help-0

[wicked plover]

what graph is this?

[alpine sable]

wdym

[wicked plover]

like

i littearlly dont know

like bar graph

[alpine sable]

[wicked plover]

like im supposed to graph a set of numbers and its supposed to look like that graph

[alpine sable]

are you given a function

[alpine sable]

o

so you want to graph that?

[wicked plover]

Yeah

[alpine sable]

like a specific graph you're looking for?

[wicked plover]

Yes.

[wicked plover]

i have to graph the set of numbers

and its supposed to look like that

graph

but i dont know what that graph is called

:'/

[alpine sable]

i'm still confused on what you're asking

[wicked plover]

cause im trying to just search up a website where i can input the numbers

[alpine sable]

seems like a regular line graph to me

[wicked plover]

Oh

Oh i see

thats what its called

[alpine sable]

i mean idk if thats the answer you're looking for, maybe plot them on a bar graph

or pie chart

or a table

cumulative frequency table

you got histograms

and whiskerplots

[wicked plover]

I have no choice because

Thats the only thing that was posted

[alpine sable]

i'm not that great at statistics #probability-statistics #advanced-probability is your go to place

[wicked plover]

Hey

Thank you

Do you know a website that I could just input numbers

and it'd make a line graph

[alpine sable]

Desmos?

I'm unsure if thats what you're looking for

oh wait

probably not

[wicked plover]

Yeah desmos doesnt make line graphs

[alpine sable]

Are you looking for something that outputs this?

thought you were talking about line graphs on the cartesian plane

https://www.rapidtables.com/tools/line-graph.html

https://www.visme.co/line-graph-maker/

Not that I know of

I just searched these up

hope they come in use

[wicked plover]

Yess!

Thank you

[warped phoenix]

we add probabilities when they're mutually exclusive right?

and multiply when they're not

if so

why is this the case

they replace the card, and picking a jack has nothing to do with picking an 8, thus it's mutually exclusive meaning we would add the probability and not multiply right?

maybe im thinking about this too hard, should i just remember that with probabilities, or means add and "and" means multiply?? what if theres a question that doesnt have either keywords then whattttt

ughhhh im confused now

[vague coral]

huh, they just applied a formula é_é

the probability that two events happen at the same time

[warped phoenix]

wait so when should we add probabilities 😟

[vague coral]

and since A and B are independant I guess its why we multiply

[warped phoenix]

oh so when its mutually exclusive u multiply

[vague coral]

what is that "mutually exclusive" ?

[vapid oak]

does order matter? do we need to pick specifically a jack, and then specifcally an eight or can it be in either order

[warped phoenix]

i dont think order matters no

[vapid oak]

because if order doesn't matter the probability would be 2/69

169**

[warped phoenix]

4/52 * 4/52 is 1/169 tho

[vapid oak]

because you have an 8/52 chance of picking either a jack or an eight, and then once the card is returnd you have a 4/52 chance of picking the card you didnt

since you said order doesnt matter

[warped phoenix]

idk she never specified

[vapid oak]

i think order doenst matter because otherwise the question should have specified

[warped phoenix]

wait so im still confused on when we're supposed to add the probability

[vapid oak]

but i wouldnt know

[warped phoenix]

you multiply dependent events too tho

theres a formula for doing so

[vapid oak]

you don't add the probability in this case, but there are where you do

[warped phoenix]

when would that be? :/

[vague coral]

remove that idea of adding or multiplying probabilities of your head xd

it's not how you should think in probability

but in combinatory yes

[warped phoenix]

yeah its getting me confused real quickly

ok

[vague coral]

I sent the formula

[warped phoenix]

what is the iEI

[vague coral]

A and B are independants event

[vague coral]

?

[warped phoenix]

under that pi, there's an iEI

[vague coral]

$i \in I$

[warped phoenix]

also whats that curve thingy

[ocean seal]

Herels

[warped phoenix]

yeah

whats the thing that looks like a C, also why is the A upside down 😅

[vapid oak]

i think theres a lot of stuff in that large formula you dont need to know, seeing as the question you posed was realtively intermediate probability

[warped phoenix]

oh ok

so i add probability when it's combinatory

[vague coral]

thats not how it works lmao

[warped phoenix]

😦

[vague coral]

I mean, just apply formula in probability, don't think about adding or multiplying

when you are dealing with combinatory (i hope its what its called in english), there are times when you should use + and there are times when you should use x

[warped phoenix]

ok

how do i know when those times ar

[vague coral]

If in the exercise, they use "and", it's mean x, and when it's "or" it's +

[vapid oak]

yep thats it

[warped phoenix]

ok ill just remember that then

im just worried there may be a problem that doesnt have either key term

idk how that would work

i guess such a problem isnt possible???? maybe it is

[vague coral]

but you will have exercise that deals with combinatory and probability at the same time

[warped phoenix]

basically i dont wanna get tricked by the question writers

oh

like "what is the probability of getting a 6 on a die and a heads on a coin, or what is the probability of getting a 2/3/4 or a tails on a coin"

idk thats just some dumb example i made

see theres like

multiple "and"s and "or"s

[vague coral]

yes something like that

[warped phoenix]

bruhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

then what 😭

[vague coral]

?

[warped phoenix]

like how would i know

what to do

when their are multiple ands and ors

[vague coral]

[warped phoenix]

WHAT

😦

[vague coral]

I don't really love probability, it bores me so much

[warped phoenix]

lol

@vapid oak do you know?

srry for the tag

[vapid oak]

sorry what was the question

[warped phoenix]

herels said that ill face questions that have both + and x operations

how would i know which one to do for which part of a question when there is mutliple uses of the words "or" and "and" in a question like that

like an example like "what is the probability of getting a 6 on a die and a heads on a coin, or what is the probability of getting a 2/3/4 or a tails on a coin"

[vapid oak]

ok so can i reword the problem and you tell me if its the same?

[warped phoenix]

sure

[vapid oak]

what is the probability of getting a 6 on a die and heads on a coin or rolling a 2/3/4 or a tails on a coin

[warped phoenix]

uh

[vague coral]

<@&268886789983436800>

[spice lintel]

its my kingdom cum

[warped phoenix]

yup thats pretty much what i was asking

wow lol

[sly mantle]

@spice lintel don’t shitpost

[spice lintel]

its not ashitpost

but ok

[warped phoenix]

someone doesnt know what shitpost means 0_0

[spice lintel]

im literally trying to do a math problem about it

[warped phoenix]

yeah..........

[sly mantle]

@spice lintel you’re on thin ice. stop trolling

[night geyser]

you're not making a good case for yourself

just drop it

[spice lintel]

yes sir

[vapid oak]

well calculating probability in these cases is quite hard, so you calculate the probability that none of these events happened and then -1.

still quite hard

[warped phoenix]

hm, ig what i want to know is if ill be covering any of that in the near future, like, within the course of alegbra II 😅

this is whats left of my unit

idk if the example question i gave is in any of these lol

[night geyser]

perhaps

[warped phoenix]

😦

[night geyser]

it's hard to tell just from names how in depth it goes

but that could certainly be covered

[warped phoenix]

true

[night geyser]

"addition rule for probabilities" could just be about linear combinations of random variables, or it could be about the inclusion-exclusion principle

if the latter then it would certainly cover questions like this

[with appropriate bracketing, since as written it's ambiguous]

[warped phoenix]

well i suppose ill cross that bridge when/if i get there hahahahah, thx for letting me know tho 😄

[night geyser]

and 5.18 sounds like bayes' law (which would also be used in this)

but it could be referring to something else

[warped phoenix]

bayes what now

😂

oh wait

is this gonna

be my first

like

[night geyser]

P(A given B) * P(B) = P(B given A) * P(A)

[warped phoenix]

formula i encounter named after someone

[night geyser]

assuming P(B) nonzero

[warped phoenix]

ok so, probability of a, knowing the probability of b, times the probability of B, is the same as the probability of B given the probability of A, times the probability of A

is that what that's saying? 😅

[night geyser]

not quite

[warped phoenix]

😦

[night geyser]

"A given B" means the probability A happens if we know B happened

[warped phoenix]

ohhh

given b occurred

right

i see now

[night geyser]

for example, lets say we're rolling a 6-sided dice, and "A" means that "we rolled an even number", and "B" means "we rolled 4, 5, or 6"

P(A) and P(B) are both 1/2

but if we KNOW B happened

that is, we KNOW we rolled a 4, 5, or 6

2/3s of those are even numbers [and they occur uniformly]

so P(A given B) is actually 2/3

and similarly, P(B given A) is 2/3 by bayes' law

"given" is often notated with a bar |

[warped phoenix]

wait

so its saying the condition of a applies to the probability of b??

because the condition of a here is the number rolled must be even

and in the probability of b, there are 2 even numbers

so then 2/3?

thats prob wrong lol

[night geyser]

i think you have it a bit backwards

P(A given B) means we're assuming that B happened

and now we're computing the likelyhood that A happened as well

if A and B are both independent (i.e. don't affect each other), then P(A) = P(A given B)

since B doesn't affect A

but if we're only rolling a single dice and our events are "we rolled an even number" and "we rolled 4, 5, or 6", then they're certainly NOT independent

since knowing we rolled 4, 5, or 6 (i.e. knowing B happened, or being "given B") means that it's more likely we rolled an even number

since our possibilities for even numbers are 4 and 6, while our possibility for odd number is just 5

and since we were equally likely to roll any of them, this means 2/3 of the time, if we rolled 4, 5, or 6, we rolled an even number.

this is P(A given B)

B - that is, the number being a 4, 5, or 6 - is given

and we care how much A happens when B is given

[warped phoenix]

so P(A | B) means that, knowing we rolled 4, 5, and 6, what is the probability that an even number was rolled?

[night geyser]

right

and that would be 2/3

[warped phoenix]

ohhhhhhhhhhhhhhhhhhhhhhhhhhhh

[night geyser]

we were equally likely to roll 4, 5, or 6

but 2/3s of those were even

so if we know we got one of them, 2/3s of the time we got one of the even ones

[warped phoenix]

so

1, 2, and 3, are completely disregarded

since B is given

[night geyser]

yes.

[warped phoenix]

since B is what happened

OHHHHH

🤦‍♂️

oh wow

[warped phoenix]

this really helped

ty!!!!!!!!!!!!!!!!!

[night geyser]

theres an alternate way to interpret this as well

[warped phoenix]

now i wont face this issue when i learn about it 😂

[night geyser]

$P(A|B) = \frac{P(A \cap B)}{P(B)}$

[ocean seal]

Namington

[night geyser]

if youre not familiar with $\cap$, here it just means ``and"

[ocean seal]

Namington

[night geyser]

so P(A and B) in this case is the probability that we rolled an even number AND we rolled a 4, 5, or 6

[warped phoenix]

the probability of a given b is equal to the probability of the intersection of A and B divided by the probability of B

that's what that's saying?

[night geyser]

right

[warped phoenix]

oh ok

[night geyser]

P(A and B) in this example is

we rolled a 4 or a 6

[warped phoenix]

(wait rq isnt "and" supposed to be the upwards u symbol? the union? 😅)

[night geyser]

do you see why? "A" means we rolled 2, 4, or 6, and "B" means we rolled 4, 5, or 6

so their intersection is 4 and 6

[vague coral]

and is $\cap$

[night geyser]

??

[warped phoenix]

he put the down one tho

[ocean seal]

Herels

[warped phoenix]

oh

[night geyser]

anyway, so P(A and B) is 2/6 = 1/3

since it means we rolled 4 or 6

and P(B), as previously established, is 1/2

so P(A | B) = (1/3) / (1/2)

by laws of fraction division, this is (1/3) * 2

in other words, 2/3

and of course, this is the same as what we found earlier

so we can verify that this "makes sense" (at least for this example)

anyway, this broadly is known as "conditional probability"

im not sure to what extent your course will cover it

its hard to tell just from topic descriptions

[warped phoenix]

ok

[night geyser]

but its pretty important to applications of probability, since it can create unintuitive results if you're unfamiliar with it

[warped phoenix]

ill prob just stick to the first explanation 😅

[night geyser]

the usual example being drug testing

[warped phoenix]

oh how are the two related

also

wait

[night geyser]

https://www.khanacademy.org/math/ap-statistics/probability-ap/stats-conditional-probability/v/conditional-probability-tree-diagram-example

[warped phoenix]

if $\cap$ is and, what's $/cap$

[ocean seal]

TheMane3

[warped phoenix]

oops

how do i do the up U? 😅

[stoic burrow]

hello, sorry to interrupt
I need help with homework

3i + 4h - 14 = 2ih

I need to find h, and i is imaginary number 😄

[warped phoenix]

channel in use

channel 1 looks free

i think

[night geyser]

/cap doesnt exist

do you mean $\cup$?

[ocean seal]

Namington

[warped phoenix]

oh

LOL

yeah

[night geyser]

"or"

P(A U B) is the probability that A happened OR B happened (or both)

so in this case, if A = "rolled 2, 4, or 6" and B = "rolled 4, 5, or 6"

P(A U B) is the probability we rolled 2, 4, 5, or 6

[warped phoenix]

union = or (either one occurring), intersection = and (both occurring)

right

[night geyser]

yes

[warped phoenix]

ohhhh

[night geyser]

well, or should maybe be (either one or both occurring)

just to be clear that it's inclusive

but yeah

[graceful lynx]

Can some one give and example of this...

u look at this example and u can see even through the series converges to 1, the sum sequence also converges to 1

[solar cradle]

a_{k} =1/2^k, which limits to 0

[graceful lynx]

oh

i didn't realize u use partial sum for proof, which is different to ur example..

thanks

[warped phoenix]

wait whaaa

so or = and but and doenst equal or?

since or is also both occurring

[glass lichen]

A or B means A happens or B happens, if both happen, then you can still say either happened

A and B means both have to happen'

[night geyser]

$A \cap B \subset A \cup B$

[ocean seal]

Namington

[night geyser]

i think this is what youre trying to communicate

"if something satisfies A AND B, it must also satisfy A OR B"

but the other direction is not true

for example, 4 is both even and ≥ 4

so it satisfies A and B from my example

and therefore also satisfies A or B

but 5 ONLY satisfies B

so it satisfies A OR B, but not A AND B

we would not use the "=" symbol to communicate this, we use the "subset" symbol

since it's not a symmetrical relationship

(as you observed)

[stray parrot]

Guys

I need help on this question lmao

Apparently this

Like i dont rly get the

Concept

Of

Similarity

[vapid oak]

would you mind translating the question?

[alpine sable]

Yo

[twin haven]

multiply both sides by x

[stray parrot]

Oh sure

A is 90 degrees

Line BM equals CM

[vapid oak]

I can read the diagram for that info. maybe just tell me what the question is asking

🙂

[stray parrot]

Ohh find the length of MH

[vapid oak]

oh well we know that DM is 1.5 because BM=CM so CD-DM=BD+BM

And we know that AD is 2 because of the similarity within the triangle

[stray parrot]

Yeah

Ohh

[vapid oak]

because 4/AD=AD/1

so AD^2=4 and AD is a length so therefore not negative so AD =2

i assume the question requires you to calculate all the lengths of the triangles and then calculate AM-AH

[stray parrot]

Then we get the length of mh

[warped phoenix]

LMFAO 💀

[stray parrot]

Hmm

[warped phoenix]

Ohhhh, "and" is a subset of "or" basically?

an intersection is a subset of a union

THAT MAKES SENSE

because the intersection is literally inside both of the things

like a venn diagram

[violet sphinx]

Can anybody tell me what's the y-intercept for a straight line passing through/intersecting the origin?

Is it 0?

[alpine sable]

x=y, but i think i dont get what you want to say

@violet sphinx

and it can be rotated

so there many ways it could pass through origin

or it cant i think

only this x=y works i think

[tight locust]

y = kx

[violet sphinx]

Let's take this graph for instance, what's the y-intercept?

[alpine sable]

y=kx not work

[tight locust]

yeah it does

[alpine sable]

y=kx means x is greater than y so it does not go through zero as he wanted

or less

[tight locust]

if y=kx then what happens when x = 0?

[alpine sable]

@violet sphinxno dont think of it this way, just look at the graph x is the same as y and so yeah y=kx for k=0 is what you asked for to go through zero

[wary stream]

K in this case, would just be the slope

[tight locust]

not just for k = 0. for any value of k

[violet sphinx]

I thought it was "m" not "k"

[tight locust]

doesn't matter lmao

letters are letters. you can call it m or k or sigma or phi

[wary stream]

Any arbitrary variable works

[alpine sable]

wow indeed u right i did not know

[violet sphinx]

So, there's no y-intercept?

[tight locust]

there is a y intercept. every function defined at x=0 has a y intercept

[alpine sable]

just y=kx and you can chose any value of k for roation, x and y don't get identified as numbers

[tight locust]

the y intercept is at y=0

[wary stream]

The general form you are used to seeing is $$y = mx + b$$ but it can be written as $$y = kx + c$$ or $$y = \theta x + z$$, or with any letter

[ocean seal]

dldh06

[tight locust]

a y intercept at 0 is different from no y intercept

[violet sphinx]

Ok

[tight locust]

a function with no y intercept would be 1/x

[alpine sable]

or yeah it is at y=0

[violet sphinx]

The problem here is if the y-intercept is 0 then how can I count the gradient by using the y-intercept/x-intercept formula? Wouldn't you just get 0 but actually the gradient isn't 0

[tight locust]

slope = change in y/change in x

you need two points

[violet sphinx]

That's an another formula

[tight locust]

you mean this:

$(y-y_0) = k(x-x_0)$

[ocean seal]

EndTimes

[tight locust]

?

[violet sphinx]

Umm... Not that

[tight locust]

then what do you mean?

[violet sphinx]

It's just y-intercept over x-intercept

[wary stream]

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

[ocean seal]

dldh06

[wary stream]

That one?

[tight locust]

if y = kx then the slope is just k

[violet sphinx]

Gimme a sec

This one @wary stream

[tight locust]

yeah that formula doesn't work if y=kx

[violet sphinx]

Wait, what?Why?

[tight locust]

ok. if y=kx then the x int and the y int are both 0

so then you get m = -0/0

[violet sphinx]

Exactly

[twin haven]

tan theta?

[tight locust]

which is an indeterminant form

wrong. actually there are infinite solutions

[violet sphinx]

That's where I got stuck

[tight locust]

if m = 0/0 then 0m = 0

then just don't use this equation lmao. it doesn't always work

there are much simpler ways to go about this

[violet sphinx]

So that formula is just a hoax or something?

[tight locust]

not a hoax. it just doesn't always work

it is true when the y intercept and x intercept are at different points

[violet sphinx]

Oic

[tight locust]

this formula you have is a special case of this formula:

$m = \frac{y-y_1}{x-x_1}$

[ocean seal]

EndTimes

[tight locust]

and the implicit assumption being made in your formula is that you have the points (x,0) and (0,y), which are presumed to be two different points

so then that simplifies to (y-0)/(0-x) = -y/x

but you can't do that when the x int and the y int are the same point.

you need two points to define a line

[violet sphinx]

You have opened my eyes

[violet sphinx]

So pretty much, the formula is like a derivation/form from the original, right? @tight locust

[violet sphinx]

I see

[gaunt magnet]

will the intervals for this graph be

[violet sphinx]

Btw, thanks for helping me out @tight locust @alpine sable @wary stream

[gaunt magnet]

<@&286206848099549185>

🥱

[alpine sable]

[stray parrot]

Isnt that 4?

[stray parrot]

Btw i dont rly get that part

[vapid oak]

ok so you know like similarity laws?

we know that the sides of the triangle are in ratio because they are similar. So the side corresponding to each other are AD-4 and 1-AD and therefore their ratios are the same

[stray parrot]

Hmm i kinda getting it

We know that

Umm AM is 2.5

@vapid oak how do we find MH again?

[lyric cedar]

The differentiation looks wrong

[halcyon geode]

Second one no, that doesn't work to prove equality. Easy counter example. Consider 5x-5=5x. They both have the same derivative yet they're not the same

(didn't really checked the derivation, just that something having the same derivative doesn't prove equality)

There for example you could have had any value, pi/2,pi,5, potato, your rhsis always gonna be zero

[lyric cedar]

Aint 5x -5 = 5x show 0=-5?

[halcyon geode]

Yeah, but let's say the question is is "prove or disprove this" and you differentiate and say voilà it's equal!

[lyric cedar]

Yea

[halcyon geode]

Mmm not completely sure I dont remember my tangents, but you have your inver trig functions there and is tan and Cotan, so my guess is check identities for something like tan (a+b)

[lyric cedar]

The differentiation. Did you apply chain rule?

Quotient rule works with multiplied terms. Here sin^-1(something) is one complete term. I think what you are doing is applying quotient rule on sin^-1 and (something) separately which is wrong

Just assume (1-x³)/(1+x³) t be k and apply normal differentiation. Then differentiate k again

[steel palm]

can someone please look at channel 2 when you are done

[whole charm]

Well, i don't think you can simply differentiate the LHS and RHS and prove they're equal. The fact that the derivative of LHS is 0 means that it is a constant term, which could be anything. Now take any x(wouldn't matter which as the domain is -inf to +inf). Consider x=1, so tan-¹(1) +cot-¹(1)= π/4 + π/4 = π/2

Since the derivative is 0, the value of the expression is π/2 regardless of x

[lyric cedar]

You wrote 1/sqrt(1-x²)

It should be 1/sqrt(1-k²)

k = 1-x³/1+x³

[vocal drum]

Sketch the graph of f(t) for t ∈ [0, 2].

What does this mean? I'm doing trig functions

[austere bridge]

it means draw the graph on the interval [0,2]

∈ is shorthand for 'in', so you could interpret it as "sketch the graph of f(t) for each value of t in the interval [0,2]"

[vocal drum]

Um would you mind showing me an example?

[austere bridge]

an example of what?

[whole charm]

which trig function are they referring to?

[vocal drum]

f(t)=4-2cos(2pit)

That's 2 "pi t to clarify

"pi"

[austere bridge]

$f(t)=4-2\cos(2\pi t)$, right?

[ocean seal]

cgodfrey

[vocal drum]

Yes

[whole charm]

right, so you'll need to sketch this for x lying between 0 and 2

[vocal drum]

Oooohhh ok

I get that

Thanks

[whole charm]

here's how it would look like

[steel horizon]

I could do the first one but not the others, if its not too much trouble, please a photo of the answers:D

[ionic jewel]

check the pinned message for the relevent expansions

[steel horizon]

thenks

[lilac shadow]

cosine is just sine but shifted by 90°/pi?

no wait pi/2

?

[soft zodiac]

I'm not sure if this question is supposed to go in a physics discord, but I'm going to ask it anyways because I feel like it involves math more than physics:

A ball is thrown on a flat ground at an angle of 48 degrees above horizontal with a velocity of 25m/s. Determine the time of flight, the horizontal distance, and the peak height of the ball? Assume that there is no air resistance.

I was able to figure out the time of flight and horizontal distance, but I'm having trouble finding the peak height.

[lilac shadow]

there is a physics discord though

i can dm invite if you need

ah ok thanks

[soft zodiac]

yes plz awsam thx

[rugged elbow]

how to

[lilac shadow]

taiga

[lilac shadow]

can use calculator or no?

[rugged elbow]

yes

[lilac shadow]

hmm

all three of us

have things

related to japan

i mean pfp

not things

if you gonna ask me

how is this train related to japan

IT WAS MADE IN JAPAN

same train

:)

anyways

hmm

im quite lazy to do it now

even though i can

nice about me

[dark granite]

This channel is open for questions

[dry berry]

how can i find the inverse function of y=x*e^x on the interval [-1; +inf)?

[placid zinc]

You can't express such a function using the "usual functions"

So we made one up. It's called the Lambert-W function

[gaunt sun]

<@&286206848099549185> I drew out a cartesian plane, failed, went to google, failed. Please help

[wanton vortex]

you can only ping the Helpers role if it's been 15 minutes since you've posted your question and hasn't been answered yet

[wanton vortex]

your answer for number 16 is correct. a reflection over the x-axis means the y values change sign. a rotation 90 degrees counterclockwise about the origin is when the coordinates go from (x, y) to (-y, x)

[reef hare]

When I would solve this equation: $\min {x{1}}\left[f\left(x_{0}, x_{1}\right)+g\left(x_{1}\right)\right]$, I would end up with a function only depending on x0 right?

[ocean seal]

benek

[vale wigeon]

it's not an equation but yes

[reef hare]

Do you have any idea on how I could solve that optimization problem in Matlab?

Thank you btw for the quick answer

all variables are vectors with five values

[flat vale]

What’s the correct mathematical term for the lower and upper value of the domain?
e.x. [2,5]
2 is the lower value

[placid zinc]

Endpoint or boundary

[vapid oak]

yeah. it would be lower and upper boundary

[placid zinc]

A lot of sets don't have these so they're not often named

Infimum or Supremum for certain cases

[nimble cave]

help

[wanton vortex]

with?

[nimble cave]

these 2

3*

[vapid oak]

have you tried drawing a diagram for Q4?

[nimble cave]

Yeah i have

[vapid oak]

do you know the cosine rule?

[nimble cave]

yes

[vapid oak]

or the sine rule?

[nimble cave]

yes

i used them i got confused

[vapid oak]

use the cosine rule

[nimble cave]

lemme show u he diagram i drew just tell me which angle's cosine should i use

Like i used of

A and b

[vapid oak]

the problem only tells you one angle so

[nimble cave]

wtf

[vapid oak]

well you would use the cosine for the only angle you have!

[nimble cave]

i did

[vapid oak]

and what did you get

[nimble cave]

then the answer comes in iota-

[vapid oak]

yeah i mean the first part looks right

oh really? let me try it mysel

[nimble cave]

ok

[vapid oak]

i dont get any complex numbers but the answer sure isnt rational

[nimble cave]

what is your answer

[vapid oak]

ill send a photo

[nimble cave]

Okok

[vapid oak]

its a bit messy sorry

[nimble cave]

Its fine

is the question just wrong then

[vapid oak]

i think using the triangle inequality you can boil it down to only one answer but my brain is collapsing rn

no the question isnt wrong

at all

[nimble cave]

ok

do yk what can i do of the 2nd ques

[vapid oak]

yep i was right. 4sqrt2 is not a viable answer. the answer is 2sqrt2**

[nimble cave]

√2?

ok

[vapid oak]

sorry 2sqrt2

[nimble cave]

2√2

So

ok

Thanks

[vapid oak]

also Q5 is kinda impossible

[jagged imp]

yeah lmfao

i assume they meant to give you one of the sides maybe?

[vapid oak]

i mean it tells you an angle but no side lengths so its impossible to know what the lengths of the reactangles are. You could work out the ratio between the length and the breadth but not their actual values

[nimble cave]

yeah I was thinking that too-

Everyone in the class said its wrong sir said he'll check but he didnt-

Nvm

So

Ok

[vapid oak]

would you mind explaining what you mean?

[nimble cave]

i

[nimble cave]

Is that a 5 or a S

[vapid oak]

a 5

[nimble cave]

oh oka

[vapid oak]

aha sorry

If it helps, the ratio between the length and the breadth is 1 : sqrt2-1

[nimble cave]

idk ill just leave that 2nd ques

[vapid oak]

yeah

[nimble cave]

That question 6 idk the rules

I

[vapid oak]

can you tell me what the first line of Q6 says. ABC is a ??? angle triangle

[nimble cave]

abc is a right angled triangle

[vapid oak]

ok

[nimble cave]

why in the worldjd

[vapid oak]

gee golly this is hard

[nimble cave]

im just a

9th grader

why am i

nvm

Ill do other ques

[vapid oak]

ill try and solve it in the meantime 🙂

[nimble cave]

okayy

[vapid oak]

yeah its a tough question

im stuck

[nimble cave]

Oh its ok

Thanks for the help

[wanton vortex]

for number 5, you can find all of the angles in the rectangle, right?

[nimble cave]

yes

[vapid oak]

yeah but there arent any side lengths so you cant work out any sides, only their ratios

[nimble cave]

I have

But the length

Cant be found out

There are many possibilities so ok

[wanton vortex]

[nimble cave]

[wanton vortex]

even if you could find the lengths, what units would you even express them in

weird question

[nimble cave]

ikr

[covert wren]

i dont think questions 5 is even possible

[warm veldt]

can anyone help with this?

[vale wigeon]

have you made any progress so far?

[warm veldt]

i can do A

but not b and c

[vale wigeon]

can you show your work for part a?

[sleek elbow]

@warm veldt ^

[vale wigeon]

great, so what is stopping you from calculating P(X=1) and P(X≥2) using almost the exact same method?

[warm veldt]

xC0 will always be 1

xC1 will be x tho

[vale wigeon]

yes, and?

were you able to at least write down the equations you need to solve?

[warm veldt]

idk how to progress from that last line

[vale wigeon]

you really should have shared this when i asked you "have you made any progress so far" btw

its a bit annoying having to find out you DID make progress but withheld it

[warm veldt]

idek if its the right thing to do tho

cause when i put it into a online calculator i get the wrong answer

[vale wigeon]

what exactly did you put in the online calculator?

[rigid island]

do i get banned if i call anne out on something

ann*

[vale wigeon]

n = 2542.19392...

[warm veldt]

^

[vale wigeon]

huh

,w 0.001 * n * 0.999^(n-1) = 0.2

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Ann#0413

[warm veldt]

ah

[vale wigeon]

oh, so that W function probably would have evaluated to 259

[warm veldt]

i c

[vale wigeon]

except that symbolab is

shitty

[warm veldt]

ahhhh ok

[vale wigeon]

try having it take the derivative of sqrt(x)*sqrt(x).

[warm veldt]

mbad

[vale wigeon]

it'll launch into a whole spiel with the product rule

and outright ignore the obvious solution path

[warm veldt]

lmao

so i should use wolfram alpha instead?

also Is there a way to do it with my calculator instead then

cause i wont have this in exam

[vale wigeon]

can you show your calculator

[warm veldt]

TI-84

[vale wigeon]

okay honestly im not sure how to do this besides trial and error

[lucid nova]

i don't understand this step

[whole charm]

take (x-2)^2 common from both brackets

does it make sense?

[lucid nova]

i am still thinking 😅

[whole charm]

so its (x-2)^2 (1-(x-2))

[tight locust]

a^2 - a^3 = a^2(1-a)

[lucid nova]

oh thx!

[tight locust]

yes. substitution is helpful

[lucid nova]

wow indeed

[high palm]

Question 6 a and b need help

Complete noob here

[whole charm]

whats a triangular and a pentagonal number?

[high palm]

are u asking me to see if i know

or asking because you don't know

it's like making the shape, e.g. first triangular number is 1, next is 3, 6 then 10

[whole charm]

i was asking cuz i didn't knwo

[whole charm]

what kinda shape? i didn't get it..

[plucky sleet]

use their formulas

Tn=n(n+1)/2

Pn=n(3n-1)/2

[high palm]

yea, but like what do i do from there

[high palm]

you can search it up

[plucky sleet]

replace n by 3n-1 to calculate T(3n-1)

and see what happens

[high palm]

k

[high palm]

sorry i don't understand

[plucky sleet]

we have Tn=n(n+1)/2

[high palm]

yes

[plucky sleet]

replacing n by 3n-1 we have

T(3n-1)=(3n-1)(3n-1+1)/2

thus

[high palm]

yes

[plucky sleet]

T(3n-1)=3n(3n-1)/2

you can check that this is 3Pn

[high palm]

I was told by a friend to substitute n with n-1

@plucky sleet ?

[plucky sleet]

i'm talking about question a

[high palm]

yes

[plucky sleet]

in b you substitute by n-1

[high palm]

OH SHOOT

MY BAD

OK I MESSED UP

ok so can you restart

sorry im really stupid

[plucky sleet]

np

we are in a or b?

[high palm]

a

[plucky sleet]

k

[high palm]

im really stupid

so try to eli5

[plucky sleet]

we have Tn=n(n+1)/2

[high palm]

yes

[plucky sleet]

substitute n by 3n-1

[high palm]

that is the formula

[plucky sleet]

you get

T(3n-1)=(3n-1)(3n-1+1)/2

[high palm]

3n-1(3n-1+1)/2

[plucky sleet]

we are good now

[high palm]

yes

[plucky sleet]

-1+1 cancel out

it becomes

[high palm]

yes

3n

[plucky sleet]

3n(3n-1)/2

[high palm]

yes

i am with you

[plucky sleet]

and that's the same with 3Pn

since Pn is n(3n-1)/2

[high palm]

yes

it stays the same?

[plucky sleet]

yeah

[high palm]

so

[plucky sleet]

don't forget that we are proving T(3n-1)=3Pn

[high palm]

yes

[plucky sleet]

and we found it :'

[high palm]

3 x n(3n-1)/2 = (3n-1)(3n-1+1)/2

[high palm]

How?

[plucky sleet]

forget about the right hand side

3n(3n-1)/2=T(3n-1)

and at the same time

3n(3n-1)/2=3Pn

[high palm]

yes

[plucky sleet]

thus they are equal

[high palm]

Wait what

wait

[plucky sleet]

what?

[high palm]

please bear with me

[plucky sleet]

what step didn't you understand?

[high palm]

T(3n-1) = 3n(3n-1)/2

[plucky sleet]

yeah

[high palm]

Pn = n(3n-1)/2

[plucky sleet]

yeah

[high palm]

so

[plucky sleet]

don't forget to multiply by 3

[high palm]

yes

so

[plucky sleet]

3Pn=3n(3n-1)/2

[high palm]

yea

[plucky sleet]

yea

[high palm]

wait thats the same

as the other one

YOOOO

THANKS SO MUCH

[plucky sleet]

you'r welcome

try to prove b in the same way

[high palm]

Ok

[plucky sleet]

calculate the rhs and lhs and prove they are the sam

same

[high palm]

I will try that but first i need to write down the answer

is it ok if i ping you if i need assistance with b?

[plucky sleet]

of course

[high palm]

thanks so much!

ill brb

[plucky sleet]

np

[viscid cove]

hey, what is the condition for an equation to be homogeneous ?

[vale wigeon]

there are multiple things you could be talking about,

but generally, it means that the right-hand side should be 0

in whatever way makes sense in context

[viscid cove]

i'm talking about differential equations

is (x+1)/y homogeneous?

[vale wigeon]

this is not even an equation

[viscid cove]

dy/dx=(x+1)/y

i dont think the 0 is relevant here

[vale wigeon]

ah. that kind of homogeneous.

no, this isn't homogeneous.

but it is separable.

[viscid cove]

so...1 no bueno?

i know the degree should be equal

[vale wigeon]

yes, 1 no bueno.

[viscid cove]

so whenever an equation can be expanded, each of the separated terms should be homogeneous too?

[vale wigeon]

dunno what thats supposed to mean

[viscid cove]

(x+1)/y: x/y + 1/y is not homo cause of 1/y. It that the general case for time an equation can be separated?

meh leave it

[upper escarp]

how to solve x?

[wary stream]

Sine

On both sides

[upper escarp]

?

[wary stream]

Also write parentheses too because that's probably confusing you too, the format

[dreamy mountain]

Sin (sin-1) gets the sin gone

So you just got x/25

[wary stream]

It's $$sin^{-1}(\frac{x}{25}) = 53$$

[ocean seal]

dldh06

[upper escarp]

oh ok thanks

[unborn dome]

isnt the answer just 1...

[wary stream]

Yeah, looks like it

[dreamy mountain]

If I’m correct yes

Actually

Isn’t it pi?

[wary stream]

Nope, pi is the period

[dreamy mountain]

Yeah

[unborn dome]

thought its just pi/pi which is 1

[untold mountain]

guys

I am year 7

can anyone

[wary stream]

Explain please?

[unborn dome]

idk i just distributed pi

[wary stream]

No need to

[unborn dome]

ah......

[untold mountain]

please tell me what the 'f' is in math equations

[dreamy mountain]

function

[untold mountain]

thxs

[wary stream]

If you mean f(x), it normally means function, otherwise it's just an arbitrary variable

[untold mountain]

can you tell me how it is used

give me some example

[dreamy mountain]

Is it f(x)?

Cause then it’s just a function with variable x

[wary stream]

To denote functions, like f(x) = x + 1

[hollow hawk]

3b

im dead inside

please help

[wary stream]

It is equivalent to y

[untold mountain]

dang thats hard

[wary stream]

The function y = x + 1 and f(x) = x + 1 mean the same

[untold mountain]

rn I am learning cosine rule

how am I supposed to know that question.

LOl

[untold mountain]

this one

[vapid oak]

have you done differentiation?

[untold mountain]

nope

not yet

[vapid oak]

so then how are you doing these questions?

[dreamy mountain]

If I’m correct you just calculate the derivative and plug in that point

[untold mountain]

because I was just curious

[dreamy mountain]

English isn’t my first language so idk if gradient is the same thing here

[wary stream]

No one needs your comments if you don't know it. If you don't know the concept, let someone else answer. Also (s)he wasn't asking you about differentiation, was asking neon

[dreamy mountain]

But since it’s dy/dx it seems to me it is

[untold mountain]

I am sorry :((

just realized

[vapid oak]

hey so if you understand it the equation of a tangent at point (t, f(t)) is:
y - f(t) = (df(t)/dx)(x-t)

i find that thinking of it that way helps me find tangents but its quite intricate if you've recently started differentiation

^^^ for constant t, where you substitute in the x value of the coordinate where the tangent will touch the graph

[cobalt sparrow]

Factorize

[hollow hawk]

@vapid oak

where do i go from here

but how get square root

[vapid oak]

cos(pi/4) is sqrt2/2 not 1

if it helps, pi/4 = 45°

[dreamy mountain]

The final answer is correct tho

[vapid oak]

sorry could you elaborate, im a bit confused

[hollow hawk]

thanks

❤️

[quaint pond]

hello could someone help me understand the solution to the following problem:

[cobalt sparrow]

Can I get some help please, i am confused what to do next lol

[quaint pond]

the solution is 20! / 10! but I can't understand it

[vapid oak]

i would love to help both of you but maybe could someone hop onto another channel so it isnt confusing?

[cobalt sparrow]

Ok sure !

[rocky atlas]

My question is

How many numbers of one digit number are there

9 or 10(if we include 0)?

I don't know if I can include 0 to be one-digit number

[vapid oak]

ok im here sorry

[quaint pond]

so could you help me understand it

[vapid oak]

yes ok so basically how many ways can you individually pair up 20 people?

well its (20C2)*(18C2) etc.. until (2C2) which is 1

[quaint pond]

wait

[vapid oak]

oh my lord this number is going to be massive

[quaint pond]

isn't it just

[vapid oak]

sorry when i said 'which is 1' i meant just (2C2)

[quaint pond]

(20C2)

[vapid oak]

20C2 is how you could pull out a single pair of people from 20

[quaint pond]

yes

ohhhhhh

yeahh

[vapid oak]

but unless i misread we want to know how many different pairings of all 20 there are

[quaint pond]

yes

okay got it

[vapid oak]

ok so we should simplify the expression now

20C2 is 20!/18! * 2! and then 18C2 is 18!/16! * 2!

[quaint pond]

yes

[vapid oak]

so notice that one factorial on the bottom will always cancel out and so that product telescopes into 20!/2^10

[quaint pond]

yes

but then why the 10!

[vapid oak]

no not 10!, every term will look like 20!/18! * 2!

sorry bad example

take 12!/10! * 2!

the 12 factorial will cancel out with the previous term, and the 10! with the next term

all that is left is 1/2! which is just 1/2

so every term has that extra 1/2

plus the 20! from the first time which we didnt cancel out

[quaint pond]

aha

that makes sense

[vapid oak]

would you mind just letting me go check if im right aha

I am

ok so now we have all of our kinds of pairs, but we actually now have to multiply by 2^10

because we have our 10 pairs, but since the arrangement of black and white pieces matters each pair can be arranged 2 ways.

so 2^10

which cancels out with the denominator of our product and the answer is just 20!

quite a beautiful problem

[quaint pond]

yes but shouldn't we divide

by 10!

[vapid oak]

oh maybe

[quaint pond]

because we don't care

[vapid oak]

why do you say

[quaint pond]

about the order of the games

[vapid oak]

huh? are we the honey badgers

OH

MAYBE

THATS A GREAT POINT

[merry plank]

i dont understand these >.>

[alpine sable]

what about them you don't understand?

are you having problems solving them?

[merry plank]

yes i'm having trouble finding the zeros and i don't understand how to find what x= at the end

the <,> signs are trippin me

[neat kayak]

anyone know this

[merry plank]

c

[lilac shadow]

C

[alpine sable]

C

[lilac shadow]

3x1+2x4=11

4*

[alpine sable]

Can anyone help me with this one?

[merry plank]

um i'm getting help with a question rn

can u ask in a diff channel?

[alpine sable]

ok

[faint minnow]

how can I do part c & d for a i just plugged in 0 and 2, then b i just did the functions Q(2) - Q(0) and Q(3) - Q(0)

[merry plank]

ask in a diff channel, i'm still waiting on one of the helpers that was helping me

[faint minnow]

all channels are being used

[merry plank]

#help-6

[alpine sable]

this isn't an eqn but an inequality, which one are you talking about?

[neat kayak]

anyone know this

[merry plank]

i'm talking about all of them but can we go over a few?

[merry plank]

for example c

[alpine sable]

ok sure.

can i see what you tried? i'm guessing you already have done some attempts

[merry plank]

okay so i found the VA which i think is -7

would the x value of the numerator be 1?

[tepid crystal]

Can someone help me solve this further? I am stuck after rationalizing

a hint would suffice 🙂

[vapid oak]

im terrible with integrals so sorry

[alpine sable]

the VA? why are you finding VA? do you mean you found when the den=0?

[jade birch]

denominator is a constant?

[tepid crystal]

Yes

[alpine sable]

@merry plank @tepid crystal please both read #❓how-to-get-help , the channel is occupied.

[tepid crystal]

Ok. Sorry

[merry plank]

?

[vapid oak]

move to channel 8

[merry plank]

i've been here

[alpine sable]

@merry plank wrong tag, meant @vapid oak

[merry plank]

o ok

[alpine sable]

you are good here

[merry plank]

also isnt the VA in the denominator?

that's why i tried to find it

[alpine sable]

i mean okay

is this your very first time to solving inequalities?

[merry plank]

kinda yeah

[neat kayak]

anyone know this