help-38

[dawn trellis]

I think I know what it means by what congruence statement but I’m not sure how to do that at all

Nvm I got it

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[halcyon beacon]

I need help with some math homework

[halcyon beacon]

Can someone help me with my math homework? Does that work with the just ask thing?

[lethal anvil]

what we're asking is to post the problem and state what you're having issues with

please

[halcyon beacon]

Okay I'll do that

I'm very bad at math

[ancient sable]

It goes from -5 to -4 so not linear if that’s the question

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[halcyon beacon]

Oh I thought there was more to it lol

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[pseudo wasp]

can someone help me with this question?

[trim lichen]

which part?

[pseudo wasp]

erm the whole thing

[trim lichen]

okay

let's say you clip the 4th and 5th columns off A and row-reduce the rest

i.e. [a_1, a_2, a_3]

what will you get?

[pseudo wasp]

identity matrix

[trim lichen]

right

now keep that in mind and read the hint

[pseudo wasp]

okai

oh wait

OH

okay lemme write the answers down

then ill sen dhere to calrify

like this?

[trim lichen]

yup

[pseudo wasp]

ah okay

then the basis for the row sapce would be the first rows

first three*

then column space would be the first three columns

[pseudo wasp]

actually how would I get the column space?

i thought i need the original matrix for that

[trim lichen]

sure you do

well, you have all the info you need actually

{a1, a2, a3} is LI in R^3

[pseudo wasp]

hmm since theyre LI, can i use the RREFed form of those vectors?

like the {1,0,0}, {0,1,0}, {0,0,1}

ah wait

[pseudo wasp]

A needs to be 4 x 5

think this makes more sense

[trim lichen]

you are conflating a vector space with its basis...

[pseudo wasp]

whats conflating

[rugged latch]

Mixing one up with the other

[pseudo wasp]

Umm where

[pseudo wasp]

Where is that happening lol

[rugged latch]

No clue, i don’t know this stuff too well sorry, I was just saying was conflating meant lol

[pseudo wasp]

Oh LOL

Okay ty

[rugged latch]

I actually just had my test on vector spaces, lin independence, basis, and that stuff today

But that’s beside the point

[pseudo wasp]

Lets wait for Ann

[rugged latch]

Yep

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@pseudo wasp Has your question been resolved?

[amber python]

hi

you need to write span

span{{1, 0, 0, 1, 0}, ...}

otherwise youve just got a basis

[pseudo wasp]

MY SAVIOUR

I mean

Me

Bht hi

[pseudo wasp]

Erm gimme 5 mins pls

Dont go

[pseudo wasp]

Bruh i ended up taking

35 mins

Ok i think i gtg

LOL

Later yes @pseudo wasp

@amber python

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[stiff prairie]

Can somebody help me with probability I am struggling

[mental tundra]

what is it?

[stiff prairie]

Question 6

[mental tundra]

ok what did you try?

[stiff prairie]

I tried doing the tree diagram but I suck at it

[stiff prairie]

Do u know

[meager surge]

I'm not the best at probability but I'm fairly certain you can just do q6 by multiplying fractions
So for example in i), with replacement the pr of two red balls would be 7/13 x 7/13

And without 7/13 x 6/12 without replacement

For part three just multiply the probability of getting a black first, then a white with the probability of getting a white first, then a black

And part five, it'd be subtract the probability of pulling no white balls from 1

[stiff prairie]

Thx

[stiff prairie]

Than answer is correct tysm

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@pseudo wasp Has your question been resolved?

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@pseudo wasp Has your question been resolved?

[pseudo wasp]

hi

but i thought they are asking me to find the basis?

[pseudo wasp]

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[untold sorrel]

Determine the domain of analyticity for f(z) = Log(−2+i−z).

[untold sorrel]

where should i go after plugging in x+yi

Is this correct?

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[brittle blade]

how does one answer this?

[fringe minnow]

so its 52.4 + 0.06991 repeating

just find 0.06991 repeating as a fraction

and then add on 52.4

@brittle blade

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[brittle blade]

how do i find this?

[fringe minnow]

do you know how to find like 0.01 repeating as a fraction or

any repeating decimal ?

its same concept

[brittle blade]

i dont recall

[fringe minnow]

urm so

set x = the decimal

so like

x = 0.99999999999999999

10x = 9.999999999

9x = 9

because the .99 repeating cancel each other out

9x = 9

x = 9/9

that might be a bit confusing because 0.9 repeating is equal to 1 lol lemme do a different one

x = 0.0111111111

10x = 0.1111111111111

9x = 0.1

0.1/9 = x

or 10/90 = x

so basically ur setting 0.06991 to x

and then finding like 10000x or whatever and subtracting

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[pseudo wasp]

Hi can someone tell me how why does this question i) use the normal dist for multiple samples?

[pseudo wasp]

If i were to see it by itself, i would think that its using the normal normal distribution

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[pseudo wasp]

<@&286206848099549185>

[zinc ginkgo]

there are 4 samples

4 is considered "multiple"

[pseudo wasp]

but i remember doing something like:
the sum of 4 pens is taken from bla bla, what is the probability rhat the total weight > 40

and i did somehting like

Let X_2 be the new random variable bla bla

~N(4 * mean, 4^2 * s,d,)

whats the difference?

[zinc ginkgo]

how do sum and mean relate to each other?

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[pseudo wasp]

Oh wait

Nvm i see it now

Thanks

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[dense hazel]

Why is this wrong

[dense hazel]

<@&286206848099549185>

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[dense hazel]

<@&286206848099549185>

Seriously no one?

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[dark lily]

I only dont understand the part circled in red. What definition is it? If they mean the sin(theta)=s/l I understand it. However theta is written without the sin. So i am confused. Elaboration will be apreciated!

[dusty saffron]

sine refers to triangles (mostly), this definition is the arc length formula s= theta* r… (or in this case r = l

[dark lily]

clear thanks

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[dark lily]

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✅

[dark lily]

@dusty saffron so, do you understand this then?

It is the same arclength formula

but why does the derrivative of theta, make the outcome of the equation be the velocity

[dusty saffron]

it’s because theta is a function of time

you can say this

[solid kiln]

Larry the Cucumber

[dusty saffron]

the length l will always remain a constant (assuming the string never is a ridgid object), so we can say that’s a constant

however, the angle theta will change as time goes on so we define both the arc legnth and theta as functions of time

[solid kiln]

Larry the Cucumber

[dusty saffron]

then if you differentiate that quantity you will get the result from above

[dark lily]

wait i understand everything youre saying but I dont have to differentiate this last one right?

We differentiate theta(t)

and thats our velocity

and then we can put that Theta(t)' into the arc length formula

[dusty saffron]

remember that velocity refers to a change in some distance, if you differentiate the theta funciton you’ll get the rate that the angle changes not the distance

also

I think you’re saying that you should differentiate just theta(t)?

but you have to differentiate both sides of the equation for it to hold true

[dark lily]

yeah I said it a bit wrong

I meant the differentiation of the x and y which are functions of theta

[dusty saffron]

ohhh

wait

I’m confused

could you repeat your question?

[dark lily]

I think you explained it very clear. Thanks a lot!

[dusty saffron]

sounds good! do you still have anything that you’re unsure about?

[dark lily]

not right now, but probably very soon

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[pearl wren]

How to graph?

[edgy cedar]

Linear equation

[pearl wren]

I'm trying to convert this into y=mx+b but failing to

[edgy cedar]

What’s your y in this case?

[pearl wren]

Im doing t for y

[edgy cedar]

Then t=-s+10 is what you want

[pearl wren]

I graphed and I got (6.5,3.5)

[edgy cedar]

What’s that?

,w plot y=-x+10

[solid kiln]

Results provided by WolframAlpha

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Requested by Pure#9389

[edgy cedar]

Ah yeah that’s right

I didn’t see the first eq

I don’t know why you’re tryna graph them

Just solve them simultaneously

[pearl wren]

I have to graph this system, teacher said so 😣

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[grave spruce]

How can I find the equation?

[grave spruce]

What’s Y for red?

Anyone help me?

I am trying to find the equation for Y and first one is green then red

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[gusty pine]

HWLP

[gusty pine]

<@&286206848099549185>

[mental tundra]

what don't you understand?

[gusty pine]

how do I solve it

Or get started

[mental tundra]

first, you want to simplify both numerator and denominator

do you know what tan(360 - x) can be converted to?

[gusty pine]

no

Is it

tan(2pi - x)

[mental tundra]

yeah but we can simplify it further

[gusty pine]

How so

[mental tundra]

tan(2pi - x) = -tanx

[gusty pine]

Ok

And the denominator goes to what

[mental tundra]

there's also a formula for that. find it out

[gusty pine]

cot x

ok

-t^2

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[glacial pike]

Why is 7^6 wrong? How does the 7^6 become negative so that it gets placed in a fraction?

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[glacial pike]

<@&286206848099549185>

[stable jacinth]

Read the explanation. "Negative exponent rule"

[glacial pike]

I did but I didn’t fully understand it

[stable jacinth]

So if the exponent is negative, you can remove the negative by just putting everything in the denominator with 1 in numerator.

a^-n -> 1/a^n

[glacial pike]

Yeah but I though I could bring 7^-4 underneath the fraction and combine it 7^9 and then subtract 7^3

[glacial pike]

If you get what I mean

[stable jacinth]

You are subtracting 7^3 - 7^9 = ?. Not the other way around. This creates a negative exponent of 7^-6 and using the "negative exponent rule" remove the negative from -6 and put the 7^6 in the denominator with 1 in the numerator which brings 1/7^6

[glacial pike]

I think I understand now I see umm

I think

[stable jacinth]

So what is 7^3 - 7^9?

[glacial pike]

-7^6 and then I have to fraction it right???

[stable jacinth]

The 7 isnt the negative. The exponent is. 7^-6

^ means exponent

[glacial pike]

Oh yes yes woops

[stable jacinth]

Totally fine. And then you get 7^-6 which you use the exponent rule.

[glacial pike]

Okay I think I get it Thank you so much!! 🙏

[stable jacinth]

Welcomee

[glacial pike]

Much appreciated!

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[steel widget]

how do i do this problem?

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[steel widget]

<@&286206848099549185>

[steel widget]

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[storm cave]

can someone please help me with c and d? i dont know what i did wrong for c and i don't know what to do for d

[storm cave]

can someone please help? thank you

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[zinc ginkgo]

Show your work

[storm cave]

so for 3c, given that volume is 4/3πr^3

i multiply 50000 by 3/(4π)

and then cube root

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[mint peak]

where is a mistake?

L are languages, h^{-1} is homomorphism

[valid moss]

you mean isomorphism?

[mint peak]

homo

[valid moss]

if h is a homomorphism then h^-1 doesn't make much sense

[mint peak]

inverse homomorphism

[trim lichen]

are we told h has an inverse?

or does the h^-1 in the first line refer to preimage

because i think it refers to preimage

[valid moss]

beat me to it

[mint peak]

we are given only homomorphism

[valid moss]

(what language is that btw)

[mint peak]

slovak

[mint peak]

no

[trim lichen]

thought so.

that means $h^{-1}(L)$ is NOT the image of $L$ by $h^{-1}$ as you're treating it.

[solid kiln]

Ann

[mint peak]

hmm

then why second inclusion works

[trim lichen]

second inclusion?

do you mean the reverse inclusion?

[mint peak]

yes, reverse

[trim lichen]

somehow i get the impression that showing you the proof and walking through every step of it will not satisfy you.

i don't know if i should read your question as

Now that you have explained the mistake in my mis-proof of the inclusion h^-1(L1L2) ⊆ h^-1(L1)h^-1(L2), I am adamant that the same reasoning can be applied to a seemingly legitimate proof of the REVERSE inclusion. Explain to me why I am wrong.

or as

I am now confused as to why the same argument does not work to brand a proof of the reverse inclusion as faulty.

[mint peak]

Second one I would say

But if it's easier I can watch some videos on this topic

Probably i wont find something related to formal languages

Maybe sets in general can be enough though

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[dense hazel]

Why is this wrong someone please help

[warm phoenix]

yes come voice call

I am an expert

@dense hazel

[dense hazel]

Uhh I can’t voice call oof

Could u just write it?

Well then, ig not

<@&286206848099549185>

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[dense hazel]

<@&286206848099549185>

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[dense hazel]

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[fallow spruce]

$x_1 ,x_2 , x_3 ,x_4$ are the roots of the polynomic eq find x_1^2 +x_2^2+x_3^2+x_4^2

[solid kiln]

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

[fallow spruce]

<@&286206848099549185>

[opaque lance]

How'd you find a^2 + b^2 + c^2 + d^2 if you knew a+b+c+d, abcd, ab+ac+ad+bc+bd+cd, abc+abd+acd+bcd. That's all I can think from relationship between roots and coefficient of a biquadratic polynomial..sorry for typing for long time..

[fallow spruce]

does a^2+b^2+c^2+d^2 even have some kind of formula can t even find it on google

[opaque lance]

I'd place my bet on (a+b+c+d)^2 formula but that seems out of place

Or something like integration as that would make square from linear function but I don't know how d we bring calculus here

[fallow spruce]

the (a+b+c+d)^2 might work

[opaque lance]

Yep might work

[fallow spruce]

yeah in the formula there are the a^2+b^2+c^2+d^2 and 2ab + 2ac + 2ad +2bc +2bd+2cd and factoring 2 from that we end up with a formula that can be used

[opaque lance]

Yes

[fallow spruce]

well thx for the help going to finish it a bit later

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[pseudo mantle]

Hello everyone, I'm having trouble with a calculus problem. I need to find the derivative of a function. y = sqrt(11x+sqrt(11x+sqrt(11x)))

[pseudo mantle]

I am using the chain rule, but cannot find the combination of f(g(h(x))) (or longer) that is correct.

obviously, the first one would be something like
f(x) = sqrt(x) or f(x) = sqrt(11x+x)
but every time I try to make it deeper it doesn't work
if its f(x) = sqrt(x) then g(x) = 11x+sqrt(11x+sqrt(11x))
which is correct, but still can't differentiate that.
if I make h(x) anything then it doesn't work
if f(x) = sqrt(x), then g(x) can be something like 11x + sqrt(x)
which so far would give y = sqrt(11x+sqrt(11x)
but then you can't go farther
idk what to do

I can solve it once I find what each chained function is

[zinc ginkgo]

you need way more functions

[pseudo mantle]

yeah i figured

[zinc ginkgo]

use f_1, f_2, f_3, ...

[pseudo mantle]

this other problem im working on has 6

but it was a lot easier since it was all trig functions

[zinc ginkgo]

go inside out

f_1(x) = sqrt(11x)

or even f_1(x) = 11x

[pseudo mantle]

yeah it would have to be that

then f_2(x) would be sqrt(x) probably

but now what would f_3(x) be

not 11x+x

my brain

thx for the help btw @zinc ginkgo

this one here is similar in that I got no clue how to separate these things

here's another one

since these are popping up then there must be some way to change it so that we only substitute certain parts?

on the last one, if the outermost one were x*sqrt(x) then obviously that wouldn't work

but if we said it was x*sqrt(a) then we can make the next lower one f_n(a) = something

are you allowed to just do that? my textbook made no mention of it

ironically, this homework assignment has video examples to help me out, yet not a single one of these seemingly unseparable equations have one :/

on second thought the last one uses the product rule

[trim jolt]

@pseudo mantle Has your question been resolved?

[pseudo mantle]

yeah still trying to figure this out

<@&286206848099549185> I need help 😦

[pseudo mantle]

ill figure it out eventually

[slow swallow]

which one you need help?

[trim jolt]

@pseudo mantle Has your question been resolved?

[pseudo mantle]

the very first one at the beginning of my help post

basically, i don't know how to break the equation down

[trim jolt]

@pseudo mantle Has your question been resolved?

[jagged chasm]

hm

[jagged chasm]

yea that’s ez

[jagged chasm]

@pseudo mantle

check my work please

that last number is 121x/8 in the sqrt

[pseudo mantle]

sry i was gone

am back now

[jagged chasm]

all good

[pseudo mantle]

hey if im reading this correctly @jagged chasm it's this?
\frac{1}{\sqrt{\left(\frac{121x}{8}\left(11x+\sqrt{11x+\sqrt{11x}}\right)\left(11x+\sqrt{11x}\right)\right)^3}}

wait hold on that didnt work at all

[jagged chasm]

bro i have no idea if it’s right

i just kind of cranked something out

[pseudo mantle]

yeah its not is the issue

thanks tho

[jagged chasm]

let me try something

maybe you have to multiply out what’s on the bottom

[pseudo mantle]

no it accepts un-simplified answers

i havent even submitted that response yet

but graphing calculator says no

[jagged chasm]

oh i see

[pseudo mantle]

well anyways my dad is home currently and hes an engineer so ill go ask him

[jagged chasm]

i’m wondering where i went wrong

i think everything is correct

up until

i try to mush the chain rule togeyher

[pseudo mantle]

graphed, it gives results that are very close to zero at all times

[jagged chasm]

yep

super tiny

[pseudo mantle]

well it should look similar to the right half of 1/x

anyways brb

[jagged chasm]

ah i see where i went wrong

it was the chain rule axtually

ok

one more time

this is good this is correct i think

now we must simplify ourselves into hell

😊

i will leave that to you

have fun

[trim jolt]

@pseudo mantle Has your question been resolved?

[pseudo mantle]

@jagged chasm My dad any I tried to solve this problem for like an hour at least and we couldn't do it, also your answer doesn't look correct still. He's taken calc III and even he's stumped. I have no idea what kind of torture problem this is but it's weird

[jagged chasm]

Mine is right it’s just not simplified

I can simplify it a bit more

graph checks out too

Yep

My answer should be good

@pseudo mantle

[pseudo mantle]

yeah, that worked. It's interesting that simplifying made it work

thanks for the help

[warm kernel]

".close" when done btw

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[devout rapids]

I have to write this in the shortest possible form

And i have the answer but i don’t know how they came to that conclusion

Its about question 10 a

[tranquil scaffold]

just keep applying these laws until you get a simple surd

they first expand the bracket

and then just keep applying the laws

[devout rapids]

What is the law of surds

I’m new to math

[tranquil scaffold]

its right there

surds are numbers in the form of
$\surd{b}$

i dont know the latex for this one oops

[solid kiln]

moik

[tranquil scaffold]

ok anyway, its just a list of facts when youre dealing with roots

it is always true

its like $aa = a^2$,
that is a fact just like \surd{b} * \surd{a} = \surd{{ab}}$

[solid kiln]

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

[tranquil scaffold]

ok i really suck at latex but you get the idea right

[devout rapids]

Yeah i get it thanks!

[tranquil scaffold]

try learn that law of surds sheet

[devout rapids]

Yeah i’ll just learn it through that

[tranquil scaffold]

yeah as you're doing through ur questions, have a check back and see if you can apply any laws

eventually try do it without the sheet to remember it

good work!

[devout rapids]

Thankyou!!!

.close

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[fallow spruce]

.close

.close

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[frosty anchor]

what is the thought process behind discriminant =0?

[long basin]

A tangent line only intersects a curve once

If it was greater than 0 it'll become a secant line

[frosty anchor]

But this is a tangent at one point, which does intersect the curve again

[long basin]

Locally

Intersects once locally

So concavity

Once it changes concavity it may intersect the function more than once

[frosty anchor]

Ive not studied concavity yet, so im not sure what you mean

[long basin]

Concave down, concave up

The pink is what we call an "inflection point"

Where the function will change concavity

A tangent line is tangent to a curve locally, is its formal meaning

Meaning a region of similar concavity

[frosty anchor]

And does the curve y=c/(x+1) have any inflection points?

[long basin]

Uh

If c is a constant

[frosty anchor]

It is

[long basin]

I mean

Not really

No

The second derivative never equals 0 so there's no inflection points

It does change concavity because it's asymptotic to x=-1 and the denominator's leading term is x with an odd power

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[frosty anchor]

alright

.close

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[drifting crow]

I need a hint for this problem

[solid kiln]

kawaii_pear

[vital linden]

idk sorry

[drifting crow]

It's a weird problem it's okay

[vital linden]

what is this lol

[drifting crow]

idk

could you post this somewhere else?

[vital linden]

ok sure sorry

[drifting crow]

<@&286206848099549185>

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[drifting crow]

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[final nexus]

$$y'''-11y''+30y'=40e^x$$

[solid kiln]

2003 Honda Accord

[final nexus]

I can't seem to to find a good guess for the particular solution.

I am aware of superposition in differential equations, but all of the guesses I've tried always seem to end up being the same as the homogenous solutions or fundamental solutions.

I have tried $$y_p=(Ax+B)e^x$$ and other relevant forms.

[solid kiln]

2003 Honda Accord

[boreal dome]

did you try y_p = Aexp(x) ?

[final nexus]

Wouldn't that end up being the same as the homogenous solution such that the particular is "absorbed"? I found the homogenous solution to be

$$y_c = c_1 + c_2e^5t + c_3e^6t$$

[solid kiln]

2003 Honda Accord

[final nexus]

Oh wait, I just realized they are raised to different exponents and so are not the same

[boreal dome]

hmm let see
Ae^x -11Ae^x +30Ae^x = 40e^x
(20A)e^x = 40e^x
A = 2

[final nexus]

long morning I guess, haha thanks

.close

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[dense scroll]

ive proven it is increasing but how do i prove it is bounded above?

[supple oriole]

Wuh

How would one easily turn that into a continuous function...

Like there is a much easier way to do that

The question was how to prove it's bounded

That is to say, that it has a limit

[dense scroll]

right so assume its bounded by assumption, then find that supremum?

[supple oriole]

Isn't trying to solve for the limit without proving it exists first how you get the -1/12 thing

[subtle lava]

1. that's series using riemann rearrangement theorem
2. in this question you need to get an estimate of an upper bound
3. Once you have the estimate you don't use the fact it converges in your proof

[supple oriole]

The initial question was how to prove it's bounded above

Nothing you've said helps with that

[dense scroll]

yh true that proves that if its bounded then it converges

[supple oriole]

So as for proving it's bounded above

[dense scroll]

i need to somehow show that each consecutive phi is increasing smaller and smaller?

or whatever that symbol is

[supple oriole]

No

Oh wait yes sorta?

[dense scroll]

how would one get to that

[supple oriole]

Well in this case I wouldn't do that directly

Just look at the rule for getting each phi_i

You're adding two things, can you bound both of them above?

One of the things is just 1 which is trivially bounded above by 1

(that's a confusing way to put it)

So can you bound $\frac{\phi_i}{1+\phi_i}$ above by something?

Texit hello

$\frac{\phi_i}{1+\phi_i}$

[dense scroll]

well the numerator will always be smaller than the denominator

i think

[supple oriole]

Right

So what does that mean

[dense scroll]

its less than 1?

[supple oriole]

Yup

[solid kiln]

Gamma is an Algebraic Number

[supple oriole]

So each phi_i is the sum of 1 and something less than 1

[dense scroll]

right

oh so its bounded by 2

[supple oriole]

Right

[dense scroll]

ahhhhh

ur a beautiful man/woman

or some other gender

thank u

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[fading ledge]

help

[fading ledge]

anyone pls helpme

plsss

[naive crest]

connect A and B by a segment, and use that the sum of the angles in a triangle is 180°

[fading ledge]

can u send the sol

[naive crest]

so you want the solution, not help

[fading ledge]

yup

[naive crest]

c)

[rugged latch]

This isn’t the right place for u then

[fading ledge]

😦

why

[civic bloom]

first find angle bca, then use sum of all the angles of quadrilateral is 360

You will get your answer

[rugged latch]

#❓how-to-get-help

[fading ledge]

ok

[fading ledge]

oki thanks

thank you so much

.close

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[true fjord]

All organisms contain C-14. When the organism dies, the amount of C-14 begins to decrease with a half-life of 5740 years. The remaining amount of C-14 as a percentage of the amount of C-14 at the time of death can be described by an exponential function, f(x)=b·a^x , where x denotes the number of years after the time of death of the organism.

a) Determine a. 5740=log⁡(1/2)/log⁡(a ) a=1/2^(1/5740) ≈0.9998792 (solved)
b) Write down the calculation formula. We are informed that in some dead organic matter the remaining percentage of C-14 has been measured at 90%.
c) Now calculate how many years have passed since the time of death

[lapis spear]

Just substitute the value of a and u get the calculation formula

For c, b.a^x at x=0 is b

At some point of time x, it's 90% of b

So b.a^x=0.9b try solving that

[true fjord]

what exactly do you mean by substitute the value of a? as in f(x)=b*0,9998792^x?

[lapis spear]

That kinda seems vague, calculation formula to calculate what? That's the formula to calculate the amount after x years, yes

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[analog sequoia]

How do u do 11

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[hoary orchid]

A parabola?

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[analog sequoia]

.reopen

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✅

[analog sequoia]

idk

<@&286206848099549185>

[wraith hinge]

No

it's a circle

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[stoic robin]

Given this f:

[stoic robin]

How do I apply the chain rule to show the following expression? Mostly, how do I apply the chain rule, I dont see any inner functions

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[stoic robin]

I have tried this:

t must then be = 1 for it to work out, but why?

<@&286206848099549185>

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[pseudo atlas]

Given sin A =12/37, find cos A and tan A.

@silk helm

Help

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[river badger]

Find W(i) and then find all the roots of polynominal. Complex numbers. I don't know what to start with

[delicate bobcat]

hint:
2z^2 = z^2 + z^2

[river badger]

Tbh it tells me nothing. It's my first time doing smh like this with W(Z) and W(i)

[delicate bobcat]

$$W(z)=z^4-z^3+z^2+z^2-z+1=$$
$$=z^2(z^2-z+1)+(z^2-z+1)$$

[solid kiln]

Modus

[delicate bobcat]

= ...

[river badger]

Can i assume that w(z) = 0 ?

[delicate bobcat]

this is what you're trying to solve

Can't you proceed what I've done?

[river badger]

Ahhh bro thanks i was so confused because of this

I'm good nvm

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[alpine fern]

whenever this happens, do i convert the other side to +- and remove the absolute value?

[merry bluff]

Do you want to solve for x?

[alpine fern]

yeah

[merry bluff]

yes, then you get 2 equations, x + 1 = 3 and x + 1 = -3

[burnt cloud]

the absolute value is just x+1 since it's the distance between. If X is a negative number then say -3 it's absolute value is 3

I think

[merry bluff]

or x + 1 = 3 and -(x + 1) = 3 which is the same

[alpine fern]

how do i know that without memorizing it?

[merry bluff]

yes

[burnt cloud]

it's just a property of absolute values

[alpine fern]

right now i just memorized that whenever theres an abs value i convert the other side to +-

after simplify ofc

[burnt cloud]

the absolute value of a number is just its additive inverse basically I believe

[merry bluff]

that works, but how would you solve |x| + 2x = 3?

[merry bluff]

no, additive inverse 3 would be - 3 and |3| = 3

[alpine fern]

idk actually

how?

[burnt cloud]

@merry bluff sorry I misworded my statement then

[merry bluff]

the trick is not to replace the other side with +- 3, but replace the |x| with +-x, or in general the thing between | |

[burnt cloud]

Also consider that the absolute value is the numbers distance from 0

[alpine fern]

yeah ik

it just gets confusing when u dont know the value (x)

[burnt cloud]

well the absolute value of X is just X

[merry bluff]

just consider it as 2 cases, one where x is negative and one where x is positive

[burnt cloud]

it can't be negative

if x is negative it will be the positive opposite of X. If it's positive, it's just X.

because it's the absolute value of the number

or just the distance the number is from 0

so for Jelle's example |x| + 2x = 3 cookie what is X

[alpine fern]

either -1 or +1?

no

1 or 3?

[burnt cloud]

|x| + 2x = x + 2x = 3x=3= 3/3=X = X=1

sorry I don't know how to use the math function to display it properly.

I could write it out and SS if that is confusing

[alpine fern]

sure

[burnt cloud]

it's not saying x is = + or - X. An equation is stating equality between both expressions. So 3 must be equal to the expression on the left hand side. All that absolute value symbol is telling you is that even if that term was a negative number, it's absolute value must be positive. So in either case it's going to be positive X.

Does that make sense?

[alpine fern]

yeah

[merry bluff]

or if x is negative then -x + 2x = 3 => x = 3 but 3 is not negative so the only solution is x = 1

[alpine fern]

OHHHHH

so u basically just remember if x is negative or positive

so the cake is a lie

.close

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[wheat violet]

Is this statement true or false ?

M = {{0, 1}} is relation over {0, 1}

Please explain the solution because I want to comprehend the solution.
And maybe 2 thoughts from me about it:

1. {0, 1} is one set, but don't we need 2 sets to create a relation ?
2. Shouldn't a relation be a tuple and consist of ( ) brackets instead of {} ?

[wheat violet]

<@&286206848099549185>

[zealous lark]

M is a unary relation over {0, 1}

not binary

In general, an n-ary relation over the sets A_1, ..., A_n is a subset of the Cartesian product A_1 x ... x A_n.

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[wheat violet]

Thanks. So in this case I would need to multiply {0, 1} with itself ? {0, 1} x {0, 1} = {0, 0, 0, 1 } ?

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[wheat violet]

.reopen

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✅

[wheat violet]

And the answer to the question would be True, right ?

[zealous lark]

If the question is talking about a unary relation, then yes.

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[wheat violet]

Ok. Thanks

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[orchid sonnet]

Hello. Could you help me, what answer is the right one? Thank you.
// Find the Domain//

[orchid sonnet]

What’s the right domain ?

<@&286206848099549185>

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[cunning belfry]

Can ik the compound intrest fomrula?

[cunning belfry]

formula

[trim lichen]

surely this is the kind of thing that you can (and should) Google by yourself?

[cunning belfry]

Yup

But I get dif answers on dif sites

[upbeat lynx]

I see one answer on google

[cunning belfry]

Ty]

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[uneven hatch]

How do i do this

[nimble quail]

substitute p and q

[uneven hatch]

P is 5 and q is 2?

Do I not do (p/p-q) + (q/p-q)

[nimble quail]

p=3-2root(2) ; q=2-root(2)

[uneven hatch]

Yeah

[nimble quail]

solve it then rationalize the denomiator . try to remove the root sign

[uneven hatch]

Ok

[uneven hatch]

How do I solve

[nimble quail]

show me how far you got

[uneven hatch]

I am at the start

<@&286206848099549185>

[nimble quail]

did you substitute p=3-2√ (2) ; q=2-√ (2) in (p+q/p-q)? what did u get?

[uneven hatch]

(5-3_/2)/1-_/2

5-3sqrt(2)

Divided by 2 minus sqrt(2)

[deep compass]

Replace what you get

Then complete the sums and substractions

And then multiply by the reciprocal of the denominator

To ratiionalize

[uneven hatch]

So numerator times denominator

[deep compass]

Yes

You multiply both parts of the fraction by the denominator's reciprocal

[uneven hatch]

(5-3sqrt(2)) multiplied by 1-sqrt(2)

[deep compass]

This way we notabel products to get rid of the root in the denominator

[deep compass]

Look

When you multiply the denominator

That's a notable product

a^2 - b^2 = (a+b)(a-b)

You will get rid of the root

And just multiply normally the numerator with the denominator recyprocal

And you will get your m + n(-/2)

[uneven hatch]

Is . Multiply?

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@uneven hatch Has your question been resolved?

[uneven hatch]

So 5sqrt(2) - 6 numerator?

Is m+n(-/2)

And I divide it by -1

So it just inverts the symbols after that

[deep compass]

Yes

[deep compass]

no?

[deep compass]

Yes

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@uneven hatch Has your question been resolved?

[uneven hatch]

What is it

Isn't (5-3sqrt(2))×1+sqrt(2) that?

[tropic smelt]

No, show your work 🤔

[deep compass]

you are missing something when multipying (a+b)(c+d)

[uneven hatch]

Multiply by 1 doesn't do anything

[uneven hatch]

Was I right

[tropic smelt]

That doesn't mean that the result is 0, it means that the term doesn't change : a x 1 = a

[uneven hatch]

Yeah

5 times 1 is 5, it doesn't do anything

[tropic smelt]

You didn't write 5 here

You omitted it

[uneven hatch]

Where

[tropic smelt]

Here, you have 5√2 but not 5

You have omitted the result of the multiplications by 1

[uneven hatch]

Oh I see

5 and 5sqrt(2)

My mistake

[tropic smelt]

Also -3√2

[uneven hatch]

I see

This is why I got confused

[uneven hatch]

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[opaque dragon]

Which graph(s) satisfies the above conditions? I'm not understanding why D is incorrect, given the above conditions I belive the graph must be decreasing and concave up

[lilac wind]

f''(2)=0, its between a concave and convex part

on D that is

[vivid hearth]

^^ it is a point of inflection in graph D

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[opaque dragon]

Oh I see, I'm assuming E satisifies the conditions? It's concave up and decreasing

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[granite breach]

Got a question again:

f(P) = g(P-tP)

Task: Differentiate the function above by t and find an expression for dP/dt.

Im a bit confused because I thought that the differentiation by t is the same as dP/dt right?
But then I was wondering whether I need to do something with the function first because the numerator is dP

The solution is very confusing to me aswell, I cant really comprehend it.

I probably misunderstood something fundamentally. Can somebody explain to me how this task is supposed to be solved?

[inland orbit]

This is implicit differentiation

which means you can take the d/dt of both sides in order to find an expression for dP/dt

"I thought that the differentiation by t is the same as dP/dt right?"
dP/dt is specifically the derivative of P with respect to t

[granite breach]

I did that and ended up with f'(P) = g'(P-tP)*(-P)

But that is quite different from the solution. Did I miss a step?

[inland orbit]

You treated P as a constant, but the question implies that it varies with respect to t

Think of P as a function of t. As if P is short for the function P(t)

[granite breach]

ahhh

[inland orbit]

In fact, go ahead and replace P with P(t) if you'd like

[granite breach]

so whenever I have something like dP/dt (contrary to d/dt) I can assume that P can be expressed as a function of t?

[inland orbit]

Yes.

Because even if you're wrong and P turns out to be constant, then it's still true, you'll just find dP/dt = 0 in that case

[granite breach]

Got it thanks

Ill try solving it now

[inland orbit]

👍

[granite breach]

so If I differentiate (P-tP) that would be (P(t)-tP) which needs to result in (P'-P) right?

[inland orbit]

The second P is also a function of t

So you'd need to use the product rule for the -tP

[trim jolt]

@granite breach Has your question been resolved?

[granite breach]

youre right

but in the end the solution does not contain any P'(t) at all

[inland orbit]

Hm

[granite breach]

so I am wondering where those went?

[inland orbit]

For clarity I'm going to write P(t) for P

$$f(P(t)) = g(P(t)-tP(t))$$
$$\frac{d}{dt} f(P(t)) = \frac{d}{dt}g(P(t)-tP(t))$$

[solid kiln]

tatpoj

[inland orbit]

This is basically where we started, right?

[granite breach]

yes

[inland orbit]

On the left we get $f'(P(t))P'(t)$

[solid kiln]

tatpoj

[granite breach]

I can see that

[inland orbit]

On the right, we get $g'(P(t)-tP(t))\cdot(P'(t) -P(t) - tP'(t))$

[solid kiln]

tatpoj

[granite breach]

ohhh

thanks

I see the error I made

[inland orbit]

👍 no problem

[granite breach]

thanks for the thorough explanation

[inland orbit]

Sure thing

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[alpine fern]

how to solve

[deep compass]

???

wdym by "solve"

that's a function

it is telling you what you have to do if you have a certain number you want to evaluate the function with

but that's it

[deep compass]

do you have the full screenshot?

[alpine fern]

i meant solve for derivative sorry

[deep compass]

oh...

then I'm out xdn't, sorry

haven't seen calculus yet

or derivatives in general

i just know they exist

[split chasm]

consider
$$f(x) = e^{\ln(x^{4x})}$$

[solid kiln]

ℝamonov

[alpine fern]

why that

[split chasm]

why i used this or why it works

[alpine fern]

why u used it

[split chasm]

its much clearer how to differentiate stuff with a base of e

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[alpine fern]

what is the theorem?

i remember this

but i dont know the theorem

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[runic trail]

How can I determine if a sequence doesn't have a recursive formula?

[scarlet escarp]

is this in general or is it relating to something more specific

[runic trail]

If there's a general rule that would be helpful. I am working on a sequence and I found the explicit formula but the recursive formula seems non-existent

The explicit formula is (n+1)/n^2

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[runic trail]

Well thanks anyway
.close

.close

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[lavish kite]

Hi i need help about the last question pls

I got (theta (20))' = 0

[worn venture]

do you know the relationship between a graph and its derivative?

here let me

[lavish kite]

uh yes i think so

[worn venture]

If you wanted to find max value in the graph

It would be at the peak of the graph right

[lavish kite]

yes

[worn venture]

do you know what the gradient (1st derivative) is at the peak?

[lavish kite]

is this the derivative?

[worn venture]

The orignal graph

as an example

[lavish kite]

oh ok

[lavish kite]

sure, 0

[worn venture]

yeah

So at the peak of a graph. The gradients always gonna be zero

Thats how you find local maximums and local minimums

To justify if its a local max or a local minimum. You take any two points to the left and right and see if they are postive or negative derivative values

postive -> 0 -> negative = local max
negative -> 0 -> postive = local min

[lavish kite]

yes that makes sense

b

but

its a property

i dont know hom im supposed to explain it

[worn venture]

for the last question?

[lavish kite]

yes

[worn venture]

you would just talk about how the maximum value would be the local max of the graph. Which is when the derivative changes sign and hits zero

[lavish kite]

is it not a global max here ?

as the values decreases after to inf

[worn venture]

could be

I havent checked out the graph

I dont think they mind if you say local max or global max if thats the case

but generally i just say local max.

[lavish kite]

aight ill figure it out

ty

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[wind saffron]

A tank has a parallelepiped (or prismatic) shape, whose base is a square of side 15 m and whose height is 16 m, rests on a platform located 2 m above the ground. The tank is filled by pumping water from the ground through a pipe that flows into the bottom of the tank.

Find the depth of water inside the tank (in meters), when work T =γ - 15^2 - 48, where γ = 1000Kgfm3 is the specific gravity of the water. Note. The work T was expressed in the form given to facilitate the calculations to be performed.

I understand the statement like this: (drawing)

[wind saffron]

It’s correct my thinking? I don’t know how to set the integration limits

.close

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[north forge]

.close

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[sick stump]

Prove that if φ is a normal external measure in X and φ(X) < ∞ then a set B ⊆ X is
φ-measurable if and only if
φ(X) = φ(B) + φ(X\B).

[sick stump]

i have proven the first part but i cant do the reverse

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[zinc ginkgo]

might want to post in #advanced-analysis as well

[sick stump]

thanks

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[sand forge]

How do I continue for q11