help-0

[alpine sable]

<@&286206848099549185> I do not find in internet :'

[dusky bluff]

@alpine sable apply Bernoulli inequality and then sandwich theorem. Then you are done

[tender anchor]

The probability of an event occuring is 5/18. What is the probability the event occurs at least 3 times in at most 5 games?
This question is really challenging me, any help would be greatly appreciated.

[dusky bluff]

@tender anchor look for binomial experiments with Bernoulli trials

[zealous basalt]

Why do they say 'root' here? Are they talking about things like square roots or cube roots? I've never heard someone calling it a root with this intermediate value theroem, kinda lost

[tender anchor]

root is just another word for x-intercept

I think that's what they're getting at

[zealous basalt]

hm I've never heard that, new to me

[dawn charm]

It's the value $x_{0}$ such that $f(x_{0}) = 0$

[ocean seal]

williammm

[tender anchor]

Just spent another 15min on the problem and I'm still stuck. 😐

[sinful minnow]

how do i do this

[rugged ocean]

Its not 4-2x3 ?

[dusky bluff]

@tender anchor calculate separately for 3,4 and 5 success

[tender anchor]

@dusky bluff I'll give that a try. Thanks

[alpine sable]

hello

hello lads ive started a new chapter in turkey, (bare in mind i do not speak turkish and im not that good in maths neither so this is going to be intresting)

i dont know the title of the lesson, neither do i understand it, if someone could explain it to me in the simplest way possible it would be very appericiated it, as this lesson would determine which highschool would i go to next year.

[dawn charm]

This looks like prime factorisation

[alpine sable]

excuse my handwriting as well im very sorry,

[alpine sable]

hm, how does prime factorisation work, is there like a simple explaination for it

[dawn charm]

Basically any integer can be factorised into prime numers (that is, numbers that can only be divided by one and themselves – like 5 or 7 or 13). The prime factorisation would just be given by multiplying all those numbers on the right of the line you drew. So, for instance, the prime factorisation for 48 is 2^4 * 3

[alpine sable]

can anyone help me with this?

im not talking about the r part, i wanna do the calulations by hand to understand this

i have the answers as well, how is the first one a 1/4?

i just asked a question ele7en....

another room please. i asked a question first.

[shell widget]

@alpine sable Recall that P(A < X < B) = P(X<=B) - P(X<=A) = F(B) - F(A).

Same for part d.

For parts b and c, try to remember what's the probablity for P(X=x) in a continuous distribution.

[alpine sable]

okay so when its P a < x < b its subtraction.... okay okay.....

For that it should be 0

i was doing addition 😆

thanks

[shell widget]

Yeah the coefficient should be a/2

[glass lichen]

Consider |a-2b|^2

[lament fog]

is x/2 an alegbraic function or transcendral

its algebraic right?

[glass lichen]

Those are properties of numbers not functions iirc

[lament fog]

so which is it? im lost

[glass lichen]

... read what I said

[lament fog]

I don't understand tbh

its transcendral then

but like

how do you tell

i thought transcendral is just sin functions

[alpine sable]

that's an expression. you might be talking about f(x)=x/2?

[lament fog]

yea @alpine sable

thats what i meant

[quaint rock]

Can we say that alpha is a variable?

[glass lichen]

Depends on the context... but yes, alpha can be a variable, do can any other symbol

[quaint rock]

Thanks @glass lichen

[alpine sable]

@lament fog algebraic function seems like an unknown term to me. f(x)=x/2 is nonetheless a polynomial rather than a trascendental one.

[lament fog]

Ty @Al3dium#4084

@alpine sable

[alpine sable]

are you still avail?

[gray oxide]

If this isn't open5

Do tell

Question:

The electric cost y £/month for a electricly warmed house is according to this formula:

$$Y = 560 * cos * 0.524(x-1.2)+640$$

[ocean seal]

!callidus

[gray oxide]

Where x is time in months starting from the new year

How much bigger is the cost from the first quarter of the year compared to the second?

AND This is how I went with it

.

First quarter = FQ is equal to this

And SQ= second quarter is equal to this

I did the calculations and got the wrong answer

What did I do wrong here?

[ancient saddle]

Hello, you should do a summation instead of an integral

[green wadi]

Question 4 both parts please

[alpine sable]

okay so

is this your first time to rational inequalities?

@green wadi

[subtle palm]

can someone help me prove this to be true https://cdn.discordapp.com/attachments/298073617621712896/702906064474996806/unknown.png

[slender stump]

True or false

[old bay]

I know that this over-determined augmented matrix is consistent, but due to it having only 2 variables wouldn't it have unique solutions and we can ignore the last row of zeros?

[slender stump]

Someone could explain

[unique ingot]

how to calculate y-intercept ?

[random ocean]

The y intersect is the result when you set x = 0

[unique ingot]

ahh that explains the 0 then

[random ocean]

(Imagine the graph, the y intersect always occurs at the middle, where x = 0)

[unique ingot]

i see! is y then left untouched?

[random ocean]

Yeah, the equation will give you y=…

[unique ingot]

thank you

[random ocean]

No problem

[slender stump]

Why is this false?

[midnight ether]

kayn sience math?

[sweet marlin]

The graph of f passes through (-1,5) and is perpendicular to the line whose equation is x=6

Can some one help me with this?

[midnight ether]

@sweet marlin

[sweet marlin]

It's asking to write an equation in slope intercept form of a linear function f

🤨

[fossil bluff]

i answered this when you asked this in a different channel

🤨

[sweet marlin]

Ah

[toxic island]

you have x > 12 not x < 12

[wild pagoda]

I need help

[simple elm]

i need to simplify (3x-5)/4+ (9-2x)/3 how do i do it? i am getting the wrong answer

i got (x-21)/12

i tried extending with 3 and 4 on both sides

[grim shadow]

bro u made a mistake in addition

do it again

[simple elm]

Oh lol

And i kept doing it over and over

[grim shadow]

it would be (x+21)/12

[simple elm]

Thanks

[grim shadow]

np

[sage tartan]

Is it possible to evaluate $\text{tan}^{-1} \left(-\frac{2\sqrt{3}}{5}\right)$ using pen and paper?

[ocean seal]

forlorn

[brave pendant]

How Many? 278x192

[grim shadow]

i dont think so that its possible

[sage tartan]

well the answer is $\frac{2\sqrt{42}}{7}$ I believe

[ocean seal]

forlorn

[sage tartan]

surely there are some identities I could use to get here

[wild pagoda]

If a group has an average IQ of 120 SD15 and there are 60 people in the group, what is the highest expected IQ in the group?

[sweet marlin]

Can someone help me with #25?

[alpine sable]

Probably being stupid, but does anyone know the answer to this?

[sage tartan]

should be -|x| - 8 i think

[alpine sable]

It worked!

I got that, but where do you get the -8 from

I thought it was -4 since you move 4 down.

[sage tartan]

Well I did -(|x| + 8)

[alpine sable]

Ohh I see

[sage tartan]

Ask yourself, which function is g a reflection of

[alpine sable]

I get it now, Thank you!

[harsh nimbus]

Hello I am attempting question 6f I got the negative of my teachers answer can anyone please help

[ancient saddle]

Hello. When you divide by x on the denominator, you have to multiply by -1 because x es inegative

[alpine sable]

the identity $\arctan(\frac{x+y}{1-xy})=\arctan(x)+\arctan(y)$ comes to mind

[ocean seal]

Al3dium

[alpine sable]

let me see, hold up a second

[harsh nimbus]

Why is x negative

[ancient saddle]

Because it goes to -inf

[harsh nimbus]

So shouldn’t the top be negative as well since you divide both by it

[alpine sable]

@harsh nimbus sqrt(x^2)=abs(x)=-x, since if you recall the defn of the abs, abs(x)=-x for x<0.

do you know about the abs value defn?

[harsh nimbus]

Isn’t it just the value has to be positive

[alpine sable]

$\abs{x}=\begin{cases}x, \quad x\geq 0\ -x,\quad x<0\end{cases}$

[ocean seal]

Al3dium

[alpine sable]

i mean yes, but algebraically things change. whenever you have abs(-2) you can directly know that it's value will be non-negative hence abs(-2)=2

[alpine sable]

but another way of saying this is: since -2 is negative, recalling this definition, abs(-2)=-(-2)=2.

[harsh nimbus]

Wait sorry why are we talking about abs value the question doesn’t have an abs value

[alpine sable]

$\sqrt{x^2}=\abs{x}$

[ocean seal]

Al3dium

[alpine sable]

at the very last step

they factor out an x^2 inside the sqrt, in the denominator

if it's still not clear, i can expand out with details and colors

explaining every step

do you want me to do a more thorough explanation and expanded out with details or no?

[harsh nimbus]

I am a bit confused
The blue colored is my work and I got the answer a-b/2 but the answer key says b-a/2
By what I understand from you is that the second last step will result -1-1=-2 not 2 because sqrt can be either value but when it approached -infinity it will be the negative 1

I am not sure if I am understanding correctly

[alpine sable]

okay so let me go ahead with this option then

[harsh nimbus]

Oh ok thanks

[alpine sable]

give me some minutes to write it down

[unborn dome]

can someone help me out with this? https://media.discordapp.net/attachments/735281673306112150/886011585846468668/unknown.png?width=1440&height=345

the vid they give for review doesnt really help :/

[alpine sable]

$$\lim_{x\to -\infty}(\sqrt{x²+ax}-\sqrt{x²+bx})$$ from the very beginning, if you see sqrt's together, the idea of conjugate should pop out first: $$\lim_{x\to -\infty}\frac{(\sqrt{x²+ax}-\sqrt{x²+bx})(\sqrt{x²+ax}+\sqrt{x²+bx})}{\sqrt{x²+ax}+\sqrt{x²+bx}}$$ $(a+b)(a-b)=a²-b²$ and simplifying $$\lim_{x\to -\infty}\frac{ax-bx}{\sqrt{x²+ax}+\sqrt{x²+bx}}$$ now $\mathbf{here\ comes\ the\ part}$:

factoring out an $x²$ inside the sqrt and factoring an $x$ in the numerator:

$$\lim_{x\to -\infty}\frac{x(a-b)}{\sqrt{x²\left(1+\frac{a}{x}\right)}+\sqrt{x²\left(1+\frac{b}{x}\right)}}$$ remember that always $\sqrt{x²}=\abs{x}$ $$\lim_{x\to -\infty}\frac{x(a-b)}{\abs{x}\sqrt{1+\frac{a}{x}}+\abs{x}\sqrt{1+\frac{b}{x}}}$$ factoring out a $\abs{x}$ $$\lim_{x\to -\infty}\frac{x(a-b)}{{\color{green}{\abs{x}}}(\sqrt{1+\frac{a}{x}}+\sqrt{1+\frac{b}{x}})}$$ and recalling the abs value defn \ $\abs{x}=\begin{cases}x, \quad x\geq 0\ -x,\quad x<0\end{cases}$, and we are dealing with the $\mathbf{second}$ case, the $\abs{x}=-x,\quad \ \text{for }x<0$, but why the second case? because we are dealing with negative values, since we are dealing with $\mathbf{negative}$ infinity. hence ${\color{green}{\abs{x}}}=-x$ $$\lim_{x\to -\infty}\frac{x(a-b)}{{\color{green}{-x}}(\sqrt{1+\frac{a}{x}}+\sqrt{1+\frac{b}{x}})}$$ and finally evaluating the limit $$\frac{a-b}{-2}=\frac{b-a}{2}$$

hold on a sec.

@harsh nimbus

[ocean seal]

Al3dium

[harsh nimbus]

Yeah

I am here

[vague coral]

that dedication tho

[alpine sable]

if you get what happened at the beginning, you can just go to the middle lines, they were just so we are clear on everything they did

[alpine sable]

ty

[grim shadow]

bro u nailed it now im feeling motivated coz of u xd

[harsh nimbus]

Wow thank you so much that makes 100% sense

[alpine sable]

glad to hear.

yw!

[dense flower]

There are 3 items, A, B, and C
if you spend 45 dollar u can get 2 of each item
if you spend 30 dollar you get 5 of a single item

I want to buy
X number of item A,
Y number of item B,
Z number of item C

if I have desired budget of M (can exceed a little), is there a formula i can make to calculate the minimum purchase of each item to buy the amount of items I desired ?

[boreal isle]

yall got any idea how to do this?

or what it means

[vague coral]

they told you to evaluate the limit of this function when x approaches 0

that means, you should take some values that are closed to 0

[boreal isle]

hmm ok

what's the point of a table of values?

why not just select a number that's extremely close to the limit

[vague coral]

just to see how the limit evolve

[boreal isle]

oh ok

cool cool

[bitter flower]

can i get help with finding the surface area of this shape?

i tried getting surface area of the 6 cylinders

then the cube

added and didnt get the right answer

[boreal isle]

there is only one circular face on each cylinder

not two

[bitter flower]

yeah

I made sure to do this formula

2πrh+2πr

[boreal isle]

also the surface area of those round faces should be subtracted from the surface area of the cube

that might be it

oh also i think your formula is wrong

[bitter flower]

i did that step at the end but does it matter in which order?

really?

[fluid sluice]

can anyone help me w this?

[bitter flower]

oh

wait

my bad

i see what u mean

[boreal isle]

should be pi r^2

yeah

[bitter flower]

thanks let me try again

[boreal isle]

the three angles in a triangle add up to 180 degrees

so 4m + 10 must be equal to 180

[fluid sluice]

ohhhh

thank u so much

[boreal isle]

👍

[vagrant frost]

Can someone explain to me how to work this out step by step?

[boreal isle]

you're familiar with y = mx + b right?

[vagrant frost]

Yes

All I don’t understand really is when to swap the negative numbers to positive

[boreal isle]

probably want to restate that in y = mx + b form

[vagrant frost]

2y = - x - 14

[boreal isle]

it would be 2y = x - 14 i believe

cuz you subtract the x, then multiply both sides by -1

[vagrant frost]

Idk

[boreal isle]

ok so you have 14 = x - 2y

then you subtract x from both sides

so 14 - x = -2y

but you want y to be positive

so you multiply everything by -1

[vagrant frost]

Ok

[boreal isle]

which basically just flips the negative and positive signs

so -14 + x = 2y

then for y = mx + b, you want to get y all on it's own

so you divide through by 2

[vagrant frost]

Alright I understand from that point

[boreal isle]

-7 + (x/2) = y

[vagrant frost]

What exactly do you subtract x from though at the beginning?

[boreal isle]

you subtract x from both sides

[alpine sable]

14 = x - 2y | +2y

2y + 14 = x | -14

2y = x - 14 | : 2

y = 1/2x - 7

first of all it shouldn't be called the gradient

but the slope, right?

[boreal isle]

yeah that's odd

[alpine sable]

because it's another concept from multi calc

the perpendicular slope to any slope is the reciprocal right?

no

negative of reciprocal

[boreal isle]

negative reciprocal i think

yeah

[alpine sable]

oh

alright thanks

good to refresh this

so in this case it'd be 1/7?

[vagrant frost]

Alright I think I understand now thanks

[vapid oak]

how does the streched out s symbol work

[boreal isle]

no

the slope is 'm' in the y = mx + b formula

[alpine sable]

@vagrant frostit's called an integral

oomg

pardon me

-2 I meant

[boreal isle]

yeah

[vagrant frost]

I couldn’t care less what it’s called

[alpine sable]

...

[vapid oak]

how are you gonna describe it to other people then or find out more information about it @vagrant frost

[boreal isle]

queens meant to respond to bobbey

[alpine sable]

the big s denotes a sum, doesn't it?

[boreal isle]

i dont think queens meant to ping you

[vagrant frost]

Ok

[boreal isle]

bobbey asked about the stretched out S, which is the integral

probably misclicked on your message

[vapid oak]

mmmm

but how does it work

[boreal isle]

do you have an example problem?

[quiet basin]

im in maths class rn

[boreal isle]

tho i havent done calc in a few years so this might be beyond my pay grade

[vapid oak]

no

[alpine sable]

is it as hard to understand as it seems?

or is it something you get explained once and you remember for ever? like the quadratic formula or something

[boreal isle]

apparently not haha

i used to know how to do it

it was fairly confusing, but everything is confusing at first

[alpine sable]

yes well I'm planing to go to the ETH so...

what is ETH

I want to study maths by myself a bit to be ahead

ETH Zurich

[boreal isle]

is that like an SAT subject test or somethin?

[alpine sable]

13th most renowned university in the world

it's like oxford and so on

[boreal isle]

we still dont know what an ETH is tho

[alpine sable]

it's an university

it's called like that

[boreal isle]

ohhhhh

i gotcha

[alpine sable]

and basically it is about CS there etc

maths too since they also do AI's

but yeah, life's gonna be hard there, hence me wanting to study beforehand to have things go easier

[arctic steeple]

Go step by step

[alpine sable]

what grade are you in hikari

I don't know in american terms

I'm 18 though

have you learned calculus yet

the thing is that I'm unsure

that's all the stuff about vectors etc right?

If so I haven't

[dark granite]

that you're 18?

[alpine sable]

no

[arctic steeple]

No

Calc is derivatives and Integrals

[alpine sable]

nope

[arctic steeple]

But only superficial stuff

Kinda

[alpine sable]

They don't teach that yet at my grade

sadly

i am 15, and i already finished multi calc

basically self study

[boreal isle]

damn that's wild

[arctic steeple]

Well you wanna go step by step

[alpine sable]

I'm mostly ahead of my class

i am halfway through linear algebra and differential equations

abstract algebra is kind of hard though

yeah, already sweating reading this terms

never heard of them

differential equations yes

[boreal isle]

most people dont do multi calc in high school

[alpine sable]

to make yourselves an idea

after going to work next year I have to study 1 year

[quiet basin]

can someone help me with sin

[arctic steeple]

Church

[alpine sable]

and do everything normal people do in 4 years but packed

[boreal isle]

post a problem if you have one

[alpine sable]

so yeah it's going to be hell

anyways y'all have a good night ^^

[arctic steeple]

Good night

[boreal isle]

seeya lata

[quiet basin]

number 5

[arctic steeple]

You might wanna cut that pic a bit

[boreal isle]

so you have sin(62) = x/25

[arctic steeple]

Your name is on there etc

[boreal isle]

also good for readability generally

[quiet basin]

oop

[boreal isle]

this is a different problem

did you mean to send these ones?

[quiet basin]

ye

[boreal isle]

which are you wondering about?

[quiet basin]

4

i have 1 min to do it

left

[boreal isle]

are you familiar with how sin works?

[quiet basin]

ye

[boreal isle]

it's opposite over hypotenuse

[quiet basin]

ye

[boreal isle]

so sin(50) = x/100

solve for x

100*(sin(50)) = x

[quiet basin]

thx i found the answer

thank you so much

[boreal isle]

👍

[quiet basin]

😆

[violet jetty]

Proving the identity is easy, but wtf does it demonstrate?

[crisp grail]

the sum of the squares of the diagonals of a parallellogram = the sum of the squares of the sides

@violet jetty

1 sec

imma draw

here we go

that should explain

got it?

[midnight ether]

https://tenor.com/view/kalculus-calculus-calculator-nigerian-exorid-gif-21249587

[violet jetty]

Oh! I had managed to make the drawing myself but never thought of the takeaway from that. Thanks!

[crisp grail]

:))

[sharp sparrow]

Can somebody help me how to convert percentage with a decimal into simplest form of fraction?

[ocean seal]

VincentBH

[crisp grail]

than just start simplifying the fraction

@sharp sparrow

[sharp sparrow]

Sorry for the distraction I made earlier. I was in a hurry.

[crisp grail]

nah I saw it all good bro

[sharp sparrow]

Thanks.

[finite mesa]

Could someone explain what I did wrong? I distributed (x-1) into ( x^2 + 9) to make the integral easier but it didn’t work

[placid zinc]

So something like
1/(a + b)
Is not the same as
1/a + 1/b

Can't "bridge the denominator".

[finite mesa]

So I can’t distribute?

In that case how would I solve? I don’t think this is a partial fraction question and I can’t use long division

[placid zinc]

It is a partial fraction problem, haha

It starts you with the best factorization

[finite mesa]

Like this?

[placid zinc]

You may have gotten a "partial fraction table" in your class or book, you'll need to refer to it

[shy thicket]

Hello, can someone help me with this question ?

Consider that the incidence of viral attachments in email messages in 1 in 259. Your malware checker will correctly identify a message as viral 98% of the time. Your malware checker will correctly identify a message as non–viral 98% of the time. Your malware checker has just flagged a message as being malware. What is the probability that the message is actually okay? Justify your answer using Bayes theorem ```

I have developed an answer

but not sure

truepositive = (1/259) * (98/100) 
falsepositive = (258/259) * (2/100) 
positive = truepositive + falsepositive
falsepositive / positive
= 0.84039087947883

[placid zinc]

I'm sus since you haven't used Bayes'

[shy thicket]

I have tried using Bayes

it gave me a wrong answer

[placid zinc]

Don't use labels like "truepositive" when you actually mean:
P(Checks as malware | Is malware)
Or might actually mean
P(is malware | checks as malware)
Two very different things

[shy thicket]

Ok

at least help me label things

Let A = “Malware identify a message as viral”
Let B = “A message is viral”

P(A|B) = 0.98 
P(A`|B`) = 0.98
P (B) = (1 /259)

How does that look ?

And we need to calculate P(B'|A)

Does that seem right ?

Do I go from there ?

[alpine sable]

how could i do this Suppose X and Y are independent random variables with standard deviations 2 and 9, respectively. What is the standard deviation of X-3Y?

[jagged imp]

if X and Y are independent, Var(aX+bY)=a^2Var(X)+b^2Var(Y)

[alpine sable]

im not entirely sure what u mean by that

[placid zinc]

@shy thicket
Yeah that looks good! So now you want to use Bayes':
P(B'|A') = [P(B')/P(A')]P(A'|B')

The problem quickly becomes
"Wait, I don't have P(A')?"

[fathom sequoia]

What mistake have I made here

[placid zinc]

Doing that is basically just a tree diagram.

Or, law of total probability

[shy thicket]

I have this

[placid zinc]

Yeah exactly

[shy thicket]

to calculate P(A')

[placid zinc]

That's just a tree diagram in disguise

[shy thicket]

Alright cool well look into it

[bitter cliff]

Hey all, pretty basic stats problem, how do I approach B in the following?

[spiral mason]

All outcomes satisfy B except rolling a 3 on the first roll. Thus, P(B) = 1 - (1/6) = 5/6

@bitter cliff

[bitter cliff]

OK, so basically you're looking for anything BUT a 3 on roll one

[spiral mason]

right, because then it will take you at least 2 trials to roll a 3

[bitter cliff]

What if it was asking about at least 3 trials?

You need a 5/6 twice, so (5/6)^2?

[spiral mason]

then your probability of failure would change. What is the probability of rolling a 3 in two rolls?

in one or more of two rolls*

[bitter cliff]

2/6?

Idk how I'm so bad at stats sorry

[alpine sable]

for Suppose X and Y are random variables with means 98 and 18, respectively. What is the mean of X-5Y? would it be 8?

[placid zinc]

,w 98 - 5(18)

[alpine sable]

yeah thats what i did

ty

[bitter cliff]

2To be clear, this is because you are looking at the probability of rolling a 3 on the first roll (1/6) OR rolling it on the 2nd roll (1/6) and 1/6 + 1/6 = 2/6?

Wouldn't that imply that once you start looking at the 3rd roll you would have 3/6?

[spiral mason]

wait, that's not quite true

hold on

[bitter cliff]

Is it though? Isn't it an independent event?

Yeah ok

[spiral mason]

no, I'm trolling, sorry

this is binomial

are you familiar with binomial distributions?

[bitter cliff]

I'm just starting to learn about it, could use an overview

[spiral mason]

it's this fancy formula, but it's really quite simple

[bitter cliff]

where q = (p-1), yeah?

and p is the probability of... ?

[spiral mason]

success

and q = 1 - p

q is the probability of failure

[bitter cliff]

Ok, so how should I apply it in this context?

x is number of successes, right?

[spiral mason]

right

and n is number of trials

so for your question of 3+ trials

we want to find the probability that get a success in two trials

and then subtract that from 1

[bitter cliff]

Ok, so how would I apply that formula?

3 choose 1?

[spiral mason]

nope, only 2 trials here

we dont want to consider the third trial

as 3+ is inclusive

[bitter cliff]

So really we're looking for failure to our condition, to then subtract that from 1 to find success?

[spiral mason]

the probability of it taking 3+ trials is 1 - probability(less than 3 trials)

[spiral mason]

correct

[bitter cliff]

?

[spiral mason]

yep @bitter cliff

<@&268886789983436800>

see above

[sly mantle]

ty

[bitter cliff]

I got 13/18, does that sound right?

[spiral mason]

13/18 for which?

[bitter cliff]

As the ending result

B is the event that at least 3 trials are required to observe a 3

[spiral mason]

mm so actually we're almost there, there's one part i forgot to include

so 5/18 is the probability of (first is 3, second is not OR second is 3, first is not)

we also need to consider the probability of both 3

which is (1/6)^2 = 1/36

[bitter cliff]

Oh gotcha

[spiral mason]

5/18 + 1/36 = 11/36

[bitter cliff]

That makes sense, 25/36 then

[spiral mason]

yes

[bitter cliff]

Cool, thanks

[spiral mason]

np, this was a very roundabout way of saying your method of (5/6)^2 was correct

I just wanted to show u why with binomials haha

bc your method works well with simple things like dice rolls and low trial #

but once you get more complicated, you'll need to rely on the binomial formula

[bitter cliff]

Yeah that was a really helpful exercise thank you

[fathom sequoia]

Hey, I was given the question:

Write A and B in terms of X

$$A\times B=3x^{2}+13x+12$$

I got to the following results:

$$A=\frac{3x^2+9x+4x+12}{B}$$

and:

$$B=\frac{3x^2+9x+4x+12}{A}$$

For some reason, when I factored to:

$$A=\frac{3x\left(x+3\right)+4\left(x+3\right)}{B}$$

$$A=\frac{\left(3x+4\right)\left(x+3\right)}{B}$$

It's saying it's not right - could someone tell me why? Have I messed up? Seems to be right??

[ocean seal]

TJ89899889

[kindred hull]

That’s not in terms of x

[fathom sequoia]

yes it is

what d you mean

[kindred hull]

But there’s still a A and B

On the right

[fathom sequoia]

it says here its right:

what do you mean bro theres a and b on the right

[kindred hull]

Shouldn’t u input what b= to

Into that

[fathom sequoia]

I did also

[kindred hull]

Did it still say it’s wrong

[fathom sequoia]

but when i factor it its saying its not right -_-

[bitter cliff]

Hey @spiral mason what are the conditions in which I am able to do P(A) * P(B ) to find P(AnB)? Is it only when the events are independent?

[fathom sequoia]

yeah

you think it's a problem with them maybe

[kindred hull]

Maybe it wants you to factor both in one step

[fathom sequoia]

I tried everything

why is it being mean to me

[wintry vortex]

would someone mind helping me figure out where i went wrong?
After that I put the equation through the cosign equation

33^(2)=52^(2)+85^(2)-2(33)(85)cos(33)

and I got 0 as the answer, but 0 doesnt really sound right

Any help would be appreciated, ive been stuck since yesterday lol.

[harsh nimbus]

why did you do law of cos with 33?

where did the 33 come from?

[wintry vortex]

I just used that

[harsh nimbus]

yeah but where does 33 come from

question says 13 degrees

[wintry vortex]

the first one was 33 N i used that for A

is that where i messed up?

[harsh nimbus]

oh you cant put 33 the side value inside cos thats where the angle goes

[wintry vortex]

oh, i only have the one angle though, what would I do for b and c?

[harsh nimbus]

be right back i will draw the diagram and share it give me a second

[wintry vortex]

ok

[wary valley]

How would I do 16 d) and 17 c)

[harsh nimbus]

i believe this is your diagram

there are two forces

with an angle of 13 between the 2

[wintry vortex]

oh, i really did not understand what was going on

ok then to fine Ax and Ay i do Ax=Acos(theta)

sin for Ay

how do I get from there to the resultant force

[harsh nimbus]

I think in this question you can directly use law of cos

[harsh nimbus]

Let’s use the first equation

[wintry vortex]

how do I know which of those numbers is a b and c?

[harsh nimbus]

a= magnitude the question is asking for
Theta = 13 degrees
b=52
c=33

b and c can be interchanged

A has to be directly opposite to angle theta

[wintry vortex]

would it be the same for the second and third equation?

would the cos(b) be angle as well?

[harsh nimbus]

Depending on how you make the diagram

[wintry vortex]

its not finding a way to run the question

when i run for degree it still comes out 0

[harsh nimbus]

Don’t write 13^2

On the left it’s a variable

[wintry vortex]

Just keep it as A

[placid zinc]

cos(13) will likely never make for the equation being exactly true

[wintry vortex]

or A^2?

[placid zinc]

"Exact" is the wrong thing to look for here. Something will be rounded

[wintry vortex]

ok well im actually getting answers now lmao, but I have 54 and -54 degrees, am i suposed to have 2?

[harsh nimbus]

Why are you getting degrees

[wintry vortex]

its the same when I just solve for a

And idk, I thought i was suppoesd to and now realize that doesnt male snese

[harsh nimbus]

This is how I approached the problem

Hopefully it is right and also helpful

[wintry vortex]

o-O

the correct answer was 85

sorry 84

[harsh nimbus]

wait really

[wintry vortex]

my original answer was 85

idk why they rounded down 0_0

ypu, going to a similar problem and trying again again again lol

[alpine sable]

just wondering what the steps to solve this are

[alpine nacelle]

expand, add, divide (be careful of signs)

or divide and substract

quicker

[wintry vortex]

🤬 got it wrong again

[alpine sable]

could you walk me thru doing it?

[alpine nacelle]

divide the inequality by -3

then you'll have: ||x+1 <= 2||

[alpine sable]

okay

now just subtract?

[alpine nacelle]

substract 1, yes

[alpine sable]

1 more just cause this one looks different

[alpine nacelle]

substract 6, then divide by -4

x < -2

[alpine sable]

thanks i got it

[cold root]

hello

what are the other classifications besides ordinary diff equations

im studyinh exact equations

and im thinking it will only apply to nonlinear ordinary diff equations

[tight locust]

stupid question time:

We typically think of calculus as an infinitesimal process, getting our answer by letting the difference quotient of a function at a certain point by letting the 'delta' become smaller and smaller: "zooming in".

What if we zoom out? Could you make sense of an infinite difference quotient?

take for instance the normal derivative: $\frac{f(x)-f(x)}{0} = 0/0$
now look at this: $(f(infinity)-f(-infinity))/(infinity - (-infinity)) = infinity/infinity$

[ocean seal]

EndTimes

[tight locust]

something like that i guess

[placid zinc]

The derivative for large x?

[tight locust]

nevermind it doesn't work become there's no guarantee on the range of f so it can simplify to just 0

[jovial breach]

do you mean the difference between the values of f for infinitely small x and infinitely large x?

[tight locust]

that divided by the delta x

[west heart]

Hi guys! I need help with question 1

i mean part a

I know we have to prove using the zero property and that it's closed under addition and multiplication

But stuck on showing that...

[glass spoke]

if a^505 + b505 = 1
then a^2020 + b^2020 = ?

[placid zinc]

So do you understand the set they've given you? Like, could you tell me if
(1,2,3)
Is in W?

[west heart]

Im confused what the x 2 0 means

i shouldve started with asking that...

[placid zinc]

x0 is the first coordinate (or zeroth I guess?)

x1 is the next one
x2 is the bottom one

In (5,6,7)
x0 = 5
x1 = 6
x2 = 7

At least, the way they've defined it. This can change

That make sense?

[west heart]

yeahh i get that

[placid zinc]

So they did provide an equation that a member of W needs to follow. In order for a member of F³ to also be a member of W:
x0² = x1•x2

That is, top coordinate, when squared, should be the same as the other two multiplied

[west heart]

omg is it x0 squared

lolll i was confused there my bad

[placid zinc]

Kek cool cool. Does that solve everything for you?

[west heart]

idk if im overthinking it but still lost on how to prove zero property

could i just say 0 vector spans W

[placid zinc]

(0,0,0) is the zero vector of F³. Is it in W?

[west heart]

yes

[placid zinc]

Done. W has a zero vector

[west heart]

omg cool cool

thank you idk why i was stuck

[sick ledge]

why is length of a vector is sum of square roots of all its components?

[placid zinc]

That's the Pythagorean theorem

[sick ledge]

but i thought pythagorean theorem only works for two dimensional triangles

i cannot visualize how it works in 3d

please help

MY BRAIN

each component in a vector represents a coordinate yes or no?

[rugged thunder]

can anyone please send me some LCM examples with answer 🙂

[sick ledge]

so basically im squaring each coordinate of the vector when i find the length?

[sick ledge]

sorry im stupid its displacement

then everything makes a little bit more sense

[fringe spindle]

basically, imagine some 2-dimensional vector on a flat level surface, restricted to 2 dimensions but protruding out at some odd angle, neither perfectly vertical nor horizontal (relative to the flat coordinate system). to find the length (magnitude) of this vector, we would have to use pythagoras; square root of the sum of the squares of its horizontal and vertical components. however if we now come out of our flat plane and extend it to 3 dimensions, we need to square it back again, and then square its "height" to find the length of its magnitude, which has components in all 3 dimensions

[alpine sable]

need help with this because i am dumb dumb

[fringe spindle]

"ordered pairs" implies a different ordering of the same pair counts as different. so non-negative integers, let's pick one component say x, x can run from 1 to 9, for each of these values y will be 10 - x, so there are 9 ordered pairs.

[alpine sable]

oh my brain stopped working, though the order didn't matter

thought

thank you

[fringe spindle]

np i literally thought exactly the same at first, until i re-read the question

[alpine sable]

but the teacher said there are more than 9 ordered pairs? idk

9 is apparently not an answer

and x and y are non negative

so hmmm

[fringe spindle]

SHIT

"≤"

so you're absolutely right

but then this just equals the sum of the first 9 whole numbers, which is 9*10/2 = 45

because there are 8 such pairs for r = 9, 7 such for r = 8 etc. etc. all the way down to 1 pair for r = 2

[sick ledge]

i can visualize like two triangles in the xy plane and yz plane
so i always think there is like two pythagoreans theorems going on
but i dont know like how sqrt(a2+b2+c2) would work
like you are making it in like one go
and i dont know how it works
maybe i am getting too fundamental here
that it goes to the proof of the theorem

[thorn kindle]

[alpine sable]

this shit confusing

i want to sleep

[thorn kindle]

On the ground picture a right triangle. What is its hypotenuse

[sick ledge]

i know

but like you are combining the hypotenuse of the two triangles

in one line

and thats very confusing
in 3 dimensional plane

[fringe spindle]

actually i was wrong

[thorn kindle]

Now picture the vertical plane going through the hypotenuse

[fringe spindle]

because you can include zero

let's try that again

[sick ledge]

yes im picturing

whats next

[alpine sable]

we had a ta/student teacher teach it today and he walked out halfway through and came back with a lot of papers

;-;

[kindred hull]

sigma

[fringe spindle]

|P_10| = 11

sorry you know what i mean

not literally P_10

but like if it's just 10

there's 11 sums

[alpine sable]

11 sums, but order matters?

[fringe spindle]

yes

[alpine sable]

so would it be 22?

wait no

confusion intensifies

[alpine nacelle]

you already have the order mattering with the 11

[fringe spindle]

the smallest sum is 0 + 0 = 0

[alpine sable]

largest would be 10 with 0+10?

[fringe spindle]

which has cardinality 1

so it would be the sum of the first 11 integers, 11*12/2 = 66

finally convinced myself i'm happy with that answer

[fringe spindle]

i'm also pretty tired oof

[alpine sable]

yooo it is 66

i rechecked my work

and submitted it

thanks for the help NOW I CAN SLEEP soon

who tf posts homework at 8pm due before the end of the day

[fringe spindle]

oh nice, glad to hear that ☺️

[alpine sable]

good night

[fringe spindle]

night sleep well

[alpine sable]

i hope your pillow is cold on both sides

[fringe spindle]

lol ty same to u

[sick ledge]

i hope your pillow is ice cold so you will have a really cool dream

[thorn kindle]

@sick ledge the euclidean metric in R^2 is the diagonal of a rectangle going through your desired points. similarly, the euclidean metric in R^3 is the diagonal of a rectangular prism going through your desired points. you start by taking the diagonal of the base of the prism. which is sqrt(a^2+b^2). then you find the diagonal of the rectangle whose base is the diagonal of the prism. yielding: sqrt(sqrt(a^2+b^2)^2 + c^2) = sqrt(a^2 + b^2 + c^2).

the diagonal of the base is the orange line, the diagonal of the prism is the purple one.

[sick ledge]

oh i was actually thinking of the same thing!
i call a b and c perfect vector as their length can be measured in terms of coordinates
like they lie perfectly on the x/y/z axis so their length is pretty obvious
then i find the two vectors of the purple line using the perfect vectors
c is perfect vector so you dont have to calculate it and can use it directly!

but what if the c doesnt lie on the axis perfectly?

oh nvm

the height must be the height so it must lie on the axis
lol im so stupid

[sick ledge]

thx a lot!!!

[thorn kindle]

a "perfect" vector as you describe it is a vector which is a multiple of one of the unit vectors:
(a,0,0), (0,a,0), (0,0,a)

and you should know that the distance between two objects does not change with the choice of coordinate system

so yes you can always just use the change in height, the change in horizontal distance, and the change in vertical distance

[green wadi]

No it isn’t

[thorn kindle]

,w 1/tan(45) = (4+x)/y, y = xtan(60)

[ocean seal]

Results provided by WolframAlpha

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

Requested by AMD#4434

[thorn kindle]

,w 2(3+sqrt3)

[ocean seal]

Results provided by WolframAlpha

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

Requested by AMD#4434

[thorn kindle]

lol

[thin berry]

This is a silly question but can someone tell me when should it be C

Or it is C or A ?

[thorn kindle]

make sure the zeros yield 0

plug in 1 for x

[thin berry]

I put x as 1 then i solve ?

[thorn kindle]

yeah

[thin berry]

Umm so A is -4 and C is 8

Maybe i did it wrong

[thorn kindle]

when x=1, y=0

(1-3)^2 - 8 = ?

2(1-3)^2 - 8 = ?

[thorn kindle]

you forgot to subtract 8

[thin berry]

Wait i mean

[thin berry]

This one is -4 right

[thorn kindle]

no

[thin berry]

I don't get it

[thorn kindle]

(-2)^2 - 8 = -4 you're right on that one my bad

but what is:
2*(-2)^2 - 8?

[thin berry]

0

Right

[thorn kindle]

right. so that one works

[thin berry]

So this one is the solution

Thank you so much

[thorn kindle]

yes

[hollow pasture]

could use help wit this

nvm

[thin berry]

@thorn kindle sorry can i ask why did we put X as 1 ? Or we do that always

I mean why 1 specifically

[thorn kindle]

Because the graph shows that f(1)=0

So therefore the function that describes that graph must satisfy that condition

1 isn't special here, it's just the points where the curve crosses the x axis

@thin berry

[fringe spindle]

3C0 + 3C1 + 3C2 + 3C3 = 2³ = 8

[thin berry]

But we can't choose 5 right ?

[thorn kindle]

You can

That would be equally valid. In general you should test both points

[thin berry]

Aah alright

Thank you 👍

[alpine sable]

@fringe spindle if you are still awake, i made a venn diagram but it doesn't add up

[fringe spindle]

my sleep's that messed up, i'm sure i can still manage this LOL

[alpine sable]

For abc and nbc we would have 8 , and for abc and cbs we would have 9, that is 17 total so how do we have 16 students watch abc???

my brain literally does not work

[fringe spindle]

hmm, looks like inclusion-exclusion principle

[alpine sable]

yeah but literally the ta didn't teach anything

was like go do ur work class is over

[fringe spindle]

(16 + 18 + 17) - (9 + 8 + 7) + X + 6 = 40

[alpine sable]

51-24+6+x=40

[fringe spindle]

solving for X we get X = 7 students watched all three channels

[alpine sable]

33+x=40

x=7

[fringe spindle]

yes

[alpine sable]

another one lol

my brain does not work

im sorry

[fringe spindle]

https://en.wikipedia.org/wiki/Inclusion–exclusion_principle

[alpine sable]

i definitely need to read this

[fringe spindle]

sure, hope it goes well for you (sorry i couldn't find a better article than wikipedia, all the others seem to assume knowledge/use too complicated notation without breaking it down into smaller steps to explain it it seems)

[alpine sable]

thank you i will try to do it ;-;

[fringe spindle]

i just got the wrong answer i'm sorry that question is too confusing. (also i hope u don't think i'm rude but i also have to help someone else on another server on a question also involving inclusion-exclusion, which involves finding the least common multiple of integers, and not sport which i have a bad history with, i'm sorry 😫 )

[alpine sable]

oof it's fine and yes it is confusing

[fringe spindle]

tysm i'm sure you'll manage it, and yeah fr

[white swallow]

hello is anyone online? I wanna ask a very simple question, I'm a little confused

[alpine sable]

Wassup

[white swallow]

Hey

I was wondering what's this symbol called in english |x+1| " | "

those lines used for absolute value

[kindred hull]

@white swallow pipe

https://gyazo.com/e2702255dbbe875f497c7eea58f8f3b5

[white swallow]

ah thanks gotcha

oh and also is it okay to write " (x+1)^2=4" as " |x+1|=2 "

[dark granite]

So X must contain elements of {1,2,3,4,5} and we already may assume X contains 1 and 2. So X can contain (in addition to 1 and 2) 3,4,or 5. So really you just need to determine the number of subsets of {3,4,5}. Which is 2^3 since for each element you can ask yourself "should this be in the subset I'm creating? yes or no?"

[oak sandal]

small question, what's the calculus of csc(x) ?

[vague coral]

,w csc(x)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Herels#1420

[vale wigeon]

"the calculus"?

[vague coral]

🤷

[hard ether]

How do you find the radius for b

[silver relic]

2 * pi * r * theta/360 = 12 first equation using the length of the curved arc
pi * r^2 * theta/360 = 100 second equation using area

solve for r using these two equations

[oak sandal]

derivative** sorry, i do math in another language

[silver relic]

its - csc(x) * cot(x)

[alpine sable]

Could someone help me simplify these 3

[hard ether]

But I don’t know theta

[silver relic]

you dont need to

[hard ether]

What

[silver relic]

because you have 2 equations

2 equations 2 variables

get it? @hard ether

[hard ether]

Um no

[silver relic]

You can find theta in terms of r from equation 1, and then put that in equation 2

then the equation you will get will only have r, then you can solve for r

This is the first equation

you can rearrange it to get

notice that the second equation also has the term theta/360, you can substitute 12/ 2*pi*r in its place and then solve for r

[alpine sable]

pls help

[fringe spindle]

D. Stack IV

[alpine sable]

how ??

[fringe spindle]

to get from the leftmost stack to the one adjacent to to it they've knocked off the top block, then interchanged the digits on each block. to get from that one to the one to the one immediately to the right of it, they've knocked out the second highest block and interchanged the digits. so to get from that one to the rightmost block you have to knock out the 3rd highest block and interchange the digits.

[alpine sable]

ohhh i see, thanks

[fringe spindle]

np

[weary slate]

Hello there! I have a question concering the order of operations.

In order to simplify this term, how do I know that I have to take (option 2), instead of (option 1) ? Is there any mathematical rule that defines that?

And also in option 2 the + (see red circle) stays after factoring... why?

Option 1:

Option 2:

[supple junco]

well you gotta do multiplication before addition

you have -6+2*sqrt(7)

in option 1 you do -6+2 first but you have to do 2*sqrt(7) first

in option 2 you take the common factor of -6 and 2*sqrt(7)

to explain option 2 in more mathematical terms:
a*b+a*c=a*(b+c)

[weary slate]

@ember mural what?
@supple junco how does the "multiply first" rule apply to taking out the common factor first?

[supple junco]

this is the common factor formula

-6 can be written as 2*(-3)

so you have 2*(-3)+2*sqrt(7)

we can see that 2 is part of both terms so we have 2*(-3+sqrt(7))

[weary slate]

yes i see that

[supple junco]

we do this so we dont have to calculate sqrt(7) since its an irrational number

and it would either take a calculator or for us to set a certain ammount of decimals

[weary slate]

so whenever I need to simplify a term, I try to factor as much as I can, before I begin to add everything together?

[supple junco]

well if its doable without, there's no need for a common term

tho sometimes it does make it easier

[weary slate]

i see

alright thanks for the help haha

[supple junco]

np

[amber marsh]

someone please help with b

[alpine sable]

hello

good?

i think i missed something plz add

still new to circle theorems tbh

[pearl marlin]

They way you have written the solution is not a proper way

[alpine sable]

yeh can u plz help me

[alpine sable]

i have a really long string in fortran, how do i make it continue from the next line?

found it. you have to put the continuation characters in column 6 otherwise fortran cries

[fathom sequoia]

What is your maths problem 🙂

[fathom sequoia]

This is not a Fortran server...

And who uses Fortrain in 2021 😂

[alpine sable]

i figured people here might have use fortran because its one of those extremely outdated pieces of software only mathematicians seem to use

[alpine sable]

fucking mit and their math software.

[fathom sequoia]

Haha no, we are not really that good at maths here also I just help Hih School kids

High*

[fathom sequoia]

Well then... Interesting

[alpine sable]

i am about to be high from all of the SIGSEGV's i have been snotring over the last 3 hours trying to compile this piece of shit

[fathom sequoia]

Ok, I dont have any background in Fortrain so I can't help

[alpine sable]

thanks anyways, i figured the line continuation out

[fathom sequoia]

Great

[alpine sable]

what calc do you have

[fathom sequoia]

Give me an example problem @alpine sable

Your question is... broad

[fathom sequoia]

I use online calculator

[alpine sable]

not you

[formal panther]

hi

[fathom sequoia]

ok

[alpine sable]

@alpine sable what calculator do you have

[fathom sequoia]

ok so you want to find y or x?

[formal panther]

same

[fathom sequoia]

I mean... You can't find the numerical value of x if you don't know 'y'

[alpine sable]

not experienced with that specific one but you need to have a graphic calculator to find roots

[formal panther]

dont u need to equations for simultaneous

[fathom sequoia]

No no you dont get it

you can't ever find x if you don't know what y is

ok so you want to find 'y' or 'x'

you said before you wanted to find 'x'

Oh k

just graph it online

https://www.desmos.com/calculator

,graph x = 2y+ 3

[alpine sable]

have you heard of algebra my friend

[fathom sequoia]

Here's the graph:

[fathom sequoia]

Again, that's not using a calculator

[alpine sable]

he can do algebra by hand

not hard

[fathom sequoia]

yeah

that's waht I was trying to say

but she is not explaining her question properly

she already has an equation for 'x'

not sure if she/he wants to find 'x' or 'y', but she/he can use simple algebra and rearrange to find 'y'

[alpine sable]

english desperately needs a gender neutral pronoun. he/she business is confusing

[fathom sequoia]

?

[fathom sequoia]

ok... and how is this relevant

[alpine sable]

not relevant at all

[fathom sequoia]

OK

[kindred hull]

they...

[alpine sable]

thats plural

[kindred hull]

it can be used as singular

[quartz oxide]

https://youtu.be/46ehrFk-gLk
I think this video explains your question

[alpine sable]

Sir Thomas "One Take" Scott...

[kindred hull]

english is my first language and ever since ive been able to speak ive used "they" or "them" as a singular pronoun

#discussion anways

this is for questions

[dreamy bone]

Hey Everyon!

I'm doing complex number rn and I can't figure out how to simply this question

please help if possible. Thank you!

[crisp grove]

what's the question? solve for z? or the shape of the curve?

[crisp grove]

well for the first part, the set of points is already given. for the sketching part, notice that **|z-a| ** is just distance of z from the fixed point a. so, all it is saying it's the set of all points where the sum of the distances from the points -3 and -1 is fixed.

you know what that shape is?

[sick ledge]

could someone explain to me the angle measure of vector?that would help a lot thx

like the formula i dont really understand it very much how it works

the feta = arccos(dot product of two vectors/multiplication of both length of vectors)

[tawdry sphinx]

it is theta btw just so you know

so you basically want a proof why it works?

[tawdry sphinx]

the geometric definition of the dot product actually is $a\cdot b=||a||\times||b||\times\cos(\theta)$

well that wasnt the dot i was looking for

[ocean seal]

NoRysq

[sick ledge]

not only proof but like maybe a graphical explanation so that i can know the logic of it rather than some plain proof

[tawdry sphinx]

so you know if the dot product is 0 then theta is 90° right?

arccos(0) = 90°

if they are parallel then the dot product will be $||a||\times||b||$

[ocean seal]

NoRysq

[tawdry sphinx]

so for this case $\arccos(\frac{a\cdot b}{||a||\times||b||}) = \arccos(1) = 0$

[ocean seal]

NoRysq

[tawdry sphinx]

@sick ledge can you follow?

[sick ledge]

oh wait

doesnt dot product gives 0 tho

[tawdry sphinx]

0 when?

[sick ledge]

oh perpendicular

[tawdry sphinx]

it gives 0 for theta = 90

yes

[sick ledge]

ohh

sorry i am pretty noob

why parallel means dot product = product of two lengths?

i dont even understand like how dot product works
like i know how to calculate it but i dont know what it does

for me it seems like dot product and the length are two different thing

[tawdry sphinx]

i mean it's hard to explain

[oak chasm]

When the vectors are parallel, they're equal, so the dot product is the square of the Pythagorean theorem, which is the square of the length.

[tawdry sphinx]

well actually true haha didn't even consider that

[oak chasm]

Well, they can be different lengths, I guess.

[sick ledge]

ohh
i forgot that vector is only about displacement rather than coordinate
and yes now that makes sense if they are equal length
but what about different lengths?

is they any different?

[oak chasm]

Then you have vectors x and ax.

The components of one will be multiplied by a compared to the other.

So, by the distributive property, the a can come out in front of the sum for the dot product.

[sick ledge]

ohhhhh

[oak chasm]

So, you get the square of the length of x times a.

Which is the length of x times the length of ax.

[sick ledge]

thx a lot thats a bit clear now!

[oak chasm]

No problem.

[gray oxide]

Hello

The electric cost y £/month for a electricly warmed house is according to this formula:

$$Y = 560 * cos * 0.524(x-1.2)+640$$

[ocean seal]

!callidus

[gray oxide]

Where x is time in months starting from the new year

How much bigger is the cost from the first quarter of the year compared to the second?

AND This is how I went with it

First quarter = FQ is equal to this

And SQ= second quarter is equal to this

I did the calculations and got the wrong answer

[gray oxide]

I was told to do summation by this guy

How do I use it in this scenario?

[alpine sable]

I saw this

What is it

[oak chasm]

An expression.

[lyric hedge]

can i ask a question?

[glass lichen]

Factor 1296

[lyric hedge]

do i need to find out square root of 1296

[glass lichen]

Read what I said

[lyric hedge]

ok.

[timid hedge]

Not necessarily, when Mosh said factor he meant

[glass lichen]

I meant factor

[timid hedge]

keep dividing till you get a product of prime numbers raised to something

In this case, x=4 so square root will get you closer to the answer

But if you have to show work, factor

[glass lichen]

Don't give answers

[vernal dragon]

hello

[lyric hedge]

36²= 1296

[glass lichen]

Yes, that's true

[timid hedge]

Sorry boss

[lyric hedge]

So is 36 the ans?

[glass lichen]

Clearly not

,calc 6^36

[ocean seal]

Result:

1.0314424798491e+28

[amber marsh]

isnt it x=4?

(6^2)^2=6^x

[oak chasm]

@lyric hedge Do you know about logarithms?

[wary stream]

Probably Taylor series

[lyric hedge]

yup

i got the ans

: )

[fringe depot]

anyone can help me to find the value of B pls

😭