help-39

[warm copper]

Imagine going to work and getting in debt for only being there 4h instead of the 8h

[compact ridge]

LMAO

yeah so he has to work more than 6 hours to gain money

is he in debt to the person whose house he is renovating

lol

it's less than 6 hours btw, like 4 or 5

[flint wyvern]

@compact ridge @warm copper are you still here i just finished part c and was wondering if you guys could check it

this is the last part btw

[compact ridge]

ok

what's part c?

[flint wyvern]

i was following a vid again for this

like all this basically but somehow i got the same answer as them

[compact ridge]

isn't that wrong

[flint wyvern]

wdyM?

[compact ridge]

should be $\frac{3(x+h)^2 - 75 - (3x^2 - 75)}{h}$

[jolly parrot]

southlander!

[flint wyvern]

man i knew it

yeah i was thinking i shouldve done that

[compact ridge]

yeah

[flint wyvern]

hold up lemme fix it

[flint wyvern]

so how would i do this

just 3(x + h)^2

[compact ridge]

yes

so $3(x+h)^2 = 3x^2 + 6xh + 3h^2$

[jolly parrot]

southlander!

[flint wyvern]

but like is it still (x+h)(x+H)

[compact ridge]

yes

you just multiply it by 3

[flint wyvern]

okay okay

[flint wyvern]

okay fixed it

how does it look

is it h(3h + 6x) there

[compact ridge]

yes and then divide by h

[flint wyvern]

so it would be 3h + 6x right

[warm copper]

Difference quotient? Is that another way of writing dy/dx

[compact ridge]

nearly

it's the definition of the derivative without the limit $h \to 0$

[jolly parrot]

southlander!

[warm copper]

So like ∆y/∆x

[compact ridge]

so yeah if you take $h \to 0$

congrats you've just done calculus, you've shown that $\frac{d}{dx} (3x^2 - 75) = 6x$

[jolly parrot]

southlander!

[compact ridge]

mhm

[compact ridge]

yes

[flint wyvern]

finallyy thank you so much

super difficult but pushed through

couldnt have done it without u guys dude ❤️

[compact ridge]

no worries!

[pearl pond]

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[fluid zodiac]

Anywone kindly help me with this graph

[fluid zodiac]

Why did the portion marked disappeared?

[compact ridge]

oh because |y| is never negative

so if sin x is negative, then the function doesn't exist cause of the |y|

[fluid zodiac]

Oh yeah thanks thanks

I was confused cz of that -sinx. Lmao now that I think -(-sinx) yeah got it

[compact ridge]

no worries!

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[tough viper]

Alright what the sigma is going on for part c

Find r where a station value means dA/dr=0 right

And we solve for r

To find max/minimum we continue solving for d^2A/dR^2 by subbing in r

I don't get the last part what do they mean by find the stationary value of a

Isint it 0...

[dusty flame]

dA/dt = 0

Essentially critical point

[tough viper]

U mean to find r right?

But how do we find the stationary value of a

[dusty flame]

Find r using this

And then plug r in the original equation for A

[tough viper]

Wait why plug into original eqn

[dusty flame]

To get A

It asks for value of A

[tough viper]

So that area represents the rate of change of area is not changing when we use that r value?

[dusty flame]

Yes

It shows max/min area

[tough viper]

Ohhhhh Alright I understand now tks

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[swift lodge]

3C b

[idle parrot]

write the problem in english pls

[swift lodge]

There is english also

I was thinking of contructing a height

[iron basin]

use the formula for area of triangle and parallelogram

both have the same heights

[swift lodge]

But how do i know i contructed a perpendicular line

[iron basin]

ok then construct a perpendicular from P to AM

it is the height for both the shapes

[swift lodge]

3D a please

[iron basin]

PORS is a parallelogram, and we can see that triangles POS and RSO are congruent

so both have same area

can you figure what area of POS is then?

[swift lodge]

11 i think i got it

Are btoh 11?

[iron basin]

yes

second triangle has same proof as the last question you showed

[swift lodge]

(≧▽≦)

Thanks

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[split bridge]

How to calculate

4^31 + 5^67?

[light helm]

not practical without a calculator

[vestal tapir]

no it's uh

you can

oh it's +

yeah + is too hard

[pearl pond]

@split bridge Has your question been resolved?

[split bridge]

Why can’t you add 31+67?

[vestal tapir]

it's not very funny

[split bridge]

What ?

<@&286206848099549185>

[midnight haven]

what's up?

[ancient lotus]

Wats the help ?

[midnight haven]

what's the problem?

[split bridge]

How to add two powers?

[ancient lotus]

Bruh , he gave funny problem

[midnight haven]

scalar?

or vector?

[ancient lotus]

If there are in multiplication I guess

[ancient lotus]

He is asking the normal one

[midnight haven]

I can't understand, the force has size and direction

[ancient lotus]

Dude , he is not asking physics question , he is asking just basic exponents

That dude ask how to calculate 5^67 + 4^31

[split bridge]

Exactly

It’s called powers

[midnight haven]

oh, you have to calc that using program.

such as C++

[ancient lotus]

Yo dude , do you want the answer in terms of power ??

Or else, I better execute answer in python

[cosmic charm]

adding two powers involve multiplication of two numbers with the same base

that is neither

[split bridge]

So I can’t?

[cosmic charm]

nope

either use a calculator or find some godly algorithm that allows you to do it by hand

[astral copper]

Hyy wassup chat

[pearl pond]

@split bridge Has your question been resolved?

[pearl pond]

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[regal herald]

yeah

should be -3x-2y+z=0

i believe

[pearl pond]

@naive marlin Has your question been resolved?

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[weary urchin]

does 0^infinity and infinity^0 indeterminate form?

[iron basin]

yes

[weary urchin]

how

or why

<@&286206848099549185>

[west vault]

0^infinity is not indeterminate

something very small to the power of something very big will always be something very small

[jolly parrot]

jewels!

[west vault]

infinity^0 is basically infinity/infinity in this way

[weary urchin]

oh thanks

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[pearl pond]

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[shadow knoll]

i need someone to explain this to me

[shadow knoll]

https://math.stackexchange.com/questions/581128/prove-that-subsequence-converges-to-limsup

i tried to think about it and worked with different sources but i somehow cant get my head around that concept

why can we just set it smaller than one half? Is it just because we get as close to the lim as we want to regsrding infinity? and why do we choose 1/2?

[plush bramble]

Follows from definition of limsup. Do you know it?

[shadow knoll]

yes

wait wrong one but same principle lol

i thought of it as the lim of the supremums going towards infinity so the smallest upper bound when n grows infinitely large right?

[plush bramble]

Yea so this tells you that there's always an n1 for which the limsup is within a given error
|xk - limsup(xn)| < error
for all k>n1

[shadow knoll]

so by this def i can just pick a series of "errors" which just converges to 0?

[plush bramble]

Yes

[shadow knoll]

ohhhhh

that totally makes sense!

thank you^^

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[jolly marsh]

Pls more help with proofs

[jolly marsh]

So i have to show that |A| =< |AuB|

So i know there must be injective function so that it will be correct

Because of cantor theory

so i defined f:A -> AuB

And i also fixed f(a)=a, where a is in A

used injection definiton such as a1,a2 in A so a_1 != a_2 => f(a_1) != f(a_2)

and i know that f(a)=a because i defined function

[fringe raft]

right

[jolly marsh]

So um is this that simple proof?

in the end i just replaced f(a_1) with a_1

[fringe raft]

yeah

just extending the domain of the identity function again

[jolly marsh]

so i got a_1 != a_2 => a_1 != a_2

I see

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[midnight haven]

the first graph represents two sin waves

oh

nvm

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[jolly marsh]

Is my proof good

[jolly marsh]

So if AcB and BcC then thanks to transitivity i know that A c C and i know that |A| = |C|, so it means set A contains same amount of elements as C then i can say that A=C so now if A=C and AcBcC then i can write that CcBcC so that means that B=C and if sets are equal then we can write it as |B|=|C|

[ocean hornet]

what if A = {2,4,..., 2n, ...} and C = {1,2,3,...}? then A c C and |A|=|C|, but A is not equal to C

[jolly marsh]

Oh crap

So i use here equuivalence of sets definition such as there has to be bijection

and then continue the proof with it

I asked it incase that proof might work aswell

Thanks!

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[quick star]

what is the volume of the largest cylinder that can fit inside a closed rectangular box measuring 12 inches by 10 inches by 8 inches?

[quick star]

What’s the justification for why the cylinder can’t be along the space diagonal of the rectangular box? is it just because it intuitively feels like it leaves empty space?

Like relative to keeping it horizontally or vertically

[indigo pewter]

just think of putting a cylinder in a rectangular box

it would be very difficult to pack along the space diagonal

so horizontal or vertical is the most efficient way to pack

[quick star]

yeah but like idk

that doesn’t justify why that can’t be a case too?

[indigo pewter]

i dont know a definitive proof, it just intuitively feels correct

[quick star]

if i want to write a solution, i have to say why im excluding a case right? i also did it horizontally and vertically

[indigo pewter]

hmm

[quick star]

but like i don’t have any justification for the other cases i excluded

[indigo pewter]

i would search it up ngl

[quick star]

okay but search what?

[pearl pond]

@quick star Has your question been resolved?

[solid pier]

well, you might think to just compute what the dimensions of such a cylinder would be. it’s not immediately obvious from the definition of “cylinder” and “box”, but one might draw a picture and compute the dimensions of the cylinder in the case where it sits diagonally in the box so that it can’t get any bigger

one principle that might be useful here is that a cylinder has equal volume as a parallelepiped with the same cross-sectional area

which is much more easily justified than the conclusion you’re trying to make

and then use that principle somehow

[solid pier]

not sure if it’s actually useful though. i’m not as sharp today but if i come up with some other easy or clever path to proving something like this

then i’ll share

[pearl pond]

@quick star Has your question been resolved?

[pearl pond]

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[midnight haven]

pp

[midnight haven]

what is happening

[tulip marsh]

Are you familiar with the formula for a sum of numbers in a geometric series? (I am trying to guess where do you have a problem in this)

[cinder orbit]

what is the prime factorization of 90 my brain is not braining

[midnight haven]

wasnt it

first value

[cinder orbit]

wait...

is this channel open?

[midnight haven]

and something n-1

i remember that yea

[cinder orbit]

is this channel open?

[tulip marsh]

afraid not

[cinder orbit]

..

[midnight haven]

2 × 3 × 3 × 5

[cinder orbit]

k thx

.close

[midnight haven]

😂

[cinder orbit]

breh

[tulip marsh]

😄 lol it wasn't yours

[cinder orbit]

didn't work

💀

fck

[tulip marsh]

let me go back to that serieees

[midnight haven]

anyways

what was the equation

[cinder orbit]

BRO I ASKED

💀

anyways

bye

[tulip marsh]

You understand here how the rate was calculated?

[midnight haven]

the rate is e^x right

[tulip marsh]

yes. We divide 2 consecutive terms, after we notice dividing any 2 consecutive terms give same result (e^x)

[midnight haven]

alright

[tulip marsh]

How about the formula for the sum of geometric series; know it?

[midnight haven]

so the rate is e^x

and the first thingy is e^x

which is u1

what was the equation again

for geometric

[tulip marsh]

I'll apply the rules used here, so:
S_n=u_1 (1-r^{n+1})/(1-r)

I dont think it's too clear to understand like this, let me find it on google so it's written nicer

[midnight haven]

alright

[tulip marsh]

https://www.cuemath.com/geometric-sum-formula/

here, a=u_1, in your exercise

on the site, you should look at "geometric sum formula for finite terms"

The font is quite small; tell me if you found it

[midnight haven]

a is first thingy

r is the rate

and n is the place

[tulip marsh]

it should be r^(n+1)

But that is supposed to be the formula (with r^(n+1) )

[midnight haven]

oh wait this is for the sum

oh year r^n+1

[tulip marsh]

yes, and now we're supposed to apply this to our exercise

by switching a and r with what we have in the exercise

[midnight haven]

so

wait

[tulip marsh]

although your exercise looks quite strange; I might have to research this a bit, as it seems there's 2 unknowns in it: you don't know neither x, nor n

[midnight haven]

e^x(1-e^x^n+1)/1-e^x

[tulip marsh]

If we check the link I sent earlier again, https://www.cuemath.com/geometric-sum-formula/,
there's also a formula for infinite series (2nd formula)

we need that one; the sum you have here is not finite (there is no n, or "n is infinite")

[midnight haven]

oh yea it must be infinite

a/1-r

makes more sense

[tulip marsh]

true, now I see why you had that solution before

[midnight haven]

e^x/1-e^x

and this equals 3

now we only have x unknown

[tulip marsh]

Yes. But we should also note that x =/= 0, for the fraction to make sense

[midnight haven]

ohhh now i get it

[midnight haven]

yea

even for log and ln right?

[tulip marsh]

True, ln and log (I suspect log is the base 10 logarithm, here) are only defined for numbers > 0.

[midnight haven]

do you have any idea if the equations are given in a levels?

[tulip marsh]

I am not sure what you mean. Could you explain?

[midnight haven]

a levels are external exams from cambridge

[tulip marsh]

oh, I cannot help you with that, I am afraid. No idea 😦

[midnight haven]

alright no worries

thanks for the help

appreciate it

[tulip marsh]

know how to get from this

to solution?

[midnight haven]

oh yea thats the easy part

i just didnt know where the equation came from

[tulip marsh]

alright 🙂 apparently, it was a formula

[midnight haven]

.close

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[neat marlin]

could I get some help? I'm stuck trying to understand Taylor and Maclaurin stuff in Calculus 2, ive been trying to do this for hours and I can't figure out what I'm doing wrong

[sharp vigil]

,rcw

[sharp vigil]

you used the maclaurin series for cos(x), but we need the series for cos(2x)

[neat marlin]

OHHHH

oh my god that so incredibly stupid of me

thank you- i might come back in a bit with more questions, but thank you

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[robust cedar]

im stuck on this problem. i attached an image of what i think the shaded region is and another image is the integral i setup to solve for the area, but it was incorrect. what am i doing wrong? last image is the greens theorem formula im using

[pearl pond]

@robust cedar Has your question been resolved?

[little swan]

The order of your inner limits of integration look backwards to me

[pearl pond]

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[buoyant garnet]

One message removed from a suspended account.

[buoyant garnet]

One message removed from a suspended account.

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[pearl pond]

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[rose sentinel]

Help me sole this system of ODEs please

[rose sentinel]

$$(D-1)x +(D^2+1)y = 1$$ $$(D^2-1)x + (D+1)y = 2$$

[jolly parrot]

Nathan

[rose sentinel]

please

Using elimination methods

$$(D-1)(D-1)x + (D-1)(D^2 + 1)y = -1$$
$$-(D^2-1)x - (D+1)y = -2$$

Cancelling:

$$(D-1)(D^2+1)y = -1$$
$$-(D+1)y = -2$$

Adding:

$$y'''+y'-y''-y-y'-y=-3$$

Simplifying:

$$y'''-y''-2y=-3$$

Auxillary:

$$m^3-m^2-2$$

Solutions:

$$\frac{1+\sqrt{7}i}{2}$$

[jolly parrot]

Nathan

[rose sentinel]

$$\frac{1-\sqrt{7}i}{2}$$

[jolly parrot]

Nathan

[pearl pond]

@rose sentinel Has your question been resolved?

[gleaming moss]

The elimination doesn’t look correct

[rose sentinel]

howso

[gleaming moss]

For x: (D-1)^2 =/= (D^2 - 1)

[gleaming moss]

.

[pearl pond]

@rose sentinel Has your question been resolved?

[pearl pond]

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[robust cedar]

i think i got the right answer here but i only have 1 attempt left so id like someone to check my work. 2nd pic is greens theorem that im using. the problem gives the curl of Z which is equal to whats used in the greens theorem. the problem also gives the circulation of C1, the outer circulation. so basically i need to find total_circulation - C1 = C2. total is 4 over the area of D which is 18 from the diamond - 1 from the square = 17. so 17 * 4 = 68 is the total circulation. 68 - 240 = -172. the question doesnt say its positively oriented so im not 100% sure on the sign but i think -172 should be the answer

[warm current]

curl of Z which is equal to what's used in greens theorem
What? nvm i see what you are saying

[robust cedar]

this is equal to the curlz

right?

[warm current]

@robust cedar this looks perfectly correct as far as i Can tell

240 is the outer circulation, C1

and total circulation is 17*4

,calc 68-(-172)

[jolly parrot]

Result:

240

[warm current]

Yeah jeff i think you are good

[robust cedar]

damn it was wrong

maybe it was positive?

[warm current]

Hmm that doesnt feel right. The orientations are all right

Oh dammit nvm C2 is also counterclockwise

Yeah i think it should have been positive

[robust cedar]

if its positively oriented then the region should be to the left of the curve right?

[warm current]

Let's see. C1=240, and it should be C1-C2=68 from what i Can see

[robust cedar]

the picture makes me think its negative but the math makes sense to be positive

[warm current]

Yeah the hollowing of the inner square made me think it was negatively oeiented, but nope. Counterclockwise

[robust cedar]

can you tell which way its oriented based on the picture? if the question had explicitely said its positively oriented would the answer have been negative

[warm current]

Both curves are positively oriented in the picture

Counter clockwise is positive

[robust cedar]

in this article https://tutorial.math.lamar.edu/Classes/CalcIII/GreensTheorem.aspx it says that "Another way to think of a positive orientation is that as we traverse the path following the positive orientation the region D must always be on the left."

if you follow the arrows of the inner square then region D is on the right which would be negative i think

[warm current]

Yeah. The region of the inner path is the inner square

[pearl pond]

@robust cedar Has your question been resolved?

[robust cedar]

it says D is inside the bigger square but outside the inner square, so the shaded region in the picture

[pearl pond]

@robust cedar Has your question been resolved?

[robust cedar]

ill close this but if anyone has a good explanation for how to figure out the direction feel free to dm me

[pearl pond]

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[flat radish]

Not really sure how to do the approximation for this one

I was thinking of doing some solutions for smaller n

such as 2 and 3

and a thing i noticed was that the sum of first (n-1) numbers to the power of 4 is a small proportion compared to the value of n^4 itself,

and thus n^4 itself is an approximation

however then again the proportion of sum of first (n-1) numbers to the power of 4 is gonna increase

so not really a good approximation

and it seems likely that the sum will overtake

n^4 value

[autumn fossil]

hmm

I'd find a function that approximates that sum to n

f(n) = f(n-1) + n^4

[autumn fossil]

this should be the recursive formula

so you will have f(n) - f(n-1) = n^4

so I'd just find a 5th degree polynomial, such that the difference between f(n) and f(n-1) is approximately n^4

if you just try n^5 - (n-1)^5, you get this:

,w expand n^5 - (n-1)^5

[jolly parrot]

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[autumn fossil]

so here it's approximately 5n^4

[flat radish]

i suppose for large values of n

5n^4 is more significant

[autumn fossil]

Yep, indeed

so we can say that it's approximately 5n^4

how do you get it to be approximately n^4?

[flat radish]

and then just divide by 5?

[autumn fossil]

yep

[flat radish]

that makes so much sense

[autumn fossil]

so n^5 / 5 is a decent approximation

you could get finer approximations by ignoring less terms

and if you ignored none, you would get the exact formual

[flat radish]

makes sense

got it

thanks a lot

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[pearl pond]

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[flat radish]

Obviously without the use of calculator

this has been my working so far

[pearl pond]

@flat radish Has your question been resolved?

[flat radish]

<@&286206848099549185>

actually nvm jus figured it out

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[distant hearth]

so i know its convergent because srqt2/2 is less than 1 but how do i find the sum?

A/1 -r? right? but whats A in this

[warm copper]

GP formula

[fringe raft]

the constant factor, but it doesn't have one in this case

[warm copper]

That's bassically it

[fringe raft]

the A*r^n

[warm copper]

Yeah a is 1

[fringe raft]

also be careful

[warm copper]

Because there's a hidden *1

[fringe raft]

the n start at 1, not 0

[distant hearth]

so what goes in the numerator?

oh i see

[warm copper]

1

[distant hearth]

so the constant is just 1 you mean?

i see ok

[warm copper]

And like rbit said, don't forget it starts at 1 and not 0

You need to do another step... I'll let you figure it out

[distant hearth]

hmmm, so 1/1-sqrt(2)/2 isnt ok as a solution?

[warm copper]

nope because it starts at 1 and not 0

You need to subtract something...

[distant hearth]

take the conjugate?? honestly im not sure haha, im probably missing something simple

[warm copper]

if you start at 1 and not 0

That means you're not using the value of n=0

so you find n=0 and subtract it away from your GP

think of the series like this:
a+ar+ar²+ar³...arⁿ
the r exponent is the nth term

therefore a is the 0th term

but you don't want all of that, you only want ar+ar²+ar³...arⁿ

[warm copper]

So you use the formula for this, then subtract a

[pearl pond]

@distant hearth Has your question been resolved?

[pearl pond]

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[livid bolt]

Hey

[livid bolt]

For part b ii i dont get it

Oh speed of the electrons in the beam is reduced to half

So the electrons are faster?

Oh nvm

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[midnight haven]

Is this correct?
lim x->a f(x)/g(x) = lim x->a f'(x)/g'(x) = lim x->a f''(x)/g''(x)........?

[calm wing]

this is l'hôpitals rule

it is correct only if you have 0/0 or inf/inf case

otherwise you can't use it

[midnight haven]

Oh

thank you

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[oak quiver]

why are you doing limits?

you have started to surpass me 💀

[midnight haven]

I ain't studying it from a book, I just found it myself

[oak quiver]

hmm

you should actually follow a book

if you wanna learn something

learning bits and pieces from here and there wouldnt help you in the long run

[midnight haven]

You have misinterpreted

I haven't learned this somwhere

I discovered this.

[oak quiver]

wdym discovered?

[midnight haven]

Like it's my rule now, not l hopitol's.

you gotta give me credit

[oak quiver]

[pearl pond]

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[cyan coral]

So the derivative of y=3x is 3, because for every value of x y increases by 3

Why is the derivative of y=xx not x, since y increases by x for every value of x

[icy narwhal]

nah

that is not how you justify the dervative

[cyan coral]

But it does increase by x the same way 3x increases by 3

[icy narwhal]

do you know about the slope formula

[cyan coral]

Maybe

what is it

[icy narwhal]

write it down

Ta(h) = (f(a+h) - f(a))/h

[cyan coral]

Isnt this the slope formula

[midnight haven]

Because x is not a constant

[cyan coral]

I know that

[midnight haven]

three is a constant
x(x) = ax
a = x not constant

[inland ivy]

the value of y=x^2 actually increases by roughly 2x*h, where h is the amount you "step forward" on the x-axis

this approximation gets better the smaller h is

[cyan coral]

where did you get the h from

[inland ivy]

meaning f(x+h)-f(x) is approximately 2x*h for suitably small values of h

[midnight haven]

Or 2xh + h^2

[inland ivy]

it's a common variable name for this sort of thing

[cyan coral]

what does it represent in e.g. y = xx

[inland ivy]

it means that the slope at any point on the curve is twice the x value

not just the x value as you thought

[cyan coral]

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[sweet oxide]

The given binomial distribution is B(100, 0.6)
a) Calculate the expected value and the standard deviation.
b) Determine the number of successes within the interval [E(X) - \sigma; E(X) + \sigma]
c) Calculate the percentage of all outcomes within this interval.

The standard deviation gives the interval [55.101; 64.899] .
The number of successes is 56 and 64
Why is 55.101 rounded up to 56 , while 64.899 is rounded down to 64 ?

[plush bramble]

55 and 65 are not in the interval [mu-sigma, mu+sigma] if you don't round and you want to keep it that way when you round

[pearl pond]

@sweet oxide Has your question been resolved?

[sweet oxide]

mu - sigma = 55.101 and mu+sigma = 64.899
Why is 55 rounded to 56 and 64.899 to 64 when you want to calculate c) for example

for c) youd need to do smth like P(56 <= X <= 64), when you want to calculate it or not?

The interval doesnt seem to be allowed to get bigger

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[karmic wigeon]

SAT math can someone pls help?

[tulip marsh]

How are the anglex x and y? (let's remember, any 2 angles on that image are either equal, or have the sum 180 degrees)

[karmic wigeon]

yes angle x and y sum up to 180\

[tulip marsh]

I am afraid not. 😦

[karmic wigeon]

oh

[tulip marsh]

They're called opposite angles.

[karmic wigeon]

okay

[tulip marsh]

And they're equal 😦

[karmic wigeon]

ohh alr

I think thats my mistake

btw when are they equal to 180

[tulip marsh]

For example, 2 angles that are next to each other sum up to 180. A way to visualize it easier is:

You can see on the image there's 4 angles bigger than 90, and 4 smaller than 90

[karmic wigeon]

yes

[tulip marsh]

x and y were smaller or bigger than 90, in the image?

[karmic wigeon]

bigger

[tulip marsh]

https://www.cuemath.com/geometry/parallel-lines-cut-by-transversal/
Here's an article, if you want to read more about their names etc (I suspect you might have their names in the notebook too)

[karmic wigeon]

alright thanks

[tulip marsh]

Yes, so they couldn't sum up to 180, since they're both bigger than 90, right?

[karmic wigeon]

ahh alright

true

[tulip marsh]

🙂 this would be a way to understand them easier

[karmic wigeon]

Okay

[tulip marsh]

Then, we can ask ourselves. how are y and z?

equal, or adding up to 180?

[karmic wigeon]

equal?

[tulip marsh]

do they seem equal in the graphic?

[karmic wigeon]

no, they are not

[tulip marsh]

or is one bigger than 90, and 1 smaller

[karmic wigeon]

yes

1 is greater and one is smaller

[tulip marsh]

Yes. so they add up to 180

[karmic wigeon]

ohh ok

Sorry I'm am not very familiar with this topic

[tulip marsh]

It's alright. I wasn't trying to rush you, was just trying to teach you how to figure it out.

Giving a bit of intuition 🙂

[karmic wigeon]

Yess, I just want to thank you so much

For your time

it really helped

[tulip marsh]

You're welcome. I am glad to help 🙂

For school, it's a good idea to also remember the names of the pairs of angles, assuming the teacher gave them names.

[karmic wigeon]

Yes true

I haven't done geometry in a while, since right now I'm currently doing calculus

[pearl pond]

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[dim bobcat]

Can somone help me pls 💀💀

[frozen lantern]

what.

[midnight haven]

uh

[dim bobcat]

I cant do this

HEELP

[midnight haven]

just use a calculator at this point

[frozen lantern]

should i ping mods

[dim bobcat]

teacher say i wont be able to use my calculator during exam

[dim bobcat]

bro i rlly suck at math

[cinder thistle]

are u refusing to do this out of spite against arethmetic?

[dim bobcat]

didnt understand

[frozen lantern]

im sorry who allowed this person on discord

they're just a troll

no?

[dim bobcat]

no

[frozen lantern]

i should ping mods

[cinder thistle]

i think little kid more likely

[dim bobcat]

bro pls helppp

[frozen lantern]

mod ping in either case?

[cinder thistle]

nah it is bad to do such stuff

[dim bobcat]

i've learnt to speak and write recently

[cinder thistle]

it feels rude somehow

[dim bobcat]

i am 16

[cinder thistle]

oh

[dim bobcat]

pls helpp

[frozen lantern]

troll

[dim bobcat]

this is all want

[cinder thistle]

such ppl exist, doesnt give troll vibes to me

[dim bobcat]

[frozen lantern]

hmm well

[pearl pond]

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[exotic gale]

Please help someone

[exotic gale]

so far, i have manage to simplify the congruence down to 11n≡33 (mod 52)

i also realize that 33 is a multiple of 11

so n=3 is a possible choice

but the question asks for the largest three-digit integer

and that's where i'm stuck

<@&286206848099549185>

<@&286206848099549185>

[sinful quest]

You know that n has to be a three digit number, so replace n with 100a+10b+c where a,b,c are the numbers 0 through 9, then reduce further

i would do that and then guess and check large digits, thats how I got it at least

[cunning comet]

11n=52k+33 for some k
as the left side is divisible by 11, the right side has also to be divisible by 11, so k = 11m

[exotic gale]

is m an integer

[cunning comet]

if you understand my argumentation you know the answer.

[exotic gale]

ok cool

i don't understand

yay i got the answer

thanks

.close

[cunning comet]

what exactly is not clear? its the same "way of solution" as in the other channel - some minutes ago.

[exotic gale]

i don't know, i guess i was just tired

.close

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[orchid cobalt]

wait im confused on the horizontal translation of k units

cuz for example

when y = (x + 2)^2 the x intercept is -2

and not 2

or am i tripping and misunderstanding this?

i think im just confusing myself ;-;

[merry carbon]

If you want to find where y = 0, you want where (x + 2)^2 = 0, so where x + 2 = 0 and x = -2

[orchid cobalt]

ohh ok

but like it says when h is greater than 0 it goes right

wont that make it 2?

[merry carbon]

But here h is negative, h = -2 so it goes left instead

[orchid cobalt]

guys im sorry im a little slow

so (x + 2)^2

the 2 is negative?

[merry carbon]

(x - (-2))^2

[orchid cobalt]

OH EM GEE

[merry carbon]

Then here

[orchid cobalt]

OK THAT MAKES SENSE

TYSM KITTEN

https://tenor.com/view/cat-bottle-milk-gif-12663346

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[midnight haven]

lol

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[raw pier]

In A level maths we do something called linear coding, which enables us to talk about means and standard deviations whenever each data point is changed by the same linear expression

[raw pier]

What if that expression is non-linear, what can we say about the new SD and Mean

For example, if i have 10 data points, with a mean of 5 and SD of 2, what is the new mean and SD if I square each data point

[plucky python]

you can work out the new mean

but you won't be able to work out the SD

[raw pier]

Why not?

[plucky python]

as in u can cook up 2 sets of 10 data points with mean 5 and SD 2 that have different SD if u square each data point

[raw pier]

Ohh okay

Would the new mean just be 25?

[plucky python]

no

in general, if i give you the mean of 10 data points

and then i square those 10 data points

u wouldn't be able to work out the mean

[plucky python]

here if u think abt what the SD^2 is

it's the mean of the squares - square of the means

so it'd be SD^2 + mean^2

if ur asking really really generally, like if i have some data points and i transform them all by some function f

[raw pier]

I don't quite understand this

[plucky python]

in general, knowing the S.D and the mean does not tell u anything about ur new sets of data points

like actually, SD and mean tells u very little information

[raw pier]

Okay

[plucky python]

i tried to find a nice picture but i can't find a picture rn

[plucky python]

have u not come across that in A level?

[raw pier]

I have but we've not done much on it

[plucky python]

oh right

[raw pier]

I just understand it to be a measure of the average variance of a data point from its mean

[plucky python]

yeah basically

were u introduced it as like sum (x-mean)^2

[raw pier]

Oh yeah we were

[plucky python]

yeah if u just expand brackets

stuff cancels and you end up with

mean of the squares - square of the means

that's the formula u'll use for most qs on the exam and like that's the mantra to remember it

[raw pier]

Ohh right of course

So you're saying non-linear transformations to data points don't tell us anything about means or SDs without being given the actual data?

[plucky python]

yh

[raw pier]

Ohh okay cool

[plucky python]

standard deviation and mean compresses a lot of our data into 2 values

but u have to remember that bcus we've 'compressed' all our data into just these 2 values, we've lost a lot of information

[raw pier]

Yeah that makes sense, can i ask just one last thing

[plucky python]

ok this was the best i could find

[raw pier]

The lower quartile Q1 is just n/4, but if that number is an int, we add 0.5, if it is a decimal, we round up. why is that?

[plucky python]

ngl i don't really remember all the rules for that

[raw pier]

Oh okay no problem

[plucky python]

i don't do stats and like i don't think it matters that much anyway

cus like in the real world, u have like way more than 10 data points lol

[raw pier]

So it's pretty much negligble

[plucky python]

so who cares if it's the 10000th or the 10000.5th data point

[raw pier]

Yeah true 😭

Thanks for your help

[plucky python]

nw

[raw pier]

.close

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[plucky python]

wait whoops i thought u typed in some weird rounding rule

ok u typed in the normal one

it's just cus like if u have a list of 11 numbers

if u write them out

the middle number is the 6th number, not the 11/2nd number

the 1/4th number is the 3rd number, not the 11/4th number

[pearl pond]

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[midnight haven]

Hello

[midnight haven]

I lowkey ned help with statistics

Random variables

Its just a broad thing im trying to learn jow to do random variabls for statistics

[plush bramble]

https://www.probabilitycourse.com/chapter4/4_0_0_intro.php

[midnight haven]

Mb for not clarifying im learning a unit withh four lessons

Random varibles 1, analyzing discrete random variables 2, binomial random variables 3, anlyzing binomials random variables

[plush bramble]

then https://www.probabilitycourse.com/chapter3/3_1_1_random_variables.php

[midnight haven]

Thanks big dog

[midnight haven]

Ill ask you if i still need clarification

[pearl pond]

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[fringe smelt]

Can anyone check if my homework is right?

[fringe smelt]

Solve the following problems. Make sure to read each problem carefully and draw diagrams as necessary. Provide answers rounded to one decimal place if they are not whole numbers. Do not forget units such as cm or degrees. Be precise and show all your calculations.

In triangle ABC, the sides and are both 5 m, the height m, and angle . Calculate the measures of angles and and the length of side .
Answer:

In a right triangle ABC, , , and . Calculate the length of the median from , denoted .
Answer:

The diagram shows two similar right triangles. Calculate the length of side .
Answer:

The diagram shows two similar triangles. Calculate the lengths and .
Answer:

In a right triangle ABC, , , and . Calculate the length of side . (Draw a diagram and use trigonometric functions.)
Answer:

In a right triangle ABC, , , and . Find the measures of angles and . (Draw a diagram and use trigonometric functions.)
Answer:

[pearl pond]

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[pearl pond]

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[main kite]

Anyone plz help in this ques..

[pearl pond]

@main kite Has your question been resolved?

[latent hill]

chatgpt is enough for definite integrals

[pearl pond]

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[raw verge]

what is the vector for x axis

[raw verge]

3d

[versed mica]

you mean the unit vector in the direction of the x axis?

(1,0,0)

[raw verge]

ok thanks

.close

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[copper mirage]

for number 16 what do I do after plugging it in

[slim verge]

Take lcm

[copper mirage]

Wym

[slim verge]

In the denominator

It will turn out option b

[copper mirage]

I still don’t understand what you’re trying to say

[dapper kraken]

what do you get from plugging it in?

[pearl pond]

@copper mirage Has your question been resolved?

[copper mirage]

uhhh I don’t know what to do after plugging it in

[dapper kraken]

what do you get from plugging it in?

[copper mirage]

6/(7/8x)+8

<@&286206848099549185>

[pearl pond]

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[pearl pond]

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[midnight haven]

One friend is 60 miles away from a city, another friend is 90 miles away from the city. What is the shortest possible distance between the 2 friends, largest possible distance, and average distance between the possible locations of the 2 friends.

I already got that the smallest possible distance is 30 miles, and the largest possible distance is 150 miles. How should I find the average distance without iteration bc iteration would take forever?

[cinder thistle]

do you know cos rule?

[pearl pond]

@midnight haven Has your question been resolved?

[midnight haven]

Yes is that how to solve it?

[cinder thistle]

i was thinking that they could means 2 possible things

what is the center of the range

and what is the median

actually they cant even as for median

[midnight haven]

Wdym

[inland lantern]

Assume the 90 miles away person is at some random point 90 miles away. This is WLOG since all points they could be at will be the same average distance. Now, where is the average location for the 60 miles person?

[cinder thistle]

since you cant take the average of a inifinite set without defining a probability measure on it

[midnight haven]

Which is why I went to iterating first

[cinder thistle]

integrating you mean right?

[midnight haven]

Yeah mb 😭

[cinder thistle]

its fine

anyway

integration isnt defined here

since you dont know what to integrate with respect to

the only thing they could be asking for is the center of range

[midnight haven]

Ok

[pearl pond]

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[young zinc]

This look correct to you guys?

[sharp vigil]

for both tests we require ln n / n to be decreasing, so you should establish that somewhere

[young zinc]

Does that mean i have to find the derivative

And if its negative in the numerator its decreasing

[sharp vigil]

that's a way of establishing it, yes

[young zinc]

Generally speakin at least

Ok

Well thats inconvenient

Shoulda just ratio tested that bitch

[sharp vigil]

the other way would be to directly prove a_(n+1) < a_n

which one is easier depends on context

[young zinc]

That way sounds confusing to me

Wait so

For both AST and direct comparison

I have to show that ln/n is decreasing?

[sharp vigil]

i misremembered, we only have to show that for alternating series

[young zinc]

Ah ok, still a pain in the ass

Just less so

This fine?

[sharp vigil]

sure

[young zinc]

Sick

Aw man that AST thing is kind of a bummer

Seems like i did my entire hw wrong for that section

Im not gonna go back n change it but still

Lemme check my notes

So, youre right it says so in my notes

I didnt doubt u, but it was more like a uh, "maybe my professor is lazy"

Cuz for some reason, in the examples, he doesnt prove that b_n is decreasing

Or a_n, my notes calls the expression b_n

[sharp vigil]

well we often consider a_n to be our original series, and a_n = (-1)^n b_n

if your professor does not establish that the series is nonincreasing in examples then it may be that you are allowed to as well. in any case it should not be too difficult to establish that it is decreasing for this particular function using calculus

[pearl pond]

@young zinc Has your question been resolved?

[young zinc]

Yeah imma just do it from now on

Just in case

Its just a small derivative

And for an exam, i got time to crank out a quotient rule if need be

Ty for your help though cloud

Actually one more thing if ur here

For this one, i shouldve done the alternating series part where i check that the expression 1/n³ is decreasing right

And then find the lim of 1/n³ as n-> infinity

Then if it equals 0 (which it does) then it converges by AST

And that 2nd part i did was the check for absolute convergence

Right?

Cuz i think i initially fucked up there

Cuz i dont think direct comparison shows abs convergence

[sharp vigil]

direct comparison doesn't show absolute convergence, but you can establish absolute convergence by computing the convergence of the absolute value

(which would involve essentially the same arguments)

i don't see where you are using the alternating series test, though

[young zinc]

Yeah thats why i mentioned i shouldve

I didnt check that b_n was decreasing and then didnt even find the limit of 1/n³

I messed up. I just noticed lookin back at my hw

[sharp vigil]

how would the AST apply? where is the alternating series?

[young zinc]

2sin(n) or at the very least sin(n)

As n approaches infinity

Sin(n) fluctuates between 1 n -1

The 2 may change that fluctuation

[pearl pond]

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[sudden badger]

Find f(x) with the condition that the line x= 2 is a vertical asymptote, the line y = -2 is a horizontal asymptote and that the intersection with the x axis is p(3.0).

[sudden badger]

I don't know how to make it so that f(x) intersects the x axis at (3,0)

[nimble osprey]

heyy marito

[sudden badger]

hi!

[nimble osprey]

you should have f(3)=0

so for example f(x)=(x-3)g(x)

[sudden badger]

yeah but idk how to make it so that:
y = -2 is a H.A
and it intersects x axis at (3,0)

fulfilling both of these conditions is whats confusing me

[nimble osprey]

g(x)= -2/(x-2) so that the limit for x approaches infinity is -2

[sudden badger]

😨

[severe quarry]

That doesn't sound right

[nimble osprey]

remember that g is inside the f above

[severe quarry]

Oh, I didn't see that, sorry

[nimble osprey]

np

[sudden badger]

oh yeah

this does it

thanks

[nimble osprey]

what 1704 stand for ?

[sudden badger]

birthday

[nimble osprey]

ohh I see

[sudden badger]

.solved

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[lethal estuary]

how did we get r of t

[coarse harbor]

In other words, C is the set of all (x, 0, z) such that x^2 + z^2 = 1 (oriented counterclockwise), so essentially a unit circle in the xz-plane

A famous parametrization of a unit circle is (sin(t), 0, cos(t)), which follows from the main trig identity

sin(t)^2 + cos(t)^2 = 1

[pearl pond]

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[earnest flint]

hey guys, does anyone know whats the correct input for my calculator?

TYPE: Casio-fx82ms
WHAT: Formula for time for compound interest :)))

What our teacher gave us:

(It worked last night but it doesnt work now and i forgot how i did it last night 😭) Please can someone tell me the order of input? Huhu...

[earnest flint]

I would appreciate it so much

[pearl pond]

@earnest flint Has your question been resolved?

[earnest flint]

anyonee?

<@&286206848099549185> sorry for pingg

[leaden jay]

Your alone on this one🙏😭

[earnest flint]

LMAOO 😭

[sinful nebula]

what even i this

[earnest flint]

this HAHSAHH 😭

Im just practicing on putting the values

for my exams 😔 🫰

[sinful nebula]

first numerator then denominator

like this (log_10(F)-log_10(P))/((n)*log_10(1+(r/n)))

[earnest flint]

omgomg hold onn ima try

[sinful nebula]

brackets important

[earnest flint]

Waitt whats _10?

[earnest flint]

yesyes tyy

[sinful nebula]

that is the base of log. But in calculator log of base 10 are generally just log

[earnest flint]

okay2 im gonna try itt

[sinful nebula]

(log(F)-log(P))/((n)*log(1+(r/n))) smth like this

[earnest flint]

OH MY GOD IT WORKS

BROOO THANK YOU

LIFESAVER

IT WORKSOKDK

THANK YOUUU 😭

[sinful nebula]

mm

nice

[pearl pond]

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[earnest flint]

TY AGAINN

.close

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[midnight haven]

@sharp walrus

[midnight haven]

bruh aint noway

im sorry

.close

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[sterile flax]

[pearl pond]

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[pulsar stump]

how is this true?

[smoky musk]

What is the basis of log? Looks strange to me.

Normally, the basis of logarithm is $10$. Logarithm with basis $e$ is written $ln$. Logarithm with basis $2$ is usually only used in computer science context, especially when discussing entropy.

[jolly parrot]

Xwtek

[oak quiver]

I think it would be base 2

[pearl pond]

@pulsar stump Has your question been resolved?

[cursive wraith]

you need "log" to be base 2 for this to be true yeah

[pearl pond]

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[warm osprey]

I just started learning about inner products and I am a little confused by the definition of the length or norm ||v|| = sqrt(<v,v>)
Consider the weighted euclidean inner product: <u, v> = sum(ui * vi * wi)
Now in R2 consider w1 = 1 and w2 = 10, then the norm of v = (2, 1) becomes ||v|| = sqrt(<v, v>) = sqrt(2*2*1 + 1*1*10) = sqrt(14)
But my intuition tells me that the length of the vector v = (2, 1,) should be sqrt(5)? What am I not understanding?

[plush bramble]

Weighted norms are not the same lengths as you learned before

It is if all the weights are 1. But your weights of (1,10) make the "length" different

[warm osprey]

Fair enough thanks

.close

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