help-28

[glacial pasture]

gn

[clever iris]

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[bleak wolf]

Hi for the last part, I don't get what the quadrilaterial being cyclical has to do with vectors

[steel solar]

Notice the relationship between angles in a cyclic quadrilateral.

[bleak wolf]

Opposite angles add to 180?

[steel solar]

Yes.

Did you do the other parts?

[bleak wolf]

Yes

These are the solutions if it helps

[round nimbus]

I haven't solved it yet but I assume they wish for you to use Ptolemy's theorem?
i.e., in a cyclic quadrilateral, product of its diagonals = sum of products of opposite sides

[bleak wolf]

Ohh I think that's it

thank you!

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[half oyster]

no idea how to start thisd

[glacial pasture]

what is f'(x)

[half oyster]

yeah I tried that

[glacial pasture]

howd it go

[steel solar]

Do you know what the product rule states?

[half oyster]

got stuck after 6x^5

[dense smelt]

What did you get

What is the product rule

[half oyster]

yes

[steel solar]

State it.

[half oyster]

d/dx fx * gx + d/dx gx * fx

[dense smelt]

Uhhh not quite

[half oyster]

meant *

[steel solar]

You multiply the last 2 terms.

[half oyster]

yeah mb mistype

[glacial pasture]

f'=(gh)'=g'h+h'g would look nicely for your problem

[steel solar]

So what will $\dv{x}x^6h(x)$ be?

[glossy valve]

;(

[half oyster]

d/dx x^6 * h(x) + d/dx h(x) * x^6

[dense smelt]

Yes

[half oyster]

oh wait lemme see

[dense smelt]

Plug in :3

[half oyster]

$(6(-1)^5 3) + (66(-1)^5)$

[glossy valve]

Paul04

[steel solar]

Good.

[half oyster]

,calc (6(-1)^5 *3) + ((6)6(-1)^5)

[glossy valve]

Result:

-54

[half oyster]

,calc (6(-1)^(5) (3)) + ((6)6(-1)^5)

[glossy valve]

Result:

-54

[half oyster]

,calc (-1)^5

[glossy valve]

Result:

-1

[half oyster]

,calc -18 + -36

[glossy valve]

Result:

-54

[half oyster]

oh

,calc (6(-1)^5 3) + ((6)(-1)^5)

[glossy valve]

Result:

-24

[half oyster]

,calc (6(-1)^5 3) + (6*(-1^(6)))

[glossy valve]

The following error occured while calculating:
Error: Parenthesis ) expected (char 10)

[half oyster]

,calc (6(-1)^5 (3)) + (6*(-1^(6)))

[glossy valve]

Result:

-24

[half oyster]

I figured it out, thanks for the help

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[elder fiber]

Idk what should I do next

I have 4 variables

[glacial pasture]

try to eliminate two variables

[elder fiber]

Ohhh

I can eliminate a from equation 1 and 2

[glacial pasture]

si, then eliminate with 3 and 4 also

and some other pair

then eliminate a variable from the 3 new equations

you could turn this into a matrix if youre familiar with gaussian elimination

[elder fiber]

I'll not get anything from 3 and 4

[fossil kiln]

oh

[glacial pasture]

how so?

[elder fiber]

Idk Gaussian elimination

[elder fiber]

Like if I add 1 and 2 then a will vanish

[glacial pasture]

sure

you can scale the equations

[elder fiber]

Oh wait from 3 and 4 I'll get 9b which I can add to 2

A and B gone

[glacial pasture]

now you just have an equation without a and an equation without b

not too helpful

you want 3 equations that all have no a or b in it if those are the ones youre eliminating

[elder fiber]

Ohh

I see

Let's find

It'll be lengthy af

There gotta be a smaller path

[glacial pasture]

not that i can see immediately if you dont know how to do this using a matrix

Id say eliminating c and a are probably the easiest though

[inland moth]

ignorant question: have you learnt inverse matrices before?

if not then ignore me and move on

[elder fiber]

Yeah ik inverse of matrix

[glacial pasture]

damn

[elder fiber]

Ohhh

[inland moth]

well then you just subjected yourself to levels of horror that no one can comprehend

[glacial pasture]

just occured to me i never looked at the original question

[elder fiber]

😭

[inland moth]

if you look at the right side

the matrix is 1 0 01

identity matrix

[elder fiber]

Oh

Yeah

Is this some property

[inland moth]

so you can slowly multiply inverses of the matrices to both sides

to find A

[elder fiber]

We know that A × inverse of A is identity matrix

[inland moth]

exactly

[elder fiber]

Im trying to comprehend your method

[inland moth]

you can group two matrices together

and the other one will be the inverse of it

[elder fiber]

It's going above my head

How can I say that it's inverse of B

[inland moth]

.

1 0 0 1 is the identity matrix correct?

[elder fiber]

Yeah

[inland moth]

so thats why

[elder fiber]

So I shouldn't assume matric A as a b c d?

[inland moth]

i mean you can

but you'll go through what you just went through

not super easy is it

[inland moth]

or if you dont understand it i'll change another way to phrase it

[elder fiber]

[inland moth]

wut

[elder fiber]

😭

[inland moth]

ok lets try this again

[elder fiber]

Yes

[inland moth]

so you have those 3 matrices

and they all multiply to the identity matrix

[elder fiber]

Yeah

[inland moth]

so that means either, the first matrix times A is the inverse of the third matrix

[elder fiber]

Their product is identity

Yeah

[inland moth]

so if we call the third matrix B

the first matrix times A is equal to B inverse correct?

[elder fiber]

Yesss

[inland moth]

so something like this

[elder fiber]

Yesss

Got u

[inland moth]

its the opposite of the previous one i showed you but its the same

the brackets doesnt matter

[elder fiber]

Then we can assume matrix A

[inland moth]

?

[elder fiber]

Like the elements as a,b,c,d

[inland moth]

no no

no need for that

[elder fiber]

Okk

[sturdy valve]

yes thats how ur supposed to solve it

[inland moth]

ok great so we know that the first matrix times A is equal to B^-1

and we know B = -3 2 5 -3

can you find the inverse of B?

[elder fiber]

Yeah

[inland moth]

1/det yadayada

[elder fiber]

Yeah

Determinant and adjoint

[inland moth]

so find it

[elder fiber]

Ok let me do this first

Im back

Now we can assume matrix A and get elementssss

[inland moth]

you can

but theres another easier way

[elder fiber]

Tellll 👀

[inland moth]

so you have another matrix equation

[elder fiber]

Huh

[inland moth]

lets call them uh

CA = D

[elder fiber]

Okay

[elder fiber]

Yess

[inland moth]

it would be good if we could "divide" C

[elder fiber]

Matrices are not divisible

[inland moth]

ik

but

we could multiply C inverse on both sides

you see what that does?

[elder fiber]

I'll have to again find inverse of C

Which mean

Determinant and adj of C

[inland moth]

yep

also you'll need to multiply it on the left of D

because C is on the left of A

so C inverse would be required to be on the left of D

[elder fiber]

So you think it's better then assuming matrix a and then multiplication

[inland moth]

i mean you're working with 2x2 matrices

which is easy to find inverses

[elder fiber]

Ohh

Yeah you're right

Intelligent

[inland moth]

larger matrices? probably not

[elder fiber]

I have a 1 min short trick for finding adjoint of 3×3 matrix too

[inland moth]

3x3 is longer but doable

4x4 and above then yikes

[elder fiber]

I have never done 4×4

Not even once

[inland moth]

eh doesnt matter lol

[elder fiber]

Maybe not in syllabus at this level

[inland moth]

anyways what you get for C inverse

[elder fiber]

You do 4×4 in uni?

[inland moth]

there are more advanced methods to find inverses quicker

like elementary row operations

[slate violet]

that's not how maths works

[elder fiber]

Now I understand why my sir used to say, pre/post multiplying inverse of any matrix

[slate violet]

that wouldn't appear in an exam

[inland moth]

yes yes

[slate violet]

if it were on your problem set you'd be allowed to use technology

[elder fiber]

I have done it a bit

[inland moth]

good

[elder fiber]

Ohhh it's that difficult that they let u use calculator?

[slate violet]

yes

the point of maths isn't to grind numbers

[elder fiber]

[inland moth]

anyways i think you got this

[inland moth]

ok good

[elder fiber]

Thank you so much ❤️

I feel intelligent

[inland moth]

answer check passed

[elder fiber]

YOOO LESSS GOOOO

Btw is there shorter method than this?

[inland moth]

not that i know of

[elder fiber]

Hmm I see

Im not yet closing this channel, I'll probably have more doubts related this topic

[inland moth]

btw this works also for right side matrices that is not identity

so if the original question was equal to like, 1 2 2 3

you can also do this

[elder fiber]

Huh how

[inland moth]

so lets say the equation is ABC = D

finding for B

[elder fiber]

We did this only because of identity matrix

[inland moth]

you can multiply C inverse on the right side on both sides

so ABCC^-1 = DC^-1
AB = DC^-1

but you would need to the matrix multiplication of D and C^-1

the question you got was D being the identity matrix, so D times C^-1 is just C^-1

no multiplication needed

but if D is not identity you would need to do an extra matrix multiplication

[inland moth]

.

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@elder fiber Has your question been resolved?

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[elder fiber]

Ohhh

[elder fiber]

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[elder fiber]

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✅

[elder fiber]

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[silver granite]

Dawg I think I need some help I got more dumber and dumber, and this homework is gonna Submit tomorrow💀 and I don't really understand English... My main language is melayu

[severe igloo]

Could you send an image of the question than?

[silver granite]

Idk if u understand but here's the questions

The number two is wrong I think 🥀

[severe igloo]

The number two looks right to me

[silver granite]

But I have the answer in my other paper but it was wrong

[severe igloo]

Could you show the answer?

[silver granite]

Sure

Those are the answers

[severe igloo]

Oh okay. Your sketching is right, you just dind't put the range for it

It doesn't say anywhere in the question for the range

Also i assume you put equal sign to make it easier for you to sketch the reigon?

[silver granite]

Yup

But I still cannot understand 🛌

I cannot just put the answers I also need the Solution and the graf thing

[severe igloo]

Okay. Well think about it like this for question 2, what values of x would produce greater than 0?

[torn jolt]

Could someone explain/help
me with this?

Im studying for my exam and asked chatgpt to make me some exams

[severe igloo]

You need to open a seperate help channel btw

[torn jolt]

And this came up and i’m pretty lost

[torn jolt]

Oh

My bad

[severe igloo]

No worries 👍

[silver granite]

Ummm 1?💀

Dawg I forgor to study

[severe igloo]

Eh okay. Why not sketch it like this? With the y-axis as well

[silver granite]

Can u use language melayu then English? Cuz I couldn't really understand hehe🛌

[severe igloo]

Makes it easier to understand

[severe igloo]

I don't understand melayu sorry

[silver granite]

It's okay

[severe igloo]

Anyways. You shold include the y axis part

just to make it a bit easier

[silver granite]

Okay

[severe igloo]

can you notice it's easier with the Y axis?

included into it

[silver granite]

Ohh okay

[severe igloo]

Btw, you should include the upper region to be shaded in as shown in the image

[silver granite]

And then?

I'm trying to understand your words 🙏 so let me think slowly

[severe igloo]

No worries 👍

After you'd shaded it in, you'd have an accurate graph

[silver granite]

So then how do I do the calculation? I have to make the solutions too

[silver granite]

Ohh okay I understand it now

[severe igloo]

So think of it like this. If it's below 0 it has to be inside the graphe where the roots are

Can you notice where the two sort of broken lines intersect at -2 and 3?

those are called roots

[silver granite]

Ouhhh

[severe igloo]

Roots are basically when the polynomial meets the x axis. (y = 0)

So in this case yours is a quadratic graph. So roots are -2 and 3

Does that make sense?

[silver granite]

Hmmm I'm thinking about it

[silver granite]

Can u do example number 2?

So I can understand

[severe igloo]

Btw your factorisation for example number 2 is wrong

it should be (x-5)(x+3)

[silver granite]

I know that's why I need some example 😭 hahahaha

[severe igloo]

again notice this time it's shaded outside the graph and the roots are -5 and 3

This is because we want y to be greater than 0

[silver granite]

Ohh

[severe igloo]

this is what it looks like if you did the roots from (x-13)(x+15)

Can you notice how the lines don't intersect compared to the previous one?

Because those are the wrong roots

[silver granite]

Ohhh I think I understand a little now

[severe igloo]

Does that fix you're problem btw?

or help you out

[silver granite]

I understand the graph thing but the calculation of it I couldn't understand

[severe igloo]

You can interpret the calculation from the graph

[silver granite]

I can't do this calculation 🥀

[silver granite]

Ohh

[severe igloo]

Oh you mean the facotrisation?

Wait ignore what i said than lol

I thought you were talking about the range of values

[silver granite]

No I already understand about that

[silver granite]

But I cannot understand how I make this calculation

If I know the calculation of the roots I know how to make the graph

[severe igloo]

So basically if we had the form ax^2 + bx + c. In order to factor, you need to find two numbers that multiply with C and also add up to B

[silver granite]

Sorry I don't understand in English I only understand my main language 😭

[severe igloo]

😭 . Yeah it makes it harder so sorry about that

You can use the quadratic formula instead for finding roots. If the quadratic does not factor

[silver granite]

Do u have like> or < examples?

[silver granite]

Nahh it's okay

[severe igloo]

It's the same process

[silver granite]

Ohhh okay

[severe igloo]

But you just replace the equal sign with either > or <

There's also completing the square as well to solve a quadratic

[silver granite]

Ohh okay I'll try

[severe igloo]

Just practice getting into factorisation and also watch youtube videos of it

[silver granite]

Ohh okay but most of them r English then my main language I used to beg my sister to help me to solve the questions but ngl I understand a lot from my sister

[severe igloo]

Yeah most them are in English

[inland moth]

yoo fellow spm student

[silver granite]

Ayo u Malaysian??

[inland moth]

yea man

melayu is on the question bro

just read that

[silver granite]

Damn nah bro I still f4 ambil steam

Stem*

[silver granite]

But I still couldn't understand cuz my teacher's straight answer person, couldn't give any reason how it make that happen u know?😭

So I have to find out myself

[severe igloo]

Do they not explain it to you how to get the answer?

[silver granite]

Yesssss

That's the problem

[severe igloo]

Yeah that can be a problem

[inland moth]

rough

[silver granite]

All of my classmates are complaining about the teacher teaching skills

💀

[inland moth]

anyways you got this now?

[silver granite]

A little🗣️

[severe igloo]

still better than nothing lol

[silver granite]

Hahahaha real

[severe igloo]

Hopefully i explained it better than your teacher lol

[silver granite]

Well true tho hahahaha

[severe igloo]

Anyways you should close the help channel like this .close

[silver granite]

Okay

.close

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[silver granite]

So this channel can magically disappear?

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[severe igloo]

Eh no, it just stays there but closing it allows others to open a channel. Also i think there's a rule to not discuss generally in the help channels so go to other channels instead

[severe igloo]

.close

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[glad void]

I forgot how to do these

The values are: a=4 b=2 c=3

[sturdy valve]

substitute a,b,c in the equations and tell the new equation

[glad void]

4sin2x + 3 = 7 - x

[glad void]

Then what’d I do after lol💀

[sturdy valve]

huh oh

i think you'll have to draw the graph

[glad void]

It’s already drawn

[glad void]

I don’t think so tho

It’s like 1 mark only

[sturdy valve]

did not see this

[glad void]

Yes

I didn’t show it lol

Cuz I thought it wasn’t needed

[sturdy valve]

yeah im kinda stumped

wait for someone to help you

[glad void]

Okay 👌

Thanks tho🙏

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[near bronze]

Question C, i just don't know how to do it.

[near bronze]

<@&286206848099549185>

[full forum]

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

[near bronze]

1

[robust slate]

Hint: Consider $\angle ACQ$ and $\angle FDQ$

[glossy valve]

Civil Service Pigeon

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@near bronze Has your question been resolved?

[near bronze]

I'm clueless i'm sorry, it's SAS right?

OHH i get it now

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[real silo]

hey guys i need help

[modest obsidian]

uhm, what help exactly?

[real silo]

how does [sin^2(theta) + cos^2(theta)]/[sin^2(theta) - cos^2(theta)] became the second line on the left side

[onyx glen]

they divided outer num & denom by cos^2(θ)

[modest obsidian]

yeah that 😔

[onyx glen]

also they seem to have withheld the first mark from you

i would have given it

can you show what it says to the right of the *M1 bit

i wanna see what the guidance is

like this bit

what does it say

[real silo]

it says "Sight of a correct common denominator, either in one or two fractions, condone missing brackets if recovered. In the numerator condone +-sign errors only."

[rain merlin]

is this caie

[real silo]

yes

[onyx glen]

it looks like A-levels stuff

[real silo]

thats true

[rain merlin]

unless mentioned they're strict about it being exactly the way in the mark scheme (other than being simplified)

[onyx glen]

yeah ngl

[rain merlin]

so the sign error in the denom is why

[onyx glen]

your only fault is that you dropped a theta at the ened

end*

[rain merlin]

the mark wasnt awarded

[onyx glen]

wait what sign error did she make tho

[rain merlin]

wait no

wait am i blind

oh yeah I am blind wait

[onyx glen]

yeah no you definitely deserve the first mark for this work lmfao

@real silo

[rain merlin]

oh yeah wait

yeah

[rose zephyr]

Mhmm

[rain merlin]

im just stupid

you do deserve that

[real silo]

wait wdym outer

[onyx glen]

like the entire fraction

essentially

they went from $\frac{s^2+c^2}{s^2-c^2}$ to $\frac{(s^2+c^2) \cdot \frac{1}{c^2}}{(s^2-c^2)\cdot \frac{1}{c^2}}$

[glossy valve]

Ann

[onyx glen]

i'm using s and c as shorthand for sin(θ) and cos(θ)

make sense?

[real silo]

i thought we are not allowed to divide the entire function bcs the equal sign has 3 lines

[onyx glen]

this is no different than going from $\frac{6}{10}$ to $\frac{6/2}{10/2} = \frac{3}{5}$

[glossy valve]

Ann

[onyx glen]

btw just so you know

[modest obsidian]

it just means identity (same thing) instead of an equation 😔

[onyx glen]

grading tests like these is part of my literal actual job

if i saw your work as part of a test that fell into my hands to grade

[eternal dock]

3 lines means the same essentially

[onyx glen]

i would have given you 1 mark

instead of the 0 you got

[rain merlin]

the equality sign just signifies that don't cross multiply

[eternal dock]

prove that x is the same as y

[rain merlin]

rather prove

yeah

work with only one side

[onyx glen]

and she did.

[rain merlin]

yes

[eternal dock]

I am replying to this, not to your comment

[rain merlin]

same

[real silo]

wow thats cool

[modest obsidian]

weird that she didn't get a mark

[still current]

Why is bro flexing

[onyx glen]

please do not call me "bro".

[real silo]

i marked myself

[rain merlin]

oh

😭

[real silo]

☺️

[rose zephyr]

Lol

[modest obsidian]

makes a lot more sense...

[onyx glen]

@still current could you edit that word out please?

[onyx glen]

anyway i'm not flexing either. i am just letting OP know that i know my way around this particular style of paper.

so that she can more readily trust my judgment

[real silo]

wait, so (s^ + c^2)/(s^ - c^2) is the same as (t^2 + 1)/(t^2-1)?

[onyx glen]

indeed, because sin(θ)/cos(θ) = tan(θ).

missing a 2 exponent on the very first s though. typo.

[real silo]

wait wheres the sin(θ)/cos(θ) there? i still dont understand

wait i think i understand

[onyx glen]

they went from $\frac{s^2+c^2}{s^2-c^2}$ to $\frac{(s^2+c^2) \cdot \frac{1}{c^2}}{(s^2-c^2)\cdot \frac{1}{c^2}}$

[real silo]

its this

[glossy valve]

Ann

[onyx glen]

yes

[real silo]

yess

[real silo]

okaayy thank you so much!!

[onyx glen]

you expand the brackets

[real silo]

alright!

[onyx glen]

anyway yeah as i said you have my approval to grant yourself the M1 mark for this question

[real silo]

yay!!

[onyx glen]

in case you're keeping track of a total or something

[real silo]

thanks again

yes im doing past papers as practice

[real silo]

anw thankuu!

[modest obsidian]

happy mathing

[real silo]

thank uu!

yes thanks ☺️

thank you so much everyone

byebye

[modest obsidian]

could you .close if you don't have any further questions

[covert heath]

are you a teacher 😭

or tutor

[eternal dock]

I didn't do anything but you're welcome

[real silo]

yes

[real silo]

wait sorry i gotta close the channel

.close

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[cinder belfry]

Hello i wanted to ask is this a question you guys would be able to help me in

A manufacturer of off-road vehicles is considering the purchase of dual-axis inclinometers for installation in a new line of tractors. The distributor of the inclinometers is temporarily overstocked and is offering them at a 40% discount from the regular cost of $142. If the purchaser gets them now instead of 2 years from now, which is when they will be needed, what is the present worth of the savings per unit? The company would pay the regular price, if purchased in 2 years. Assume the interest rate is 10% per year.

[cinder belfry]

Helloooo!

[glacial pasture]

what have you tried

[cinder belfry]

If you would buy it right now with the 40% discount then it would be 85.2

In 2 years with an interest rate of 10% at regular price it would go from 142$ to 171.82$

Okay so 171.82 - 85.2 would be 86.62$

Isn’t that the amount I saved

[glacial pasture]

i may have misunderstood, what is it meaning by the interest rate here

[cinder belfry]

What did you understand from the question here

Because I think I may have misunderstood

Isn’t it how much the 142 would go up by every year

[glacial pasture]

its either the product price raising, or it could be the price stays the same but the value of the currency increases

i mainly lean to the former

[cinder belfry]

English isn’t my first language

Leaning to the former means the first one or the second one

?

[glacial pasture]

first

[cinder belfry]

Can we try both

[glacial pasture]

sure, we've done it for the product

but if we're saying the value of the dollar increases by 10% per year then we need to find what 142 two years from now would be in todays money

which would be 142/1.1^2 ~ 117.36

[cinder belfry]

How do you get 1.1^2

[glacial pasture]

10% interest is the same as multiplying by 1.1

doing it twice is 1.1^2

[cinder belfry]

Oh yeah okay

So with this way you would have saved 24.62 by subtracting it from the original 142?

[glacial pasture]

it would be 117.36-85.2=32.16 as the difference

since we're looking at the discount

[cinder belfry]

Oh yeah

So that’s the answer if the value of the currency increases but if the price of the product is raising then my first answer would be correct?

[glacial pasture]

yeah, do you have a picture of the question?

[cinder belfry]

It’s exactly like the text

Here

Q3

[glacial pasture]

im relatively sure this is what its asking for

which is what we did the second time

just because it says present value in the questions

[cinder belfry]

Okay yeah

I think so too

Okay thank you for your help

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[stuck fiber]

y = 4x/3 - 5/3

[2cos(2t)-1] = 4[2-3sin^2(t)]/3 - 5/3

2cos(2t) - 1 = 5/3 - 12sin^2(t)]/3 - 5/3

2cos(2t) - 1 = -4sin^2(t)

2cos(2t) - 1 = -4(1 - cos^2(t))

2cos(2t) - 1 = -4 + 4cos^2(t)

2cos(2t) = -3 + 4cos^2(t)

2(2cos^2(t) - 1) = -3 + 4cos^2(t) [Not sure if this identity is correct]

4cos^2(t) - 2 = -3 + 4cos^2(t)

-2 = -3

So close QQ

[grave elm]

what are you trying to achieve here?

[stuck fiber]

Subbing in x(t) for x and y(t) for y

WAIT I see my mistake

[void magnet]

here's the mistake lol

[stuck fiber]

2cos(2t) - 1 = 8/3 - 12sin^2(t)]/3 - 5/3
2cos(2t) - 1 = 1 - 4sin^2(t)
2cos(2t) - 1 = 1 - 4(1 - cos^2(t))
2cos(2t) - 1 = 1 - 4 + 4cos^2(t)
2cos(2t) = -2 + 4cos^2(t)
2(2cos^2(t) - 1) = -2 + 4cos^2(t)
4cos^2(t) - 2 = -2 + 4cos^2(t)
-2 = -2
😎

Thank you!!

❤️

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[lavish cradle]

What are options and futures in quantitative finance?

[lavish cradle]

can anyone please help me understand this?

[dense minnow]

do you just want a general overview?

[lavish cradle]

yeah

can you help me

[dense minnow]

Okay 🙂
A option is a contract that will give a buyer a right but not a obligation to buy/sell a asset at a certain prices. People like them in quant finance because they have lots of flexibility.

A future is a contract in which both people are locked into buying or selling a asset at a certain price on a future date.

[lavish cradle]

hmm

[dense minnow]

does this help or

[lavish cradle]

if i expect a share to drop its price, why would i use the option feature??

[dense minnow]

heres a chart I found online that could help you

[lavish cradle]

??

@dense minnow

[dense minnow]

because you have more leverage essentially. you could buy like a put option (which allows you the right to sell the stock at a certain price) and is way cheaper then shorting a stock. If the share you have drops as you think then your percentage gain will exceed the stocks decline

[lavish cradle]

shorting a stock??

what does that mean??

[dense minnow]

rather then betting on a stock to increase your betting on it to decrease

[lavish cradle]

is that what shorting means??

[dense minnow]

yep 🙂

[lavish cradle]

shorting a stock? as in a future??

[dense minnow]

yes

shorting a stock is a future. a put option is a type of option

[lavish cradle]

put future is a type of shorting of stock?

i know absolutely nothing and am trying to learn but am finding it hard, really appreciate the help bro 🫶

[dense minnow]

a put option is a thing. A put future is not a thing. Shorting a stock is related to futures. A put option is realted to options

Both of these strategies are good if you are betting on a stock to drop

[lavish cradle]

how exactly?

[dense minnow]

Here is a chart.

[urban flame]

plz help with this

it won t take long

[idle kelp]

You need to read the definition of an option and a future contract and specify what exactly you don't understand, this whole conversation is jumping all over the place.

[dense minnow]

I was just trying to help him with these definitions 😂

[median gust]

Read the rules

This channel is occupied

[urban flame]

?

[median gust]

You have to open your own channel to ask your qustion

[urban flame]

ohhhh

[median gust]

Another person opened this channel to ask their quedtion

[lavish cradle]

see, what i dont understand is why would i use an option when i can just sell the stock (considering i predict the stock price is gonna drop)

[median gust]

#❓how-to-get-help

[urban flame]

BUT CAN YOU ANSWER ME QUICKLY

[dense minnow]

When you use a option theres a cap on how much you can lose/gain. It's less risky then an option. If your buying a future/short selling then you can lose a unlimited amount of money

[urban flame]

i really need top go and i will stop typing

[lavish cradle]

81/256

[urban flame]

ty very much

[urban flame]

one last question how did yopu know it

[lavish cradle]

how unlimited?

[idle kelp]

There are a ton of reasons why you might want to use one or another, but its just a matter of modifying your expected payoff functions. Trading options gives you much more options to be able to control your risk if used correctly.

[lavish cradle]

okay lemme explain my thought process

maybe youd understand better

so

[dense minnow]

Okay so lets say you buy stock A at $1 with a future. If this stock goes to $100 then you make $100
However, lets say this stock instead goes from $1 to $.10 . You would lose all the money you have

You buy stock B with a option.
Your option is capped at $50 and $.50 max loss
This stock goes from $1 to $100 you make $50
This stock goes from $1 to $.10 you lose $.50

Does this help?

[lavish cradle]

what is the future set for the stock ?

[dense minnow]

thats the thing that makes futures very risky. you could gain and lose an unlimited amount of money

[lavish cradle]

bro do you do stock market?

[dense minnow]

Learned a lot from my grandfather 💯 he does it more then me. I do it for fun sometimes but not super seriously 😂

[lavish cradle]

ohh

bro

what is a future?

[dense minnow]

!

[lavish cradle]

no but you need to set a certain price for a future

when you call a future you need to set a certain price

[dense minnow]

thats a option

future you dont need a certain price

[lavish cradle]

then? can you explain it a little more simply

[dense minnow]

@lavish cradle this is about as simple I can explain to you.

https://www.youtube.com/watch?v=-efa99L9J08

Maybe this video can help you as well

[lavish cradle]

ok thanks

will see this

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[urban flame]

A box contains 18 balls numbered 1 to 18. What is the minimum number of balls you must take to ensure having at least three prime numbers?
A) 11 B) 12 C) 13 D) 14 E) 15

[full forum]

Please don't occupy multiple help channels.

[urban flame]

<@&286206848099549185>

[fast aspen]

Mf

You have the same name as me

Wtf

[urban flame]

how

[fast aspen]

Yahya

[urban flame]

yeah from morocoo

[urban flame]

can you help me

[fast aspen]

From Algeria personally

[fast aspen]

Response D

[urban flame]

khawa khawa

[fast aspen]

You get it from searching the number of prime numbers from 1 to 18

7

You then try

Worst case you get only one

Best you get three

[urban flame]

opk so mine is true

[fast aspen]

Yeah

It’s 14

D

😄

[urban flame]

i know ty

[fast aspen]

Yeah

[urban flame]

can take a photo

[fast aspen]

You’re studying what ?

[fast aspen]

Yeah of course

[urban flame]

can we go on a call i have a lot of questions

[fast aspen]

Nah

Im with family rn

Anyways

Goodbye

[urban flame]

ok wait plz

one last question

.close

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[vale cipher]

i dont think my mind is thinking straight

[vale cipher]

oh wait nvm my friend might help me rn

.close

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[kindred galleon]

Guys can anyone help me
The problem here is undetermined forms,in my country I can't calculate each one then add,we have to try to factorize x or e(-x) to get it done,can anyone help me plz

[gritty flax]

!help

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[tepid jacinth]

when finding the equatoin of a ellipse, how come if the eccentricity is 2/5 that a doesnt =5 and the distance to focus doesnt = 2

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[tepid jacinth]

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[torn jolt]

Hi. I need help with this problem statement. I can code, but I want someone to explain me the problem.

Aim: To explore the application of the **Central Limit Theorem (CLT)
using a binomial distribution by:

1. Generating multiple random sequences of binomial data for n
   trials with probability p of success.

2. Calculating the mean of each sequence and analyzing its distribution.

3. Visualizing the distribution of the arithmetic means using histograms.

4. Verifying the theoretical expectations of the mean and variance.

[torn jolt]

Can someone please help

[sand escarp]

do you know what the CLT is?

[torn jolt]

Yes, I know the theorem

But I don't understand the aim of this problem, specifically the question about mean

In problem 2, they've asked me to find mean of the sequence. So, should I divide the binomial sequence (with 1000 elements) by 1000 or do I have to divide this by n (no. of trials)

@sand escarp

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[boreal pagoda]

I need some help understanding example 2. When it says x=2, why do we plug in 16 into the general solution?

[boreal pagoda]

Shouldn't we just plug in 2 into the general solution?

And the derivative of x^(1/4) at x=2 is not 1/32

[lime ether]

$g’(2) = \frac{1}{f’(g(2))}$

[glossy valve]

knief

[lime ether]

if f and g are inverses

in general, [g’(x) = \frac{1}{f’(g(x))}]

[glossy valve]

knief

[lime ether]

if by inverse do they mean g?

i assume they mean g

[boreal pagoda]

yea i know about these, but when it says x=2, i assume thats x=2 on the inverse right? but that derivative is for x=16 on the inverse

[lime ether]

i assume they want this

g(2) = 2^{1/4}

then f’(x) = 4x^3 so f’(g(2)) = 4(2^{3/4})

but perhaps they mean the other way around

[boreal pagoda]

yea i looked into that formula yesterday and figured it out, but the one weve been using is g'(f(x))=1/f'(x)

[lime ether]

it’s the same thing

take the reciprocal of both sides

and you get the exact same thing

since f and g are inverses of each other it’s symmetric so it doesn’t matter

what you call g or f

[lime ether]

this is just what i committed to memory and rings nice in my head

g’ = 1 over f’ of g

had a nice ring to it

[boreal pagoda]

the formulas not what im confused about, its the general solution to inverse equations. So the inverse is x^(1/4), the derivative of that would be 1/(4x^(3/4)). If I put x=2 into that, it finds the derivative for the inverse at x=2 on the inverse function. but the derivative we found (this is a lesson) was at x=16 on the inverse. Is it just bad wording?

[lime ether]

if x = 16 for the inverse then that means x^4 = 16 so x = 2

anyways i have to go

[boreal pagoda]

yea i mean thats what im confused about, why am i finding the derivative at x=16 on the inverse when it seems to ask for the derivative at x=2. I know that (2,16) is (16,2) on the inverse, but how do i know what point to solve for in a question like this?

it just seems very plug and chug for derivatives of inverse equations and i dont like that

[clear pumice]

honestly just bad wording in the problem

[clear pumice]

yeah it's more of a simpler way of finding the derivative of an inverse

you can always just derive it yourself but that'll take you more time

as long as you understand why it's true

[boreal pagoda]

yea ig, ima just study this a bit more and see where i get lol

thanks

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[clear pumice]

(helps to go through the proof if you haven't already)

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[desert bane]

so in this Qs I know that we have to use circular permutations, so there are 10 people in total which amounts to a total of 9! ways of arranging them, to satisfy the condition that they seat adjacent to there wives, i treated them as 5 pairs leading to 4! ways of arranging the couples and 2 ways of changing their positions in the couple, amounting to 4!x2^5
This should give me a probability of 4!x2^5/9!

[desert bane]

but that is 2/945

which isnt in the options

am i doing something wrong?

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@desert bane Has your question been resolved?

[desert bane]

<@&286206848099549185>

[languid junco]

the key idea for this is to imagine pairs of american men and their wives as points on a circle, maybe label each of them as P. then the Indian man and his wife can be labeled I and W. you just wanna find out in how many ways you can make I and W adjacent around the circle, which you can easily just count

[desert bane]

huh but like i shouldn't treat each american as a separate individual?

isnt that absurd?

oh shooot its given

bruhhh i misread the question

ugh

thanks a lot for your help!

[languid junco]

yeah np lol, didn't realize you misread it

[desert bane]

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[unique wagon]

alright do you know how the right riemann sum is defined

[fierce linden]

I know that you need to solve the area under the curve

with the rectangles

[unique wagon]

lets first find Δx

[fierce linden]

it would be 1

[unique wagon]

correct

now right end points are such that x_i = a+iΔx

a being the lower bound of the interval

what would x_1 be from this logic?

[fierce linden]

I don't know

[unique wagon]

x_1 = 0+1*Δx for example

you sub in your i value into the place for i

[fierce linden]

what is my i value?

[unique wagon]

you take i from 1 to 4

,w right endpoint riemann sum

[glossy valve]

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

Requested by _mia_34

[fierce linden]

ohh

[unique wagon]

x_i being a+iΔx in right endpoints

[fierce linden]

icic

[unique wagon]

f(x_i) would be
16-(x_i)^2

[fierce linden]

that's the part that kinda trips me

[unique wagon]

yes it is often the most difficult to understand but let us understand a function as something that takes an input and produces an output

[fierce linden]

yeah, taking a input and producing a output

[unique wagon]

if f(x) = x^2 for example,
f(k) = k^2
because it took input k and it mapped to k^2

does this make sense?

[fierce linden]

yup

[unique wagon]

now try this:
if f(x) = ln(x)sin(x)+5

what is f(a+iΔx)?

[fierce linden]

you would plug in the value and replace the x in the first equation

the value within the bracket in the 2nd equation

[unique wagon]

could u try writing it out

typing*

[fierce linden]

how do you type out the triangle?

[unique wagon]

oh right just call it d instead of Δ

so dx

for this example

it is not proper notation

but just for convinience

[fierce linden]

alright

f(a+idx) = ln(a+idx)sin(a+idx)+5

[unique wagon]

absolutely

[unique wagon]

so lets try this now

∑f(a+iΔx)Δx from i=1 to i=4

could you compute that now? after finding Δx, the first step would be to find a general way to compute f(a+iΔx) based on your expression

[unique wagon]

like you did here

[fierce linden]

wait, what was a = to again? I figured out that it's f(a+(i = 1 to 4)(1))

if I'm not wrong

[unique wagon]

a = the lower bound of the interval so 0

[fierce linden]

so if I plugged in and did 1 to 4, my answer would be 1, 2, 3, 4

is that right? it feels off

so basically like f(1) + f(2) + f(3) + f(4)

[unique wagon]

lets see
dx = 1
x_1 = 0+1
x_2 = 0+2
x_3 = 0+3
x_4 = 0+4

yes indeed

[fierce linden]

so is that it or there's still more to the problem?

[unique wagon]

you need to compute f(1) + f(2) + f(3) + f(4) and multiply it with dx

[unique wagon]

as the sum demands

[fierce linden]

could you help me on that part?

[unique wagon]

what is f(1)?

[fierce linden]

if I multiply that with dx, it'll still be 1

[unique wagon]

no based on f(x)

what is f(1)

[fierce linden]

oh mb

it would be 16-1^2

16-2^2

[unique wagon]

yes

[fierce linden]

and so on

[unique wagon]

basically u r computign
(f(1) + f(2) + f(3) + f(4))*dx

but dx = 1 so u dont need to put ur attention to it

[fierce linden]

yeah

so after computing all dat, it would be 34 for my answer

is it a overestimate or a underestimate?

[unique wagon]

,w integral of 16-x^2 from 0 to 4

[glossy valve]

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[unique wagon]

it depends on the function's monotonicity

is the function icnreasing or decreasing?

on x in [0,4]

[fierce linden]

0 to 4

it is increasing

[unique wagon]

let us compute the derivative

f'(x) = -2x

from 0 to 4, is f'(x) negative or positive

[unique wagon]

good so is it increasing on that domain or decreasing

[fierce linden]

decreasing

[unique wagon]

if a function is decreasing on the interval then the right riemann sum is an underestimate

while i have explained u the algebraic way of finding right riemann sums, i would suggest u to go through youtube to look at the geometric visuals of right end points to get an intuition for the above statement

[fierce linden]

alright, and one last question

[fierce linden]

where did you get this?

for the algebraic way

[unique wagon]

the derivative of 16-x^2

-2x

[fierce linden]

ohh

that makes a lot of sense

thanks, you helped a lot

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[half oyster]

see below

[half oyster]

can someone please check and lmk if this is correct definition for limit

[full forum]

@half oyster Has your question been resolved?

[half oyster]

lim x→a f(x)=L ⟺ ∀ε>0, ∃δ>0 ∋ 0<∣x−a∣<δ ⇒ ∣f(x)−L∣<ε

the limit as x approaches a of f(x) is L if and only if for every epsilon greater than zero, there exists a delta greater than 0, such that whenever the absolute value of x-a is between 0 and delta, it follows that the absolute value of f(x)-L is less than epsilon

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@half oyster Has your question been resolved?

[onyx glen]

using ∋ as 'such that' is pretty cursed

but like yes this is essentially the right copy of the defn from your textbook

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[torn jolt]

Start with exponential function I think it's the easiest

[atomic hare]

which one do you have trouble with

[torn jolt]

Uh-

All of them

I'm not used to the formulas yet

[atomic hare]

huh its differentiate not integrate

do you know the chain rule at least

[torn jolt]

What's a chain rule??

[atomic hare]

ok you know what a derivative is right

[torn jolt]

Yes

[sudden condor]

you know what are composite functions ?

[pure basin]

ok so just differentiate everything from left to right

so you wanted exponential so differentiation of e^x is e^x itself

differentiation of e^ax is ae^ax

@torn jolt

[torn jolt]

What..

I don't understand

[pure basin]

ok so $\frac{d }{dx}e^x=e^x$

You know this?

[glossy valve]

devthemasked

[pure basin]

Mai Mai?

[pure basin]

?

[torn jolt]

Wait I was answering it

!status

[full forum]

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

[pure basin]

ok lemmesee

[torn jolt]

4

[pure basin]

hm

so for

5> you cannot subtract

and 6> also same thing

[torn jolt]

So just 5e^5x - 2e^2x is the answer??

[pure basin]

yes

[torn jolt]

Also 6e^3x - e^-x

[pure basin]

yes

[torn jolt]

Okay what else??

[pure basin]

ok so exponential is done?

[torn jolt]

Is everything correct??

[pure basin]

yes

[torn jolt]

WOAHHH THAT WAS EASYYY

[pure basin]

yep

[sudden condor]

well time for trig

[pure basin]

let them go log

[torn jolt]

I'm bad at trig and log

[pure basin]

log is pretty simple

differentiate of ln(x) is just 1/x

So try log and ping me when ur done

[torn jolt]

Okiii

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@torn jolt Has your question been resolved?

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[torn jolt]

Done!!!

[sudden condor]

send

[torn jolt]

@pure basin

[onyx glen]

may want to watch out for your opening parenthesis accidentally looking like the letter C

also in (5): cos^2(x) - sin^2(x) isn't equal to sin(2x)/2 like you seem to have written

and in (12), you could have simplified the fraction by factoring out x from the numerator and then cancelling it with one of the x's in denom

[pure basin]

1/2 (sin(2x)) is your y and you have to differentiate that @torn jolt

[onyx glen]

on the handwriting side, your spacing's somewhat wide overall -- though this is better than it being cramped

(but i do have some suggestions for which places you could make the spaces shorter and have it look better, if you're open to that)

[torn jolt]

But it's just a draft.

Please stop judging about my writing

That makes me sensitive.

[onyx glen]

my bad.

[torn jolt]

It's just a draft..

[onyx glen]

the derivative of cos(x) is -sin(x)

she got it right

[torn jolt]

What's happening to number 11-

[pure basin]

nothing

[onyx glen]

oh yeah just to be clear aside from the ones i commented on everything else is correct

11 is correct

[torn jolt]

I don't get it

[pure basin]

so

y=sinxcosx

y= 1/2 of 2sinxcosx

[torn jolt]

I don't think I can do that...

[torn jolt]

I don't get it

[pure basin]

y= 1/2 of sin(2x)

look at what I wrote above

but yea u got the answer

cos^2x-sin^2x

that is same as cos2x

[onyx glen]

can like able or can like allowed?

[torn jolt]

Yeah my answer is cos² x - sin² x I can still differentiate it around 2x i think??

[pure basin]

uh no

you dont need to differentiate again

that will be the d^2y/dx^2

cos^2x-sin^2x= cos 2x

[torn jolt]

Kasi sin x is cos x and then x² will be the numerator just before cos x also taking note if the sin x which will be 2x sin x so they are connected I don't know how much can I simplify it

[onyx glen]

kasi?

[torn jolt]

Sorry filipino pop out

[onyx glen]

... i think you are overthinking it somehow hold on

[torn jolt]

Kasi in english is because

[pure basin]

u mean taking x common and denominator x^3?

[torn jolt]

There is nothing to simplify

[pure basin]

oh u can tke x common

[onyx glen]

oh but there is something.

[pure basin]

take x common from numerator

[onyx glen]

$\frac{x^2 \cos(x) - 2x \sin(x)}{x^4} = \frac{x[x \cos(x) - 2 \sin(x)]}{x^4} = \frac{x \cos(x) - 2 \sin(x)}{x^3}$

[glossy valve]

Ann