help-10

[haughty coyote]

factoring out x from the first column makes a nice 1 in the bottom left
Then doing R2 <- R2 - (x-1)/x R3 yields
((x-2)/x (x-1)² x^3)
(0 x² - (x-1)(x+1)²/x (x+1)^3 - (x-1)(x+2)^3/x)
(1 (x+1)² (x+2)^3)

Then R3 <- R3 - x/(x-2) R1 yields
((x-2)/x (x-1)² x^3)
(0 x² - (x-1)(x+1)²/x (x+1)^3 - (x-1)(x+2)^3/x)
(0 (x+1)² - x(x-1)²/(x-2) (x+2)^3 - x^4/(x-2))

Now C2 <- C2 - ( (x+1)² - x(x-1)²/(x-2)) / (x+2)^3 finally yields, after multiplying back C1 by x
((x-2) (x-1)² - x^3( (x+1)² - x(x-1)²/(x-2)) / (x+2)^3 x^3)
(0 x² - (x-1)(x+1)²/x - ((x+1)^3 - (x-1)(x+2)^3/x) * ((x+1)² - x(x-1)²/(x-2)) / (x+2)^3) (x+1)^3 - (x-1)(x+2)^3/x)
(0 0 (x+2)^3 - x^4/(x-2))

Hence the determinant is
(x-2) * ((x+2)^3 - x^4 / (x-2)) * (x² - (x-1)(x+1)²/x - ( (x+1)^3 - (x-1)(x+2)^3/x) * ( (x+1)² - x(x-1)²/(x-2)) / (x+2)^3)
= ((x²-4)(x+2)² - x^4) * (x² - (x^3 +2x²+1 - x²-2x-1)/x - (x^3+3x²+3x+1 - ((x-1)(x^3+2x²+4x+8)/x) * (x²+2x+1) - x(x²-2x+1)/(x-2)) / (x+2)^3
etc

Or don't be an idiot like me

and notice you're asked for the coefficient of x, so you can disregard anything above x

[ember monolith]

wait

wait

this question is THIS BIG?

[haughty coyote]

then the matrix becomes
(x-2 -2x+1 0)
(x-1 0 3x+1)
(x 2x+1 12x+8)
Which is much simpler

[ember monolith]

(´。＿。｀)

[haughty coyote]

don't forget your fundamentals: if they're asking for something computationally obscene, it's that there's a trick

[ember monolith]

um so where should i start from?

like the first step?

[haughty coyote]

,w det(((x-2, -2x+1, 0), (x-1 ,0, 3x+1), (x,2x+1,12x+8)))

and I messed up again

[ember monolith]

oh

I FEEL SO GUILTY OMG'

[warm shale]

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Requested by mateo713

[haughty coyote]

there, same coefficient of -2

[ember monolith]

from where zero came,?

[haughty coyote]

this

then just compute the determinant with your algo of choice, immediately disregarding terms of power > 1

[ember monolith]

im sorry but howಥ_ಥ

is there any vc in this group so u can explain?😭

[haughty coyote]

-(x-2) (3x+1)(2x+1) + (2x-1)( (x-1)(12x+8) - x(3x+1))
-(x -6x - 2)(2x+1) + (2x-1) (8x-12x-8 -x)
-(-5x -4x -2) + (-16x +5x+8)
-2x + 10, as expected

so if you know what you're doing it's not that bad at all

[ember monolith]

well ,i do not know what im soing :))

doing*

[haughty coyote]

do you understand why?

[ember monolith]

can we solve it with polynomials tho?

[haughty coyote]

we're handling polynomials, wdym?

[ember monolith]

nah not like tht i meant
5ax^4+4bx^3+3cx^2+2dx+e

something like tht

idk tbh thats wht my teacher said to do but i have no clue''

[haughty coyote]

yes that's the pain and suffering option, i think

[ember monolith]

oh

[haughty coyote]

another option would be interpolation
at x=0 this gives
(-2 1 0)
(-1 0 1)
(0 1 8)
Whose determinant is 10
And at x=1 it gives
(-1 3 0)
(0 0 4)
(1 3 20)
whose determinant is 8
Hence the only line giving these values is -2x+10, no polynomial computations involved

[ember monolith]

how did u find determinant in this??

solving it one by one? like -2(2)

something like tht?

[haughty coyote]

hell no
The whole point is to find a method to not compute the whole thing

[haughty coyote]

may I repeat my question?

[ember monolith]

oh yah ,i didnt understand :))

[haughty coyote]

when you're computing the determinant the naive way
You're gonna end up with terms of all orders: 1, x, x², x^3, ...
But those greater than x are irrelevant for the coefficient of x: a term in x² will add something of the form x²(...) to the determinant, whose x-coefficient is 0

[runic cypress]

What do you want?

[ember monolith]

?

[haughty coyote]

so you can disregard the terms in x² since computing them will inevitably yield 0, so spare yourself the effort

[ember monolith]

oh so which method should i follow?

[haughty coyote]

does that make sense?

[ember monolith]

kind of ngl

[haughty coyote]

then you can just expand each entry and say "thus, everything above x I disregard"
Giving the much simpler matrix I gave

that's a determinant you can compute more easily already

especially if you keep in mind that you still don't care about higher terms, so you might as well ignore terms above x as soon as you find them

[ember monolith]

ohhh

[haughty coyote]

which is why you find things like (x-2)(3x+1) = (x-6x-2) here, because they're equal as far as the relevant coefficients are concerned

[ember monolith]

can u give an example?

[haughty coyote]

you're basically computing everything modulo x²

[haughty coyote]

this is an example
(x-2)(3x+1) = 3x²+x-6x-2 = x-6x-2 mod x²

[ember monolith]

so we ignore higher values of x

[haughty coyote]

because they can't possibly change the answer, you only compute the relevant part

[ember monolith]

thts why u changed it into 0?

x^2?

[haughty coyote]

then this is another method saying "I expect an answer of the form ax+b, which is determined by its value at 2 points"
So if I just compute it at 2 convenient points, I find the answer without polynomial computations

actually I'm not sure how that 2nd one even worked

[ember monolith]

ohh

[ember monolith]

tbh this is something my sir did but i was clueless like how u get determinant

also how u get determinant 10 from this??

u there?

um im sorry but i gotta tag u

@haughty coyote

[haughty coyote]

sorry currently interrupted

[haughty coyote]

not even sure about the theory

[ember monolith]

oh but how u managed to get determinant?

umm'

actually lets leave this question pls explain me summation

[haughty coyote]

with just numbers it's not hard
Just pick the formula you prefer

[ember monolith]

,

[ember monolith]

i tried but didnt get the answer thts why im asking

[haughty coyote]

-2 (0*8-1*1) - 1 * (-1*8 - 1*0) = 10

[ember monolith]

OH I WROTE 9 INSTEAD OF 8

,

[ember monolith]

thank iu!

[haughty coyote]

it's just factoring k out

[ember monolith]

can u explain?m0ore? abt summation?

[haughty coyote]

it's no different, except you're summing n terms

k+k+...+k, n times
is indeed k*(1+1+...+1)

[ember monolith]

then this?

[ember monolith]

ohhhh

[haughty coyote]

that's the d-linearity of the determinant

[ember monolith]

wht does tht means?

[haughty coyote]

because the other rows are common, you can sum the different row

I recommand you read up on what you're supposed to know about the determinant

[ember monolith]

i need to first know abt summation?

[haughty coyote]

i'm not the one structuring your classes

and I'm gonna have to go by now, bye

[obtuse pebble]

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[stuck isle]

hello

[stuck isle]

the options are 1, -1, 3, -3

[obtuse pebble]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[stuck isle]

i dont know where do begin

well i kinda do

i know you must differentiate the function to get the tangent

[lapis charm]

yeah so what would that be in terms of b

[stuck isle]

2x + b?

[lapis charm]

yea

[stuck isle]

= 0

[lapis charm]

wait hm?

why 0

[stuck isle]

wait no

nvm

my bad

not 0

ok so 2x + b

now what

[lapis charm]

so what is it at the point (1,1)

[stuck isle]

2*1 + b?

[lapis charm]

yes

so how do you find the equation of the tangent line

[stuck isle]

isnt this the equation of the tangent?

[lapis charm]

that isnt an equation

its the expression for the slope

[stuck isle]

oh shit

ohh

so we use the point slope form

[lapis charm]

yea

[stuck isle]

fuck i forgot the most basic thing

so (y -1) = 2x + b (x -1) + c

what do i do after this

[lapis charm]

thats not quite right

[stuck isle]

oh

now?

[lapis charm]

no lol idk how youre getting that

[lapis charm]

this is the slope

[stuck isle]

yeah?

[lapis charm]

so its y-1 = (2+b)(x-1)

[stuck isle]

oh

so i substitute the x in the slope

[lapis charm]

yea thats what happeend here

the slope of the line tangent to (1,1) is 2+b

so the line has that equation

[stuck isle]

alr

[lapis charm]

so from there find the intercepts

do you see how to solve from here

[stuck isle]

oh wait

yes

so i find the x and y intercept

and 1/2(base)(height)

and itll equate it to 2

[lapis charm]

yea

👍

[stuck isle]

nice

alr

thankyou very much

[lapis charm]

gl

[stuck isle]

.close

[obtuse pebble]

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[stuck isle]

yessir

[obtuse pebble]

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[warm frost]

can anyone provide me solution of this?

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[timid silo]

yeah no

We give explanations, not solutions

[warm frost]

ok.. thn pls just explain this

what should i do here?

[warm frost]

can anyone explain this what should i do here?

[tardy marsh]

so we need ordered pairs for P^2

did you do it ?

calculate P^2

[warm frost]

yea i did

[warm frost]

i did

[tardy marsh]

equation the values that you got

with - i

i = identity matrix

[warm frost]

i did but not getting anything

like i got 2 relations but don't know what to do next

[tardy marsh]

didn't you get a relation like this

[warm frost]

yea i did

but idk what to do nxt

[tardy marsh]

okay
so u know z is actually omega
and

r could only be

odd

that that equation to be truee

according to the property of of

so r = 1, 3

[warm frost]

y 'r' could only be odd numbers?

[tardy marsh]

uhh
lemme just simply it for you

now compare it with

standard equation of omega

can you see

s = 1

??

[warm frost]

yea

[tardy marsh]

and then r also 1

[warm frost]

but what happened to 4s? y did u take just s in place of 4s in 2nd equation?

[tardy marsh]

no

[warm frost]

can u explain this pls?

[tardy marsh]

do you know this ?

[warm frost]

ahh.. ok I got it

thnk u

[tardy marsh]

yeah 🙂

[warm frost]

can I dm u? I hv some other ques too

@tardy marsh

[tardy marsh]

yeah sure

I am also preparing for jee

it seems like a jee question

[warm frost]

yea it is

[tardy marsh]

maybe I have done it before as well

[warm frost]

cool

[warm frost]

thnk u

[obtuse pebble]

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[fleet stag]

I have no idea how to do this question

[obtuse pebble]

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[wanton oriole]

hello, I am really struggling with diff eq and need help with this problem

[wanton oriole]

this is the beginning of the problem from lecture

i do not know where to go from here

[obtuse pebble]

@wanton oriole Has your question been resolved?

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@wanton oriole Has your question been resolved?

[obtuse pebble]

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[dim copper]

wondering how to simplify this into just terms of n

if possible

is this a factorial?

or something like it

[cunning breach]

Do the inner sum first, then the outer one (think of arithmetic sequence).

[obtuse pebble]

@dim copper Has your question been resolved?

[dim copper]

this shouldn’t be too complicated right?

like these can be done with simple formulas

[cunning breach]

Yeah

[obtuse pebble]

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[ripe hazel]

ik the function is right but im still confused

[dusk widget]

looks like you might've just forgotten an = sign?

[dusk widget]

yeah, and I'm saying you might've just forgotten an = sign

[ripe hazel]

where does the = sign go in an inequality

[dusk widget]

<=

[ripe hazel]

ah

im stupid

ty

.close

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[empty salmon]

how do I take (n+2) common after doing this?

[empty salmon]

<@&286206848099549185>

[obtuse pebble]

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[runic frigate]

Hello! Im in elementary statistics and we are in the confidence interval unit. We are talking about stating conclusions and errors, and there is a lot of wording that makes it a little hard to understand. I want to make sure I am understanding it right, so i will post the question below.

[runic frigate]

my question is that if the null hypothesis is true, do you have evidence proving it? Its hard to explain... but like for this question, it says to state the conclusion if the null is true... so dows that mean we do have evidence?

[cobalt shuttle]

thats not exactly how it works. The null hypothesis is your default hypothesis so its a lack of evidence. You don't support the null hypothesis. Your alternate hypothesis is what you're trying to build confidence in!

So in the absence of any evidence, you have not been able to reject the null hypothesis in favour of the alternate!

[runic frigate]

so is there a lack of evidence because the null is true?

i think im hella overthinking, but there are a lot of words that mean a lot of things and im just trying to wrap my head around it all

in this scenario i mean. so would it be A?

[cobalt shuttle]

oh sorry I didn't even read the question lol!

so anytime you're hoping for a result, you're hoping for the alternate hypothesis right

so your alternate hypothesis is that the peanut butter manufacturer is underfilling

now its saying the null hypothesis is true so it is saying that at the 5% level of significant, there is no evidence to show that the peanut butter manufacturer is under filling the jars

you get to the null hypothesis if your evidence does not show the alternate!

but its weird to say that your evidence shows the null hypothesis, that's what I'm cautioning against and indeed thats the difference between A and D

[runic frigate]

okay, so if the null is true, then we assume there is no evidence to suggest any different?

[cobalt shuttle]

exactly right

[runic frigate]

thats what i was getting confused on lol

because thats originally what I thought but then i second guessed myself. Again, lots of words haha

[cobalt shuttle]

haha it is confusing

just remember null is default, it doesnt need evidence

alternate is what requires evidence

[runic frigate]

Okay so this is a similar one, except is says the probablitiy was more than 5%. This doesnt make sense because would we state its unusual at the 10% level if its more than 5%

assume the questions are A-D like the last one

my professor doesnt really explain this part.

im just confused. Because we are stating the probability of the sample result occuring was more or less than 5% which doesnt make sense to me.

can you explain what that means? Or like how i would look at a question like this?

<@&286206848099549185>

can someone please help i really dont understand whats going on

with the question

[obtuse pebble]

@runic frigate Has your question been resolved?

[runic frigate]

No

[obtuse pebble]

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[native garden]

help needed-

[obtuse pebble]

@native garden Has your question been resolved?

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[exotic drift]

Does any1 know how to solve this question?

[exotic drift]

I'm confused on how to formulate the net profit random variable

is it -20X?

or is it 15X

like if Y is the net profit random variable

like the parameters means that he will be able to sell 25 papers

and each paper of selling has 40% chance

<@&286206848099549185>

<@&286206848099549185>

[strange bone]

im tryin it

[exotic drift]

oh ok

[obtuse pebble]

@exotic drift Has your question been resolved?

[exotic drift]

<@&286206848099549185>

.close

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[ebon moth]

in a triangle ABC, if AB = 13, AC = 25 and tan(BAC) = 3/4, then there are two possible values of BC, right?

[ebon moth]

since cos(BAC) could either be 4/5 or -4/5

[vapid kite]

but how would an angle be negative?

[ebon moth]

the output of trig functions can be negative

doesn't mean the angle is negative

[vapid kite]

oh u said cos bac mb

i thought u meant the angle itself

[glass wolf]

The output of a trig function can indeed be negative, but only the positive output has any meaning for right triangles.

[ebon moth]

that's not my question

is the triangle in my question ambiguous?

BC^2 = 13^2 + 25^2 - 2*13*25cos(BAC)

but $\cos(BAC) = \pm \frac45$

[warm shale]

Typo

[ebon moth]

I don't see anything preventing BAC from being obtuse

[glass wolf]

As far as I can tell, it does appear to be ambiguous.

[ebon moth]

alright thanks

.close

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[cerulean crag]

Is constant tension throughout the rope a valid assumption

[tawny copper]

yeah

Hint: a) ||14 * 18 * cos(25)||

b) ||1. Constant tension
2. No friction or friction is neglectable (ice)
3. Constant angle? ||

[obtuse pebble]

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[cerulean crag]

thanks a lot 🙂

[obtuse pebble]

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[toxic echo]

need help carrying out a statiscal testing. superficially chi - squared test
one to find out whether there is a correlation/relationship between place visited and and ehtnic group i got a secondary data to if needed
just need help carrying out a statistical testing should i just go with primary data or add secondary data find the expectred and soemthing need someone to talk to

[obtuse pebble]

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@toxic echo Has your question been resolved?

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[timid silo]

A

[obtuse pebble]

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[molten gull]

I need help with a and b

[molten gull]

u sure?

[sharp narwhal]

wait a min

lemme just solve it

[molten grove]

solve for 3sqrt(x)

then square both sides

for part a

you'll get a quadratic

[molten gull]

alr lemme try that and say what i get

[molten grove]

alternatively, you can just notice what you have written is a quadratic in sqrt(x)

[molten gull]

4x^2 -9x -196 = 0?

[molten grove]

that's not how you square it

you are missing a bunch of terms from distributing if you do it that way

but solve for 3sqrtx first

so you get $3\sqrt x = 2x - 14$

[warm shale]

chebyshev's infinite pee norm

[molten grove]

square both sides of this

[molten gull]

i thought that what i did

did i do it wrong

[molten grove]

what did you get for (2x-14)^2

[molten gull]

oh wait

i squared 2x individually

and -14 individually

[molten grove]

yes

[molten gull]

mb lemme fix it

[molten gull]

4x^2 - 56x +196

[molten grove]

yes

and 9x on lhs

[molten gull]

yh

now shift it over

4x^2 -65x +196 = 0

now i jus solve it like normal and put solutions?

@molten grove

[molten grove]

yh

[molten gull]

for the not relying on ur calc part

if i state quadratic formula

then jus put it in calc its good/

?

or i gotta like complete square and stuff

@molten grove

[molten grove]

huh

it's just a quadratic

solve it however you want

[molten gull]

it says i cant rely on calc tho

alr nvm that

how would i do part b

@molten grove

[molten grove]

it's the same manipulation as part a

solve for the thing with the root

and exponentiate to get rid of it

[molten gull]

what should i be expecting to get

@molten grove

i got just 8

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[humble halo]

i got 2 solutions what am i doing wrong

[humble halo]

since we know x^2+3x>0 right?

[tranquil sonnet]

no

[humble halo]

well how

[tranquil sonnet]

what if x=-2?

[molten grove]

x = -1

[humble halo]

oh right

[molten grove]

split it up into regions and consider what happens in each region

[tranquil sonnet]

what i would do is take cases on whether each term is negative or positive

[tranquil sonnet]

oops i thought this said positive 7

well absolute values always give a non-negative value

so the sum of 2 absolute values is always non-negative

[humble halo]

oh

yeah

so 0?

[tranquil sonnet]

yep

if it said positive 7, another valid method could be graphing |x^2+3x| and 7-|4-3x| and counting their intersections

[molten grove]

oh it's -7

[obtuse pebble]

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[latent torrent]

What is the anti derivative of secxtanx

[latent walrus]

sec(x)

[prime night]

secx

oops

[latent torrent]

How

Is that something u just memorize

[prime night]

mhm many people do...the proof is pretty long

[latent torrent]

Oh

[prime night]

wrong image sorry!

[latent torrent]

I’ll just memorize it thank you

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[warped zinc]

.close

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[latent torrent]

What did I do wrong here the correct answer is 2/7x to the power of 7/2

plus c

[latent torrent]

Sorry

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[latent torrent]

I made a mistake

Let me try again

[obtuse pebble]

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[brisk sable]

How do you know which one it is

?

[obtuse pebble]

@brisk sable Has your question been resolved?

[timid silo]

look at the lines and see

[brisk sable]

huh

[timid silo]

yeah

one of the line is when x=4 y=0 and x=0 y=4

and its a straight line

[brisk sable]

😀 ❓

[timid silo]

[timid silo]

look at what the graph and look at the answers

put in the values from the graph to the answers

see if they are true

[brisk sable]

ok

[timid silo]

do you know what a dashed line is?

like the one in the graph

[brisk sable]

i suck at reading graphs in general

[timid silo]

woh

so did ya do it

[brisk sable]

ill figure it out but thanks anyways

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[sacred goblet]

does a mapping of two sets $A \mapsto B$ necessarily include all elements of A

[warm shale]

ChiliLion

[sacred goblet]

im stupid thats the definition LOL

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[lofty hare]

help pls

not sure how to do this

this is my working

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[last gorge]

where would I start?

no f(x) is given

[flat anvil]

Well to determine 2 variables you need 2 equations right

[obtuse pebble]

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[last gorge]

.reopen

[obtuse pebble]

✅

[last gorge]

ok

and it didn't say "so the function is continuous at x= ( )

so how would i find the hole here?

[obtuse pebble]

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[obtuse pebble]

@last gorge Has your question been resolved?

[obtuse pebble]

@last gorge Has your question been resolved?

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[weak forge]

can someone telll me whether im right or wrong

[weak forge]

im confident the first one is true

just not the second one

[glossy basalt]

Consider
f=x²
A=[0,1]
B=[-1,0]
and check for validity of
(i) and (ii)

i remember this from the textbook, not sure if it works here through

[obtuse pebble]

@weak forge Has your question been resolved?

[weak forge]

hmmm

if a = {0,1} and B = {-1,0}
then lets union it and become {-1, 0, 0, 1}
and put this thru the function we get {1, 0, 0, 1}
if done seperately,
f(a) will have {0,1}, b will have {1,0}
and union those two will also get {1, 0, 0, 1}

so i guess its still correct

[obtuse pebble]

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[fresh pebble]

A town has a population of 8400 in 1990. Fifteen years later, its population
grew to 12 500. Determine the average annual growth rate of this town’s
population.

[fresh pebble]

anyb know how to solve?

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[prisma whale]

i dont able to understand why discrete mathematics needed help me please by showing wher used this stuff

[timid silo]

Combinatorics and probability are used in ur Daily life and many branches of of mathematics

i think it goes without saying u might need to know the amount of ways u can do something

Graph theory is used extensively in topics relating to computer science

you can really make further arguments about a lot of the stuff discrete math covers

[prisma whale]

and group theory?

[timid silo]

group theory is often more so related to abstract algebra than discrete mathematics

[prisma whale]

from where i can easyly start learn?

i found books very hard and lengthy

[timid silo]

try looking into introductory harvard courses about abstract algebra

[prisma whale]

ok thank you

[obtuse pebble]

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[flint pike]

Can anyone show me the solution to this task?

[obtuse pebble]

@flint pike Has your question been resolved?

[alpine verge]

recall that curvature is equal to $\frac{||x’(t)\times x’’(t)||}{||x’(t)||^3}$

[warm shale]

y0shi
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[alpine verge]

also i’m assuming that the equation is meant to be in terms of t not r

[obtuse pebble]

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[turbid fog]

Two people have one day decided to meet at a certain place at lunchtime. However, as both are somewhat unsure of when they can get there, they have agreed to wait up to 30 minutes for each other at the meeting point, before giving up and leaving. What is the probability that the people will actually meet, if both can be considered to arrive at the meeting place independently of each other at a random time uniformly distributed between 12:00 and 13:00.

[turbid fog]

The solution say

I know I can use areas: Meets = Square - lower triangle - upper triangle.

But can I integrate to find solution? How do I do that?

Or is that just unnecessary?

[obtuse pebble]

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[turbid fog]

<@&286206848099549185>

[zealous dragon]

that can be solved using integration or other standard mathematical operations

[turbid fog]

Okey, I don't know how to set it up really.

[obtuse pebble]

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[sterile venture]

I need help with this linear algebra question. Im stuck at (2), where i need to show that <P_E\phi(x),\phi(v_k)> = <\phi(x),\phi(v_k)>.
I have tried using some definitions for the orthogonal projection P_E(\phi(x)) = <\phi(x),\phi(v_k)> for all v_k, but im pretty lost tbh :(

[obtuse pebble]

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[sterile venture]

Nvm i think i figured it out

[obtuse pebble]

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[vague elk]

heya

[vague elk]

do i distribute the 1/2 to the other term aswell?

or only the first one?

this part here

[buoyant igloo]

Distribute to both

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[modern bison]

How to do this?

[grizzled shore]

so if we want to find the monthly wage

and we know what the hourly wage is

what would we need to know about this worker?

[modern bison]

His total work time

[grizzled shore]

right, how many hours did he work?

ok let's see if the other pieces of information can help us get this

[modern bison]

Okay

From what I attempted I got 216.67 hrs

[grizzled shore]

yes

[modern bison]

Then I multiplied it with 600

[grizzled shore]

that sounds right

and we dont get the answer

right

[modern bison]

And got answer 130002

But answer didn't match from the book

So I was then confused on what I did wrong

Maybe answer in book is wrong?

[grizzled shore]

i see the problem

i dont know why it says that

i think the book might be wrong

[modern bison]

Mine was correct then?

[grizzled shore]

if he is paid 30000 a month, and the hourly wage is 600, then he worked 50 hours

there is no doubt about that

i dont see how you could make the number 50 from "30", "13" and "500"

[modern bison]

Okay thank you

[grizzled shore]

yes i think you are correct

[modern bison]

.close

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[grizzled shore]

it should be 130 000 though

no 2, that comes from rounding error

[modern bison]

Yea

Thanks

[obtuse pebble]

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[latent torrent]

If u had to choose 4 to do for each 3 and 4 which ones would u choose for practice

[versed stratus]

why do you ask?

is this part of a test?

[hybrid gyro]

I think they just want to practise 4 questions from each section but not all of them, and can't decide which ones are harder

[versed stratus]

if I had to chose, I'd obviously chose the easier ones though

like g,h

[latent torrent]

It’s not apart of a test I just don’t want to waste time doing them all

[latent torrent]

Yes

[latent torrent]

I don’t want to practice easy ones

[hybrid gyro]

tbh I glimpsed at all of them and the only one I can't think of an answer right away is 3(h) [nvm i figured it out]

[high lily]

all the questions employ the principle of chain rule
whether you go through the sub is optional
just take a mix of questions that involve
exponential, fraction, radical,

[latent torrent]

Thank you

[latent torrent]

Mm ok so

How about 3 m h e n q

Then for 4 a e h g d

[high lily]

dunno why those aren't in alphabetical order but yeh,
that looks like a good selection

[latent torrent]

Lol I just choose

Thank you guys

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[proven needle]

Hiya! This is very likely a stupid question but i really suck at math like no one else. What i have to do is prove an equation using complete induction. Im currently stuck at proving that my n+1 equation is equal to the one ive marked in yellow. I dont know if I made a mistake or if i just dont know where to go from here. Id really appreciate someone helping my dumbass out here haha

[proven needle]

so the last equation there is the closest ive gotten lmfao

[obtuse pebble]

@proven needle Has your question been resolved?

[obtuse pebble]

@proven needle Has your question been resolved?

[obtuse pebble]

@proven needle Has your question been resolved?

[proven needle]

<@&286206848099549185>

[alpine verge]

i would say distribute the yellow bit and the answer you have

and see if it lines up

[proven needle]

did that a few times

still didnt work out, close but didnt work out haha

i get ((4n²+8n+3)n+1)/3

as opposed to ((4n²-1)n+12n²+12n+3)/3

[alpine verge]

oh i found the error

[proven needle]

oh shit nice

[alpine verge]

the yellow bit is wrong

[proven needle]

ohhh ye the n+1 missing

[alpine verge]

you plugged in n+1 only for the n^2

not the n outside

[proven needle]

yep fixed that

[proven needle]

gave me this

[alpine verge]

then it should line up now

[proven needle]

sadly not

[alpine verge]

can you show your work

cuz i just graphed both on desmos

they line up perfectly

[proven needle]

wha

imma redo it rq bc as is its kind of unreadable

this is how i got to my solution

excuse my handwriting lol, best i can do

[alpine verge]

you forgot the minus 1 from the first line

$(4(n^2+2n+1)-1)$

[warm shale]

y0shi

[proven needle]

ohh nice catch tyty

sadly cant be the only thing i did wrong, still doesnt seem to add up at all

[warm shale]

y0shi

[alpine verge]

if we cancel out the 3’s

[warm shale]

y0shi

[alpine verge]

that’s what we have for the left side

[warm shale]

y0shi

[alpine verge]

and that’s the same as the left hand side

[proven needle]

im sorry i dont get this step

[alpine verge]

do you understand where i got the first line from or no

[proven needle]

yeye thats the one i almost got missing the -1

[alpine verge]

alright so we just distribute

[warm shale]

y0shi

[alpine verge]

that’s from distributing the parenthesis out

and then just combine like terms here

to get what i have up there

[proven needle]

oh shit ye idk what i fucked up last time

lemme just to the entire thing from scratch and see if i really got it now haha

[alpine verge]

alright

induction is just a lot of algebra honestly

[proven needle]

i just started my math heavy semester

i may have skipped class a little too much back in high school lmfao

knew that was gonna come back to bite me some day

[alpine verge]

haha i see

yeah you need like algebra in a lot of math courses

[proven needle]

i do computer science

in my opinion kinndddaaa bullshit that they want algebra and analysis to this level but what do i knowww

[alpine verge]

haha

ig you do need it for writing programs and stuff

[proven needle]

hardly but i guess so

[proven needle]

alright finally got it

ty so much for the help yoshi, theres a good chance youll catch me on this server a tad more often haha

thanks!

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[mint oak]

how do

[mint oak]

you solve cos(-pi/4)

cuz i get the degree is -45 so wheres that on the trig circle

[restive gorge]

cos(-x) = cos(x)

[mint oak]

so its square root 2 over 2 ?

[restive gorge]

yes

[mint oak]

what about sin(-x) ?

[shut lagoon]

sin(-x) = -sin(x)

[mint oak]

oh ok

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[untold flower]

hi

need help with this

[obtuse pebble]

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[fiery spire]

Trying to graph a circle from scratch (programatically) using x^2 + y^2 = r^2. Question is how do you graph the 3rd quandrant since requires both negative x,y?

Using
x = sqrt(r^2 - y^2)
y = sqrt(r^2 - x^2)

while x,y < r

[gilded needle]

should be:
x = +/-sqrt(r^2 - y^2)
y = +/-sqrt(r^2 - x^2)

[fiery spire]

I'll give that a shot thanks

.close

[fiery spire]

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[untold flower]

sorry

dont close

Just need help with this

Home work question

@gilded needle

[gilded needle]

you need to open your own doubt channel, see #❓how-to-get-help

[fiery spire]

.close

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[tidal ravine]

How could i use a comparsion test to prove this is convergent

[rugged barn]

How does the comparaison test work ?

If you had a sum of a_n

[rugged barn]

.

[tidal ravine]

So i have to find the sum of this ?

[rugged barn]

No

But in general

[tidal ravine]

if the sum is finite its convergent ?

[hybrid gyro]

he's asking you to state the comparison test basically

[rugged barn]

Yes

Using a generic example

But if you can state it directly it will be easier

[tidal ravine]

I usually just find a larger series to compare to that is convergent to prove convergence
and a smaller one that is divergent to prove its divergent

is that what you mean

[rugged barn]

Sure

But you don’t compare the series

You compare the term

Like 1/n^3 is smaller than 1/n^2 so the série of 1/n^3 is convergent since the series of 1/n^2 is convergent

[tidal ravine]

yea like that

[rugged barn]

Okay so here

How could you find something bigger than 1/n(1/2)^n

Just try thing easy

It might work

[tidal ravine]

n+1

?

[rugged barn]

Sure but is the série of (n+1) convergent ?

[daring ravine]

did you notice that part of the series is a geometric series

and that you're just multiplying it by 1/n

[tidal ravine]

yea but i thought in order for geometric series to work the index has to start at 0

[daring ravine]

no it can be anything

as long as the common ratio is the same

2 more questions: is that geometric series convergent? and is it bigger or smaller than the series you have here

[tidal ravine]

the geo is conv cause its r = 1/2 < 1

the series would be bigger wouldnt it ?

[daring ravine]

yes

the geo series is bigger

and if it converges... what does that say about your original series

[tidal ravine]

that it converges as well

thats weird , i just thought because its being multiplied by a divergent it would be divergent

[daring ravine]

you cant really determine conv or div for product / quotient of series

for sums it is obvious because finite + finite = finite and etc

[tidal ravine]

yea thats why i thought that because i had a question with the sum of a div + conv

wait so my geo series doesn't need to start at index 0 ?

[daring ravine]

no

[tidal ravine]

wait so for a question like this

i can just say its a geo series and r < 1 so conv ? and it wouldnt mess up the sum when i try to do it later on

[daring ravine]

yes

btw it's |r| < 1

[tidal ravine]

thank you

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[weary heart]

why can't I solve it like this?

[obtuse pebble]

@weary heart Has your question been resolved?

[pseudo swift]

well your solution is fine

the book just gave a smaller square for some reason

@weary heart

[weary heart]

thx

.close

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[mint oak]

How am i supposed to find the base and height of the triangle assuming we dont know 4costheta and 4sintheta

[hybrid gyro]

base and height of the triangles in terms of theta?

[mint oak]

Yeah

[hybrid gyro]

well you have found the height, which is 4 sin(theta)

[mint oak]

No this is other students work

[hybrid gyro]

ah right

[mint oak]

I dont know how they found 4sintheta

[hybrid gyro]

so do you know SOH CAH TOA?

[mint oak]

Yes yes

But im not given two pieces of information ?

[hybrid gyro]

well you are told the angle, and the hypotenuse, that's two pieces of information. It's just that theta is unknown, but if you want the answers in terms of theta then it's fine

[mint oak]

So we know the angle is theta and the hypotenuse is 4 so what do we do next ?

[hybrid gyro]

don't mind the horrible diagram drawn using a mouse

the angle is theta, O means opposite and A means adjacent

[mint oak]

😂 😭

So would i do this ?

[hybrid gyro]

yes, sin(theta) = opp/4

[mint oak]

ohhhhhh ok

OMg ur amazing

Life savor

SAVOUR

SAVER ?

HOLY CRAP

[hybrid gyro]

idk if I'm edible but you're welcome

[mint oak]

😭 😭

[teal turret]

[mint oak]

theres no way i forgot how to say saver

[teal turret]

happens to the worst of us

dw

[mint oak]

[mint oak]

what the hell is this

[teal turret]

not "what"

"who"

thats Buford

[mint oak]

WHO IS THAT??

..

buford..

who gave him that name.......

[mint oak]

best*

[teal turret]

didnt stutter

[mint oak]

Alright.

.Close

Shit

.close

[obtuse pebble]

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[high pebble]

help

[serene fossil]

cant if you dont ask a question

[fickle shell]

maybe he needs help in asking the question

[tranquil sonnet]

maybe he needs help in help in asking the question

[fickle shell]

maybe he needs help in asking for help to ask for help to ask the question

[hybrid swan]

maybe the question is so complex she’s trying to put it into simple words so mere mortals can understand

[obtuse pebble]

@high pebble Has your question been resolved?

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[wary solstice]

Hey, can someone help me?

[wary solstice]

It is about dimensioning a joint

[plain stag]

,rccw

[obtuse pebble]

@wary solstice Has your question been resolved?

[obtuse pebble]

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[nocturne pike]

like here

[nocturne pike]

oh, wow

Ok then:
Im at like, 11th grade (3rd year on Brazil high school), still learning english and with HUGE difficulties at math

[chilly wagon]

I see you were unsure about the identity

$\sin^4-\cos^4=\sin^2-\cos^2$

What have you tried to make sense of it so far? Do you have any scratch work? Proving the identity should illustrate it well

[warm shale]

wraithlord_komplications

[chilly wagon]

Why did you delete that

Good first step keep going

[nocturne pike]

i know jack shit

like, i have the formulas

[chilly wagon]

Bullshit you just said something vital to the problem

[nocturne pike]

some of them

[chilly wagon]

start listing your facts

[nocturne pike]

the sin² + cos² = 1

tgx = sen / cos

[chilly wagon]

Cool, earlier we mentioned difference of squares, can you write that one down?

[nocturne pike]

1 / cos = sec (idk the translation)

[chilly wagon]

No translation (needed), that's how we say it

[nocturne pike]

a² - b² = (a-b) * (a-b)

this?

[chilly wagon]

Close, it's (a+b)(a-b)

[nocturne pike]

oh, yeah

[chilly wagon]

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

[nocturne pike]

missed the signal

[chilly wagon]

Just look long and hard at that, and at the original question you had

Tell me if you can figure it out

You officially have all the puzzle pieces

[nocturne pike]

oh

sin^4-cos^4 = 1 * sin^2-cos^2

since sin^2 + cos^2 = 1

is this it?

so in the question that follows:
1+cos(alpha)+cos²(alpha)+cos³(alpha)+cos^4(alpha)+... = 5, with 0 < alpha < (pi/2), so, sin2(alpha) iquals to:

i would need to use 2sin * (alpha) * cos(alpha)

i cant seem to find a way to connect theese two things

like, the sin problem dont vanishes, i stil dont have it

i know that it is less that 90°

because it is less than pi/2

[chilly wagon]

Yes, big old QED

[nocturne pike]

yes!

3 more to go

[chilly wagon]

The key here is that it's a geometric series

Each term gains a factor of cos(alpha)

Since you know the initial term and what it converges too, you can figure out the factor

Then use inverse cosine to find alpha (given the restriction on domain)

I don't actually remember how geometric series work well enough to help with the actual computation part of that ATM, I could do some recap I suppose

[nocturne pike]

ook

oh, wow

i do not remember seeing this in his class

is it Sn = a ( (1-r^n)/(1-r))?

[chilly wagon]

Maybe I'm leading you astray with an unintended method

[chilly wagon]

That looks right from what I remember

[nocturne pike]

i mean, there is a big chance that i do not remember it

[chilly wagon]

I'm getting a burger, when I get home I'll open one of my calc books and look for it

[nocturne pike]

oh, there is no need for that

im going to sleep soon, so

already 11pm around here

[chilly wagon]

Well I'm going to either way, because I want to know now

[nocturne pike]

good luck with it, ill give up college and... yeah, just that. good night

[obtuse pebble]

@nocturne pike Has your question been resolved?

[obtuse pebble]

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[slow vale]

i need help on my get more math questions

[outer glade]

Since the line is parallel, you know that the gradient of the lines are the same

[slow vale]

what that mean

im so cooked i need 75 points

[outer glade]

gradient is rise over run

so u know that line equations are of the form y = mx + b - gradient is the m value

[slow vale]

bro im sorry i dont like understand what i do

its fine bro i give up

[outer glade]

so you see the equation they gave- (5x +2y = 12) , you can rearrange it for y

then the number in front of the x is your gradient- which you know is the same for the other line

now you just need the extra constant term (b in y = mx + b) , so plug in (x=-2, y=8) since that point lies on the other line

and rearrange for the constant and youre done

[slow vale]

so do i get -10 plus 16 = 12

[outer glade]

nah you plug in as a step when finding the other line- you dont know the equation for the other line but the question wants you to figure it out-

[slow vale]

2y=-16+12

[outer glade]

nah, when you rearrange it- you get (2y = -5x + 12)

[slow vale]

im actually so cooked

[outer glade]

so dividing both sides by 2 , y = (-5/2)x + 6

(-5/2) this bit in front of the x is the gradient of the line

[slow vale]

it didnt work

what did i do wrong

[outer glade]

What did you get for your equation?

[slow vale]

y=-5/2x + 6

since u said divide by 2

[outer glade]

nah thats just a rearranged version of the first equation- its asking for the equation of a new line with the same gradient that passes through (-2,8)

[slow vale]

damn im stupid

bro i think imma call it quits

[outer glade]

so we know immediately the new equation is gonna be of the form y = (-5/2)x + b where b is some constant we dont know

now just plug in (-2,8) and solve for b and ur done

[slow vale]

wait so how exactly

[outer glade]

since the coordinate (-2,8) just tell you here x = -2, y = 8 sine its an (x,y) coordinate

so u get 8 = (-5/2)(-2) + b

[slow vale]

do i just solve

[outer glade]

yeah

[slow vale]

i dont get it tho

how do i solve for b here exactly

[outer glade]

just rearrange the equation to get b on its own

there are no other variables

[slow vale]

ohh

b=3

[outer glade]

yeah so u get y = (-5/2)x + 3

[obtuse pebble]

@slow vale Has your question been resolved?

[obtuse pebble]

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