help-0

[fresh bolt]

^ this is easy

[heady notch]

i know

[sleek elbow]

get 2 equations first @heady notch

lets see if you can do that

[fresh bolt]

an equation is like 1 + 1 = 2

let first game be x

let second game be y

[heady notch]

i cant

oh oh

[fresh bolt]

5x + 2y = 24?

4x + 4y = 30?

then you simultaneous it

solve for x and y respectively

[heady notch]

wow i love smart ppl

[alpine sable]

:sus:

[fresh bolt]

i need help

[alpine sable]

🧐

with what

[fresh bolt]

is 2 ^lg lg n = lg n

[fresh bolt]

do u know if 2lg lg𝑛 + ∛n is log-logarithmic, logarithmic or radical?

[alpine sable]

seems like radical from desmos

as n->∞

[fresh bolt]

ok thanks

[viral raptor]

Hello, I am doing an investigation about chess. I need to find the minimum number of moves a knight has to do to get from one corner to the the other, for each board of side n. So for a knight to get from one corner to the other in a 3x3, 4x4, 5x4 grid.

[dim bough]

Not me but for a friend

[ionic musk]

suuuure

[ancient creek]

sorry we cannot help you in a quiz/test. Read #rules

[orchid coral]

Uhmm help?

[alpine sable]

use alegbra

we first break down the shaded area into 3 parts

two identical triangles and one rectangle in the middle

if we take the base of the two triangles as x

we can have the equation of

9-2x=width of rectangle

[orchid coral]

yeah i label that as y

and then the area of triangle is 2(1/2 times x times 3)

is it?

[alpine sable]

yep

but rn we dk the y value

so u need to come up w another equation

[orchid coral]

from where?

[alpine sable]

lemme check if my understanding is mathmatically correct

[orchid coral]

alrighty

[alpine sable]

How did Galileo know that the pendulum swings at the same frequency regardless of the amplitude?

[alpine sable]

nvm some things dont add up using this method

[subtle mantle]

He measured it

[alpine sable]

im sure that the method is still valid but u just need to come up w another equation relating y

omg

i figured it out

[subtle mantle]

You know the height is 3 because it’s the height of the rectangle

[alpine sable]

How?

[subtle mantle]

He got a couple of pendulums with different lengths,, and timed the frequency

[alpine sable]

How did he time it?

[alpine sable]

if u use the hypotenuse of the triangle, u can come up w the equation of (x+width of rectangle)^2=x^2+3^2

[subtle mantle]

He used his pulse iirc

[alpine sable]

Oh, but that's not accurate?

[subtle mantle]

Accurate enough

[warped phoenix]

is this channel taken?

[orchid coral]

yeah

wait @alpine sable ]let me draw that first

[subtle mantle]

I highly doubt he was able to solve d^2(theta)/dt^2 = sin(theta) back then

[alpine sable]

aight i need to do sth else so hv fun

[orchid coral]

alright thank you so much i think i get it

[warped phoenix]

can someone help me understand what i did wrong?

i performed synthetic division as i was supposed to but my answer was wrong...

[untold sequoia]

@warped phoenix

it shd be 12

[warped phoenix]

omfg

you're right

LOL

[alpine sable]

damn.

[mossy berry]

f(x,y) = 2/3 { 0 < x < 1 ; 0 < y < 3x }
I have to integrate f(x,y) over {y< x < 2y}
What will be the limit of y?
I am getting limit of y as: {0 < y < 1/2}
But my answer is lower by a factor of 2.

[warped phoenix]

so the correct answer would be $x + 16 = \frac {29} {x-3}$?

oopsie

[subtle mantle]

Why are you getting a set as your answer

[ocean seal]

TheMane3

[warped phoenix]

there we go

[subtle mantle]

Oh never mind I understand now

[mossy berry]

I am getting limit of y as: {0 < y < 1/2}

the answer I am getting is 1/12. Correct is 1/6

[subtle mantle]

Yeah I didn’t realise you meant the integral bounds

[warped phoenix]

i dont think ive simplified a polynomial with 4 "results" at the bottom of the synthetic division so im not sure if im supposed to add the 4 and 12

i know the first one, 1, would be the coefficient of the x

but im not sure if i did that right

but im not really sure where else the 12 would go

[mossy berry]

I am getting $x^2 + 4x + 12 + \frac{29}{x-3}$

[ocean seal]

ImperfeKt

[warped phoenix]

really? how

what do i do when i have 1, 4, 12, and 29 as the results of synthetic division?

I know the 29 is the remainder, and ik what to do with that

oh waitttt

i get it

if it was 3, 6, 11, and 36 for example, it would look like

$3x^2 + 6x + 11 + \frac {29} {x-3}$

[ocean seal]

TheMane3

[warped phoenix]

so the more terms you end up with, it basically follows the chain of a polynomial

i see

[warped phoenix]

@mossy berry if that bit outside the fraction was factorable, would i factor it?

ik x^2 + 4x + 12 isnt factorable but if it were would i do it

also in that picture are you subtracting by x^3 or x - 3? 😅

[restive anvil]

What's up nerds xD

I'm dumb myself.

[mossy berry]

x^2 + 4x + 12 = 0 gives imaginary solutions, cannot factor it

[mossy berry]

oh, in the second line, it should be $x^3 - 3x^2$

[ocean seal]

ImperfeKt

[warped phoenix]

ah yeah ik ik but if x^2 + 4x + 12 was replaced with something factorable, like im talking a different polynomial we're simplifying, would i factor it?

[mossy berry]

I had re written it for clarity, ate up the ^2 while writing

[warped phoenix]

like if it was factorable

hahah lol no worries

[mossy berry]

upto you, factored polynomials looks neat

[warped phoenix]

got it, thank you so much!!!! @mossy berry

[mossy berry]

np

[warped phoenix]

sorry the picture is shitty but how would i solve this?

i know i need to find the LCD, but how do I do that when there's an x?

also the RHS has two different things being multplied with each other, (x-3) and (x-1)

[mossy berry]

(x-3) on both side will cancel each other

take (x-1) from RHS to LHS, then LHS will become quadratic.
RHS is also quadratic, shift the whole equation to one side and solve for ax^2 + bx + c = 0

[warped phoenix]

oh so x - 3 is the LCD, how did you figure that out? doesn't (x-3) being multiplied with (x-1) change the LCD?

[mossy berry]

answer should be x = 0 or 3
But x = 3 do a NO NO.

[alpine sable]

New York and Los Angeles are about 3000 mi apart; the time difference between these two cities is 3 h. Calculate the circumference of the Earth

Is it correct assume that traveling to the 12th time zone will put us approximately 12k miles from NY, and so the circumference would be 24000pi?

[pale haven]

hey guys, what does it mean for a number to be exact in this context:
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. this is one of the instructions on Cambridge's maths exams

[alpine sable]

It means if you are working with significant figures in your calculations

[shell widget]

Exact means w/o decimals

[pale haven]

are you sure?

[shell widget]

Yes

[pale haven]

ok thank you very much

but the problem is that I found one of the answers with a decimal and hasn't been rounded in the model answer

this is in the model answer:
237.25

[gray isle]

depends on the question

[pale haven]

can you please clarify

[gray isle]

e.g there will be errors when measuring stuff like distances, speed, time.
(unless stated otherwise, calculations involving them won't be exact)

how you round depends on the full context of each question

[pale haven]

so when should I round, i don't get it

I should round when I am sure that the number I get isn't accurate for example using cosine and root?

but there are other questions that want me to calculate the mean, the answer is a recurring number but it has been rounded to 3 sigs

[gray isle]

trig and radicals is a different context to what you wrote earlier

[pale haven]

this is one of the instructions on the front of the exam paper. How can I apply this instruction in my exam paper

[gray isle]

gonna take too long to explain rounding for every single situation

[pale haven]

isn't there a general rule of thumb

[gray isle]

different places have different rounding practices

leave stuff as nice radicals where possible I guess unless told otherwise

[pale haven]

ok thanks

[warped phoenix]

“The sum of the reciprocals of two consecutive integers is 11/30, find the integers.”

Wouldn’t that be x/1 + 1/x = 11/30 ?

[gray isle]

no

[queen wigeon]

the integers are consecutive, so it would be $\frac{1}{x} + \frac{1}{x+1}=\frac{11}{30}$

[warped phoenix]

[alpine sable]

1/x + 1/(x + 1) = 11/30

[ocean seal]

mchen10

[warped phoenix]

Ohhhh consecutive as in they’re right after each other

🤦‍♂️

Right, thank you!!

[alpine sable]

What was your original interpretation of the problem?

[warped phoenix]

I thought by consecutive they meant it was just going to be back to back, so literally just 2 of the same integer, one normal and one the reciprocal

Sorry my brain is really dumb dumb lol

So uhhhhh

I’m pretty sure I did something wrong lol

I multiplied everything by the LCD 30(x + 1)

[gray isle]

why are you using the incorrect setup?

[warped phoenix]

Wdym?

Bro

Omg

Nvm

I’m so retarded wtf????

Well

I’m stuck again 😦

How do I do 30(x + 1) / x ?

[queen wigeon]

try multiplying the equation $\frac{1}{x} + \frac{1}{x+1} = \frac{11}{30}$ through by $x(x+1)$

[ocean seal]

mchen10

[warped phoenix]

But I thought you could only multiply it by the LCD which was found by multiplying two unique factors in the denominators?

I did 30 (x+1) because x already is in x+1 so it’s not unique

[queen wigeon]

you can still multiply through by x(x+1), since you're doing it to both sides of the equation it will be equal nonetheless

[warped phoenix]

Hm

Well now I have this

[queen wigeon]

that looks right. there is still a denominator of 30 on the right side, so how can you get rid of it?

[warped phoenix]

Multiply both sides by 1/30?

Wait

No that’s not right

30/1?

[queen wigeon]

yes

[warped phoenix]

Well now I have this :/

@queen wigeon

[queen wigeon]

check your calculation of $\sqrt{(-49)^2-4(11)(-30)}$

[ocean seal]

mchen10

[warped phoenix]

Oh

Not even gonna remark on how embarrassing that is

But I get it now

[warped phoenix]

THANK YOU @queen wigeon @pale haven !!

[pale haven]

I guess this is it

Could you send me where you get such questions. I really need to solve stuff like this

[warped phoenix]

Hmm..this is an online course I’m taking but this specifically is called “Problem solving with rational equations”

[warped phoenix]

Maybe search up something like that? ^ 🙂

[pale haven]

Yeah I mea n where do you get them from i need them for my exams

[queen wigeon]

artofproblemsolving.com has something called alcumus, and you can practice questions from a variety of subjects. its free but you need to make an account

[warped phoenix]

You could just search up “problem solving with rational equations questions” or something like that

@queen wigeon quick question, my solutions are 5 and -6/11 to the above question I asked

But uhhh the only answer choices are 4 and 5, 5 and 6, and 5 and 7

[pale haven]

K thanks

[queen wigeon]

your question asks for integers, so 5 would be the only acceptable one. also you need consecutive integers, and the equation was of the form 1/x + 1/(x+1), so the consecutive integers are x and x+1 @warped phoenix

[hardy crest]

can someone help me with some geometry on question 1 real quick

[warped phoenix]

If 5 is the only answer why are the answers in pairs of 2

[queen wigeon]

because they are asking for consecutive integers, so you need 2

[warped phoenix]

Ohhhhh

5 and 5 + 1

Right

LOL

[alpine sable]

Can anyone help with this

[warped phoenix]

hey guys, just want to double check

if f(x) = a fraction, we can find the x intercepts and y intercept in the numerator only, because the asymptotes are found in the denominator, right?

[rigid smelt]

Not sure what you mean by in the numerator only

For example (x+1)/(x+3) has y-int of 1/3

You know that because (0+1)/(0+3)=1/3

Where you "used" the whole thing

If thats what you meant by "use"

[warped phoenix]

ah, is what i said not the same thing as what they're saying here?:

would you only find x intercepts in the numerator?

and not the denominator

[rigid smelt]

No, because of the fact that you added the term "y-int"

[warped phoenix]

ah

but without y-int., it is true?

[slim bone]

That's not the answer but ty

[rigid smelt]

But yes, the x-int of the fraction if it exists, is also the x-int of the expression in the numerator

[warped phoenix]

woah thats cool

because it makes things waaaaaaaaaaaaaaay less complicated than setting the whole fraction to 0

thank god it doesnt have to be like that

LOL

[rigid smelt]

Thats just like a shortcut...

[warped phoenix]

ik

you could do it by setting the whole fraction to 0

[rigid smelt]

Its not more complicated or anything

[warped phoenix]

but you dont HAVE to

is what im getting from this

[rigid smelt]

I mean you do have to...

[warped phoenix]

well i mean

by using the shortcut you dont have to set the whole thing to 0

[rigid smelt]

But since its just so obvious that its not mentioned

[warped phoenix]

😦

😭

the one time i understand something it was meant to be something extremely obvious ofc LOL

[rigid smelt]

Dont try to memorise stuff, its really tedious

Try to understand it if you can

By setting the fraction to 0, you know that the fraction is only 0 when the numerator is 0. And by doing that so many times it becomes a habit

Just when you instantly see a fraction you would know what to do to find the x-int

But thats just my view

It varies among people

[warped phoenix]

so numerator/denominator = 0 because denominator must = 0?

[rigid smelt]

No

The numerator is 0

And the denominator is not

[warped phoenix]

oh mb

yeah

[rigid smelt]

Also you should be careful

[warped phoenix]

i meant the other way around

yeah because if denom is 0 then its undefined

[rigid smelt]

There are cases where both of them are 0

[warped phoenix]

:0

[rigid smelt]

(x^2-1)/(x-1) is one

x=1 is not an x-intercept

[warped phoenix]

you mean x = sqrt(1)?

[ocean seal]

returnoflibrary

[rigid smelt]

Yes...

[warped phoenix]

bro why tf am i so dumb

thats the same thing

LOOOOOOOOOOOOOOOOOOOOOOOOOOOL

anyway lemme rephrase that, most of the time, numerator/denominator = 0 because numerator must = 0

[rigid smelt]

AND denominator != 0

Dont say most of the time, its just a statement with a condition

[warped phoenix]

@rigid smelt wait but if denom. = 0 then its undefined?

[rigid smelt]

Yes

[warped phoenix]

so then how does that work

0/0 = 0?

because 0/0 = undef. not 0

?

[minor elbow]

Oh crap soz I wasn't looking at question properly
Btw is the answer 1.13?

[warped phoenix]

"there are no holes since the numerator and denominator dont share any common factors"

wtf does it mean by holes?

[fallen venture]

Discontinuities probably

[minor elbow]

Uhhhhh English?

[warped phoenix]

how do we know if a rational function how a right branch?

or 2 branches for that matter?

Apparently there are two branches, I got the left one because I knew which points it passes through, but I had no clue there was a right one/second one, and what info in the function even tells me that there was

[alpine sable]

How does (a) differ from (b)?

[warped phoenix]

<@&286206848099549185>

[alpine sable]

@warped phoenix Your question isn't really clear I think

[warped phoenix]

oh

well my question is really just how do we know how many branches a rational function is

[alpine sable]

How do you define what a rational function is?

As a quick example, f(x) = (x - 1)(x + 1)/(x - 1) is just a line without any branches. Does that count?

[woven pollen]

The Earth is not a perfect sphere. It appears the question is asking you to account for that. In a previous section, did the talk about how to make this correction?

[alpine sable]

No

[woven pollen]

Then, numerically they will be the same. It's a nice built in check then..

Is this an Astronomy class?

[alpine sable]

No chapter 1 of a physics textbook

"Measurement"

[woven pollen]

It's a square centered on the given lat/lon then. I think they just want you to make the square and and add +/- 0.25" to find the "edges".

(c) is then, somewhere in the square.

[alpine sable]

But how does (a) and (b) differ then?

[woven pollen]

one is north south, the other is east west.

( btw, cthulhu lives at 48°52.5′S 123°23.6′W )

[alpine sable]

But why would the uncertainty be different?

[woven pollen]

It says the accuracy of these determinations (plural) is +/- 0.5". The uncertainty is the same for each.

1. draw a square. 2. label the center point of the square with the give lat/lon. 3. add and subract half the error (0.25) to the center and find the edges (or corners) of your square.

[alpine sable]

I think I don't understand what you are saying.

We're asked for the uncertainty

But that's given to us at ± 0.5''

[woven pollen]

They want you to say between what two points the tanker lies in each direction. So the answer is the coordinates of the corner's of the square, give the error of +/- 0.5".

basically, add and subtract half (0.25") from the given lat/lon, and figure out the corner points.

for examples, what is 43 degrees 36 minutes 25.3 seconds +/- 0.5 seconds -- for one direction

then do the same with the latitude, and find the corner of the square.

[alpine sable]

Useless problem.

[woven pollen]

Have you drawn a picture yet?

[alpine sable]

No, I get it I just don't see the point of the problem now.

[woven pollen]

that's a conversation you need to have with your teacher

[alpine sable]

I only have a textbook without a teacher but I get your point

[crisp cave]

Can someone help me with this question

[warped phoenix]

Is that a test? @crisp cave

[woven pollen]

It says "practice test"

[warped phoenix]

Oh didn’t notice that ty

[woven pollen]

When you take partial derivatives with respect to one variable, you treat all the other variables as "constants".

So in a) the y is "constant" and it is -4y^4 + 4

we only did the x. then in the next part you change based upon the "respective" variable.

[rotund pulsar]

I have a simple question about area of a segment

[crisp cave]

What is up with how the functions are defined I know how to do Partial Differentiation.

@woven pollen

[fossil prawn]

Which is this!?!?!? Helpme pls xddd

[warped phoenix]

@fossil prawn @rotund pulsar @limber shard please read the rules, this channel is in use

[rotund pulsar]

Oh ok sorry

How do you know when it’s not in use

[fossil prawn]

Okl

[warped phoenix]

If someone is not mid conversation, has not asked a question, or if the last message in a channel was sent 30 minutes ago@rotund pulsar

[limber shard]

I know the rules. I just thought that the other person's doubt was clear. My bad.

[rotund pulsar]

Ok I’ll go to #help-5

[crisp cave]

Guys can someone solve my doubt

[warped phoenix]

That’s fine 🙂 @rotund pulsar

@crisp cave you can tag the helpers role if you haven’t received help after 15 mins

Otherwise you gotta wait for someone :/

[crisp cave]

<@&286206848099549185>

[warped phoenix]

Though tbh no one from the helpers role ever responds hahaha

[glass lichen]

what do you mean?

F is clearly defined

[crisp cave]

Yes

[rotund pulsar]

Can you applicate to be a helper

[crisp cave]

But it has like g(x) and f(x)

[glass lichen]

yeah.. and?

[crisp cave]

IDK what to do about those

[glass lichen]

it just says g=f'

[warped phoenix]

@rotund pulsar yes you can, how to do it is somewhere in the rules I think

[crisp cave]

Well what will be partial derivative of F wrt x

[glass lichen]

chain rule and find out

[crisp cave]

IDK how to apply that chain rule

[glass lichen]

Same way you would for single variate stuff..

[crisp cave]

Also what does it mean when F: r2 to r?

[glass lichen]

R not r

and it's just the mapping statement

[crisp cave]

yea

[glass lichen]

F maps from R^2 to R

[crisp cave]

Okay what does that mean

[glass lichen]

you put in an element of R^2 and get something from R

[crisp cave]

Can you write the formula for the chain rule and what do I have to differentiate wrt what

[glass lichen]

So.. do the question for you

[crisp cave]

I mean yes because I am so clueless out here

[glass lichen]

formula for chain rule: Google it if you dont know it
differentiate wrt to: Read

[crisp cave]

Aren't there like multiple chain rules

[glass lichen]

No

there's chain rule.

[crisp cave]

based on how the functions are defined and stuff

?

[glass lichen]

???

what are you even talking about

$(f\circ g)'(x)=g'(x)(f'\circ g)(x)$

[ocean seal]

Mosh

[crisp cave]

Like F=f(x,y) and then x(t)= something and y(t)=something

And stuff like that

[glass lichen]

yes, but F isnt parameterized

so you just need regular chain rule for partials

since you hold the other variable(s) constant

[crisp cave]

I don't understand

I am not trying to get the easy way out but it would really help if you showed it to me @glass lichen

[glass lichen]

Have you taken Calc 1?

[crisp cave]

Yes

[glass lichen]

so you know what chain rule is

[crisp cave]

So f'(g(x)) is f'og(x)

[glass lichen]

yes

(f'og)(x)

[crisp cave]

and f'(x) = g(x)

[glass lichen]

in this question, yes

[crisp cave]

so that means g(g(x)) = (f'og) (x)

correct

[glass lichen]

no

[crisp cave]

but f'(x) = g(x)

[glass lichen]

I gave you the general chain rule formula.. nothing to do with the question

[crisp cave]

in the question

[glass lichen]

the f and g I used in the chain rule are not the ones from the question

[crisp cave]

oh

Can you use them as per the question then?

[glass lichen]

Assume a is differentiable and $b(x)=a(2x^2)$ what's b'?

[ocean seal]

Mosh

[crisp cave]

a(2x^2)?

oh b'

[glass lichen]

yes.. cause you're struggling with chain rule apparently

[crisp cave]

4xa

its 4xa

[glass lichen]

no

[crisp cave]

ohhh

wai

[glass lichen]

$b'(x)=4xa'(2x^2)$

[ocean seal]

Mosh

[crisp cave]

what?

[glass lichen]

it's chain rule.. from calc 1

[crisp cave]

god i feel so dumb

[glass lichen]

you should probably review your notes on chain rule.. then try and do the question..

[crisp cave]

so keep a = const we get 4x

4x*a

[glass lichen]

NO

a IS A FUNCTION

[crisp cave]

oh

ok

how does that help?

[glass lichen]

cause I was trying to see if you could do chain rule from Calc 1

[crisp cave]

oh

can you tell me how to apply chain rule in the question I asked

[glass lichen]

it's literally the same way you do for chain rule in Calc 1

[crisp cave]

ok let me try

[glass lichen]

you just.. hold the other variable constant since it's a partial

[crisp cave]

It would help if you just did the question

I tried and i got g(-4y^4+4x) [4-16y^3]

is this correct/

?

[glass lichen]

for which..?

[crisp cave]

no wait i did wrong

i think i know what youre saying let me try one more time

@glass lichen

I did it 🥲

thanks

@glass lichen I have another question

[glass lichen]

ok...

[crisp cave]

How to make the matrix

[glass lichen]

compare co-efficients of left and right side of the equation, and you get the linear equations to make the augmented matrix

[crisp cave]

but there are 4 equations how do i get 3 rows

so they defined 4 functions

[glass lichen]

there are 3 co-efficients..

so you get 1 for the constant, linear and quadratic

[crisp cave]

then i dont get the mew r1 mew r2

[glass lichen]

$c_1(1+3t+t^2)+c_2(3+10t+2t^2)+c_3(1+t+4t^2)=1+7t-t^2$

[ocean seal]

Mosh

[crisp cave]

ok

so this is like one line of the augmented matrix?

[glass lichen]

no...

that's how you get the system of equations you need to solve..

[crisp cave]

can you give me one line of the augmented matrix

[glass lichen]

sure

1 3 1 1

[crisp cave]

3 10 2 7?

2nd line

1 1 4 2?

3rd line

correct?

[glass lichen]

no

[crisp cave]

then?

[glass lichen]

where are you getting 3 10 2 7?

[crisp cave]

after c2

and then middle of q

[glass lichen]

why did you just take the co-efficients from r_2?

the equations are in {c_1,c_2,c_3}.. so you need linear equations in those variables

[crisp cave]

so is 3 10 2 correct

for c2

[glass lichen]

no

[crisp cave]

3 10 4

[glass lichen]

No, stop guessing

what's the co-efficient of t on the LHS?

[crisp cave]

3 c1 10 c2 c3

correct?

[glass lichen]

missing +'s but yes

[crisp cave]

got it

so that means

[glass lichen]

$(3c_1+10c_2+c_3)t$

[ocean seal]

Mosh

[crisp cave]

3 10 1 7?

2nd line

[glass lichen]

yes

[crisp cave]

ohhh

1 2 4 -1

[glass lichen]

doesnt matter which line since row swapping doesnt change the solution space

yes

[crisp cave]

ahhh

ok

ok wait

let me do this much there is a second half also

@glass lichen

[glass lichen]

what are you stuck on..?

[crisp cave]

how to find if they are linearly independent or not

I know what the polynomials are

they are 1, 3+x and 1-2x+x^2

Correct?

Also whats a leading coloumn

@glass lichen

[glass lichen]

what??

[glass lichen]

The co-efficient matrix has RREF of I

[crisp cave]

yea yea

so the polynomials aew correct

[glass lichen]

My guess is analogous to pivots, so 1 in 1 entry and 0 else for the column in the RREF

[glass lichen]

why do you have polynomials though?

[crisp cave]

wdym?

its a continuation of part 1

See we made the matrix there they have given us the matrix here

[glass lichen]

Im asking where they came from

given you were solving for the mu values..

[crisp cave]

?

[glass lichen]

? means nothing

use words

[crisp cave]

wait so is the polynomial 1+3x+x^2 = 1

[jagged rapids]

Lmao now I'm enjoying this conversation

[glass lichen]

No

[crisp cave]

sorry

[crisp cave]

sir i already have low self confidence

[glass lichen]

dont comment if you're going to be disrespectful.

[crisp cave]

its okay man

Lets just continue

[glass lichen]

Ok, do you understand what the matrix from part 1 was to solve for?

[crisp cave]

yes

i do

[glass lichen]

what is it?

[crisp cave]

we took coefficient and then evaluated

[glass lichen]

yes, but when you solve the augmented matrix, what are you going to get

3 numbers that are what?

[crisp cave]

mew 1 mew 2 mew 3

[glass lichen]

yes

Now, please tell me where you got 1, 1+3x, whatever the last one was

[crisp cave]

okay so

[crisp cave]

this

[glass lichen]

yep

[crisp cave]

can you retype

[glass lichen]

$c_1(1+3t+t^2)+c_2(3+10t+2t^2)+c_3(1+t+4t^2)=1+7t-t^2$

[ocean seal]

Mosh

[fast timber]

could any1 help

[glass lichen]

the c's are mu's but I digress

[glass lichen]

in use

[fast timber]

oh

mb

[crisp cave]

yea first line was 1 3 1 1

first row

[glass lichen]

right

[crisp cave]

correct

so now if you go down a column you get the quadratic

[glass lichen]

$\begin{bmatrix}1&3&1&1\3&10&1&7\1&2&4&-1\end{bmatrix}$

[ocean seal]

Mosh

[crisp cave]

so 1 3 1 is our first quadratic

[glass lichen]

ok but why would you do that?

[crisp cave]

because

[glass lichen]

and you dont get a quadratic

[crisp cave]

what?

[glass lichen]

since there's no variable^2

[crisp cave]

so whats p1 p2 p3

they are mew?

[glass lichen]

they're just the row reduced linear equations

yes, they are the mu equations

[crisp cave]

so can you write what p1 =?

[glass lichen]

Yeah idk why they wrote p_1 p_2 etc

just ignore it lol

[crisp cave]

now each of them is a polynomial

in p^2

thats why I was like the first polynomial is 1 3 1

[glass lichen]

$\begin{bmatrix}1&3&1&1\3&10&1&7\1&2&4&-1\end{bmatrix}\to\begin{bmatrix}1&3&1&1\0&1&-2&4\0&0&1&2\end{bmatrix}$

[ocean seal]

Mosh

[crisp cave]

WHat????

[glass lichen]

they just glossed over the process of doing that

the matrices are row-equivalent

[crisp cave]

oh they did gaussian elimination?

[glass lichen]

yes

[crisp cave]

okay

i see

1 3 1 is actually mew 1 mew 2 mew 3

thats what we are solving for?

[glass lichen]

$\mu_1+3\mu_2+\mu_3=1 \ \mu_2-2\mu_3=4 \ \mu_3=2$

[ocean seal]

Mosh

[crisp cave]

ok

so now we take these and make the polynomials?

because now we know mew 1 2 and 3

[glass lichen]

No, you write the linear combination $\mu_1 r_1+\mu_2 r_2+\mu_3 r_3$ that gives q like the question asks

[ocean seal]

Mosh

[crisp cave]

ok

if it is equal then independent?

[glass lichen]

they're independent since you can row reduce the augmented matrix into the identity matrix

[crisp cave]

what?

got it

[glass lichen]

if you can row reduce a matrix A into identity, A is invertible and thus it's columns and rows are independent

[crisp cave]

okkk

let me solve the question and then get back to you

[woven pollen]

you can invert that matrix too.

it's determent = 1. huh.

[solid urchin]

question regarding probability

If from a deck of cards i pull out three cards what is the probability that i pulled out 2 kings at most

2 kings at most means i pulled 2 kings or less

I believe this has to be done finding the probability of the opposite

what is the opposite of pulling 2 kings or less?

[woven pollen]

S = { 1king, 2kings, 3kings, 4kings}. P(at most 2kings) = 1 - [P(3kings) + P(4kings)]

What is left over is drawing 1king or 2kings, which is at most 2.

[solid urchin]

0 kings also?

[woven pollen]

ah! yes.

[solid urchin]

Thanks

[woven pollen]

S = { 0kings, 1king, 2kings, 3kings, 4kings}.

[solid urchin]

My professor did it differently

P(at most 2 kings) = 1 - P(3 kings)

that's what he did

[woven pollen]

looks like he left one out too.

4 kings is definitely a possibility.

oh wait!!! I just read your question again. You only pulled out 3 cards.

oops. sorry about that. but you get the idea right?

[solid urchin]

Ohhhhhh

[glass lichen]

yeah, I had already pointed out it was invertible

[woven pollen]

cool

[solid urchin]

Yeah

Thanks for pointing that out, I was stuck on it too 🤣

[crisp cave]

@glass lichen

[glass lichen]

what?

[crisp cave]

Can you explain what I did wrong

i dont know how to do the last part

[glass lichen]

not sure since there's no solution

[crisp cave]

can you tell me whats p1 p2 p3

by looking at the augmented matrix

[glass lichen]

No, since you have no information to know anything about p's

[crisp cave]

now you can do it?

this is part 1 the previous one was part 2

[glass lichen]

yeah I really dont get what the p's are... you're better off asking your teacher

[crisp cave]

ok

[spring harbor]

Consider the points O(0,0) , P(a,0) and Q(0,a) in an orthogonal coordinate system. The circle inscribed in the triangle with vertices O , P and Q has radius 1 . What is the area of this triangle?

Could someone help me out with this? I'd appreciate it

So far I know the circle should have middle point (1,1) so it has the following equation:
(x-1)^2 + (y-1)^2 = 1

Not sure how to progress

<@&286206848099549185> ^^

[fossil roost]

is this in Cartesian coordinates specifically? Or is the key to this question the fact that it is orthogonal?

[spring harbor]

It is in Cartesian coordinates

[fossil roost]

ah then I can be of assistance

[spring harbor]

thanks!

[fossil roost]

just let me have a play with it, I'll be back to you in 2 mins

[spring harbor]

Take your time

[limpid spade]

He should be back

[fossil roost]

ok Im back

so if you consider the hypotenuse of OPQ, see if you can express it in two different ways

[glacial hedge]

The answer is false right?

[spring harbor]

Move to another channel

[fossil roost]

sorry elon please can you go to a different channel

[glacial hedge]

yeah mb

[fossil roost]

@spring harbor how can you express the hypoteneuse?

[spring harbor]

In terms of..?

[fossil roost]

a

[spring harbor]

Oh, 2a^2

[fossil roost]

well yeah the square of the hypotenuse is indeed 2s^2

now

[spring harbor]

Oh shooot yeah

sqrt(2)*a

my bad

[fossil roost]

precisely

now as we know that the circle is inscribed in the triangle

[spring harbor]

mhm

[fossil roost]

the hypotenuse is tangent to the circle

[spring harbor]

uh-huh

[fossil roost]

what do we therefor know about the radius of the circle

[spring harbor]

it's perpendicular to the tangent line

[fossil roost]

yes

can you find the length from 0,0 to the hypotenuse

which is perpendicular

[spring harbor]

yes

one sec

sqrt(2)/2 a

[fossil roost]

oh I mean not in terms of a

just as a length

think about how you can construct it from the radius of the circle

[spring harbor]

dont we have something like this

[fossil roost]

yeah perfect

[spring harbor]

we got a 90deg. angle

so i thought we could use pythagoras to find the perpendicular line

[fossil roost]

you can

[spring harbor]

isnt that what you're asking for?

[fossil roost]

but then you wont get the hypotenuse in two different ways

[spring harbor]

hmm

soh cah toa then?

[fossil roost]

no you can use pythagoras

just not with a

have a look at the part of the perpendicular which is not the radius

[spring harbor]

yeah

[fossil roost]

can you work out that length?

do you need some help?

[spring harbor]

yeah please im probably missing something obvious

i keep getting sqrt(2)/2 a

wait doesn't that mean the perpendicular line equals the half of the hypotenuse length?

[fossil roost]

what im getting at

is that this diagonal length

[spring harbor]

ohh

[proper copper]

yo guys i eed help

[spring harbor]

i thought that whole one

abdul go to some other channel, we're busy here

[fossil roost]

is the hypotenuse of a triangle with two side lengths 1

[spring harbor]

@fossil roost we get sqrt(2)

[fossil roost]

perfect

now taking this information

[spring harbor]

ohhhh

[fossil roost]

can you get a second expression for the hypotenuse of OPQ or whatever it was

[spring harbor]

wait

i get it

i get it

[fossil roost]

:D

[spring harbor]

sqrt(2)/2 a = sqrt2+1

[fossil roost]

yeah you can do that

what do you now get for the area?

[spring harbor]

a = 2+sqrt2 so A = 3+2sqrt2

[fossil roost]

perfect

good job!

[spring harbor]

amazing :D

thank you

you made it very clear

[fossil roost]

thanks

[spring harbor]

i was looking at the big triangle as a whole and not that small little line you showed me

that was probably what i missed

[fossil roost]

so what I would say as a pointer for future questions

is that when considering lengths, angles and areas, stick to geometry and trig

when considering intersections and such then you can start using coordinates

obviously this line gets blurred

but I would always say keep it simple

another thing would be to try to take into account all the information give

given*

for example the key to that question was that you had to use both a and the radius 1 to construct the same line

[spring harbor]

yeah good points

thank you i will really need these

[fossil roost]

have a good one!

[proper copper]

@fossil roost can you help me now?

[fossil roost]

perhaps

[proper copper]

The last part is killing me

[fossil roost]

ok

let me just google some latex real quick

so I would use $y - y_1 = m(x - x_1)$

[ocean seal]

Zac

[fossil roost]

have you come across this before?

[proper copper]

yes

but why did you use that tho?

[fossil roost]

so instead consider $A(t) - A_1 = m(t - t_1)$

[ocean seal]

Zac

[fossil roost]

as A(t) is on the y axis and t on the x

we can then subsitute values in

we know that at t = 150, A(t)=32000 so we have t1 and A1

[proper copper]

so can you use the numbers so i can use them

[fossil roost]

and m is -1000

I'd rather not do it for you

I would rather help you understand so that you can do it yourself

[proper copper]

right right

sorry i asked that that was dumb

[fossil roost]

you see how we know a point and the gradient of the last line?

[proper copper]

i am just tryna figure out why did you use that formula

[fossil roost]

sorry Yuma occupied

ok

so the reason you use it

is because you know a point and you know the gradient

[proper copper]

so y1-y=x(x-x1)

[fossil roost]

y-y1=m(x-x1)

[proper copper]

so y1 is the height and x is the time

x1

[fossil roost]

yes precisely

[proper copper]

ok let me try

[fossil roost]

its all to do with the idea of transforming the line y=x

to move it up y1 you take y1 from y

to move it right by x1 you take x1 from x

[proper copper]

but wait hold on

we dont know the time

[fossil roost]

we do

[proper copper]

it just says start decending at the rate of 1000

[fossil roost]

we know where it was before then

it cant jump around

we can consider the start of this line, the end of the last

[proper copper]

142 min

[fossil roost]

hm?

[proper copper]

wait sorry its the 32000 height and the time is 142 min

and then its start decreasing 1000

[fossil roost]

not quite hold on

@pseudo egret sure

just pipe down for a minute

so the time isnt 142

what could it be?

instead

[proper copper]

150

[fossil roost]

yep

nice

[proper copper]

wait seriously?

[fossil roost]

yes?

I think

I hope

[proper copper]

ok lol let me try aand get it

oh fuck me but the slope is missing

[fossil roost]

you have the slope

think about it

as t increases by 1

A(t) decreases by -1000

sorry

1000

[proper copper]

right there fore the slope is 1000

[fossil roost]

-1000

sorry I confused you there

[proper copper]

-1000 becuease the plane is going down

[fossil roost]

because its decreasing its negative yes

have you got an equation ?

[proper copper]

one sec

y-32000=-1000x-150000

[fossil roost]

not quite

close

you have to remember to multiply the minus signs

[proper copper]

oh let me try one more time

y-32000=-10000x+150000

[fossil roost]

well yeah pretty much

you ahve added a zero in -1000

[proper copper]

y-182000 = -1000x

and divide -1000 to both side?

[fossil roost]

I wouldn't

remember that y=A(t), x=t

[proper copper]

so then that should be answer

[fossil roost]

you want A(t) on its own I believe

[proper copper]

How to get A by itself? When we have t

[fossil roost]

well y=A(t), x=t

so A(t) = -1000t + 182000

and that should be your answer

[proper copper]

you are absoultley correct

[fossil roost]

you understand why?

[proper copper]

i thank you from the bottom of my heart bro

[fossil roost]

thats no problem really

[proper copper]

i subtracted them wrong

[fossil roost]

ah I see

[proper copper]

it shoulve been the other way around no?

[fossil roost]

?

[proper copper]

y-32000=-1000x+150000 i should ve added 32000 to -15000]

[fossil roost]

ah yes you got it

[proper copper]

i appreicate it man. ill ask whenever i have a question its nice to know there are people who are willing to help.

[fossil roost]

$y-y_1=m(x-x_1)$ should be abused for these types of questions

[ocean seal]

Zac

[proper copper]

ill let the other guys ask his question before i ask my other one

@pseudo egret all you bro

[fossil roost]

He's got someone else helping him now

[proper copper]

oh then ill ask my other question

[fossil roost]

ask away

[proper copper]

sorry for the crappy image quality

[fossil roost]

looks like you've done it to me

[proper copper]

i did but i sstill need further explantation

[fossil roost]

for the first half?

I dont quite understand the question: I don't play baseball

oh I think I understand

yep I got it

so

you understand why for the first 5

its 18t?

[proper copper]

yes becuse 5 * 18 = 90

[fossil roost]

yeah nice

so now we need to use Pythagoras's theorem to work out the second part for t>5

[proper copper]

a^2+b^2=c^2

[fossil roost]

indeed

[proper copper]

so a is 90^2

b is undefined

i dont know what c i ether

[fossil roost]

ok

so lets take this in step

you correctly identified that a=90

[proper copper]

yes

[fossil roost]

now how can we get the distance from first base to where Manny is?

[proper copper]

it says he hits double

so 9+4.5?

[fossil roost]

I dont know what hits double means

[proper copper]

i am guessing running one a half as much

distance wise

[fossil roost]

I thought it could mean that he runs to second base (which works with the solution)

[proper copper]

so the original answer was \sqrt{90^2+\left(18\left(t-5\right)\right)^2}

boy that didnt come out clean

[fossil roost]

$\sqrt{90^2+\left(18\left(t-5\right)\right)^2}$

[ocean seal]

Zac

[fossil roost]

lets ignore that for now

[proper copper]

Yes thank you

[fossil roost]

so

what is the distance from first base to manny at time t when t>5

[proper copper]

90 ft

[fossil roost]

not quite

so imagine him starting at first base when t = 5

[proper copper]

oh when it great than 5

108

[fossil roost]

we need to include t

[proper copper]

what you mean?

[proper copper]

so 18t

[fossil roost]

yes 18t is almost correct

however if we try some values

for example at t=5 it should be 0

[proper copper]

so at 5 t should be 90

[fossil roost]

sorry its late in england

[proper copper]

beach when t is 1 then he is 18 ft in

[fossil roost]

no I mean the distance from first base to manny

not home base

we're ignoring the first 90

[proper copper]

so by the time t is 6 he is 108 ft

[fossil roost]

yes exactly

but how can we generalise this

with t

[proper copper]

90t^2-5? beacuse we are ignoring the first 5 seconds

[fossil roost]

just walk me through your thinking there

[proper copper]

so by the time he reaches seond base (giggity) he is reached 108 ft

so t=6

[fossil roost]

not quite

we dont want to know how far he has travelled

[proper copper]

ahh

[fossil roost]

we want to know how he travels as time changes

[proper copper]

so 6 seconds then and he is at the second base

[fossil roost]

you correctly identified that his distance along the line is given by 18t

no not quite

we are trying to get the

we are trying to get the distance MB

(where A is the home plate)

this is so that we can use Pythagoras to work out MA

[proper copper]

wait

its 18t^2 right

[fossil roost]

what is

[proper copper]

the a part of Pythagorean equation

[fossil roost]

we got that a = 90

where a = AB

in that diagram

we're trying to work out MB in terms of t

[proper copper]

right i am all over the place here

[fossil roost]

shall we start over

[proper copper]

sure

[fossil roost]

okay so you understand why the distance from A is 18t when t <= 5

[proper copper]

90t is where he runs

[fossil roost]

90t?

I think you may have misunderstood the question perhaps

[proper copper]

18 * 5 = 90 so he should be at the end of the first base then

yea i think so too

[fossil roost]

no thats right

what then is his distance along CB and AB from A when t>5?

[proper copper]

What is cb and Ab?

[fossil roost]

this diagram

[shadow ledge]

In case of having the following series of sales, what forecasting method do you think is the most appropriate to project future demand?

[fossil roost]

sorry @shadow ledge we're occupied

[shadow ledge]

sorry

[proper copper]

So 18t then?

[fossil roost]

yeah its still 18t

[proper copper]

beacuse we know he runs 18ft but it doesnt explicitly say when he will stop

wait

[fossil roost]

can you work out MB from this then

[proper copper]

10

[fossil roost]

he stops at second base or C

thats the idea of hitting double

I think

[proper copper]

is he tho?

[fossil roost]

yes

[fossil roost]

can you work out the distance MB in terms of t

[proper copper]

i think he is stoping at the point

[fossil roost]

no that point is just an example

on my diagram thats M

M moves from A to B

then from B to C

[proper copper]

ok so from 1st base t M is t=6

so if he wanna reach third base thats 12?

[fossil roost]

no

[proper copper]

A to b 6 B to c 12

[fossil roost]

how did you get t=6?

[proper copper]

wait no its 5 actually

% seconds to reach the end of the base no?

5*

[fossil roost]

at t=5

he is at B

[proper copper]

yes t=5

so by the time he reaches second base he is t=10

[fossil roost]

yes

but what is the distance from him to first base as 5<t<10

[proper copper]

yea i have no clue

[fossil roost]

ok

so we know that AB = 90

[proper copper]

Yes

[fossil roost]

and we know that the distance A to B to M is 18t

[proper copper]

Right

[fossil roost]

so its 18t - 90

in other words 18(t-5)

and now we can use Pythagoras's theorem to get $\sqrt{90^2+18^2(t-5)^2}$