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[ocean seal]

Salt

[worldly skiff]

that's a small typo which is easily fixed, but yes

This is nitpicky, but you use lambda before you define it

[cunning raven]

what is lambda?

[worldly skiff]

And I could cite Bezout's lemma when using it. Lemme keep looking at it

$\lambda$

[ocean seal]

3K

[worldly skiff]

if that's just a sick ass looking h then my bad LOL

[cunning raven]

it is XD

oh wait

I wrote h

[worldly skiff]

hahahahaha then yeah. Nitpicky thing of you use h before defining it

and didn't cite bezout's lemma when used

usually in proof writing

[cunning raven]

what does lambda mean?

[worldly skiff]

Lambda is just enough variable

In physics it has some significance

And in linear

[cunning raven]

do I have to use lambda in euclidean proofs?

[worldly skiff]

and nope

[cunning raven]

oh you just saw my h as lambda?

[worldly skiff]

there are common things people use as variables, but there's not a variable naming format you have to follow

yeah. your h had too many sick waves. I thought it was a lambda

[cunning raven]

haha i see

so here's my frame of mind now for euclidean proofs:

If want to prove x=y

1. Take gcd(b,c) = a and turn it into a|b, a|c, as well as other theorems
2. Manipulation using theorems and algebra 
3. LH allowed to group integer; RH allowed to exclusively multiply
4. Target is to reach x|y and y|x

[worldly skiff]

I think a problem is that you can't say gcd(na,nb) divides n * gcd(a,b) from what you had

gcd(na,nb)=(na)s+(nb)t isn't true necessarily. this is because you're saying there are SOME s,t to satisfy the whole gcd(a,b)=as+bt

And some s,t means specific ones although unknown. so these aren't necessarily gonna be the same for gcd(na,nb)

[worldly skiff]

If you want to prove x=y and it involves divisibility, then yes this seems fine

[cunning raven]

Is there anything missing from my framework

[worldly skiff]

I gotta go for now, so I'll be off for the rest of the day. But I hope your studying goes well. If you have any other questions another time lemme know and I'll try my best to help if I have free time

[cunning raven]

Aight thanks a bunch

saved my a$$ so hard

[worldly skiff]

And I think your framework is fine. But there'll be other exceptions ofc and a lot of proofs are weird af

[cunning raven]

yeah

[worldly skiff]

Luckily divisibility ones are GENERALLY intuitive

[cunning raven]

just a quick question before you go

how does lcm weigh into all of this

[worldly skiff]

But there's some that still don't make sense to me intuitively although the proof makes perfect sense

In this case lcm doesn't factor in for this, but I can get you the lcm def rq

[cunning raven]

aight

[worldly skiff]

The Euclidean Algorithm focuses on gcd anyway. You usually use lcm for divisibility manipulations again

Def practice some basic Euclidean Algorithm computations to get used to it

As some proofs will require you to do it algebraically

Hopefully your professor doesn't give you too many induction proofs involving it

[cunning raven]

This is the only thing I know for lcm basically rn

[worldly skiff]

Because those are a fucking pain

That's really good that you already have that

That's a classic thing teachers make you prove

[cunning raven]

omg induction proofs kill me these euclidean and divisibility proofs aren't even induction at this point

[worldly skiff]

😔 ✊

I had one question in a number theory class involving Euclidean Algorithm with induction on Fibonacci numbers

Was not a fun time for a good 4-5 hours

Blurgh. Small again, but these are helpful to know

[cunning raven]

aight thank you so much

[worldly skiff]

Good luck fellow mathematician in your journey to pass your class

And for sure

[cunning raven]

👍

[jovial adder]

Hello, I was wondering how I could solve the following:

[obtuse yoke]

you should first translate it into exponential form

[oak chasm]

@jovial adder This channel is busy. Please see the rules on how to get help in #❓how-to-get-help.

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[hardy mirage]

How should I do this?

[hardy mirage]

These are the steps I've tried

Those circled ones

And I don't even think I'm close to the answer

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[hardy mirage]

<@&286206848099549185>

Let me type out the question:

There is two cylinder, P and Q. P has radius r and height 5, while Q has radius (r +2) and height of 3.

Their volume adds up to 488 pi.

The question asks for r.

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[hardy mirage]

<@&286206848099549185>

.close

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[candid summit]

Help with these two qns

[alpine sable]

Are these vectors?

Or classical geometry?

[candid summit]

Vectors

[alpine sable]

Think of AB as a resultant

Which two vectors can be added

To get AB?

[candid summit]

15a*

.clear

[alpine sable]

14 is clear?

[candid summit]

Ye

someome else tot me earlier

Irl

[alpine sable]

Again

Which 2 vectors can be added or subtracted

To get OB?

[candid summit]

oa plus an

an

ab*

[alpine sable]

Good

AB is the same as OC

Do you know length of any of them?

For MN, it is also simple

Just take care of the directions and

Focus on triangle CAB

[candid summit]

Aite

[alpine sable]

Using midpoint theorem,
MN is half of CA

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[light tusk]

Can anyone tell me what mistake I've done?

[light tusk]

I wanted to find a, but there's no answer, its a dead end

[remote mirage]

i don't think you change u back into 2 + sinx since you already changed the bounds

[light tusk]

Ohhh

[remote mirage]

just integrate in terms of u

[light tusk]

So that's what changing the bounds does

[remote mirage]

yeah

[light tusk]

Neat! I finally found it

Thanks

.close

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[lament pilot]

how do i do this

[remote mirage]

what have you tried so far?

[lament pilot]

I tried getting the radius of the circle

and using tan30 = √3/x

but then i realised that the circle doesnt go all the way across the rhombus

[remote mirage]

good observation

do you know the definition of a rhombus?

[remote mirage]

you can easily find the radius of the circle since the question gives you the area of the circle

[lament pilot]

ye

[lament pilot]

hmm

idk

oh wait all sides are same length?

[remote mirage]

yeah

and the area of a rhombus is half the product of its diagonals

[lament pilot]

mhm

how do i find its diagonals?

[remote mirage]

if you know the radius you can use trig functions to find the lengths of half of the diagonals

the radius forms two right triangle where the hypotenuse is half of the diagonal

[lament pilot]

ohh

OH

[remote mirage]

hope that makes sense :) you can keep me updated if you're still confused

[lament pilot]

thanks so much

i got the diagonals as 6.93 and 4?

is that right?

[remote mirage]

hm

[remote mirage]

i think that's half of the diagonals

[lone heart]

@lament pilot Has your question been resolved?

[lament pilot]

oh

so how would I write it in a√b ?

[remote mirage]

oh so you wouldn't evaluate the diagonal as 6.93 but instead leave it as a radical in simplest form

[lone heart]

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[lyric flax]

Is -14sqrt(cos^(3)x) = -14(cosx)^(3/2)?

[karmic rapids]

no

only for x>0

[lyric flax]

Since my answer is -14u^(3/2), where u = cosx

should it be -14cos^(3/2) x?

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[mortal heath]

help please 🙂

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[wary stream]

Don't ask in an occupied channel next time
Read #❓how-to-get-help

Also a performance task, sounds like a progress check meaning it's a method to see how well you are performing in the class, so are you allowed to get help on that?

[lone heart]

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[zenith olive]

hi

[last ether]

Nice picture

What's the question

[spark creek]

Where are you stuck?

[last ether]

That is a pyramid

With base 12 and 8, height 15; all in meters

You're welcome

[zenith olive]

ask ing for the surface area

whoops

[last ether]

Is it a right pyramid?

[zenith olive]

right?

[last ether]

Like

The apex is directly above the center of the bottom base

[zenith olive]

its a pyramid

yeah

[last ether]

Okay so you can use properties of right pyramids to solve this

First, do the easy shit: what's the area of the bottom base?

[zenith olive]

96

[last ether]

Good

[zenith olive]

well

my answer was

414

[last ether]

Now one of the priorities is that the height is the perpendicular bisector of the lengths of the right pyramid

[zenith olive]

idk where i went wrong

[last ether]

For the bottom rectangle you got 414?

Uhhh, well no, I don't think that's right lol

96 is the bottom rectangle, as you've gotten

[zenith olive]

no like

[last ether]

With this information, you can find the respective hypotenuses, which will be the height of their respective triangular side

[zenith olive]

the

surface area

for the whole pyramid

my answer was 414

over all

[last ether]

I'm in a tour bus so I can't check

[last ether]

For now, find the 4 hypotenuses

[zenith olive]

o

one is

square rt of 241

other is sqrt of 261

[last ether]

Lemme check

Yeah

Now use those as the height of the triangular sides

[zenith olive]

i did

my working out

[last ether]

Lemme check using desmos, which is slow as fuck because I'm using a tour bus wifi

Oh no don't cut the lengths in half when finding the area of the triangles

Well

Actually hold on

I guess you're fine because you put the 2 • in front

Which would undo your halving

[zenith olive]

yeah

???

[last ether]

I got 412

[zenith olive]

yeah thats prolly the answer

idk where i went wrong tho

[last ether]

Prob calculator did a dumb

[zenith olive]

o

is my working out okay?

[spark creek]

Yeah that's correct

[last ether]

Just note, to show the work on screen (because it'll just cut off), 1/2 • 2 = 1

[zenith olive]

yup

that was my working out

[last ether]

I guess your calculator sucks

Idk

[zenith olive]

lol

i have another one

i got like 195

[last ether]

Or

Well

I mean

You're given the height (of each trapezoid) and a square base so

Big square + small square + 4(trapezoid)

[zenith olive]

i think there something seriously wrong with my calculator-

but it seems fine jhghfgvhjdfgh

.close

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[forest helm]

not too sure how to calculate the area and perimeter

[spark creek]

Perimeter should be easy enough

[spark creek]

Where are you stuck for the perimeter?

[forest helm]

the curve and that dotted line

its 12am probably not the best time to do but imma try

ive done that

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[acoustic swift]

Given the vector (2.4,-5.6,4.2) can I get cosines directors using x/magnitude?

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[visual badger]

for a what angle is this?

and for this why isnt the dot product $\overrightarrow{BA} \cdot \overrightarrow{BO}$

[ocean seal]

HenTie

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<@&286206848099549185>

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[visual badger]

.close

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[wheat prism]

Hello. I have some trouble proving this fact. If gcd(m,n)=d then in this succession: n,2n,3n,...,(m-1)n,mn m divides exactly d terms

[wheat prism]

I know that d divides all terms in the succession since they are multiples of n

And I know that m divides at least one term

But I'm stuck

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[wheat prism]

.reopen

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✅

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[frail rivet]

guys does it suffice if i write for the reflexive attribute that f(a1) = f(a1)?

[frail rivet]

and if its not enough what is missing?

.close

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[lost saddle]

<@&286206848099549185>

[short cobalt]

could u take a more clear photo? its a little hard to read. also please ping helpers after 15 min!

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[dense gust]

@lost saddle

?

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[sour breach]

How do i go about proving this? I have tried everything I could think of xd

Tried converting it to row echelon form but it turns into a monster

[tacit arch]

try writing the third column as a linear combination of the first two

[sour breach]

Where do i go from here?

[bitter vault]

Note that third column is a linear combination of first 2. So the columns are linearly dependent, which means the determinant is zero

[sour breach]

I see! The third column can be reduced to zero

Thanks

.close

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[noble coyote]

i reversed and add, found the closed formula x = 533
so now im at the 2s = 234(538)
but the answers there dont line up with my math

[noble coyote]

ignore the selection i was trying to screenshot

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[lost saddle]

I didn’t understand

You need explanation or final answer

btw you know sigma ?

[tight locust]

OK! this is simple

9 = 5 + 4

13 = 5 + 4(2)

[tight locust]

17 = 5 + 4(3)

[lost saddle]

I used some code to solve it 😅

Answer is 1

[tight locust]

no

[lost saddle]

What no

[tight locust]

your code is right i see

but you just said that the answer is 1 lmao

[lost saddle]

Yes option 1 ?

[tight locust]

oh ok

[lost saddle]

lol

[tight locust]

you were referring to the first answer choice

[lost saddle]

Yes ofc answer is not 1 since we have + and the first number is 5😅

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[grim flower]

help

[grim flower]

<@&286206848099549185>

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@grim flower Has your question been resolved?

[tacit arch]

.close

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[versed trench]

Question:
A rocket is travelling in a straight line, with an initial velocity of 140 ms-1. It accelerates to a new velocity of 500 ms in two stages. During the first stage its acceleration, a ms-2, after t seconds is given by a(t) = 240 sin(2t), where 0<=t<=k.

1.Find an expression for the velocity.vms-1, of the rocket during the first stage.

The first stage continues for k seconds until the velocity of the rocket reaches 375 ms-1.

2.Find the distance that the rocket travels during the first stage.

3.During the second stage, the rocket accelerates at a constant rate. The distance which the rocket travels during the second stage is the same as the distance it travels during the first stage. Find the total time taken for the two stages.

[versed trench]

Attempted solution

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[versed trench]

For 3 I assume I have to derive the equation of v I got from 2

[versed trench]

.close

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[muted tinsel]

Given coprime numbers a, b, c, show that a+b+c is coprime to ab+bc+ac

[muted tinsel]

I'm trying to use the fact that if a,b are coprime then a + b is coprime to ab, and then using that for b+c and a+c as well and then summing a + b + b + c + a + c, or 2a+2b+2c but I don't think that's actually accomplishing anything.

TLDR: I'm stuck and my method doesn't do anything I think

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[muted tinsel]

<@&286206848099549185>

Alternatively I was thinking about using a contradiction where I assume some p divides a+b+c and ab+bc+ac and then show that that p cannot divide a b or c

[sterile ravine]

I found it

[muted tinsel]

found it?

[sterile ravine]

I used reduction to absurdity

I supposed that a+b+c and ab+bc+ac are coprims

so p a prime number different from 0 divide a+b+c and ab+bc +ac

I used the linear combination property

in the end I found that if a+b+c and ab+bc+ac are coprims so p divides b^2 -ac

and I used the Bezout theorem to prove that the supposition is absurd

[muted tinsel]

jeez okay, I think this might just be beyond my number theory abilities

[muted tinsel]

how did you use this?

[sterile ravine]

the property is if a divide b and a divide c so a divide mb+nc with m and n integers

so I took m=b an n =-1

[muted tinsel]

so is this based on a contradiction? Why does a divide b and a divide c?

[sterile ravine]

the prove yes but the property say that if a divide b and a divide c so a divide mb+nc

[muted tinsel]

oh ok

[muted tinsel]

is n = -a? or just -1

[sterile ravine]

just -1

[muted tinsel]

oh ok

I think I kinda get it

[muted tinsel]

so in the way you mentioned it, p is our a and b = a+b+c and n = ab+bc+ac?

[sterile ravine]

if you mean c instead of n=ab+bc+ac yes

[muted tinsel]

yes yes my bad

why does p divides b^2-ac matter?

why is that absurd

[sterile ravine]

here we will use the Bezout theorem

it says that if a and b are coprimes so an+bm=1

and vice versa

we have a and b coprimes so taking n=b and m=-c

so b^2-ac=1

so p divide 1 which is absurd

[muted tinsel]

wait

how did you get b^2-ac = 1 from an+bm=1

are n and m swapped?

[sterile ravine]

yes

I said the property in general

[muted tinsel]

oh ok

[muted tinsel]

why does this imply p divides 1?

oh

because

I see

I see

cool that makes sense

thanks so much

[sterile ravine]

you're welcome thank you too because I revised my number theory lesson

[muted tinsel]

haha

if you're interested, the question came from this

it's from a pset I'm writing right now, but I just wasn't sure how to solve my own problem 🥴

[sterile ravine]

ok tnx

[muted tinsel]

,close

.close

[lone heart]

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[fleet tiger]

help

[short cobalt]

question?

[fleet tiger]

@short cobalt

[short cobalt]

have you tried anything?

[fleet tiger]

n op

I missed the days of school because I have outpatient therapy and I just simply have no clue what to do

[short cobalt]

well to see if its linear, you can see how the x and y values increase

if you see a constant increase in the values its linear

[fleet tiger]

So this would be linear?

[short cobalt]

i do not think so

the y output are not increasing at a constant rate

[fleet tiger]

How so?

[short cobalt]

10-(-8) =__

25-10=___

increasing by 18 in the first one

and then 15 in the second jump

is not constant

[fleet tiger]

Ohhhh

ruh roh, this question looks scary

I don't think you can do it

[short cobalt]

all you are doing is looking for constant change in x values

and constant change in y values

[fleet tiger]

Ohhh

Wait

Then how would this work,

Because it says, an additional $800 installation fee

At a constant rate

[short cobalt]

can you show the question part?

[fleet tiger]

Yeazh

And this

Thats the first question

[short cobalt]

alright

so in this question

you are given two linear eq but in different methods

to find the higher rate per sq foot u need to find slope

do u know how to?

in either case?

[fleet tiger]

Slope

Like slope intercept form?

Isnt that y=mx+b?

[short cobalt]

yes

but you just need the slope

or the m part of the eq

[fleet tiger]

The slope would be

Rise over run correcT?

[short cobalt]

yes

[fleet tiger]

So, 100/10

Because the Y is going up by 50

And the X is going up by ones

[short cobalt]

which company?

[fleet tiger]

Compant A

And then for B it would be 100/5

Because on B the X is constant of 5

And Y is a constant of 100

[short cobalt]

I am not 100% sure how u got this answer

I think of slope as change in y over change in x

so i pick two points on the graph

[fleet tiger]

Agreed

[short cobalt]

and take their cords

and find the change in the y value

and put it over the change in x

if u did that, your answer should be good

[fleet tiger]

I think that's correct

I mean basically what I did was I got the X on the left and the Y on the right

And saw the Y was going up by 100

Each time

So 100 was it's constant

And the X on the right was rising by 5 so, the constant of that was 5

And if slope is y/x I got 100/5

[short cobalt]

for company A, i see change in y being 1250-1000 (choosing the farthest points on the line)

[fleet tiger]

I'm confuzzled

[short cobalt]

choose two points on the line

and tell me their cords

[fleet tiger]

Alright

100, 0

wait

1000,0

and

1150,10

[short cobalt]

(0, 1000) and (10, 1150)

correct?

[fleet tiger]

Yes

[short cobalt]

so think of it as (x1, y1) and (x2, y2)

and try doing (y2-y1)

[fleet tiger]

150

[short cobalt]

and (x2-x1)

[fleet tiger]

10

[short cobalt]

(y2-y1)/(x2-x1)

[fleet tiger]

si

[short cobalt]

that is slope

[fleet tiger]

(1150-0)/(1000-10)?

[short cobalt]

1150-1000

and (10-0)

[fleet tiger]

So how would I answer this

[short cobalt]

so you find the slope of the two companies

and whichever company has a greater slope has a higher rater per sq ft

does that make sense?

[fleet tiger]

Uh

Okay so

The slope for A is 150/10?

[short cobalt]

yes

[fleet tiger]

And

B is 5/100

[short cobalt]

did u do the same method?

[fleet tiger]

si

[short cobalt]

then it should be good. ill double check?

[fleet tiger]

alr

[short cobalt]

this is all good

actually

flip it

100/5

[fleet tiger]

Soooo

A

A charges higher

Okay

So nowww

Don't worry

We're almost done

Sorryyyy

Thank you for helping me so far thoughhh

[short cobalt]

which was a greater slope?

[fleet tiger]

A

[short cobalt]

150/10 --> 15

100/5 --> 20

[fleet tiger]

Wait then 100,5?

[short cobalt]

?

[fleet tiger]

nothin

Anywho

[short cobalt]

you already know slope

from the first problem

[fleet tiger]

Mhm

[short cobalt]

now find the y int

[fleet tiger]

1000,0

Because that's where the line crosses

[short cobalt]

yes

so what what the function look like?

[fleet tiger]

y=1000/5

[short cobalt]

y=mx+b

b will be the y-int

m is the slope

y and x just stay the same

[fleet tiger]

uhh

wait so

1000=150/10+1000/0?

[short cobalt]

y=15x+1000

[fleet tiger]

OH

It's 150 because 150/10 is 15

Ahhh

I'm getting it now :D

[short cobalt]

yes

great!

[fleet tiger]

AND THEN

B WOULD BE

[short cobalt]

B has a greater slope for the first question

[fleet tiger]

y=20x+1000?

[short cobalt]

for company B

[fleet tiger]

ye

[lone heart]

@fleet tiger Has your question been resolved?

[lone heart]

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[open folio]

sin(2x-17) = cos(6x+9) I wrote this as sin(2x-17) = sin(90deg - (6x + 9))

[open folio]

Now I am unsure of what to do next

Can I just cancel Sin? But that would make no sense because wtf does 90deg mean anyways

<@&286206848099549185>

[tight locust]

Use the sum identities

Or wait no you can just directly solve

[gray isle]

90deg means 90degrees

[tight locust]

You should be using radians

[open folio]

I know but

[tight locust]

So that 90° is just π/2

[open folio]

When I cancel out sin

[open folio]

That works sure

So 2x - 17 = pi/2 - 6x + 9

Can I solve like this?

[gray isle]

based on the values, it seems that the question intends for you to work in degrees

[open folio]

How

??

[gray isle]

do you have a pic of the original problem?

[open folio]

2x - 17 = 90deg - (6x + 9)

It was sent by text

The problem is sin(2x-17) = cos(6x+9)

[gray isle]

2x - 17 = 90deg - (6x + 9)
that'll only give you one of the solutions

$2x-17\deg = 90\deg - (6x+9\deg)$

[open folio]

I don't understand what 90deg - (6x + 9) even means though

[gray isle]

based on the values, it seems that the question intends for you to work in degrees
i.e. it feels that those 17,9 are also in degrees

[open folio]

When you solve it what do you get?

[gray isle]

i get a crapton of solutions

[open folio]

name a few

is 12.25 one of them?

[gray isle]

yes

[open folio]

Ok

thats the only one i got

.close

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[blissful gate]

I don’t know how to solve this problem

[last ether]

Expand it out

@blissful gate Expand 10(10y^2 - 110)

[blissful gate]

Should I multiply (10y^2-110) all by 10

[last ether]

That's the same thing

[blissful gate]

So I have 100y^2-1100

Or am I doing this completely wrong?

[last ether]

No that's correct

Now you combine like terms

[blissful gate]

oh thank you so much

am I done after that?

I got 6432+200y^2 i

is that correct?

[last ether]

Well yeah

Now you gotta match terms

[blissful gate]

so b=6432 and a =200^y

[last ether]

no y for a

But yes

[blissful gate]

oh i meant 2 my bad

[last ether]

a = 200

[blissful gate]

ohhhhhh

thanks

that's all I needed have a good one

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[lucid wadi]

Hello

Can anyone confirm if I did this right? I can’t check my answer cause mathway doesn’t do these problems 😞

[short cobalt]

Im not sure if this site does either, but have u heard of symbolab? that site is really great. even if it can't help with this specific problem. (just recommending it!)

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@lucid wadi Has your question been resolved?

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[alpine sable]

the x-27 is throwing me for a loop innit

mandem get me ya

mandems only question innit

cmonmande

[simple turtle]

I am looking at it

[alpine sable]

Thanks Bruv

[simple turtle]

3 sounds about right, but I thought you have to take derivative of cube roots for the second part. I am trying to figure out how you derive 1/27. I just got 27. Let me double check

[alpine sable]

i have to approximate it to nearest decimal

how would i do that

the derivatives are correct

[simple turtle]

you are correct

[alpine sable]

the derivatives are correct

[simple turtle]

Yes

[alpine sable]

i dont know how to apporximate in decimal

that is my question

[simple turtle]

I see. It is given x = 27.01 so plug into your equation and round it's answer to 3 decimal place.

f(27.01)

Do you agree?

[alpine sable]

YES

it worked

wtf

3 was the answer

Holy hsaufhafa

this is extra credit

but its fairly easy i think

but im not grasping it

[simple turtle]

Great! I got 3.000 too. You followed the formula. I think the derivative was the had part. I can find the link for you if you want.

[alpine sable]

which link

[simple turtle]

Here is the example of Taylor with degree of 3, but this example did not provide f(x = number) https://socratic.org/questions/how-do-you-find-the-third-degree-taylor-polynomial-for-f-x-ln-x-centered-at-a-2#159574

[alpine sable]

wow

Thank you so much

good template to follow along

[simple turtle]

Great work. You take care now. 😃

[alpine sable]

Thank you

you as well

Much appreciated!

.close

[lone heart]

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[final badge]

is this right?

[final badge]

it is. huh

[slow hearth]

yes i calculated it and its right

[final badge]

Really doubtful it's 65

this is a pain

[wary stream]

Concept of vertical angles

[final badge]

?

[wary stream]

That's how you solve it

[final badge]

huh

[wary stream]

Vertical angles

[final badge]

115 = 90
-115 -115

Is that how?

[wary stream]

Do you know what vertical angles are?

This thing

[final badge]

ok?

[wary stream]

Apply that

[final badge]

so it's just 115 = 115?

[wary stream]

Yes

[final badge]

ty

Is it 124?

yes

[carmine oar]

yes

you are correct

[final badge]

I'm guess it's 47?

mk

[wary stream]

Submit and check

You're using a website that looks like it autogrades

[final badge]

it does

It gives you a score for many right answers you get... i gotta get a score of 100 but if i make a mistake, the score drops.

paiiiiiiin

not sure bout this one

[carmine oar]

I think you're good to go

but does this interfere with academic honesty? @wary stream
idk if this is a test of your school or other organizations
no offense though

[wary stream]

If you don't get a score of 100, it just means you need to review more

[final badge]

not a test.

[wary stream]

Idk, could be a homework site

[final badge]

a homework assignment

[carmine oar]

@wary stream I'm not too familiar with the rules

[final badge]

I'm guessing it's 70.4?

gah these decimals are throwing me off

ah ####

so close to 100.

Back to 89

back to 83 now

ugh

.close

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[sharp spire]

I'm of the understanding that according to the above notes that the limit of An to infinity = the limit of Sn to infinity, assuming convergence. However let's say we have the scenario that the limit of An to infinity equals 0. Assuming it converges at 0, are there any series that show that the limit of Sn = 0 as well? All the infinite sequences that converge to 0 (some harmonics/alternating) typically have Sn not exist.

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@sharp spire Has your question been resolved?

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[ripe zenith]

hi I was wondering how you do the partial derivatives of this function

[solemn grove]

pd for x or y?

for d/dx consider y as constant

and d/dy, consider x as constant

everything else is like doing normal differentials

[ripe zenith]

either one I just know how to do it, something about this one is throwing me off.

I tried the product rule but got something different

got it with the quotient rule

issue was trying to use product rule

.close

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[alpine sable]

Is this correct solutions?

[ripe zenith]

is that triangle a triangle or the number 1?

169/91?

b doesnt seem right

since 2/5 is not the same as 21/55

c and a are right

try dividing by 3 for b

3 is a common factor for 21 and 55

[lone heart]

@alpine sable Has your question been resolved?

[ripe zenith]

any easy way to see if you are right is to put the fractions in a calculator. if they evaluate to the same thing then you can say they are equivalent. Otherwise you made a mistake.

example would be 21/55 if you put that in a calculator ~0.38 if you put 2/5 you get 0.4. To be correct they both need to equal ~0.38

[ripe zenith]

hope this helped

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[unreal kettle]

hi all, can I check how do i solve this question

[unreal kettle]

i) cond mean = 5, cond sd = 1, prob = 0.8413
ii) Yi ~N(8, 27), prob = 0.7373136708

(these are my answers, but i'm unsure if they're correct)

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[unreal kettle]

<@&286206848099549185>

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[white ferry]

Can anyone help me understand why - Discrete Math

[white ferry]

x-y != 0 is not transitive

[bitter vault]

Take $x=2$ and $y=1$. Then x ¬ y as $x-y=2-1=1\neq0$. Similarly, y ¬ x. But x is not related to itself.

[ocean seal]

1345631

[bitter vault]

Used weird symbol ¬ (logical not) for tilde, since bot wasn't showing it

[white ferry]

Sorry isnt being related to itself reflexive?

[bitter vault]

Yes. But you have x ¬ y and y ¬ x but not x ¬ x. So it is not transitive

Remember transitivity means: if x ¬ y and y ¬ z, then x ¬ z. Take x = 2, y= 1, z=2 in this.

[white ferry]

ok let me do the working. thank you ill report back in a sec

ok so x ¬ z is false

we you found an example of it being not transitive as all three parts of the equation have to be true?

so even though it is possible to have say x = 3, y=4, z=5, in this scenario it would be transitive. But overall it is not transitive for all x y and z?

[bitter vault]

not sure what you mean by we you, but yes. this is a counterexample

[bitter vault]

transitive means it holds for any x,y,z

[white ferry]

ah right

ok so I understand this. But how do I find a counter example without brute force

this seems easy enough, but what if the counter example was more obscure

[bitter vault]

this wasn't really brute force. you just have to think about the example

[bitter vault]

you just have to try it out and see if it is transitive. there is no trick unfortunately

[white ferry]

right ok

so if we were given
x = 3, y = 4, z=5 see if x-y!=0 is transitive, you would say it is in this case?

but x-y!=0 is always not transitive

without being given specific numbers to input

!close

.close

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[alpine sable]

How to solve this long problem

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[alpine sable]

<@&286206848099549185>

<@&286206848099549185>

Uhh.

.close

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[rose osprey]

help

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[jade fox]

Did I do these right? I’m pretty confused with the second one

[tall hearth]

your first answer is wrong
your second answer has the right expression but you've evaluated it wrong

[jade fox]

How so?

Where did I go wrong for the first?

[tall hearth]

well you havent shown any working

just written an expression

[jade fox]

Did I have the right expression for the first?

[drowsy lagoon]

the first one is missing pi in the answer

but the formula is correct

[jade fox]

So it’s just 81pi/7?

[drowsy lagoon]

yes

second is missing pi as well

[jade fox]

Is that it?

[tall hearth]

$\frac{\frac{2π}{7}}{2π} × πr^{2} = \frac{πr^2}{7} = \frac{81π}{7}$

[ocean seal]

kinglacto

[tall hearth]

$\frac{5π × 1.5}{9} ≠ \frac{5}{6}$ btw

[ocean seal]

kinglacto

[jade fox]

So then how do I set up the second

[drowsy lagoon]

rmb pi is actually a constant

[tall hearth]

it is correct

[drowsy lagoon]

it is a number

[jade fox]

So 5pi/6 is correct?

[drowsy lagoon]

yes

[tall hearth]

yes

[jade fox]

Alright thanks

[lone heart]

@jade fox Has your question been resolved?

[lone heart]

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[drowsy scroll]

Does anyone know what this means when x is in this weird box

[drowsy scroll]

|x| whats this means?

[placid zinc]

Absolute value function

|| takes whatever is in them, and returns the positive version

So |3| = 3
|-2| = 2

[drowsy scroll]

if x was negative it would come back as positive?

Ohh okay

.close

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[ocean seal]

Juia

[solemn grove]

so do you have x or y of the point where the rectangle/square touches the graph

/ are you sure it’s a square

@cunning bolt

if it is 100% a square

y = x

[cunning bolt]

It is a square 🙂

[solemn grove]

$x = -x^2+3x +4$

[ocean seal]

Rylo

[solemn grove]

$x^2 -2x = 4$

$(x-1)^2 = 5$

find x

and square it

[ocean seal]

Rylo

[rare verge]

aaaaa

[cunning bolt]

@solemn grove Can you elaborate?

[solemn grove]

^^ cuz it’s a square

[cunning bolt]

I should find an expression that is the area of the square to A = side * side

[solemn grove]

yeah, so x = y ?

because they’re both sides

[solemn grove]

so you get that

find the positive value for x

that’s your side

[lone heart]

@cunning bolt Has your question been resolved?

[lone heart]

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[haughty fiber]

"You have just 8 hours to prepare product for this sale. You start with a plain white T-shirt. This is your most popular color. But you can dye the white T-shirt blue, yellow, or red—but only one shirt at a time. Your current inventory is 50 white T-shirts and you have enough dye to make 12 red shirts, 10 yellow shirts, and 15 blue shirts. Based on experience, you know that at a sale like this, you will be able to sell all 50 shirts. Use the data in the table below to determine how many shirts of each color you should bring to the sale to maximize your profits"

So my thinking is

X = 7a + 8b + 8c +6d

X being the maximum profit and the other variables being each color

[haughty fiber]

This is linear programming

I want to learn how to format it, I don't want someone to solve it for me

I am most confused on how to plug in the time required

[lone heart]

@haughty fiber Has your question been resolved?

[haughty fiber]

So my constraints are time

and t shirts

=< 50
=< 480

[next brook]

Are you positively required to use a linear programming solver? The numbers look like it's easier to just wing it.

[haughty fiber]

Yeah need to show the work

[next brook]

And an argument in prose won't cut it?

[haughty fiber]

Idk what the heck I'm supposed to do with cost of materials because there is no money constraint?

[haughty fiber]

It may if I'm not able to figure it out 😅

I'd rather get some points than non

none*

[next brook]

Well, ||red shirts are a losing proposition -- leaving a shirt white rather than dying it red will save you time and net you an extra dollar of profit.||

On the other hand ||each time you dye a shirt blue or yellow, you make another dollar in profit. You don't have time to spend use all your blue and yellow dye, so you'd just do as many of those as you can.||

Though, at a marginal profit of $3 per hour of work, I would seriously consider just playing video games for the whole 8 hours and sell the shirts in white.

[haughty fiber]

LMFAO I agree

Sadly I don't think my instructor wld like that answer

that was the first thing I thought when I was this

[next brook]

The cost of materials is relevant inasmuch as you'll still have the materials you don't use afterwards, so that will mean you can save on purchasing more supplies later.

But I think the "cost of materials" and "selling price" columns are in fact irrelevant for the calculations, since they're both counted into the "profit" column which is what you really want to maximize.

[haughty fiber]

Yeah I'm starting to think that too

In linear programming do you only have 2 constraints everytime?

Or can it be more / less?

[next brook]

No, there can be as many as you need.

[haughty fiber]

That makes it more confusing because what if I accidently miss one

ahhaha

crap

So far though I think it should look like this:

Constraints
0a + 20b + 20c + 40d <= 480
50a + 15b + 10c + 12d <= 50

Objective
Z = 7a + 8b + 8c + 6d

Is that how you type out "less than or equal to" ?

[next brook]

You get constraints like b >= 0 and b <= 15 too.

<= is common enough, yes.

[haughty fiber]

Wdym?

In this problem specifically, or you meant as an example for other problems

[next brook]

In this problem specifically.

In particular, unless you tell the solver you cannot make a negative number of red shirts, it will tell you to dye minus a billion shirts red, and sell the billion white shirts that earns you as they are.

50a + 15b + 10c + 12d <= 50
This looks like a misunderstanding.

You want b <= 15 and 10 <= c and 12 <= d.

Since it doesn't make sense to say 15b -- that would mean "multiply the number of blue shirts you make by the number or blue shirts you could have made", which is neither here nor there.

[haughty fiber]

Now I'm omega confused 😅

[next brook]

What you do want for the 50 is a + b + c + d = 50.

The "you have enough dye to make this many shirts" column doesn't say it takes 15 units of dye to make one blue shirt. It says you will run out of dye if you try to make more than 15 blue shirts.

[haughty fiber]

hmmm okay

that KINDA makes sense

[next brook]

Another way to see that 50a + 15b + 10c + 12d <= 50 is not a constraint you want is this: One thing you could decide to do -- not necessarily optimal according to the problem, but possible -- is to leave all the shirts white. That would have a=50, b=0, c=0, d=0. But then your proposed constraint would read "2500 + 0 + 0 + 0 <= 50" which is not true. So the constraint would exclude this perfectly valid outcome.

[haughty fiber]

Ah okay this makes more sense

[haughty fiber]

I'm a little confusedo n these, why did the variables swap sides?

[next brook]

That was a typo, sorry. It should be d <= 12.

[haughty fiber]

Ah okay

hmm

[cunning bolt]

Can someone help?

[alpine sable]

uh i have a simple question do i ask it here?

[haughty fiber]

@cunning bolt @alpine sable You guys have to ask in an available channel, this one is occupied

Check out #❓how-to-get-help

[alpine sable]

@haughty fiber yeah i figured that out mb

[haughty fiber]

No problem!

@next brook So my constraints would just be?:
(time)
0a + 20b + 20c + 40d <= 480
(shirts)
a <= 50
b <= 15
c <= 10
d <= 12

[next brook]

Yes, but you still also need a >= 0 and b >= 0 etc.

As well as a + b + c + d = 50.

[haughty fiber]

Man that's a lot of constraints no

? *

I feel like we're doing something wrong if we have that many constraints

[next brook]

Nah, pretty much par for the course.

It's routine to have an upper and lower bound for each variable, and you only have two constraints that mix variables.

[haughty fiber]

Do we really need lower bounds if we only need the max profit?

Is that so if we do no red shirts?

[next brook]

Yes, I think so.

The solver doesn't know it makes no sense to have a negative number of shirts unless you tell it to.

And without a lower bound it looks like "decrease reds by one and increase whites by one" is always a win.

[haughty fiber]

Ahhh that makes sense

[next brook]

Solvers are pretty good at ignoring bounds that are not really relevant to finding the optimum, so just throw everything that makes sense at them.

[haughty fiber]

Solvers?

[next brook]

In practice, linear programming problems are solved on computer using specialized linear-programming solving software. Hundreds of variables and thousands of constraints is a small problem for them.

[haughty fiber]

Ahhh okay

So we have all the constraints figured out right?

(Objective)
Z = 7x_1 + 8x_2 + 8x_3 +6x_4
(time)
0x_1 + 20x_2 + 20x_3 + 40x_4 <= 480
(shirts)
x_1+x_2+x_3+x_4=50
0 =< x_1 <= 50
0 =< x_2 <= 15
0 =< x_3 <= 10
0 =< x_4 <= 12

[next brook]

a+b+c+d=50 too.