help-42

[velvet osprey]

it sounds like you did some bullshit

[gleaming lark]

nah I didn't write it down

[velvet osprey]

[gleaming lark]

😦

I am just kinda lost on this one

ok I'll type out everything I am trying to do

so x is food containers and y is water

each food container is 175 pounds and each pound of food is worth 8 dollars a pound

so revenue per container is 175 times 8 = 1400

each container of water weighs 60 pounds and each pound is worth 4 dollars

so revenue per container is 240

so the revenue function should be max=1400x+240y

max weight is 27000

so 175x+60y greater than or equal to 27000

max space is 575

so 5x+y < greater than or equal to 575

and I think I am supposed to graph this out right?

I am not sure how to get at it from here

do I graph it?

[velvet osprey]

so 175x+60y greater than or equal to 27000
other way around

175x + 60y should be less than or equal to 27000

[gleaming lark]

sorry my bad

thank you so much for the help btw

I know I am kinda dumb

so with all this written out how do I get the answer?

I am lost at that part

[velvet osprey]

to wrrite this all out in a less messy way, you are looking at the following problem:

maximize 1400x+240y

subject to the constraints:

175x + 60y <= 27000
5x + y <= 575
x, y >= 0

[gleaming lark]

so can I put this into a graphing calc?

[velvet osprey]

dunno, probably depends on the calc

i'm putting it into desmos

three corner points

[gleaming lark]

ok so those are my points

so my max is 450K

and its 275 units of food and 115 units of water?

wait they would go over the weight limit

so 60 units of food and 115 of water

nah that would only be 17400

275 units of water

and 0 units of food

and then I calc profit after that?

I am not sure what points I take for my food and water here

wait

450 times 60

=27000

on the dot

so

I think its 450 units of water

0 units of food

so

108000 is profit

450 units of water and 0 units of food

I believe is the answer is that right?

nah I got it wrong 😦

[calm coral]

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[late crane]

u = (-1+i✓3)/2

Calculate u² then u³ then u²⁰⁰⁸
Then calculate
s = u + u² + u³ + ... + u²⁰⁰⁸

[vagrant oak]

did you manage to do the u^2, u^3, u^2008 part?

[late crane]

I managed to calculate the square and even the cube, but it seemed illogical to me to calculate 2008

[dull wagon]

how did you calculate the u^2 and u^3?

did you do binomial expansion?

[late crane]

u² = (-i✓3 - 1)/2

[late crane]

I expand the powers

[remote mural]

Notice that number has a magnitude of 1

Hence you can rewrite it as e^(ti) (pretend t is theta)

What did you get for u^3?

[late crane]

Which number?

[remote mural]

u

Again, what did you get for u^3?

By the way I typically don't pay too much attention to notation but ✓ is a tick, not a square root symbol, you can simply write sqrt(3)

[late crane]

u³ = 1

[late crane]

Ok

[remote mural]

Doesn't that ring a bell for how to calculate any arbitrary power of u?

[late crane]

Oops , i think it's wrong

[remote mural]

❌ It's not only correct, but it's also essential to the question

[late crane]

Yea

Can u give me minute to calculate it again?

[remote mural]

Eh... Sure?

[late crane]

Nvm , i check again it's 1

[remote mural]

Mhm

[late crane]

So what about u^2008

[remote mural]

Notice u^2008=u^3*u^2005

[late crane]

And u^2005?

[remote mural]

Notice u^2005=u^3*u^2002

*a couple days later*
Notice u^4=u^3*u^1

[late crane]

Yeah 😅

[remote mural]

You might be wondering how I knew we would end up with u^1 and not u^2 or u^0

Well it turns out 2008=3*669+1

I just took the remainder mod 3

@late crane Do you understand everything up to that point? If so, let's go onto how we calculate s

[late crane]

So it's will be u¹

[late crane]

@remote mural yea

[remote mural]

Using the insight we found about how to find any arbitrary power of u, do you see a pattern in the sum?

[late crane]

No , but i think we will use u^3, right?

[remote mural]

Mhm

[late crane]

How might I find the pattern?

[remote mural]

Think of how we would use the fact that u^3=1 to simplify, say, u^4+u^5+u^6

@late crane Hmmm, did I lose you?

[whole saddle]

its binomial expansion right?

[late crane]

I'm here

[late crane]

Just think how to write :u² like u³

So I take out whatever I can get out of power ^e like 2008 = 3*669 + 1

[late crane]

I think yea

[remote mural]

@late crane So...? How would you simplify u^4+u^5+u^6?

[late crane]

(u²)²+u⁵(idk)+(u³)²

[remote mural]

Can you think of a way that makes use of u^3?

Similar to how we just showed u^2008=u^1

[late crane]

u⁵ = u^(3 + 2) = u³u²?

[remote mural]

Mhm

Can you do the same for u^4 and u^6?

[late crane]

u⁶ = (u³)²
u⁴ = (u^(3+1)) = u³u¹
Right?

[remote mural]

Yep

That's the basic idea

Then if you take into account that u^3=1, what does u^4+u^5+u^6 become?

[late crane]

so S= u + u² + u³(1+u+u²+...+u⁶⁶⁹)?

[remote mural]

That is correct but you can do easier

[remote mural]

First answer that question

[late crane]

u⁴=u¹
u⁵=u²
u⁶=1

[remote mural]

Mhm

Obviously u^1+u^2+u^3 also gives these 3 numbers

What about u^7+u^8+u^9?

[late crane]

u⁷=u
u⁸=u²
u⁹=1

[remote mural]

Notice a pattern yet?

[late crane]

I get it

So How often will it be repeated

[remote mural]

Look at the largest powers of each bits

u^3, then u^6, then u^9, etc...

All the way up to u^2007

[late crane]

So 669 repeated

?

S = 669U + 668U² +668?

@remote mural

[remote mural]

Why did the other 2 become 668?

[late crane]

I try With a series of four, five, six terms, i found
If we have 4 consecutive numbers like u + u² + ..+u⁴ it's and try to find How much it will we have this 3. Number (u + u² + u³) by calculate 4/3 i found 1.333 it's mean it's repeat 1 time and + 1 number (which is u)

Then i try use with 5 number (u+u²+...+u⁵) and 5/3 = 1.666 so it's mean it's repeat 1 time and +2 number (u+u²)

And if we have 6 numbers (u+u²+...+u⁹) and 6/3 = 2 so it's will repeat 2 times and we Will not have other number (it's will stop in number 1

I've only heard something like this before and it crossed my mind now, I don't know if it's true

[remote mural]

the what

[late crane]

Just don't care about it, I think it's wrong

[remote mural]

Okay so by your logic 2007/3=669 so it will repeat 669 times

Which is true

Hence... Where does 668 come from??

[late crane]

@remote mural 770* not 668

S = 669U + 669U² +670

[remote mural]

???

Where does 770 come from?

Same for 670

where does that come from

[late crane]

From here

2008/3=669.3333

[remote mural]

No no

The top power is always a multiple of 3

Hence the pattern goes up to u^2005+u^2006+u^2007

[late crane]

I think will have (u + u² + u³)669 + u

[remote mural]

Close enough

u^2008 actually becomes u^1

Like we found earlier

So 669(u+u^2+u^3)+u

[late crane]

Opps , it's like this

It was my fault

[late crane]

I was thinking of it as u³ 😅

[remote mural]

yeah I got that

[late crane]

😅

Well , so S = (u + u² +u³)669 + u

[remote mural]

mhm

[late crane]

Alright

Tysm 😁 @south hill

[remote mural]

bruh

[late crane]

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[stark cloak]

I would really appreciate some help with a game theory proof. Its about ehrenfeucht fraisse games but I think one can also understand the problem and help me with some good graphtheory knowledge. Question follows

[stark cloak]

Question: I need to show that for every m in N there are two Structures A_m and B_m such that A_m is a connected graph and B_m isnt and they are m-equivalent. (I can explain this term if needed)
So I thought I would show that there is the C_n with n = 2^m , so its an exponentially big circle graph which is supposed to be A_m and then B_m is build of two disjunct C_n/2 graphs. So its not connected. (I'll send an example picture)
Now I would have formulated the invariant that in every round of the m round game the duplicator has to pick as follows :

if the spoilers pick is closer or equal to 2^(m-i) to any already chosen node then the duplicator has to pick the node in the opposite structure that has the exact same distance to every corresponding node. And if not the duplicator can pick anywhere.

Now from my understanding this should always work for the duplicator as the circles are exponentially big and my problem now is that I cant really explain why the duplicator would always find a node to pick that satisfies the invariant

Sorry for this huge post. If anything is not well explained please let me know and I will try my best to explain the details. Thanks in advance

[crude solar]

I don't think anyone can help you in here @stark cloak ...

[stark cloak]

how did you come to that conclusion

I mean in the end its a mix of gametheory and graphtheory

[crude solar]

not alot of people in here who can do high level math

ping the helpers

[stark cloak]

hm

yeah well then

[crude solar]

<@&286206848099549185>

[stark cloak]

tomorrow is a lecture where they will explain it

but I am literally trying to prove this for this entire day

and also tried throughout the entire week

I feel like I know the answer but I cant formulate it

its so frustrating

[crude solar]

have you tried chatGPT?

[stark cloak]

lol didnt have good experience regarding math

but thanks for the suggestion

[crude solar]

no problem

[stark cloak]

._.

its definitely not definable

lol

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[hot kindle]

We have triangle ABC with three median lines AH, BI, and CK. Prove that the intersection of the three median lines is the centroid of the smaller triangle HIK

[hot kindle]

also note that I have not proven:
1/ The intersection of two midpoints on two sides is 1/2 of the otehr side

2/ The intersection of two midpoints on two sides is parallel to the other side

and also no trig cuz well

grade 9

and no pythag

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<@&286206848099549185>

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<@&286206848099549185>

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[short anvil]

Can someone help me on question 4? The answer is 0.00169 rounded but I’m having trouble getting to that answer.

[leaden thunder]

,rotate

!show

[calm coral]

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

[short anvil]

Yes thank you. just 4

I did all the other ones

Using the binomial probability formula

But this is different bc it says “fewer than” instead of an exact amount

What do u do in that situation?

[amber bolt]

it's kinda obvious

i don;t mind telling but maybe knowing that it's obvious helps idk

[short anvil]

I get like fewer than 4 but how do u do that

Do u just add them all up?

I tried that but it wasn’t the correct answer

[amber bolt]

you just addthemallup

[short anvil]

Ok I’ll try again ig

[amber bolt]

if it still doesn;t work ||you must be doing 1, 2 or 3 instead of 0,1,2 or 3||

[short anvil]

Wow it works. I wasn’t including 0 like u said lol.

Thanks

.close

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[inland heron]

Let a_1, a_2, a_3, … be an arithmetic sequence.

If a_1 + a_3 + a_5 = -12 and a_1a_3a_5 = 80, find all possible values of a_10.

[wise moss]

have you tried anything?

[inland heron]

I don’t know where to start

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[inland heron]

<@&286206848099549185>

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[remote mural]

how did the " = " sign in the red part gone??also how did they change the green highlighted part?

[dreamy shale]

could be a typo

also sketch the graph and it should make sense that the inequality is that way around for the green bit

[remote mural]

idk that

i will just speedrun that chap

then do this qn again

.close

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[bitter creek]

What is Y in
4x - 2y = 10
y= -2x + 5

[craggy whale]

Well you solved it already

[bitter creek]

I need to get Y by itself

[craggy whale]

You did

[bitter creek]

Wait I read it wrong mb

I need to know how many solutions it has

One, none, infinite

[craggy whale]

Infinite

As x can be any number

[reef nimbus]

I don't think so...

[bitter creek]

Likewise. That would render half my homework too easy.

[reef nimbus]

plug the expression for y into the first equation, solve for x. then solve for y

[bitter creek]

4x - 4x + 10 = 10?

[craggy whale]

Oh okay that was a stupid of me

[reef nimbus]

check your signs

[bitter creek]

?

[reef nimbus]

you have a sign error

[bitter creek]

Where? I can't find it

[reef nimbus]

look more closely when you substitute

[bitter creek]

oh is it actually
4x - -4x + 10 = 10?

[reef nimbus]

not quite, one of the signs is right though

-2 times y, where y = -2x + 5

[bitter creek]

4x - 4x + -10 = 10?

[reef nimbus]

no...

what is -2 * -2x

and what is -2 * 5

[bitter creek]

idk

[reef nimbus]

you don't know how to multiply those?

[bitter creek]

dude it's midnight for me and I want to sleep

I got school in 7 hours

-2 * -2x = 4x because - * - = +

-2 * 5 = -10

[reef nimbus]

yes

[bitter creek]

4x - 4x + -10 = 10

[reef nimbus]

you changed a sign again. you just had it correct

[bitter creek]

4x + 4x + -10 = 10

[reef nimbus]

yep

[bitter creek]

so uh

infinite solutions?

[reef nimbus]

no, just solve for x

[bitter creek]

I need to know how many solutions

one, none, or infinite

[dreamy shale]

u are literally like 2 steps from solving it just solve for x

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[opal comet]

In a survey of 60 students, 25 said that they enjoy science class. what is the ratio of students who enjoy science class to those who don't?

[opal comet]

i already tried the question '

but i got a decimal instead of a whole number im so confused

wait

maybe it is n:1

ok nvm

.close

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[remote mural]

will y=e^x touch y=x at infinity?

[alpine stone]

Depends on how you define two functions touching at infinity

If you mean both functions approaching the same value or infinity, then sure

[remote mural]

i am solving this qn

the answ given is c

[alpine stone]

1. As you can see, they don't intersect anywhere; Thus the intersection of A and B is an empty set
2. Even if "they touched at infinity", infinity is not an element of R

[remote mural]

ok

thx

👍

i thought infinity will be considered in R

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[hallow python]

hi

[hallow python]

,w [FerrersDiagram][{3,1,1,1}]

[potent lotus]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by 13wrc#1722

[hallow python]

I am trying to make the ferrers diagram for all possible partitions of 6

,w ["FerrersDiagram"][{3,1,1,1}]

[potent lotus]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

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[hallow python]

can someone tell me how to do this thing? What is the correct query?

,w [FerrersDiagram][{3,1,1,1}]

[potent lotus]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by 13wrc#1722

[hallow python]

,w["FerrersDiagram"][{5, 4, 2, 2}]

,w ["FerrersDiagram"][{5, 4, 2, 2}]

[potent lotus]

Results provided by WolframAlpha

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[hallow python]

.close

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[calm coral]

Channel closed

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[obtuse flicker]

.reopen

.close

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[olive wigeon]

i don’t get it

[calm coral]

@olive wigeon Has your question been resolved?

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[olive wigeon]

<@&286206848099549185>

[olive wigeon]

can someone help

[calm coral]

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

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[olive wigeon]

bro can someone help me please

I don’t get what it wants me to do

[calm coral]

@olive wigeon Has your question been resolved?

[potent shoal]

For the first one, the volume of a rectangular prism is length * width * height or V=lwh. If you double any one of those measurements (for example length), you would get (2l)wh = 2lwh = 2V, so the volume would double. You would apply a similar idea to the other problems

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[steady palm]

How do I do No.18? Instructions: simplify each expression. Give answers in simplest radical form

[solar spruce]

write $24 = \sqrt[3]{24^3}$ so you get $$\frac{\sqrt[3]{24^4}}{24}=\sqrt[3]{\frac{24^4}{23^3}}$$

this should be easier to solve

[potent lotus]

maximo

[steady palm]

? What did you do there?

[solar spruce]

where

[steady palm]

How did you get this

[solar spruce]

which part

[steady palm]

When you rewrote

As

[solar spruce]

substituted the cubed root of 24^3 for 24

give me a minute

[steady palm]

Ok

[solar spruce]

$$\frac{\sqrt[3]{24^4}}{24}= \frac{\sqrt[3]{24^4}}{\sqrt[3]{24^3}} = \sqrt[3]{\frac{24^4}{23^3}}$$

[potent lotus]

maximo

[solar spruce]

and then we just write the cube root around everything.

[steady palm]

Ah ok

Wait how did 24 become 23

[solar spruce]

oops a mistake

its supposed to be 24

[steady palm]

Ah okie

Bye! God bless! Jesus loves you so much!

.close

[calm coral]

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[crude solar]

am I right? All the answer options are the same on the right side of the problem.

[potent igloo]

this a test?

[crude solar]

no.

[high igloo]

It looks like a test.

[crude solar]

it's not a test..

I took a snip and left out the title(in a rush). Would you want me to retake the snip with the title?

[exotic falcon]

sure

What are the points for if it's not a test?

[crude solar]

a minor grade (schoolwork)

the points correspond with the slide

[calm coral]

@crude solar Has your question been resolved?

[calm coral]

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[stiff copper]

I have to make a gemetrical interpretation of the matrix
(1 4|-3)
(0 0|0)

The last vector equation "(-3 0) + λ(-4 1)" is the solution
i don‘t get how i can calculate the solution from the given matrix

[solar spruce]

the solution to what

[stiff copper]

the solution of my geometric interpretation

i don't see how i get from:
(1 4|-3)
(0 0|0)
to the last picture i sent which is a vector that does not intersect with the origin

[calm coral]

@stiff copper Has your question been resolved?

[stiff copper]

<@&286206848099549185>

[solar spruce]

the solution line does not pass through the origin

if it did, your matrix times 0 would give you <3, 0>, but any matrix right multiplied by the zero vector results in 0

@stiff copper is there anything else that confuses you

[stiff copper]

i only have the matrix i dont see how i can get to the vector equation from only the matrix. that's what i should do but i don't know how eventhough i go the solution

[solar spruce]

you solve the system x + 4y = -3

which gives you x = -3 - 4y

then for a vector of the form <x_1, x_2>

we get x_1 = -3 -4x_2

so our solution set is the vectors of the form

$\langle -3 - 4x_2, x_2\rangle$

[potent lotus]

maximo

[solar spruce]

does that make sense

[stiff copper]

ohh i see now and the bottom part is irrelevant since the equation is 0 0 =0

[solar spruce]

yes

[stiff copper]

thx

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[calm coral]

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[strange grove]

subs {x -> f(y)}
∀y (p(f(x))&∀x p(x)), substitute should throw: NotApplicableException

[strange grove]

can someone explain me why this substitution is not applicable?

x is free variable in a first half

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[worn elbow]

plss help

i was trying to use integrals

[tardy harness]

can you show your work

@worn elbow What is the value you need for X

[worn elbow]

bruhh

okie

lemme

show

but first you know its physics

[tardy harness]

i suppose this is from wheatstone bridge concept

specifically meter bridge

but the difference is that the resistance offered by the conducting wire is non-uniform that is it changes with respect to the length

[worn elbow]

yes

i just want to know

what is the realtion between

lenght

and radius

how can i find the function

of lenth and radius are related

this line

[tardy harness]

$R=\frac{\pho \cdotl}{A}$
$dR = k \frac{dl}{dr}$

[worn elbow]

bruhh

i know that

but i think

there is no function given

of l

to integrate it

and find the area

without resistance we cant use

meter bridge concept

[tardy harness]

is the answer 1

[worn elbow]

lemme check

[tardy harness]

if it is then i can explain

otherwise , i suppose not

[worn elbow]

actually answer is not given in paper

can u tell how you do it

?

i think you are right cuz

thi is given

[tardy harness]

see this

,rotate

,rotate

,rotate

[tardy harness]

btw there is a constant k

which i didn't put in there because it just cancels out

[worn elbow]

0.6?

[tardy harness]

ahh wait

[worn elbow]

actually length is constant

[tardy harness]

i assumed the wrong thing

[worn elbow]

throughout

the wire

[tardy harness]

area is varrying

[worn elbow]

yes

[tardy harness]

wait let me do it again

[worn elbow]

i told ya area need to be find here

[worn elbow]

how?

[tardy harness]

my bad

[worn elbow]

element cutting?

[tardy harness]

think of it as a differential eq

then integrate it

answeer should 5

@worn elbow

[worn elbow]

why did u taken 0.6?

[tardy harness]

cause it is changing linearly, and since the galvanometer is showing no reflection at midpoint then that should be the part of difference between area 1 and area 2 which account for the change in the resistance respectively for each of them

thus making a wheatstone bridge

@worn elbow

doubt clear ?

[worn elbow]

umm

yes

thanks

you solved it very easily

you are a genius bro

[tardy harness]

i suppose i do know some physics

[worn elbow]

where you from

?

[tardy harness]

kindly refrain from asking such question in channel, if you want then dm me

.close

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[tepid willow]

3x - 7 = 2

3x = -5?

[tender coral]

Nope

You need to add 7 on both sides to get rid of it

[cerulean compass]

a way to approach questions like this is to think <<How can i get this term to be 0?>>

so you'd add 7, as 7-7=0

3x = 9

[calm coral]

@tepid willow Has your question been resolved?

[tepid willow]

why?

i thought otherwise...

[rugged pivot]

wsg

[calm coral]

@tepid willow Has your question been resolved?

[tepid willow]

I was always taught you just move to the other side and change the sign (ex -7 to 7, 7 to -7) @tender coral @tender coral

Why is this so different now?

[tender coral]

Yeah, you "move" the -7 to the other side by adding 7 to the right side

[tepid willow]

But sometimes you don’t

[calm coral]

@tepid willow Has your question been resolved?

[potent smelt]

@tepid willow can you explain what your confusion is exactly?

what do you mean by "but sometimes you don't"?

[tepid willow]

I always was taught to only minus one side

I’m now totally confused with algebra..

[tepid willow]

.close

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[shut ermine]

how do I get ordered pairs

[shut ermine]

I am curious on how this happens

[calm coral]

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@shut ermine Has your question been resolved?

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@shut ermine Has your question been resolved?

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[ionic condor]

hey

[ionic condor]

is there a way i can calculate this

the black part not the blue area

I don't know how to use integrals for this

<@&286206848099549185>

[strange lichen]

U want arc length

[ionic condor]

yes

@strange lichen

[strange lichen]

Ok, just search it up

[ionic condor]

found it

thanks

.close

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[arctic cove]

I can't see how the answer comes about for this question; I have used the method where u do simultaneous equations and check if the direction vectors work, but I end up that they don't work. Am i missing something, an error, or is the question wrong given that the source of questions is known to make many errors. The vector intersect was said to be (6, -7, 4).

[arctic cove]

i've reversed that lambda is -3 but it doesn't work when i tried to find mu and got -8 = -6

maybe someone has a calculator which could check this sort of thing?

[upper sparrow]

,w solve 2 + u = 3 - w, -1 -2u = 2 + 3w, 2 - 3u = 4

[potent lotus]

Results provided by WolframAlpha

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Requested by chartbit#3171

[upper sparrow]

Think you're right about there being no solution

[arctic cove]

yeah i was struggling with a few other qs from this source which im guessing also would have been wrong, damn. Thank you

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[noble thunder]

hey can someone help me out with this

[white urchin]

Try and construct a summation using only the positive numbers, and another summation using the negative ones.

also notice that each number is a multiple of seven

as well as a power of 2

[swift laurel]

you should be able to find an expression for the nth partial sum

[gray leaf]

It's a geometric series

[calm coral]

@noble thunder Has your question been resolved?

[noble thunder]

i tried this

but i couldnt get any of the answers

could someone work it out for me

[calm coral]

@noble thunder Has your question been resolved?

[noble thunder]

<@&286206848099549185>

[calm coral]

@noble thunder Has your question been resolved?

[cold pier]

7-14+28-56+...………[phone]
= 7 (1+4+16+...…..+1024) - 7 (2+8+32+...….+2048)
= 7(1+4+...…+1024) - 14 (1+4+...….+1024)
= -7 (1+4+.....+1024)
sum of gp = a(r^n - 1) / (r - 1)
Here r = 4 and a =1 and n = 6
= -7 (4^6 - 1) / (4-3) = -9555
Hope u understood (hope i'm correct lol)

[calm coral]

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[lapis thorn]

not sure if its okay to ask to explain a mathologer vid but here it goes

[lapis thorn]

https://youtu.be/ZIQQvxSXLhI?t=807

my man says the rubber we are stretching is 1 unit long

we wrap it around a wheel

but apparently a little calculus tells us that the circumference of the circle is ln(10)

[bronze adder]

,calc ln(10)

[potent lotus]

The following error occured while calculating:
Error: Undefined function ln

[bronze adder]

,w ln(10)

[potent lotus]

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Requested by NEONPerseus#2128

[bronze adder]

Close enough

[lapis thorn]

to what?

[calm coral]

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[solemn scarab]

I just need help on c-e

i wrote the above for c and d

was wondering if you could tell me if it looks ok, and how to stsrt e

[calm coral]

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[calm coral]

@solemn scarab Has your question been resolved?

[solemn scarab]

.help

[calm coral]

Commands:
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consensus: .poll
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[solemn scarab]

.close

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[tight locust]

<@&286206848099549185>

[potent igloo]

Do you know your implicit differentiation?

[tight locust]

Kinda

I know what i need to find, but i don't know exactly how to implicit differenciate 90K^(2/3)L^(1/3)

I know we need to find dK/dt

[calm coral]

@tight locust Has your question been resolved?

[tight locust]

<@&286206848099549185>

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[tight locust]

.close

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[sudden nebula]

Anyone see my mistake,

[hollow totem]

You split it up into 0-3 and 4-6

what happened to 3-4

[sudden nebula]

oh shit

I need 3?

alrighty

makes sense

ty

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[frank gull]

no what they're saying is that you should do it between 0 - 4 and then 4 - 6

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[sudden nebula]

doesn't that conflict with this though?

[sudden nebula]

cause for the top part, 4 wouldn't be included right?

Assuming I'm wrong about the above, can anyone see what I did wrong with my computation?

figured it out! had my sign wrong towards the end

.close

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[sudden nebula]

The option on the top right isn't true because I'm including everything right? Not just one side ? Or what's a better explanation for that?

[calm coral]

@sudden nebula Has your question been resolved?

[reef nimbus]

looks right

[sudden nebula]

Do you think you could reword it

I feel like my explanation is sub par

[reef nimbus]

why sub par

[sudden nebula]

What do I really mean by everything?

Like

is the whole area shaded because of the intervals I used?

Top right doesn't make sense because the interval isn't from 0 , 3 ?

[reef nimbus]

what intervals?

[sudden nebula]

oh

I computed them from the function

cause I was given that y = 0

so I plugged in y and found my x's

-3 and 3

[calm coral]

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[civic dirge]

If you're told to "eat this apple" do you ask "wait, do you mean only half the apple?" It's a bit of a weird question

"Integrate this region"
"Wait, do you mean only half the region?"

It goes without explaining

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[white skiff]

Hey guys

[white skiff]

It says the answer is b not a

Im curious why its not a

It semes like both works

[halcyon ore]

its only a 2nd degree

its 1+2x-2x^2/2!

which is B

@white skiff

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[wise tangle]

why is it x - 50 = y

if there's 50 more men than women

shouldnt it be x + 50 = y

[slender cove]

think about it

[wise tangle]

if it's a -, doesnt that mean theres 50 less men than women?

[slender cove]

theres 50 extra men than woman

[wise tangle]

yes

[slender cove]

so i gotta remove those 50 to make them equal no?

x - 50 = y

[velvet osprey]

the number of men is 50 more than the number of women

x = y+50

@wise tangle you're putting the +50 on the wrong side there

[wise tangle]

hm alright

[velvet osprey]

is it just me or does that sound like you are not entirely convinced

[wise tangle]

yeah

im still not fully understanding

because

lets say, theres 1 man and 1 woman

and if theres 50 more men than women

it'll be x + 50 = y

which is 51 = 1

whichis 50 more men than women

[velvet osprey]

theres 1 man and 1 woman
and if theres 50 more men than women

these two sentences contradict each other

"1 man and 1 woman" would mean the numbers of men and women are EQUAL.

[velvet osprey]

51 is not equal to 1

[slender cove]

ok lets say

theres 51 men

and 1 woman right?

so how do i make em equal?

remove 50 men

x-50=y

which is correct cuz 51-50=1

[wise tangle]

i mean like

theres a 50 difference

[velvet osprey]

"theres a 50 difference"
is NOT the kind of thing you communicate with the = symbol

[wise tangle]

oh

my bad

[wise tangle]

i see

[calm coral]

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[errant vigil]

can someone give me the steps for lagrange error bound

[tepid dune]

you mean the error?

Like the formula?

[leaden thunder]

https://www.youtube.com/watch?v=lY0LzJXTgeo

[errant vigil]

just the order of things you do to apply it

[calm coral]

@errant vigil Has your question been resolved?

[leaden thunder]

did you watch the video

[errant vigil]

yes he isnt specific at all

and he puts an equal when its less than or equal

[leaden thunder]

then you need to ask a more specific question or work on an actual problem

[errant vigil]

bro theres specific steps you can have that video is literally useless

he just assumes a bunch of things and doesnt even have a question hes solving

[leaden thunder]

and until you ask a more specific question, there's no way to answer your question

[errant vigil]

yes there is

i literally asked the steps of applying lagrange error bound

[leaden thunder]

only you understand what you want

[leaden thunder]

more specific meaning an actual function or order of polynomial

[calm coral]

@errant vigil Has your question been resolved?

[calm coral]

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[cerulean compass]

hey

[cerulean compass]

how should this question be interpreted?

what does the question mean by "find the projection of the diagonal OB onto the line y=-x"

so far i've constructed a line (form y=mx) that goes through the required points for OB but I do not know what to do from here

$\vec{OB} = \frac{1}{4}x$

[winged smelt]

$\vec{OB}$

[potent lotus]

ColdTee

[cerulean compass]

ah thanks, was just looking that up lol

[potent lotus]

Zouni

[nova cave]

so do u know the basic projection formula

[cerulean compass]

yeah

[nova cave]

you already have vector OB right

[cerulean compass]

yeah

vector OB or line OB?

[nova cave]

and you want to project onto the line y = -x

line ig

[cerulean compass]

will that work?

[nova cave]

wait isn’t that what the question asked for tho

projecting the diagonal OB onto the line y = -x

[cerulean compass]

yeah

but I haven't projected it yet

[nova cave]

ye

so how do you convert y = -x into a vector

and also the same for OB

[cerulean compass]

How would I know the magnitude

actually it would be bounded by the parallelogram right?

[untold sigil]

Can u help w my question ?

[nova cave]

wait do you know about projection matrices

[untold sigil]

Sorry to interrupt

[cerulean compass]

go to a different help channel

yes i know about projection matricies but that would make things messy

[untold sigil]

I've created mine

U may help if u want

[nova cave]

well

[winged smelt]

Isn't $\vec{a} \cdot \hat{b}$ the projection formula or am i missing something?

[potent lotus]

ColdTee

[nova cave]

well

[cerulean compass]

no

produces a scalar which is not what we need atm

[nova cave]

that’s just dot product

wait mb

[winged smelt]

We can easily find OB vector and

y = -x is just $-\hat{i}$ if im not wrong

[nova cave]

that’s uh

a bit off

[cerulean compass]

$-\hat{i}$

[potent lotus]

Zouni

[cerulean compass]

but close enough

[nova cave]

-j is x=0

[potent lotus]

ColdTee

[nova cave]

-i is y=0

[cerulean compass]

well that's if the vector has a magnitude of one

which I don't think works in this case

[nova cave]

idk how to type latex but you want a unit vector in the direction of y = -x right

[cerulean compass]

yes

[nova cave]

so what does that look like

[cerulean compass]

$well -\hat{i} $ is fine but it wouldn't reach from the origin to point B which is at (4,1)

[nova cave]

uh

[cerulean compass]

uhh

[nova cave]

-i looks like a horizontal line

[cerulean compass]

yes

[nova cave]

y=-x is a diagonal line

[cerulean compass]

yes

[nova cave]

so what’s a unit vector for y = -x

[cerulean compass]

it would be -i + j

[winged smelt]

Oh yeah

[cerulean compass]

but that's of length one

[nova cave]

k that would have a magnitude of sqrt2 tho

[cerulean compass]

yeah which is the issue

[nova cave]

so

do you remember how to convert a vector to its corresponding unit vector

[winged smelt]

$\frac{-i}{\sqrt{2}} + \frac{j}{\sqrt{2}}$

[cerulean compass]

you mean $\vec{e}$

[potent lotus]

ColdTee

Zouni

[nova cave]

pre much this

[cerulean compass]

$\sqrt{5}$

[potent lotus]

Zouni

[cerulean compass]

is the magnitude

to reach from the origin to point B

[nova cave]

ok

so what’s the vector OB

with magnitude sqrt5

[cerulean compass]

wait no

it's $\sqrt{17}$

[potent lotus]

Zouni

[nova cave]

o ok

[nova cave]

and OB is this right

[cerulean compass]

$17 = a^{2} + b^{2}$

[potent lotus]

Zouni

[cerulean compass]

??

[nova cave]

mb mb

ok find the vector OB

with magnitude sqrt17

[cerulean compass]

$\vec{OB} = \frac{1}{4}x$

[potent lotus]

Zouni

[nova cave]

well

basically [4; 1] right

[cerulean compass]

yes

sorry was afk

[nova cave]

and now you want to project the vector [4; 1]

onto the line y = -x

[cerulean compass]

wouldn't the line -x also have to be a vector

[nova cave]

yes

you can either use the projection formula or a projection matrix

r u uh

solving it

[cerulean compass]

what should the magnitude of the y=-x be though

yeah just typing it now

[nova cave]

if you use the projection formula

it shouldn’t matter because

when you project onto the line the length of the line itself doesn’t matter

only the magnitude of the thing you’re projecting matters

if you use the projection matrix

then converting it to a unit vector makes it easier to find

idk if i’m being confusing

[cerulean compass]

yeah but the magnitude is the length of the vector

[nova cave]

well like

[lime harbor]

projection of OB on y+x=0 is OB.(y+x) / |y+x|

[cerulean compass]

lol jpeg sent a jpeg

[nova cave]

if you’re projecting onto the line y = -x

the magnitude of y = -x doesn’t rly matter

[lime harbor]

it does?

for the projection formula

[cerulean compass]

apart of the projection formula has the magnitude of -x in it

[nova cave]

r u sure

[lime harbor]

yep

[nova cave]

like you see in the two scuffed drawings i made

the projection of A onto B is equal

regardless of the length of B

[cerulean compass]

$\frac{\vec{OB}\dot{\vec{-x}}}{||\vec{-x}||^{2}}$

[potent lotus]

Zouni

[cerulean compass]

lmao tf

[lime harbor]

well you can make it as y+x=0 and then take the magnitude as a whole

https://www.youtube.com/watch?v=MdfArHlKWZc

here is the derivation

[cerulean compass]

what do yopu mean

[lime harbor]

might help

[lime harbor]

y=-x can be written as y+x=0

[cerulean compass]

yes

[lime harbor]

so the projection of OB on y=-x is

[cerulean compass]

how am I supposed to do a dot product with an algebraic equation

[nova cave]

you can convert y = -x into a vector

[cerulean compass]

yes

[lime harbor]

you have to find OB in terms of x and y

then you can take the dot product

[cerulean compass]

$OB = \frac{1}{4}x$

[lime harbor]

yeah so in this y is zero

[potent lotus]

Zouni

[cerulean compass]

How is that useful

[nova cave]

ok so

[lime harbor]

just a sec

[nova cave]

you wanna do this right @cerulean compass

project OB onto the line

[cerulean compass]

yes

[nova cave]

and how will you do that

[cerulean compass]

I have to convert -x into a vector

[nova cave]

ok

[cerulean compass]

my issue is that the answer will change depending on -x vector's magnitude

[nova cave]

whats y = -x as a vector

[cerulean compass]

which i Don't know what to set to

[nova cave]

uh

does it

[cerulean compass]

bruh

yes

[nova cave]

i just checked and it doesn’t matter tho

reasoning being

the projection of OB is basically like the shadow of OB onto the line y=-x

and the shadow of OB doesn’t change at all

no matter what the length of y = -x is

[cerulean compass]

okok

well thank you then

that answers my initial question

.close

[calm coral]

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[amber whale]

dont see where sqrt(x^2+y^2) comes from

i assume i have to convert from polar to cartesian right?

i mean i kinda get the idea

x dot id the velocity along the x axis

so we divide by r = sqrt(x^2 + y^2) to keep r =1?

how do i justify this well?

[calm coral]

@amber whale Has your question been resolved?

[amber whale]

also

<@&286206848099549185>

[calm coral]

@amber whale Has your question been resolved?

[calm coral]

@amber whale Has your question been resolved?

[calm coral]

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[calm coral]

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[autumn pollen]

I was wondering on how to make a start on this question

I had an idea of using the dot product of ba and bd

But it doesn’t seem to work

[calm coral]

@autumn pollen Has your question been resolved?

[calm coral]

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[shy iron]

How do o know something has no solutions or infinite solutions

[calm coral]

@shy iron Has your question been resolved?

[calm coral]

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[calm coral]

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[tepid meteor]

How are this limits solved?

[tepid meteor]

I have to do one-sided limits to see the continuity

[alpine stone]

You can use squeeze theorem (-1 <= sin(1/x) <= 1)

[tepid meteor]

and to do the calculus, how is this theorem applied?

[spark relic]

Study the domain of the function first

[tepid meteor]

the domain is R

[spark relic]

Correct

Then, you only have to study the one-sided limits in "punto de ruptura"

I know you can understand me

Limit when x->0+ and x ->0-

[tepid meteor]

do you mean, "punto de discontinuidad" no?

[spark relic]

Yes

[tepid meteor]

how? ahahah

[spark relic]

x = 0

[spark relic]

We know spanish

[tepid meteor]

that's what i have done, but i don't know how to solve this limits