help-17

[jagged cargo]

same concept though

i blame my handwriting for making 3 look like 5

[balmy delta]

Now do i do 5x-20=3^2?

to get 29/5

[jagged cargo]

just do it normally?

whats 3^2

[balmy delta]

9

[jagged cargo]

right

$5x-20=9$

[twin meteor]

FungusDesu

[jagged cargo]

now bring -20 to the rhs, what will the rhs be?

[balmy delta]

x is 29/5 right?

[jagged cargo]

correct

[balmy delta]

Thank you

Also did i do this one right? The problem is 4+(2^3x)=16. I got x=(ln6)/3

[vocal sleet]

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[sinful marsh]

Please help

[hushed pewter]

[sinful marsh]

How is the answer not 0.54? I did 1 - 0.46

[severe current]

I’m trying to see where you went wrong myself

[sinful marsh]

Yea u think this software broken?

[severe current]

Oh

Nvm

Read the question

Slowly

You went wrong somewhere

Under the blue

The blue part isn’t the question to solve

[sinful marsh]

U think they want one of the whole numbers?

[severe current]

Do you want me to paste the question they want the answer for

[sinful marsh]

Yers

yes

[severe current]

The fisherman doesn’t catch one or more fish when x fish are caught

[sinful marsh]

isnt that 0.54 than ?

since 1 - 0.46

or 1- 0.33 - 0.18 - 0.02 - 0.01 ?

[severe current]

How many fish are caught when 1 fish is caught

[sinful marsh]

0.33

[severe current]

That is the probability you caught one fish

That isn’t how many fish you caught when you caught one fish

[sinful marsh]

Oh shit , so 1?

[severe current]

So what’s the answer to the first question

[sinful marsh]

this one?

[severe current]

This

How many fish does the fisherman need to catch so the number of fish he has isn’t 1 or more

[sinful marsh]

would that be the sum of this?

[severe current]

No

[sinful marsh]

0?

[severe current]

Yes

Because 0 is the only amount of fish he can catch that isn’t 1 or more

The question wasn’t about probability lol

[sinful marsh]

Holy shit you were right

Thanks spenny

[severe current]

Np

[hushed pewter]

Spenny ftw

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[white hare]

This is gibberish to me 😭

[ancient knoll]

even if you skipped all the lectures on optimisation you can pretty quickly get to the answer just through linear algebra

(mostly because the constraint and objective here are both extremely lax)

[white hare]

i have no idea. we have no lectures and are just expected to know it. i don’t even know what linear algebra is 😭

[thin vale]

I severly doubt that is true

Do you have a textbook or assigned readings?

[white hare]

no. we were not provided with either.

[thin vale]

Again, I really doubt your class is giving you no lectures, no book, no readings and no notes or any relevant teaching material

[worthy citrus]

Use the technique developed in this section

?

[thin vale]

also the, **Need help? Read it / Watch it **

Have you clicked either of those

[white hare]

with all due respect, you are not at my school, nor in my class. we do not have any access to anything

[white hare]

yes. it’s a broken link

[thin vale]

These courses typically sell the homework and online textbook as a package deal

[white hare]

yes. we weren’t told what books to purchase because it “wasn’t necessary”

[thin vale]

Do you have a canvas course page?

[white hare]

a what?

[thin vale]

Your course

it is hosted online right?

What is it hosted on

[white hare]

webassign

[thin vale]

The homework is hosted on webassign

[white hare]

i’ve been in this class for a bit now. i know 100% there is no access to outside materials.

[thin vale]

but how did you get to the webassign page?

[white hare]

all students get a login code

gives us our course content

i appreciate y’all essentially calling me a liar about my school situation instead of helping me understand the topic. such great ppl 🫶

.close

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[white hare]

i already said it’s a broken link.

[vocal sleet]

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[plain aurora]

wait why is this line a contradiction again>

for proving divison with remainder

[thin vale]

because r-a is smaller than r, but r was the minimal element

[plain aurora]

thanks!

[plain aurora]

wait, but for this to make sense, wouldn't we require b-(q+1)a ≥ 0?

since otherwise, it won't even be an element of S

[plain aurora]

so how do we guarantee this

oh is it because q is undetermined

so pick, say, q=-1

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[plain aurora]

<@&286206848099549185>

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[vocal sleet]

@vast shale Has your question been resolved?

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[late jewel]

why is the answer a for 13?

[summer lichen]

It says that it’s concave up on that range so it makes sense that the velocity has a positive rate

[late jewel]

when its asking for when velocity of particle is increasing is it just asking for possitive acceleration?

[crisp zenith]

Yeah

When the second derivative(acceleration) is positive

[late jewel]

oh ok, that makes much more sense

im still having trouble with this one

the answer is w

e*

same graph from above sorry

i am having trouble mapping what this is asking to which derivative and what to look for

[jolly epoch]

speed is magnitude of velocity

[late jewel]

am i just looking for if velocity is possitive?

[crisp zenith]

I was kinda confuse about it also but aysob is right, since speed is magnitude of velocity you want to look for where the slope of the tangent line is increasing in magnitude. Magnitude is the size of the velocity, or its distance from zero. So it’s asking where |velocity| is increasing I believe. Which you can see from the graph of the original function but I can’t think of any way you could tell from the graph of the second or first derivative .

It looks like you might be able to tell from your extrema and inflection points. Maybe the trend to find the interval is you find an extrema and approach the next inflection point.

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[twin meteor]

to get positive k

can i divide by (x2-x1)

and then transfer the -k to the other side?

[crisp zenith]

Solve for k you can divide both side by (x2-x1) yeah and then multiply both sides by -1

[twin meteor]

ty!

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[sinful current]

idk how to do any of it and its due in 3 hours

q3 doesnt have to be done

pls 😦

[tidal dock]

which one specificially do you need help with

[sinful current]

all

my understanding is of sets, binary operations, modulo, truth tables etc but i missed a few weeks and i dont want to fail

the weeks missed couldnt be helped

[tidal dock]

which one do you want to start with

we won't give out answers here btw directly

[rancid turtle]

Since we are taking the set $5\mathbb{Z}$, to prove $(i)(a)$, Addition is closed given that the additional constant added is $5$, and since $5|5 \land 5|x \forall x\in 5\mathbb{Z}$. It is also associative. To find the identity element $e$: $a \bigoplus e = e \bigoplus a = a$. So, $a + e + 5 = a$ So, $e=-5$ is the identity element and $e \in 5\mathbb{Z}$. To find the inverse of $a$ which is $a'$: $a \bigoplus a' = a' \bigoplus a = e$. So, $a+a'+5 = -5 \implies a' = -10-a$. Since $-10\in5\mathbb{Z}\land a\in 5\mathbb{Z}$, all elements have an inverse as well. It is obviously commutative too and hence $(5\mathbb{Z}, \bigoplus)$ is Abelian $\blacksquare$

$\bigotimes$ is associative obviously (just prove it yourselves). The identity element $e$ is to be found such that $x\bigotimes e = x \implies \frac{xe}{5}+x+e = x$. So, $e = 0 \in 5\mathbb{Z}$ is the identity.

[twin meteor]

Marin Kitagawa

[tepid plinth]

u should go to youtube and learn basics of group theory

then try these questions

[sinful current]

i have 2 hours

is this doable

[tepid plinth]

thats more than enough

[sinful current]

okkkk

[tepid plinth]

seems to be basic

good luck man. hit me up if u need help

[sinful current]

will do ty

[tepid plinth]

well.. honestly its not really basic. but at least you'll be able to solve some of the complete thing bythe end of 2 hrs

• group properties
• abelian groups
• general and special linear groups
• permutation groups
• rings

[vocal sleet]

@sinful current Has your question been resolved?

[vocal sleet]

@sinful current Has your question been resolved?

[sinful current]

this has helped the most

i got 49 mins left to do it

learning permutation now

[vocal sleet]

@sinful current Has your question been resolved?

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[limpid geode]

how do i find a simple equation for this question

it seems that this is not simple IBP

[obsidian stream]

Not really clear why integration by parts wouldn't just work there, it'd help if you showed some work

[limpid geode]

i have work wait

here

Im not sure where to go from here or if I'm even correct

[obsidian stream]

well for one, x^n+1/x is not x

[limpid geode]

i just remove the +1

not the whole x^n+1

its still equal in the row

the x^n was just not placed

[obsidian stream]

I don't know what you mean by x^n was just not placed

[limpid geode]

whats the problem with my equation rn

except for the fact the x^(n+1)/x=x^n which i fixed already

[obsidian stream]

Well, for one, if you fixed something but then post something that has an error in it that you already knew about, that's annoying.

[limpid geode]

I saw it once you pointed it out... do you want me to post it again?

[obsidian stream]

No, your phrasing makes it sound like you already knew that and you just posted an old image

[limpid geode]

alright

[obsidian stream]

At this point that a-1 is inconvenient and stopping you from solving the problem neatly, either way you're going to need to use that recurrence relation

I would at least start by assuming that a is a positive integer and write down the form of the integral in that special case. Once you have that written down you can at least use it to see if it gives any hints for the next steps

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[near vigil]

how do i proof that this relation is symmetric relation?

[near vigil]

i dont understand how the left side is equal to right side

[tidal dock]

multiplication is commutative

[near vigil]

yeah, but the negation symbol above z2 and z1

[obsidian stream]

Write z_1 and z_2 as R1e^itheta1 and R2e^itheta2 and just multiply them and apply Euler's Formula

The fact that cos is even implies the relation is symmetric

[near vigil]

.close

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[warped rain]

hi

[warped rain]

what is that sign in the middle called

?

[mild flower]

which sign

[warped rain]

where. ?lim x-->0

[warped rain]

.

[mild flower]

limit?

oh the s thing

[warped rain]

yeah

[mild flower]

that's $\delta$, it's lowercase $\Delta$ and I don't know why they're using it

[twin meteor]

hayle-girl

[warped rain]

yes this d

so the name of it is delta

?

[warped rain]

?

[mild flower]

yes

it just means change, like uppercase delta

[warped rain]

but what sign is used in partial diff

[warped rain]

yup

[warped rain]

?

[mild flower]

$\partial$

[twin meteor]

hayle-girl

[warped rain]

are they same

?

[mild flower]

$\partial\delta$

[twin meteor]

hayle-girl

[mild flower]

they're different

[warped rain]

ohhhhhhhh...

🫡

omg ....

what is the name of the one on the left

[warped rain]

?

[mild flower]

it's not a greek letter

[blissful fable]

i think we just call it "partial" or sometimes "del" although "del" can also have another meaning

[warped rain]

no but it has to have a name

if i recall correctly its called something like dough

[warped rain]

?

what do u think

[blissful fable]

oh yeah some people call it "doh"

[warped rain]

oooooohhhhhh kkkkk

thanks both of ya

[vocal sleet]

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[vivid frigate]

I GOTTA SOLVE THE DIFFERENTIAL EQUATION

[keen umbra]

ok

chill

[vivid frigate]

im gonna kms

gawdam pressure

[keen umbra]

so this is a seperable equation

[vivid frigate]

indeed is

[keen umbra]

So do you know how to start?

[vivid frigate]

i do

[keen umbra]

how

[vivid frigate]

i gotta find the I.F.

[keen umbra]

wait what is I F

[vivid frigate]

integrating factor

[keen umbra]

oh oh

yeah

[vivid frigate]

@mild flower i got something for you

excuse the ping

[keen umbra]

k

[vivid frigate]

yea yea do u have it

i mean

did u find it lol

[keen umbra]

We don't need the I F here

since it's a seperable diff. equation

[vivid frigate]

oh

right

right

okay

[keen umbra]

We can just 'multiply both sides by dx'

[mild flower]

[vivid frigate]

ok ok

and

we

divide both wsides by x^3

im so smart

eee

[vivid frigate]

hey, i think you're smart

[keen umbra]

yeah

[jagged cargo]

🤨

[mild flower]

oh, thank you! i just know a lot of things tbh

[vivid frigate]

that's hot

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[zinc quail]

If I'm given a matrix A and a matrix B, is it hard to solve for a matrix C such that C^-1 * A * C = B?

[zinc quail]

my specific case: (although curious whether there is a general approach)

[random peak]

i dont see any other way than the tedious one by assuming C to be some 2x2 matrix with elements a,b,c,d and brute force multiplication

[hard atlas]

well given that B is diagonal this boils down to finding whether A has the correct eigenvalues -3 and 1

in general you can boil it down to finding the eigenvalues and their multiplicities

[random peak]

perhaps you can modify this to AC=CB

kinda less work that way if you're doing the tedious method

[zinc quail]

hm, will try both, I also first started with the tedious one, kind of didn't bring me anywhere :D

tx

[meager verge]

.wait C^-1 *C =
[ 1 0
0 1]

[zinc quail]

ys?

[random peak]

you should get a pretty beautiful system of equations

[meager verge]

ye

[zinc quail]

for the original one C^-1 * A * C = B or AC = CB?

@random peak for the second one I received

a+c = 0 & b+2d = 0

the first one yielded a conglomeration of cases

[random peak]

you should get 2 more

[zinc quail]

if I'm not mistaken the others are the same

[random peak]

one more, then

[random peak]

then the 4th becomes the same

[zinc quail]

these only give two

both left ones result in a+c=0

and the right ones b+2d=0

[random peak]

perhaps this just implies there are infinite solutions to this and any matrix satisfying these 2 conditions can be C

[zinc quail]

hm I'll insert some

my direct approach was definitely messier

it does seem to return the same, however I couldn't exclude the case a=-2c or b=-d

[zinc quail]

hm it didn't =c

I tried
1 1
-1 -2

for C

[random peak]

b+2d doesnt seem to be 0 here?

d+2b is 0 instead

[zinc quail]

oops

[random peak]

yeah im pretty confident now it should have infinite solutions

should have been confident earlier as well

[zinc quail]

yay it returns B

[zinc quail]

I find it odd how when not modifying the equation it's really unclear what the set of solutions is

[random peak]

just check another thing, can C become a singular matrix ever if a=-c and b+2d=0

if that ever happens exclude those cases

[zinc quail]

well if a=0 or d=0

which would also mean b=0 and/or c=0

essentially a,b,c,d must be nonzero

[zinc quail]

got the according eigenvalues, how does it give me the possible solutions for C though?

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@zinc quail Has your question been resolved?

[zinc quail]

@hard atlas should I close or do you happen to be available for your approach :)

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[placid pier]

Hello

[placid pier]

So we have a starting value of 45 each minute it decreases by 1,7% calculate after 1,2,5,60 min

So i got sumn like

f(0)= 45

f(1)=44,235

but is the formula, f(x)=45*0,973^x?

[half imp]

do you mean .983?

[placid pier]

ah yes

[half imp]

45*0.983^x

should be right

[placid pier]

and then the x i just put in the amount of min correcct?

and how can i calculate after how many min the value has reached half

[half imp]

Set the function equal to 22,5

[placid pier]

thank you

.close

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[upper nexus]

Looking at this problem regarding LaGrange Mult.

wondering how to know whether the extrema is a rmin or rmax

this ex is easy

but just wondering the typical approach

would you just do your derivatives and second partials test if applicable?

[full arch]

you can use the hessian or also just check the value of the function around the point,

[upper nexus]

oof that math is above my pay grade (didnt learn it yet)

ill make note of it though

ill stick to checking points but it hurts because it feels fake

thanks

[full arch]

second partials test is the determinant of the hessian :D

[upper nexus]

ahhhh i see

all these special names

alright cool

i suppose i will do these "hessians"

thanks again

.close

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[orchid pier]

how can i set domains in desmos?

[dry yacht]

f(x) = function {domain}

[orchid pier]

@dry yacht this doesnt show anything

[dry yacht]

If you zoom out and try looking for the graph.

[orchid pier]

oh nvm

i found my error

.close

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[lapis plume]

I ended up getting negative time for the first one and completely thumbled the second, please help

[urban valley]

idk what times mean

but i got 6s

[tidal umbra]

!status

[vocal sleet]

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

[lapis plume]

Same…. 😭

Makes no sense

[lapis plume]

1?

[urban valley]

what answer is given

[tidal umbra]

okay do you know equations of motion

[urban valley]

I got 6s

let me try for 11

[lapis plume]

How?

[lapis plume]

Suvat?

[tidal umbra]

what is that sorry i dont know

oh yea

yea suvat

[lapis plume]

Mhmmm

But how do you get both numbers?

Why are there two times?

It’s travelling in a straight direction

Not up

[tidal umbra]

well you know s,v and a

v^2=u^2+2as

from here u can get u

and then from v=u+at you can get time

[lapis plume]

But that will still only give one time

[tidal umbra]

one time/?

[lapis plume]

Yeah huh

[chilly sparrow]

hi guys

sorry to interrupt but its important

you should drink water

stay hydrated

[lapis plume]

Thanks bro

🙏

[chilly sparrow]

your welcome

[lapis plume]

Does anyone know how they got 11.6?

[urban valley]

idk

yet

[lapis plume]

Hmm

Surely it would only have one time though

[urban valley]

try to make quad

[lapis plume]

I’m still confuzzled

[urban valley]

with t

s=ut+1/2at^2

ig

might

work

let me try

[lapis plume]

But why would the particle go from a to b twice and take two different times to do it?

I think imma assume the question is wrong

How do I do 7? Because

Acceleration = -9.81N/m-2

Time = 3.4

You only have two things to work with

So how do you do it?

[urban valley]

btw

I got 11.6

[lapis plume]

Ahhhh

What?!

How

[urban valley]

but it's in negative

idk

[lapis plume]

Yeah that’s what I got earlier

[urban valley]

ig it's 6 only

[lapis plume]

It really confused me

[urban valley]

true

[lapis plume]

How would I do 7, you don’t have enough information

[urban valley]

you can use time of flight formula

[lapis plume]

What’s that?

[urban valley]

or

just

divide time in half

and add the equations of time of upward abd downward

or just use

t=2u/g

@lapis plume

[lapis plume]

I think we’re supposed to use suvat equations though

[urban valley]

ofc

it's derived from that only

do you want me to show yiu

?

[lapis plume]

Please 🙏

[urban valley]

@lapis plume

ping if you can't understand something

[lapis plume]

I uhh

!help

[vocal sleet]

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

[lapis plume]

Lemme show you

!suvat

I give up

https://images.app.goo.gl/3AU7nKNtPgM8qnTp7

Which one of these do I use?

@urban valley

[urban valley]

ok so see

when we throw a ball up

we give it initial velocity

but when it reaches maximum height

it's final velocity will be zero

cause

no motion

it's still for a fraction of second

since gravity is not an impulsive force

therefore

we consider v= 0 when ball reachea maximum height

@lapis plume are you getting

what I'm trying to say

try to visualise

you'll understand

[vocal sleet]

@lapis plume Has your question been resolved?

[lapis plume]

but then which equation do i use?

[urban valley]

1st

2 times

use 1st equation

[lapis plume]

kk

ty

u = 33

its not right though

0 = u + (-9.81)(3.4)

[urban valley]

it's 16.66

t=2u/g

[lapis plume]

v=u+at

[urban valley]

don't use t given

divide it in half

[lapis plume]

oh yeah cuz we doing the second half

[urban valley]

since we are first calculating for upward time taken

then calculate for doanward

then add them

[lapis plume]

Quick quesiton

if you are ignoring air resistance,

will the objects acceleration always be -9.81m/s?

[dark kiln]

sure

any object takes the same time to fall from height X in other words

[vocal sleet]

@lapis plume Has your question been resolved?

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[half yew]

Unsure if that’s the right equation

Can I just get a confirmation?

I get an answer the seems wrong

Would I just use keplers law?

<@&286206848099549185>

[vocal sleet]

@half yew Has your question been resolved?

[vocal sleet]

@half yew Has your question been resolved?

[vocal sleet]

@half yew Has your question been resolved?

[half yew]

<@&286206848099549185>

[half yew]

<@&286206848099549185> :D

[vocal sleet]

@half yew Has your question been resolved?

[hoary arch]

2π IS BEING MULTIPLIED BY THE ROOT THERE,

BUT YOU SUBTRACTED IT , INSTEAD OF DIVIDING

[half yew]

Right

Ty

Did I use the right equation to begin. With?

[hoary arch]

PRETTY SURE YEAH

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[tall ore]

I wondered if anyone could help me with this proof, I know how to prove it without the law of the excluded middle, but am struggling to see how that law helps here

[tall ore]

I started by assuming ¬p -> ¬q

[tidal dock]

that's wrong

[tall ore]

oh ok, how should i start?

[tidal dock]

-> is not commutative (a->b doesn't mean b->a)

[tall ore]

oh my bad that was a typo sorry

¬q -> ¬p

i meant that

[tidal dock]

well

yes

[tall ore]

and then i assumed p

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@tall ore Has your question been resolved?

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[languid venture]

How can I find lim x>inf of this

[languid venture]

Its 0 x inf i dont see how to do it

[sharp lynx]

how rigorous do you have to be?

as x tends to infinity, this thing behaves like x/e^x

[vocal sleet]

@languid venture Has your question been resolved?

[languid venture]

Yes but

E^-x

Thats 0

[sharp lynx]

indeed

[languid venture]

So 0 x inf

[sharp lynx]

can you compute the limit of this ratio?

[languid venture]

Wdym

Ah wait

I get it

Its 0

[sharp lynx]

$\lim_{x\to\infty} \frac{x}{e^x}$

[languid venture]

Thx

[twin meteor]

Steakanator

[languid venture]

0

[sharp lynx]

if you agree with this statement, and you conclude the limit is 0, then you can hopefully conclude that the original limit is 0

[languid venture]

If x>+inf

But if x>-inf

Isnt the result -inf

[sharp lynx]

i'm not sure i agree with that

where is -inf coming from?

[languid venture]

X>-inf

E^(-x)

So e^+inf

[sharp lynx]

careful

[languid venture]

Ok no thats 0

[sharp lynx]

the original equation involves e^-|x|

[languid venture]

Ahh

Ok

So its

Wait but

Its -x if x<0

No?

[sharp lynx]

what's "its"

[languid venture]

The module

|x| is -x if x<0

X if x>0

No?

[sharp lynx]

no that's fine

so if x<0 we have e^-|x| = e^-(-x) = e^x

however since we're taking the limit as x tends to -inf, it still goes to 0

[languid venture]

Yes but we have xe^x

[sharp lynx]

would it help to rewrite that as x/e^-x?

[languid venture]

Wdym?

[sharp lynx]

xe^x = x/e^-x

[languid venture]

Ok

So thats 0 yeah ok

[sharp lynx]

indeed

[languid venture]

And for x +inf

We have

Uhh

[sharp lynx]

we did that first

[languid venture]

The same thing

Basically

Right?

[sharp lynx]

well both limits are 0

[languid venture]

Yes but earlier i djdnt think it through

Because

If x > +inf

We have x/e^x

Ohhh

Yeah

Thx bro

Weird exercise

[sharp lynx]

np

[languid venture]

.close

[vocal sleet]

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[hybrid garnet]

so uh what does the round symbol mean

[vocal sleet]

@hybrid garnet Has your question been resolved?

[hybrid garnet]

sure

[vocal sleet]

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[vocal sleet]

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[rapid birch]

hi

[rapid birch]

i don’t know what i should do now

<@&286206848099549185>

[amber parrot]

multiply 2 * 15 = 30

[rapid birch]

then?

[amber parrot]

after that 15/30

answer 2

[rapid birch]

what

why 30/15

[amber parrot]

do you know $sqrt(4)= 4^(1/2)$ you can write\

[twin meteor]

S$PYDE-07

[rapid birch]

i didn’t understand

😥

yess

is it correct?

@amber parrot

[amber parrot]

ya it also correct

[rapid birch]

thx

[vocal sleet]

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[vocal sleet]

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[novel moss]

I need to find

[novel moss]

\sqrt[5]{i + 2}

ok that doesnt work : I Need to find the 5th root of (i+2)

my idea was that z^5=i+2
but now i am stuck

does it help to transform into polar coordinates?

[whole beacon]

yea

re^iθ

r=sqrt(1+4)

θ=arctan(1/2)

[twin meteor]

DinVin95

[whole beacon]

,tex transform $i+2$ to $\sqrt{5}e^{i\tan^{-1}{\frac{1}{2}}}$

[novel moss]

and z^5 has to be = to that , right?

so i will have 5 solutions i guess?

[twin meteor]

DinVin95

[whole beacon]

,tex so z=$\sqrt{5}e^\frac{{i\tan^{-1}{\frac{1}{2}}}}{5}$

[twin meteor]

DinVin95

[whole beacon]

i think you can add 2npi if you want to find other solutions

but this is one of them

[novel moss]

ahh yeah now i got it! thank you very much!

but i have 5^(1/10)

because you want to find z

[whole beacon]

what do you mean by that?

[novel moss]

wait a second

[whole beacon]

CRAP

I FORGOT

[whole beacon]

there you go

yea you can include 2npi

but this is the principal root

[novel moss]

yeah exactly

great easy !

tyty!

[whole beacon]

welcome

[vocal sleet]

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[mighty breach]

In degrees

[meager verge]

idk i think it have betterway

sin(x+20) = sin(90-2x)

[meager verge]

did they give u range?

[vocal sleet]

@mighty breach Has your question been resolved?

[mighty breach]

Initially I tried De moivre but I realised I was over complicating it and it's just working out the general solution with co ratios, thank you

[vocal sleet]

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[indigo karma]

I need help

[tidal dock]

factor 180

[indigo karma]

6 root 2

I got there so far

[wary mantle]

5 = sqrt(5) * sqrt(5)

[wary mantle]

Do you want to rationalize the denominator?

What's the exercise

[indigo karma]

I want to get it to the form a + (root5/b)

[wary mantle]

$\frac{6 \sqrt 5 - 2 \sqrt 5}{5 \sqrt 5 - 5} = \frac{\big(5 \sqrt 5 - 5\big) + 5 - \sqrt 5}{5 \sqrt 5 - 5}$.

[indigo karma]

Now i got it

Thank you

[wary mantle]

Ah, you want just root(5) in the numerator?

This'd give you 5 - root(5)

[wary mantle]

Yep

I got that too, after rationalizing the denominator

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[earnest briar]

I need help with getting the indefinite integral of this, I know partially how to solve by integration by parts but I'm not exactly sure what to do when you have ln()

[vale ermine]

look for substitution

[earnest briar]

I'll be honest, I don't know what that means in this context. I sort of learned calculus via example so I'm not exactly familiar with the terminology

They taught me integration by parts using this formula

[worthy citrus]

You'll want to search up "integration by substitution" or "u-substitution"

by parts is not the way to go here

[earnest briar]

...okay I see what you mean

I know how to do integration by substitution, I'm just not familiar with the terminology so I did have to look it up but yeah, that makes sense

it's a bit sloppy but I got it

Thank you!

.close

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[cyan shadow]

I mean yes? but the incident matrix is unique if you label the nodes/edges and keep it consistent

of course if you change the labels the incident matrix also changes

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[vast shale]

Prove xarctanx>=ln(1+x^2) for every x in [1,2]

[vast shale]

Without using functions

I know x>=ln(1+x)

And x>=arctanx

For every x in [1,2]

[tidal dock]

wdym without using functions

[vast shale]

How can I use these inequalities

[vast shale]

Without differentiability

[median crane]

i guess u cant do xarctanx - ln(1+x^2)

[vast shale]

Yes

Any idea how I can use these 2 inequalities

<@&286206848099549185>

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[hard wadi]

I need help figuring out if I'm calculating error right

[hard wadi]

I havent done it in so long I cant remember how to do it

I've got the average of all the velocities, then I take the average and subtract it from the velocity, then I square that difference and I add them all up and divide by the number of points that data was collected at, then I take the square root

which gives me a graph with error bars looking like this

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@hard wadi Has your question been resolved?

[hard wadi]

<@&286206848099549185>

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@hard wadi Has your question been resolved?

[vocal sleet]

@hard wadi Has your question been resolved?

[vocal sleet]

@hard wadi Has your question been resolved?

[hard wadi]

<@&286206848099549185>

[sullen moon]

it seems like u are calculating the standard deviation

can you show ur calculation?

[sullen moon]

so send the input in your excel sheet here

additionally, error bars are common, which is what appears to be shown in your second image.

Each bar shows the range within which you can expect to find the true value of each measurement with a certain level of confidence

it's not an "error"

[hard wadi]

Uncertainty is what I mean, I think. I’ve described what I’ve done. Average is the sum of all velocities/19. Difference is each velocity - the average. Diff^2 is différence squared. Then I added up all the diff^2’s and divided by 19. Then I took the sqrt of the last one

[hard wadi]

I’m just not sure if it’s the right way to be finding what I’m looking for

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[vagrant gale]

not sure how to further solve

<@&286206848099549185>

<@&286206848099549185>

[vocal sleet]

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[vagrant gale]

<@&286206848099549185>

[slow summit]

hi

RHS is -26*5^n

LHS, replace pn with an*5^n

then compare

gl with ur lab test

[vagrant gale]

@slow summit always saves me

bro is omniscient

[slow summit]

nah I'm dumb

[vagrant gale]

no ur not

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[crude swan]

Can someone help me solve this question?

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[brittle zealot]

For question b)

Why is the answer not 1/3 + 3/4?

[brittle zealot]

Sorry @sage gazelle I’ve occupied here

Since the question asks “or”, the probability can only contain addition operations, right?

[dark kiln]

they intersect though

it's like the probability of rolling an even number or a number below 4 from 1−6

[brittle zealot]

Oh, so does this mean it’s a non-mutually exclusive combined event?

[dark kiln]

sounds right

[brittle zealot]

But how does this apply for this question? It’s food and drinks

They’re 2 separate cats George’s

Categories*

[dark kiln]

you still can order fried rice and not coffee at the same time

so those events would be counted twice when you add them naively

[brittle zealot]

I don’t get it

It’s asking to find “or”

Can you give like an example

[dark kiln]

example of what

[brittle zealot]

I don’t get what you were trying to say

[dark kiln]

there are 12 orders you can make

[brittle zealot]

right

[dark kiln]

(1/3) × 12 = 4 orders have fried rice

( 3/4)(12) have not coffee

so 9

[brittle zealot]

I still don’t get it, why are you multiplying it

I just realised the working:

1/3 + 3/4 - 1/4

I don’t get what’s the 1/4 doing here (it’s intersection I know but I don’t know what this represents)

[dark kiln]

fried rice and not coffee

[brittle zealot]

Let me try to process

[dark kiln]

size of the whole shape equals size(circle 1) + size(circle 2) − size(the thing in the middle)

[brittle zealot]

Yeah I understand that but I’m trying to think why- 1/4 is there

[viral copper]

frownyfrog out of context

[brittle zealot]

I can pick fried rice and not coffee

Let me think from there

So that means

I havé a possibility of picking fried rice and coffee, but the question only ask for or, so I can’t include this

therefore I have to subtract 1/4

Alright makes sense now

Thanks

.close

[vocal sleet]

Channel closed

Closed by @brittle zealot

Use .reopen if this was a mistake.

[dark kiln]

.reopen

ouch

[vocal sleet]

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[vast shale]

aa

[vast shale]

Something is wrong with my steps. The answer is supposed to be A

[viral copper]

dv is 2e^(2x)

[vast shale]

So I change my u and v

Oh

Wait

[viral copper]

you didn't differentiate e^2x right

[vast shale]

So i need to replace u and v

[vast shale]

Yeah coz I took it as dv

[viral copper]

oh right

[vast shale]

I should take it as u to differentiate it

[viral copper]

you didn't integrate it properly

[vast shale]

im lost

[viral copper]

your choices are right

[vast shale]

Alr

[viral copper]

dv = e^2x so whats v

[vast shale]

Ok integration of it

2e^2x

Wait

Then when I integrate it again

Oh wait

[viral copper]

whats the integral of e^(2x)

thats v

[vast shale]

Yeah its e^2x/2?

Is it right?

[viral copper]

indeed

[vast shale]

Will I have to integrate it again according to the formula of integration by partsv

[viral copper]

nope

oh

yeah

[vast shale]

Then how will I end up getting e2x/4

[viral copper]

mb I didnt get what you meant

you do you do

[vast shale]

Right lemme try

got it, thank you

[median crane]

.close

[vocal sleet]

Channel closed

Closed by @median crane

Use .reopen if this was a mistake.

[vocal sleet]

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[sterile latch]

I have no idea how to solve these kinds of problems, so why is 2 x 0,5^6 correct for the first one and how do I solve the others? (Note: this was originally in German so I used google translate but the numbers on the right side (eg 3*0.56 is wrong, the 6 should be a superscript)

[sterile latch]

<@&286206848099549185>

[timber kestrel]

if I ask you what the the probability of getting 2 heads when you throw the coin 2 times instead, do you know the answer?

[vocal sleet]

@sterile latch Has your question been resolved?

[sterile latch]

Sorry, was offline for a minute but im back now

It’d be 0.5 x 0.5 right?

So 0.25

[timber kestrel]

that's correct, so you know the basic

then what do 'the coin always lands on the same side' actually means?

[sterile latch]

The coin lands 6 times in a row on either heads or tails

[timber kestrel]

exactly, there are 2 cases, the first one is 6 heads and the second one is 6 tails

so can you compute the probability for each case?

[sterile latch]

Ahhh I think I get it now (at least for the first question), it’s basically always the same side (so 0,5 x 0,5 x 0,5,… or just 0,5^6) and you have 2 possible solutions so 2 x. Then the last question must be 0,5^6 because there’s just 1 correct solution right?

[timber kestrel]

you got it for the first question, for the last question, what is the 1 correct solution you think of?

[sterile latch]

Heads - tails - heads - tails - heads - tails

[timber kestrel]

that is a valid case, but I think you have missed another case

[sterile latch]

Ahhhh

And of course tails - heads - tails - heads etc

[timber kestrel]

yes

[sterile latch]

So it’s 2x 0,5^6 as well

[timber kestrel]

perfect

[sterile latch]

I think I got it now but how do I solve the other three?

(Btw, the 2nd question should be: the coin shows tails only at the first throw)

[timber kestrel]

for the second question, what is/are the valid case(s)?

[sterile latch]

THHHHH

[timber kestrel]

yes

so what is the probability of getting this case?

[sterile latch]

Is it Like that? If yes, then it’s just be 0,5^6

[timber kestrel]

yes, there are 50% for getting tail at the first toss and 50% for getting heads for the remaining tosses, so it is 0.5 * 0.5 * ... * 0.5 = 0.5^6

[sterile latch]

And for the 3rd it’s hhthhh, so 0,5^6 again?

[timber kestrel]

I am not sure about what do the 3rd and the 4th question mean. can you translate it for me?

[sterile latch]

3rd: the coin shows tails only at the third throw
4th: the coin shows tails exactly one time

[timber kestrel]

perfect

[sterile latch]

But how do I solve the fourth? Tails could happen anytime

So thhhhh hthhhh hhthhh hhhthh hhhhth hhhhht

[timber kestrel]

yes

you got it

[sterile latch]

No wait that’s 6 x 0,5^6 right?

[timber kestrel]

right

[sterile latch]

Thanks so much omg! You saved me from ruining my grade cause we’re having a test about that tomorrow

Honestly, thank you!

[timber kestrel]

you're welcome

[sterile latch]

.close

[vocal sleet]

Channel closed

Closed by @sterile latch

Use .reopen if this was a mistake.

[timber kestrel]

remember to first list all the possible cases and second compute the probability for each case then finally add up the probabilities for this kind of question

I think you have mastered it

[vocal sleet]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[sage gazelle]

<@&286206848099549185>

[sage gazelle]

please help me here <@&286206848099549185> ❤️

[terse hatch]

Hi

[sage gazelle]

I just need to verify that these are correct 🙂

[terse hatch]

Woah

Good luck with that 😂

[sage gazelle]

is there something wrong

[terse hatch]

Too hard for me…

[sage gazelle]

oh ok

maybe it's just intimidating

[astral needle]

It seems correct

[sage gazelle]

both?

[astral needle]

But you basically did this s| 20n + 7 and s | 15n + 4 => s| gcd(20n+7, 15n+4) => s| 1 => s = +1 or s = -1

Use euclid agorithm to show gcd(20n+7, 15n+4) = 1

[sage gazelle]

we're not supposed to do that for this assignment

[astral needle]

I mean

[sage gazelle]

this is year 10

thank you for bringing it up though

i havent really heard of that algorithm before

[astral needle]

Can you use gcd( a*b + c, a) = gcd( a,c)?