gets really huge?

[toxic lion]

But I can try.

[wide onyx]

do i just sub

numbers in

t

and show

[slate vortex]

No

[wide onyx]

if its growing

[slate vortex]

No

[wide onyx]

or shrinking

help

[slate vortex]

$c(t)=9-90000 \frac{1}{10000+3t}$

[ocean seal]

Ari

[slate vortex]

As t gets really large, notice how the fraction gets super small?

like 1/21834918273412047 or something

[wide onyx]

ya

so concentration

is

decreasing

as time goes on

more time = less concentration

[slate vortex]

Well yes, but the concentration approaches a certain value over time

[wide onyx]

thatswhat im confused on

[slate vortex]

As t gets really large, c(t) is just 9 minus a really small number

[wide onyx]

what is that galue

value

[slate vortex]

do you get this

[wide onyx]

no

[slate vortex]

Look at this

[wide onyx]

-90000 and after is one whole thing

and 9 is alone

[slate vortex]

Yes

but the -90000 gets really small as t gets really large

because t is on the denominator

[wide onyx]

so if t is in den

it gets small

[slate vortex]

The $-90000\frac{1}{10000+3t}$ gets really small yes

[ocean seal]

Ari

[slate vortex]

So what happens is that as t gets really large

$c(t) = 9 - $ (some really small number $\approx 0$)

[wide onyx]

0?

[ocean seal]

Ari

[slate vortex]

As t gets really large you're essentially just subtracting 0

[wide onyx]

it cant equal zero

its always 1/x

[slate vortex]

No but the answer to this problem is

"The concentration approaches 9 (whatever unit) as time goes on"

It approaches but never really reaches 9

[wide onyx]

how is it approaching

nine

im so confused

so just sub numbers in

.close

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[waxen turtle]

Is it 11

Or uhh

5.4

Omg it's chartbit im a huge fan

Ty

.close

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[sterile hare]

I’m really confused in how to approach question 21.2 parts a,b,c I’ve done work for all I just don’t know the correct way to do it. All the online resources point towards row reduction but Stanford doesn’t teach us that

[granite pilot]

So for (a) and (b) you don't need row reduction per se

(c) it could help but you can do it without it

So what did you have for a and b? Do you want us to confirm your work or what's the question?

[alpine sable]

he moved to #help-1

[granite pilot]

sorry I missed that!

[alpine sable]

its alright man any help would be greatly appreciated.

if you can.

.close

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[uneven rivet]

was wondering if som1 could check this idt i did it right

[uneven rivet]

i j did it using regular line integral cuz i think thats easier than stokes for this

[lone heart]

@uneven rivet Has your question been resolved?

[uneven rivet]

<@&286206848099549185>

[uneven rivet]

why cant u do this

i j did the integral, plugged in r, then dotted with r't with every segment

wait

i forgot last segment back to origin

hmmm

i got 10

[granite pilot]

and that's not the answer I'm guessing? or what's the issue?

[granite pilot]

no one said you can't

[uneven rivet]

yeah

i got 10 but thats wrong

not sure what i did wrong

[granite pilot]

can't really help if we don't see your work but let's try working it out

[uneven rivet]

i split it up into 4 line integrals

did F(r(t)) dot r't

[granite pilot]

yea

[uneven rivet]

dt

[granite pilot]

no your method sounds right

its just a calculation error it sounds like

[uneven rivet]

maybe but im not sure

[granite pilot]

you're also probably right that Stokes theorem makes this harder, not easier

[uneven rivet]

yeah by glance thats j what i thought

for the rt functions i got

<2t,0,0> , <2,3t,1> <2-2t,3,1> and <0,3-3t,1-t>

each integral for 0 to 1

for derivative which i dotted each F

i j took d/dt

[uneven rivet]

any idea or nah

[granite pilot]

for shits and giggles if we did use stokes theorem though, you get Curl F = 10y i + 2z j + 2y k
it's a little hard to imagine the surface you want to integrate over but you can parametrize this plane by x = 2u, y = 3v, z = v for 0 ≤ u, v ≤ 1
so Curl F is now (30v, 2v, 6v)
you have partial_u = (2,0,0) and partial_v = (0,3,1) so you get their cross product is (0,-2,6)

Your integral actually becomes ∫∫[0,1] x [0,1] (30v, 2v, 6v) dot (0, -2, 6) du dv
= -4v + 36 v =∫[0,1] ∫[0,1] 32 v du dv = 16 so it does show that you must have had an error somewhere

not sure if its 16 or -16 but one of those is right lol didn't quite check compatible orientations

[uneven rivet]

got it

ty

[granite pilot]

no worries 🙂

[uneven rivet]

how did u get the plane

[granite pilot]

hahaha

I gotta be honest there's no good way

I kind of noticed that (0,0,0) and (2,0,0) are the same as (0,3,1) and (2,3,1) i.e. you just transpose by (0,3,1) to move the first set ot the second

the first set is descrived by (2u,0,0)

and the transposition is given by adding (0,3,1) so you get (2u,0,0) + (0,3v, v)

(2u, 3v, v)

it's just a square with 4 corners so I was trying to figure out how to map (0,0,0), (0,1,0), (0,0,1) and (0,1,1) to those 4 points and this made sense

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[brave ermine]

any1 wanna help explain slopes

[wheat isle]

What don’t you understand

[brave ermine]

ok so

like im acc so lost

?

[cedar oracle]

Slope is the amount y increases per an increase of x, so for the first one you can see m increased by 30 for every increase of s so the slope is 30

But m=30s doesnt work in this case because when s=0 m should equal 30 but it equals 20

So because m at every plotted point is smaller by 10 then it should be using the slope equation, it means the y intersection must be at -10

Meaning the graphed line would be 10 positions below the normal graphed line if its y intercept was at 0

So the equation would be m=30s-10

Where the 30 is the slope and the -10 is the y intercept

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[slow pendant]

hello, i was wondering how i could change the bases to all be equal

[coarse marlin]

notice how the bases are all powers of 2

[slow pendant]

yup

[coarse marlin]

so, if you write 16 as 2^4, you get (1/4)*log(2, x)
similarly for 4, you get (1/2)*log(2, x)

[slow pendant]

woah

[coarse marlin]

the exponent of base comes out of log func as 1/n

[slow pendant]

woahhh thank youuuu

[coarse marlin]

welcome!

[slow pendant]

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[naive sorrel]

BTW this is easily proven using change of base formula

which u should probably know and use

here

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[cold gyro]

if i have two equation like this

[cold gyro]

6x+3y=0

3x+2y=0

i can subtract one from another e find 3x+y=0

so why when i put x=1 and y=-3 those equations above the result is note zero?

i dont undersant

[fickle heath]

That's not how you solve a system of equations

[cold gyro]

what i did wrong?

[fickle heath]

By the same logic, you could also put x=2 and y=-6, or x=-3 and y=9

[cedar oracle]

If you subtract y from both sides you get 3x=-y which tells you that x must be -3 times y

So that doesnt work because 1 isnt -3 times 3

Doesnt*

[fickle heath]

Wrong

[cedar oracle]

Oh sorry wait

I saw 3 not -3

[cold gyro]

and i dont know why it doesnt work

[fickle heath]

Try multiplying both sides of the second equation by 2, and then subtract one from the other

[cold gyro]

ok

-y=0

jesus

why

im taking calc class and im having problem with it

no way

so how do i solve it?

[fickle heath]

That's correct

You have y = 0, now plug that in one of the initial equations to find x

[cold gyro]

oh i see

x=0

so

just (0,0)

its the only critical point

omg

[fickle heath]

It's the only solution

[cold gyro]

ok ok

but

look at this

[fickle heath]

These two equations represent straight lines, (0,0) is their intersection

[cold gyro]

6x + ay=0 and ax + 2y=0

for any value of a this is true?

theres only one solution?

[fickle heath]

No

If a = sqrt(12) or a = -sqrt(12) then there are an infinite number of solutions

Otherwise the only solution is x=0, y=0

[cold gyro]

ok

how did you find it?

[fickle heath]

Find what? The sqrt(12)?

[cold gyro]

yeah

im trying here

but im going nowhere

[fickle heath]

The two equations have to be the same

So 6/a = a/2

-> a^2 = 2*6

-> a = +-sqrt(12)

[cold gyro]

well

you helped a lot

thanks

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[mellow iris]

why cant we assume that the bottom base angle will also be the same

[naive sorrel]

do u have the original problem

just for better context

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[lone heart]

Please don't occupy multiple help channels.

[white gust]

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[north wren]

Hey people im dumb asap and tomorrow i have a math exam of early math in highscool so anyone can explain me factorization

[north wren]

Dont mind i just understand it

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[alpine sable]

Why is it using sine and cosine

its just r = 0 mult 2 and r = -5

omg bruh

i am dum

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[wet lodge]

From t.P outside of circle k, the secant PCA and the tangent PB were built. To prove that РВС~ РВА. Its a task for description with words.

[wet lodge]

The task is about similar triangles

This is how the drawing looks like

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[raw bolt]

can anyone explain in depth how to use weierstrass factorization to get the infinite product of sin(x)

[raw bolt]

what I've gathered so far is that you need to find the zeros of sin(x) which are just $n\pi$ but I understand very little after that, like how we use $1-\frac{x^2}{n^2\pi^2}$ instead of just $1-\frac{x}{n\pi}$ and all that

[ocean seal]

Triaxyz

[tacit arch]

They're grouped in pairs of npi and -npi

(x-a)(x+a) = ?

[raw bolt]

so when locating zeros you're effectively finding both positive and negative integer multiples?

instead of just positives

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@raw bolt Has your question been resolved?

[tacit arch]

sin(x) has zeros for x<0 yes

[raw bolt]

would it make sense to think of this as kind of like an extension of expressing polynomials as the products of their roots, but using it on periodic functions with infinite roots?

[tacit arch]

Yes that's exactly what's happening

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[tacit arch]

sine being periodic doesn't really have anything to do with the infinite product of (x-roots)

.reopen

[lone heart]

✅

[tacit arch]

Sine being periodic just makes the product look nice

[raw bolt]

makes sense

ty

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[alpine sable]

How did 6 get here

-6

[rich quiver]

-9+(-8)+9-(-2)

[zinc haven]

extract the "normal" numbers from the factor

you calculate $9 \times 5 \times 3$

[ocean seal]

FungusDesu

[zinc haven]

-3 becomes 3 because it is in absolute value sign and had the minus removed

then you calculate the "factor" one

$\frac{10^9 \times 10^{-9} \times 10^{-8}}{0.1^2}$

[ocean seal]

FungusDesu

[zinc haven]

this gets 135

[zinc haven]

and this gets $10^{-6}$

[ocean seal]

FungusDesu

[zinc haven]

hence, $135 \times 10^{-6}$

[ocean seal]

FungusDesu

[alpine sable]

Ah I see

Kinda ckmplicated

complicated

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[earnest pine]

how does this turn into this?

[earnest pine]

where does the pi r ^2 go