help-36

[hybrid heath]

Just a name choice

[oak kraken]

Does it line up with another formula?

Or are you still referring to L(x) by name choice

[hybrid heath]

Yes

L(x) is still point slope form, just L(x) instead of y

[oak kraken]

But why not keep it as “y”? What’s the reason to change it?

L(x) is more descriptive towards what it is doing? It could be P(x), g(x) doesn’t matter, it’s still y (output)?

[hybrid heath]

It's not uncommon for the original equation to be written, say, y=x^2

[oak kraken]

Ya I noticed that too. Changing y to f(x) on the fly

[hybrid heath]

Better to do L(x) and avoid name collisions

[oak kraken]

I guess it depends if it’s needed or not

I suppose in this case it is? To show linearization instead of point slope formula?

[hybrid heath]

Not really. You can call it whatever you want

[oak kraken]

AFAIK linearization formula and point slope formula are exactly the same? Just different names?

[hybrid heath]

Yes and no

[oak kraken]

How so with no? The derivative part for slope?

[hybrid heath]

Linearization formula uses derivative for slope and applies to functions. That's right. Point slope is just generic for lines

Linearization formula is an application of point slope

[tranquil pine]

Just to highlight that it is, well, a linear approximation function i suppose? semantics/notation like this change absolutely nothing to the core idea of the thing you're trying to do, but they help clear up confusion

in fact

if you search up "linear approximation" in google right now

google would show you this

did google commit an unforgivable sin by renaming the L(x) to a y? no

[vital crag]

,tex .point slope

[soft zealot]

riemann

[vital crag]

I have nothing to add, just flexing factoids

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@oak kraken Has your question been resolved?

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[oak kraken]

I don’t know quite understand the notation with this

[oak kraken]

It starts with y=f(a) + blah blah blah

But doesn’t y = f(a) to begin with?

m is f’(a) and x is a

[tardy warren]

not if they say it doesnt

[oak kraken]

Wdym?

[tardy warren]

why do you think y is equal to anything

before they tell you its equal to anything

[oak kraken]

y is the same thing as f(x) for example if f is the name of the function

[tardy warren]

no y is just a variable

and in this case a function of x

y(x)= blablabla

[oak kraken]

Confused 😐

[tardy warren]

its ebcause you think y has some predetermined meaning

its like if someone tells you x=6

[oak kraken]

Y is the output, isn’t it?

The range

[tardy warren]

and you say wait but in this otehr problem you told me x= 15!

y doesnt mean anythign

its just notation

[oak kraken]

Generally y variable is reserved for output like x is reserved for input and i is reserved for imaginary

[tardy warren]

okay and they use y as an output for the points on their new line

[oak kraken]

When I look at point slope formula, which is kinda the same as linearization formula, y is included in the point slope formula

And you can find y from that formula

y-y1 blablabla

[tardy warren]

they are different y's then

[oak kraken]

But for linearization formula i read it like it says y=y-y1 blablabla

Is that how I should read it?

[oak kraken]

Yes for sure, y and y1 are different

[tardy warren]

no the y's themselves are

[oak kraken]

y is unknown for point slope but y1 is known

[tardy warren]

they would probably name them something different

to avoid confusion

[oak kraken]

So this is bad notation or it’s fine?

L(x) would be better instead or y?

[tardy warren]

its fine if you understand what they mean

[oak kraken]

Well, I’m confused by that first line lol. Underneath the formula:
y=f(a)

That’s like saying I can replace y with f(a)

[tardy warren]

sure it might be confusing so its just bad notation

but at that point arent you just deliberately trying to misunderstand it?

cause you technically know what its suppoesd to say

and what every expression means

[oak kraken]

so I read this as f(a) = f(a) + blah blah blah and that doesn’t make any sense to me

It’s like using an equality operator when it’s not equal

[tardy warren]

im sorry but get used to it

its harsh but symbols will repeat

A LOT

[oak kraken]

How would you write it instead?

[tardy warren]

you can write a new function g(x)

or just L(x) to show its a linear thingy

[oak kraken]

Is this just because math ppl are lazy?

Don’t want to write more clearly

[tardy warren]

no you kind of just run out of symbols

[oak kraken]

our professor today was showing derivative formulas with just the letter d

Product rule; quotient rule etc

It’s not notation I have seen before

d/dx is the only way I’ve seen derivative with d

[oak kraken]

So maybe that’s just being lazy

[tardy warren]

if its obvious you might aswell omit dx.

sure but i think its a weird thing to focus on

[oak kraken]

But let’s say you multiply d with x. Now you have dx/1.

But that should be dx/dx

1

[tardy warren]

i dont get taht

[oak kraken]

or d multiplied with y. Now it’s dy/1, when it should be dy/dx

[tardy warren]

so? why are you writing /1 btw

[oak kraken]

To show the denominator

There should be dx in the denominator

[tardy warren]

but your prof didnt type it right

just did d x^2

[oak kraken]

Lol well that’s why I’m asking. Is it being lazy, or normal to write things this way? If we run out of symbols or whatever

[tardy warren]

what meaningful relevance would the dx have

[oak kraken]

dx/dx = 1
dx = dx

[tardy warren]

lol

is dx^2/dx = x

[oak kraken]

The product rule was written as
d(a)b + ad(b)

Never seen it that way before

[tardy warren]

i have

sometimes D() also

[oak kraken]

[tardy warren]

but like theyre telling you its the derivative right

and you know what that is

why does it matter to you if they write D() d() or d/dx

or f'

[oak kraken]

I guess so.. but what’s so hard about using actual notation rather than making this stuff up on the fly? I feel like it’s lazy imo

[tardy warren]

all notation is made up

[oak kraken]

Are they pretending to be Newton or something

We should go with the 4 derivative notations

AFAIK there are only 4

[oak kraken]

But it was made by the ppl that discovered the work

[tardy warren]

idk if thats always true

[oak kraken]

Which part?

[tardy warren]

that the notation we use is made by whoever discovered the 'subject'

[oak kraken]

That’s like saying instead of cm I will just write c. I used a ruler and measured 30c distance

[tardy warren]

sure

[oak kraken]

Ppl will just be confused for no reason, and will think they are too lazy to write correct notation

[tardy warren]

i mean you do that all the time in math

[oak kraken]

How so?

[tardy warren]

there is no correct notation

[oak kraken]

We are taught notation at the beginning of the class and then they basically throw it out the window anyways lol

[tardy warren]

the world is a big place

almost every1 have been taught different stuff

just explain it and move on

instead of insisting everything is written exactly like you want it to

which would be how your notation is and then other people might be as confused

and you just explain it and move on

[oak kraken]

True, and there are no standards with math. Like with the web we have W3C and all the browsers must comply. With math it’s like the wild Wild West shoot from the hip and keep riding 🐎

[tardy warren]

its just that notation is ncie and all but please never get to ofixated on it

you learn nothing of value its a waste of time

[hybrid heath]

It's better to think of notation as flexible

It's like you're saying "English sentences always need a noun and a verb, but you can literally choose any noun or any verb. It's the wild wild west of language"

[oak kraken]

Well, that’s what browsers and developers do not want. It used to be this way like the wild west but now it’s a lot better

But I guess math and programming are different disciplinarians and I just gotta be OK with that

Tim Berbers Lee was thinking ahead and W3C was put together from the very get go. It may be too late for something like that for math. And perhaps mathematicians are more than happy with their ways and do not want strict compliance

[hybrid heath]

Nah strict compliance would not be great imo

Math is a language of rigor that still offers flexibility in its writing

Also, it's very far from "wild wild west"

I think you are still learning

So new things come as a surprise to you

And W3C is nice, in theory, but every professional web page has to make 1,000 different configurations for all the different browser options and versions out there

In short, nothing is 100% compliant, and the more you try to enforce it, the further you get

There's an xkcd comic about this somewhere...

[final saddle]

@oak kraken Has your question been resolved?

[ocean lintel]

you're welcome

[hybrid heath]

bless

@ocean lintel, is there an XKCD for when you don't know an appropriate XKCD for a situation, but the mere mention will always bring someone who does know?

[ocean lintel]

https://thomaspark.co/2017/01/relevant-xkcd/

unfortunately not an xkcd

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[ocean lintel]

. somewhat relevant: https://xkcd.com/1447/

xkcd: Meta-Analysis

Life goal #29 is to get enough of them rejected that I can publish a comparative analysis of the rejection letters.

[eternal iron]

I have this problem
"Ilan and Justin are competing in a math competition. They work independently and each has the same two problems to solve. The two problems take an exponentially distributed amount of time with mean 20 and 30 minutes respectively (or rates 3 and 2 if written in terms of hours). (a) What is the probability Ilan finishes both problems before Justin has completed the first one. (b) What is the expected time until both are done?"

[eternal iron]

What i've tried for A is by using exponential races, I used the probability that Ilan finishes P1 before Justin finishes P1 times probability Ilan finishes P2 before Justin P1 giving $\frac{1/3}{2/3} \cdot \frac{1/3}{1/3 + 1/2} = \frac{1}{5}$

[soft zealot]

heheitsop

[eternal iron]

For part (b) , I have it that on average the total solve time can be seen as 1/3 + 1/2 = 5/6 but i'm not really sure how to proceed fr this

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@eternal iron Has your question been resolved?

[eternal iron]

<@&286206848099549185>

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[sturdy tusk]

The question is to find the nature and position of stationary points

Apparently my coordinate is MENT to be (-1, 5)

And also (-1, 5) is meant to be the minimum not maximum somehow

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[maiden whale]

Pls help… 99% sure what I did was illegal

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[leaden ember]

Yo

[leaden ember]

Wassup y’all

I’m back

I need help on this

Please tell me step by step on how to do it

I already did the other

But this one is hard asf

Hello? 🍔🍔🍔

https://tenor.com/view/oh-hello-hello-gif-15362273

Anyone

Realty

🗿

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[oak kraken]

are these equal?

[worldly vale]

yes

[oak kraken]

could I rewrite the first term to be 4^x?

[worldly vale]

no

why do you think you can

[oak kraken]

hmmmm

good question

i can only do that if powers are the same, ya?

[worldly vale]

yeah

[oak kraken]

otherwise it's like two different terms

2^1 and 2^x

now I gotta find the d/dx

[worldly vale]

you need to just have a exponent rule table in front of you

until you know them by heart

[oak kraken]

I should know these by now

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[oak kraken]

And I think I do

It’s just x-1 I need to remember

.close

[worldly vale]

if youre not comfortable with them its gonna fuck you over for the rest of your maths career

[ocean lintel]

And when it's no longer a problem in math it will be in physics

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[digital pebble]

how would i work this out?

[magic sparrow]

how do you expect us to help you without just giving you the counter example :p

[digital pebble]

i was wondering if there's a fast method to solve this , because what if i subsitute 10 different values for n and they all agree with toms statement

[worldly vale]

well you should always just try n=1 to ~10

no harm

[magic sparrow]

the counterexample is quite immediate

for this one

[digital pebble]

fair enough , so if i was to subsitute n = 8 into the equation that'd get me 255 , how will i know if thats a prime number or not?

[magic sparrow]

n=8 is not an odd number

and 255 is not prime, because it clearly has atleast a factor of 5 and 51

if not more

a number is prime if its only factors are itself and 1

3 is prime

5 is prime

7 is prime

9 is not prime , it has factors of 3*3

etc...

all even numbers have factors of 2 i.e not prime

[digital pebble]

oh i see , so in this case , i could subsitute a value n of 9

that'd would me an answer of 511

[magic sparrow]

which is ___ prime

prime or not?

[digital pebble]

not prime

[magic sparrow]

so would n=9 then be a counter-example?

[digital pebble]

yep , it would thanks for the help

just 1 last question

[digital pebble]

how did you find out 255 has a factor of 51 , i get 5 since all numbers which end in 5 or 0 have factors of 5

but how did you figure out 255 was divisible by 51 fast

[magic sparrow]

because I saw the 5 like you did

and then I knew it had to be 5 * something

5*50 = 250

so 5*51 = 255

so 5 and 51 had to be factors

[digital pebble]

ohhh , i see now 🤔 🤔

it makes much more sense

[magic sparrow]

I can also see that 3 and 85 are factors

[digital pebble]

right , well thank you for your time and help

[magic sparrow]

yeah no problem

[digital pebble]

i'm going to do a bit more extra practice on this

have a good day 😁

[magic sparrow]

good luck!

you aswell

[digital pebble]

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[maiden whale]

Could I get some help with 13(i) this is my working so far

[maiden whale]

<@&286206848099549185>

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[maiden whale]

I’m stuck… I’ve done this so far

<@&286206848099549185>

Please 😭

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[maiden whale]

It’s been an hour and a half 💀

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[gleaming scaffold]

How do you solve this one?

[rain compass]

have you heard of implicit differentiation?

[gleaming scaffold]

yeahh we do that here?

[rain compass]

yes

then isolate y’

[gleaming scaffold]

ohh okay

so how do we start? do we start with differentiation or do we have to simplyfly?

[rain compass]

differentiate implicitly

then isolate y’

[gleaming scaffold]

oh okay

so would it become 3x * y * y' +y^5 *y'=o?

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[unique jolt]

why does my hw have like

[unique jolt]

100000 parts on weak topology tf

[rain compass]

why not

[unique jolt]

idk I don't wanna see it again for a while tbh

Does C_X here just denote the closed neighborhoods in X?

for 4.16e)

[rain compass]

hm don’t know

[unique jolt]

ok nvm i did some digging it is

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[sour spear]

I dont get what I am doing wrong

[tulip coyote]

The series are
[
\sum_{n=1}^{\infty} \frac{6^{n}}{4^{n} - 1}
]
and
[
\sum_{n=1}^{\infty} \frac{ (n^{4} - 6) \cos(n\pi) }{n^{5}}
]
right? They look a bit blurry

[soft zealot]

@tulip coyote

[tulip coyote]

for here, what did the ratio test get you?

[sour spear]

yes those are correct

ratio test was an educated guess

it looked like it would be an apllication of it

and alternating test because of cos

@tulip coyote

[tulip coyote]

But did you try to apply it?

[sour spear]

nope

does that test not work?

[tulip coyote]

Try it and see

[spoiler: the fact that I'm asking you to try it and that I'm not questioning convergence should tell you what should happen]

[sour spear]

it doesnt work

yea

i tried it

it didnt work

but what otehr would work then?

[tulip coyote]

well worth a comment is that the alternating test should work because cos(pi * n) = (-1)^n and (n^4 - 6)/n^5 has a limit of zero

[sour spear]

right

and it converges correct?

[tulip coyote]

[it's also decreasing from a certain point too, and those are the requirements for alternating series]

[sour spear]

so the alternaatiing and converges test should work for that one

wait

so

integral test as well?

decreasing

ohpos

its not always positive

so alt test converging

[tulip coyote]

The "it" I'm referring to is the (n^4 - 6)/n^5

[tulip coyote]

But of course thee whole thing is not always positive

[sour spear]

yea i forgot about the cos

thank you that made sense and worked

what about the other one?

comparsison test

diverges

diverges is solid info i know that

i dont know which test to use however

[tulip coyote]

Well what does the comparison and limit comparison test state for you?

[sour spear]

the limit comparison test shows that the original series is divergent

or convergent

well not really

but it could also tell you if it could be either

if the end result =0

[tulip coyote]

so basically

Tl;dr if a series converges, then the sequence it's made up of must converge to zero, so if the sequence does not converge to zero (for whatever reason), the series cannot converge either
is what you mean, taking note that the converse isn't always true?

As for the comparison test?

[sour spear]

wait so

the limti

goes to inf

so we can use the test to say that the series is not zero

?

[tulip coyote]

Let me restate this:
if
[
\sum_{n=n_{0}}^{\infty} a_{n}
]
converges, then $\lim_{n\to\infty} a_{n} = 0$ \
The contrapositive is that if
[
\lim_{n\to\infty} a_{n} \neq 0
]
then the series $\sum_{n=n_{0}}^{\infty} a_{n}$ does not converge, which is also true \
however, if $\lim_{n\to\infty} a_{n} = 0$, that is not enough information to conclude the convergence or divergence of $\sum_{n=n_{0}}^{\infty} a_{n}$

[soft zealot]

@tulip coyote

[tulip coyote]

As mentioned before, the limit of the sequence is zero, but that isn't enough information for convergence or divergence

[sour spear]

Ohhhh i get ot now

so we can use it but it wouldnt help find convergence or divergence

ok i thnk i got the answer now

yea i got it it was b,d,e,f

thank you so much for helping me

i really appreciate it

now i can sleep peacefully

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[vocal spire]

Given system of PDE \
$\frac{\partial z}{\partial x} -ax-bx-c=0 \
\frac{\partial z}{\partial y} -bx-dy-e=0$ \
is know to be compatible. \ What is the common solution?

[soft zealot]

Welf

[worldly vale]

common solution means a solution that solves both the equations

[fresh star]

for these, you just integrate, and you just see which parts of one is in the other

when you integrate dz/dx, you get something + f(y)

when you integrate dz/dy you get something + f(x)

then you see if the f(y) is located in the other equation

and same with f(x)

[vocal spire]

Given system of PDE \
$\frac{\partial z}{\partial x} -ax-by-c=0 \
\frac{\partial z}{\partial y} -bx-dy-e=0$

[soft zealot]

Welf

[fresh star]

dz/dx = ax + by + c

z = ax^2 + byx + cx + f(y)

dz/dx = bx + dy + e

z = dy^2 + bxy + ey + f(x)

you can see that the f(y) in the first one

is the dy^2 + ey in the second one

and the f(x) in the second one, is the ax^2 + cx in the first one

so z = ax^2 + dy^2 + byx + cx + ey

[vocal spire]

So the full solution is
z = ax² + dy² + bxy + cx + ey

I see

[fresh star]

once you find what f(y) is, or what f(x) is

you can just pick one of the equations

and sub it in

so if you pick z = ax^2 + byx + cx + f(y)

and sub in f(y) = dy^2 + ey

you get z = ax^2 + dy^2 + byx + cx + ey

same with if you picked the other one

also

i meant to have 1/2

on the ax^2

and the dy^2

so the answer should be z = 1/2 ax^2 + 1/2 dy^2 + byx + cx + ey

[vocal spire]

Okay I get it

But I have question

If we have that z(x,y)
Can we do ∫y dx?

[fresh star]

wdym

[vocal spire]

And I assume the one can't be solved is
∫z dx since z(x,y)

z is function of x and y

When we work on multi variable function, we can take the other variable as constant when we're not working on it

I only get that on derivative

But no one told me it's work on integral too

[fresh star]

have you not done multivariable integration

[vocal spire]

I have

But most of the case we always have ∫f(t) dt

[fresh star]

infact heres a pretty nice rule

[vocal spire]

Okay

Thanks Doc

Thanks for helping me out too (⁠-̩̩̩⁠-̩̩̩⁠-̩̩̩⁠-̩̩̩⁠-̩̩̩⁠_⁠_⁠_⁠-̩̩̩⁠-̩̩̩⁠-̩̩̩⁠-̩̩̩⁠-̩̩̩⁠)

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[obtuse zinc]

help, this is my attempt sofar, i couldnt come up with anything else

[ocean lintel]

the last step is illegal because you remove the limit but not its variable

try looking at the log of it instead

to use the limit of a product property

since you probably know it for products but not exponents

[obtuse zinc]

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[unreal juniper]

simplify ( p^4 times q^8)^1/4

[dry light]

!status

[final saddle]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[unreal juniper]

i know how to get answer but i just want to know that should i put absolute sign after p

[dry light]

You would yeah

|p|

[unreal juniper]

Ohk my textbook didn't had that so i was confused

Thx

[unreal juniper]

Do you know any material that can have more real world application based questions ?

[dry light]

Light refraction/integration

Uh

Chemistry tends to be stupid

[unreal juniper]

Ohk

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[tranquil pine]

why can we say that

[tranquil pine]

wait hold on

yeah no idk why can we say that 4 divides x^2 - 4x

[void crest]

hm

u can think of it saying

for all x in Z, x^2 is not ~ 2(mod 4)

to check just try x when x is ~ 0 (mod 4)

1 (mod 4)

2 (mod 4)

3 (mod 4)

[tranquil pine]

right just returns itself

im ngl i am SUPER bad at modular arithmetic

[void crest]

just

treat it as normal squaring

then divide by 4 n get the remainder

[tranquil pine]

okay

also the product of two irrational numbers is not always rational right

[worldly vale]

im sure you can come up with an example

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[tacit relic]

Can anyone solve me this its for my sister's friend in university and I really dont know what all this means

[tacit relic]

<@&286206848099549185>

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[tacit relic]

Not yet

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[desert mantle]

well throw simplex algorithm at it but it helps no one if we solve it instead of your sisters friend

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[neat igloo]

How do i solve this

Number 1

Hello

Just the number 1

Im gonna solve the other problem

[neat igloo]

,w

[neat igloo]

Find the area of the shaded region

[tranquil pine]

is that a circle with r=2 ?

and is it a square (?)

if so area of square - area of circle + area of triangle

[neat igloo]

Huh?

Can you solve number 1

@tranquil pine

@tranquil pine

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[neat igloo]

The number 3

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[half swan]

sin(u) tan(u) + cos(u)

[half swan]

i got 1/cos(u)

but it's wrong

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Show your work, and if possible, explain where you are stuck.

[half swan]

nevermind i got it

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[tranquil pine]

Im confused how we showed f'(x) has a root

didnt we just show that f(x) has a root at c?

[worldly vale]

You showed f'(c)=0

[tranquil pine]

yea but f'(c) = 0means theres an extrema

on f(x) at c?

not

on f'(x) at c?

no?

[static blade]

not completely

[worldly vale]

You have directly shown that f'(c)=0 for some c, this literally means f' has a root at c

Regardless of what else it implies

[tranquil pine]

what is a root again?

just that it is zero

at some point?

[worldly vale]

A point that makes the function zero

[tranquil pine]

oh shit i got definitions messed up i was thinking something else

basically graphically

its saying if theres two zeroes

the derivative needs to be zero

so that if it goes above or below zero at some point

that it will come back to zero

right?

[worldly vale]

Yeah that's the right intuition

With the edge case of f having a repeated zero

Like x², but that still gives you the derivative being zero at some point

But what Paul is showing you is why that's true, specifically using MVT to make the intuition rigorous

[tranquil pine]

kk thanks

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[keen depot]

How to find the inverse laplace of this?

I got this sheet:

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[half mirage]

Why -4 became -2 here?

[tranquil pine]

It's because you made a u-sub

u = 1+ 2t

[half mirage]

Many thanks

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[vale reef]

Can anyone explain 12b

[versed crater]

So B is on the circle

On of the points of b is on the circle

Its tangent (if you know calculus)

And it also passes through A

[vale reef]

Oh wait

Can u use centre’s coordinates and point A to get gradient

Then get reciprocal for tangents gradient and get the eqn?

Oh but I don’t c how that tells what A is

*B

[versed crater]

Ok we know where A is

[dusk hamlet]

why you want to use the gradient ?

[vale reef]

i dont get how to find distance AB without B's coords

[vale reef]

idk im just trying to use the info there😭

nvm i got it

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[tranquil pine]

Heya! I need help solving

[rain crane]

Solving what

[tranquil pine]

Just simplifying it

I mean rationilizing it

[rain crane]

What's the square root of 39?

[tranquil pine]

Sorry

There is no square root of 39

[vital crag]

multiply top and bottom by the conjugate

[tranquil pine]

RAHHHH

Ok

Well that work doesn't even work

Let me post original problem

[vital crag]

!show

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Show your work, and if possible, explain where you are stuck.

[tranquil pine]

The thing is, it all started out with sum and difference formulas

But I think I did something wrong at the beginning so now I am forced to return to the beginning

Let me try and do this again

🧟‍♀️ \

Ok

SO

Im almost done

[worldly vale]

you should show the original question and then show your work

[tranquil pine]

Ok I will

It's REALLY hard to read though because ive erased so much

;-;

Ill see if you guys can read my already terrible handwriting xD

[vital crag]

learning how to write readable math and english is an important life skill

[tranquil pine]

Sorry about the blue ink, I dont want people seeing my name

;-;

I don't know if I'm doing it right so far q-q

Ok Im doing something wrong I think

LET Me JUST RESTART ENTIRELY !

😭

Maybe I got the sides of the triangles wrong?

AHA

I THINK I FOUND IT

IT IS SQUARE ROOT OF 17 NOT 17

SMH

Uhm

You know what

I give up

I cant figure it out

[vital crag]

are you working on a new problem?

[vital crag]

did you get anything after doing this fix?

[tranquil pine]

nothng that makes sense ;-;

ill just ask my teacher for help tomorrow because im too stupid for this i guess...

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[limber plover]

I need help with (b)

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[thin cradle]

ok so for this question I put
x = distance travelled (yds)
and y = height (yd)

[thin cradle]

I got 2 as X

so im trying to find the vertex

So I currently have
(2, max height)

and i need to find max height

except when i plug 2 into the equation I get 2.8

and that isnt the right answer

wha tam i doing wrong?

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[cinder ore]

A fluid initially at 100C is placed outside on a day when the temperature is -10C, and the temperature of the fluid drops 20C in one minute. Find the temperature T(t) of the fluid for t>0.

T(t)=

I am just having issues attempting to make the problem

[modest birch]

are you told anything more about the shape of the temperature curve? or are you to just assume that it drops 20 C per minute?

[cinder ore]

Nothing more, i would have to assume drops 20 per minute

[modest birch]

so what don't you understand about the problem?

[cinder ore]

Just having issues, I thought it would be

T(t) 100e^-20t -10 but I was wrong

And I dont know what I am missing here

[modest birch]

oh so it's not that it drops 20 C per minute

it just drops 20 C in the first minute yeah?

[cinder ore]

I think so, the instructions fon fuses me a bit

[modest birch]

okay so did you try something like writing T'(t) = -k(T(t) + 10), T(0) = 100, T(1) = 90?

[cinder ore]

Wait, we are supposed to write it that way?

I don't really understand

[modest birch]

well

how did you get what you wrote?

[cinder ore]

I went from the initial value of 100, and knew I needed a equation that when inputting T, it would remove 20 every time.

@modest birch

[modest birch]

honestly this question is missing a lot of information

but your answer isn't it

you're going to need to get information about how the temperature changes

[cinder ore]

This is all it gives

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[cinder ore]

<@&286206848099549185>

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[dark wind]

So I need to solve this triangle. I found the angle C by law of cosines. C = 27.
Now I want to find the angle A. But when I use the law of sines to find the angle A I get 57. The law of cosines on the other hand yields 122. Why?

[final tangle]

ambiguity from the sine law

[dark wind]

So I should only use the law of cosines when trying to find the angles?

[final tangle]

if you don't want to bother with ambiguity yeh

[dark wind]

As in sine can yield 0 1 or 2 solutions?

[final tangle]

well there isn't an issue for the angles that aren't opposite the longest side

$\textbf{ambiguity of the sine rule / law of sines:}$ \
there are two solutions to
$$\sin(k) = c$$
where $0<c<1$ \
for $0 < k < 180\deg$ or $0 < k < \pi$

[soft zealot]

ℝamonov

[dark wind]

I remember now. Thanks

I can do 180 - 58 to get a second solution

[final tangle]

well there isn't an issue for the angles that aren't opposite the longest side
.e.g. 17m isn't the longest side, so you could determine B using the law of sines without worrying about ambiguity

[dark wind]

thanks

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[solar frost]

x²+9x+2=0
The answers are x1 and x2
x1>x2
Find x1-x2 without Solving quadratic formula

[solar frost]

We using vieta theorem

[amber holly]

Recall that $(x_1 - x_2)^2 = (\underbrace{x_1 + x_2}{-\frac{b}{a}})^2 - 4\underbrace{x_1x_2}{\frac{c}{a}}$

[soft zealot]

A Lonely Bean

[solar frost]

I think it's just x1-x2

Not in quadrat

Hello?

[amber holly]

So $x_1 - x_2 = \sqrt{(x_1 + x_2)^2 - 4x_1x_2}$

[soft zealot]

A Lonely Bean

[amber holly]

What's wrong

[solar frost]

Idk I have no idea keep going

[amber holly]

Just plug in the values of x1 + x2 and x1x2 according to Vieta's theorem

[solar frost]

9 and 2m

2*

81-8

It's 73

So √73?

Is answer?

[amber holly]

Should have been (-9)^2 - 4*2

Oh, right

Yeah this is it

[solar frost]

My math tutor didn't Tell me these formulas

😭

[amber holly]

This you mean?

[solar frost]

Yes not even that

[amber holly]

They shouldn't have given you an exercise with Vieta's theorem if they have not explained it yet

Although usually you are expected to come up with something like the first equation that I presented

[solar frost]

It's my first month going to tutor I ain't experienced with math

Anyways there are more like this

Look

We did 4th one

How do I do other ones

[amber holly]

x1^3 + x2^3 is even easier if you remember how to factor a^3 + b^3

[solar frost]

Remember? Never been taught

[amber holly]

a^3 + b^3 = (a + b)(a^2 + ab + b^2)

[solar frost]

Hm

[amber holly]

Alright wait I will write down all of those algebraic manipulations that you need

[solar frost]

Okay

[amber holly]

1. $x_1^2 + x_2^2 = (x_1 + x_2)^2 - 2x_1x_2 \$
2. $x_1^3 + x_2^3 = (x_1 + x_2)(x_1^2 + x_2^2 - x_1x_2) \text{ (relies on part (2) )}\$
3. $x^4 + y^4 = (x + y)^4 - 2xy(2(x^2 + y^2) + 3xy) \text{ (relies on part (2) again))}\$
4. Already showed you
5. $x_1^2 - x_2^2 = (x_1 - x_2)(x_1 + x_2) \text{ (relies on part (4) )}\$
6. $x_1^3 - x_2^3 = (x_1 - x_2)(x_1^2 + x_2^2 + 2x_1x_2) \text{ (relies on parts (1) and (4) )}\$

[soft zealot]

A Lonely Bean

[solar frost]

I'll save this thank you so much

[amber holly]

Hopefully this helps

[solar frost]

It surely will

You are such a good person

I'll go do the other ones on my own now

Thanks again

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[amber holly]

Dzma dzmistvisao shavi dghistvisao

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[strange shore]

1 is also a root of z^3 - 1

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[past mesa]

I've gotten to z³+az+iaz-a+2ai+a=z³-3z²+4z-2

[scarlet sequoia]

Normally you would need to apply cardan's method, but given that the question gives you an important piece of information...

[void valley]

c o n j u g a t e

[scarlet sequoia]

^ as he said, and that's because the polynomial has real coefficients

then, given two roots, just use a nice property roots have to find the last one...

[past mesa]

I've done that

(z-(1-i))(z-(1+i))(z-a)=z³-3z²+4z-2=0

[scarlet sequoia]

that's one possibility

you can then develop and get the answer easily by coefficient identification

but you can also use the fact that the sum of all the roots is...

[past mesa]

-b/a

Wow im dumb

[scarlet sequoia]

no it's alright

no one is dumb, we just sometimes forget stuff

[past mesa]

I constantly feel worried sick (literally) that im too stupid for exams and that I'm letting everyone down

[scarlet sequoia]

There might be a lot of pressure on you, but everyone has the potential to succeed in exams! You're not letting people down because at least I can see you're trying hard. Wishing you the best of luck for those exams in any case

[modern sentinel]

can you clear my doubt in help-16 if you are done here?

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[pure pollen]

$\int_a^b f(x) dx = \lim_{n\rightarrow\infty} \Sigma_{i = 1}^n f(x_i^*)\Deltax$

[soft zealot]

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

[pure pollen]

i dont understand this formula (i kinda wrote it wrong)

as in, where did each part come from

i just need some link to a website or video that explains this

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[wanton sentinel]

How was it solved i dont understand it

[tulip coyote]

Differentiating both sides of the original and using the FTC retrieves you f(x) in multiple places, and then rearrange for it by itself

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[atomic geode]

Need an answer check, I got B

[fossil geyser]

This seems like an exam or something?

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[marble cobalt]

And what happens with b * log(x) cause it disappeared

[marble cobalt]

Excersise A

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[tranquil pine]

So

I've gone ahead and done cosx(tan^2x-16) = 0

then I got cos x = 0

and tan^2 x - 16 = 0

then tan x = + or - 4

I went ahead and found the reference angle which is about 75.964 degrees

I think there is still one more oslution I can find for tan^2x - 16 = 0 but I am stuck there

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[rain crane]

yes?

[viscid bramble]

Yo what’s good Fucktalogist

@rain crane

I need to solve for x

[rain crane]

!status

[final saddle]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[viscid bramble]

6

[rain crane]

U never solved for x?

[viscid bramble]

I have

[rain crane]

whats troubling u

[viscid bramble]

This requires distributive law

And I got a answer but it’s wrong

If you use distributive law

You get:

4+4-2x = 3-10+2x

Am I right?

[rain crane]

yes

[viscid bramble]

Then group like terms?

[rain crane]

simplify both sides

[viscid bramble]

So therefor 8-2x = -7+2x

[rain crane]

yes

now bring x alone to one side

[viscid bramble]

Therefore if you add want to isolate 8 then you add 2x so then the equation will lead to -7+2x+2x which will be simplified to 8=-7+4x. Then to isolate 4x add 7 to both sides to make it 8+7 = 4x. Therefor 15 = 4x. So x = 15/4??????

[rain crane]

,w 8-2x=-7+2x

[soft zealot]

Results provided by WolframAlpha

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

Requested by Gooaaa#5829

[rain crane]

yes

https://tenor.com/view/well-done-congratulations-congrats-animated-gif-26559269

t!rep @viscid bramble

[fast palm]

Gooaaa has given @viscid bramble a reputation point!

[viscid bramble]

So if we substitute this into the equation we get the same answer

[rain crane]

both sides will be equal yes

[flint echo]

who here helps with math?

[rain crane]

no one

[tranquil flume]

y!rep @tranquil flume

[flint echo]

huh

[tranquil flume]

Lmao I kiss the mirror

[rain crane]

no one helps with math in mathematics server

[flint echo]

then whats the point

[viscid bramble]

Thanks broski. Sorry for wasting your time

[tranquil flume]

#❓how-to-get-help

[rain crane]

its not like i was helping ahmad few seconds ago!!!1

[viscid bramble]

😅😅

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[vale python]

i was trying to prove this by saying that the dimension of the eigenspace corresponding to lambda 2 is greater than or equal to 1, and that the sum of the dimensions for both eigenspaces is at most n. so then i could manipulate those two statements along with the assumptions to say the dimension of the eigenspace for lambda 2 has to be 1, making A diagonalizable

[worldly vale]

Pretty much it yeah

[vale python]

okay, but is it actually true that the sum of the dimensions is at most n? and if so, why? i was hoping there was a theorem in my textbook that stated something along those lines directly but I couldnt find anything

[deep vector]

eigenspaces of different values form direct sum

[vale python]

what is a direct sum?

[deep vector]

bruh why are so many curriculums so bad, determinants before direct sums

it means what A \setsum B is linearly independent

[vale python]

im looking at the textbook and it looks like direct sums is the next section

[worldly vale]

A shorter argument is just that there is some eigen vector in the λ_2 eigenspace, linearly independent from any n-1 LI eigenvectors in the λ_1 eigenspace

[deep vector]

where A is a basis of V_1, B is a basis of V_2

[worldly vale]

So you have n LI eigenvectors hence diagonalisable

[vale python]

oh yeah i like that

that makes perfect sense, thank you!

[worldly vale]

You don't technically need to prove the 2nd eigenspace has dimension 1

Even tho it is true

[vale python]

yeah that makes sense

thanks abunch!

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[mystic badge]

im confused on how the chain rule works with implicit differentiation - why can you take the derivative of the inside term if the variables disagree and then add dy/dx in that case?

[worldly vale]

y is really a function of x

Its (y(x))^3

A composite of two functions

Hence the chain rule

[mystic badge]

why do you add the dy/dx tho?

[worldly vale]

That's what the chain rule tells you to do

"Derivative of the outer function times the derivative of the inner"

[mystic badge]

ohhhh i think i understand

i dont know if i fully grasp it but i think i will if i do some more practice with examples

thank you so much

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[shell seal]

I don't understand how I would make the equation to solve this

[north inlet]

Can somebody please help me with this?

[north inlet]

bruh

<@&286206848099549185>

here first

[final saddle]

Please read #❓how-to-get-help

[hybrid heath]

ah

[grim badger]

First, read #❓how-to-get-help, someone else has this channel

Second

[hybrid heath]

sorry merc

[final saddle]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[hybrid heath]

anti-simp barely beat you

[north inlet]

dang

[hybrid heath]

What are you trying to find? NM? x?

[shell seal]

first the x value which i would plug in to find nm

I understand how to do this one, but i am not sure how i would do it with the two equations in the previous image.

[hybrid heath]

hmmmm

[cold gorge]

How would you do this one?

Because it's exactly the same...

[shell seal]

12^2 = 8 * x
144 = 8x
x = 144/8
x = 18

[cold gorge]

Not quite.

It should be 12^2 = 8 * (8+x)

[shell seal]

oh ok

so i would get 10

[cold gorge]

Similarly, you can use the same for your problem.
MN^2 = ML * MK

Can you atleast form an equation for this?

[shell seal]

(x+3)^2 = 16 * ( 16-3)

[cold gorge]

That's wrong.

The LHS is right.

What's the length of ML?

[shell seal]

9?

[hybrid heath]

Are we assuming that the line KN goes through the center of the circle?

[cold gorge]

No.

We are assuming MN is a tangent.

That's all.

[cold gorge]

No.

ML is x-3 as in the figure. Unless we are looking at different figures.

[shell seal]

So just x-3 * 16

For rhs

[final saddle]

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[oak arrow]

transitive means if a < b, and b < c, then a < c, right?

[oak arrow]

on more question. So according to my notes, if X is the set of all students at my school, and xRy means y takes the same course as x, i have that this statement is reflexive, symmetric, and not transitive.

Then I have that if X is the set of all students at my school, and xRy iff y has the same birthday as x is reflexive, transitive, and symmetric

but those 2 statements seem identical to me (logically)

is the second one only all 3 because it's an if and only if?

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[violet compass]

Need help with some calculus multiple choice questions.

[violet compass]

Can someone confirm this?

[fickle crater]

asrk

what are indeterminate forms in calculus?

@violet compass

[violet compass]

Forms that are undefined

[fickle crater]

there are a total of 7

can you name them?

@violet compass

0/0
∞/∞
0 * ∞
∞ - ∞
1^∞
∞^0

these are indeterminate forms

do you know logically why 1^inf is indeterminate?

[violet compass]

Yeah ok, I knew all of these I was just confused at option 3. Forgot that infinity - infinity is the indeterminate form

ty .close

.close

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[fickle crater]

aight

gl

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[unborn wave]

part c