help-0

[alpine sable]

@modest dragon just try l'hospital

[carmine ermine]

soo that's all to it?

[plucky crow]

exsec is just sec - 1

[modest dragon]

okok

[glacial hedge]

@Jatron there is a second part

[plucky crow]

whats l'hospital lol

[glacial hedge]

uh its a person

[alpine sable]

french dude

[glacial hedge]

he created l'hopitals rule

[strong furnace]

false

[glacial hedge]

?

he also wrote a calc book

[shut tartan]

You work as a quality control agent for a company that produces light bulbs. From a box of lightbulbs that have been produced, you select one lightbulb. If the odds in favour of selecting a defective lightbulb are 1:60, what is the probability of selecting a lightbulb that is not defective? Respond to the nearest tenth of a percent

can someone help

[plucky crow]

whats the total probability

[shut tartan]

1

[plucky crow]

whats the probability of getting a defective one

[glacial hedge]

1/60

[plucky crow]

no

[glacial hedge]

its 59/60???

[plucky crow]

no

[shut tartan]

1.666666 chance

[plucky crow]

1/61

the p of not defective is 59/61

i mean 60

60/61

[glacial hedge]

anyone know how to do this stupid multi calc problem

[shut tartan]

so i do 60 divide by 61

and round to the nearest tenth

?

@plucky crow

[plucky crow]

ye

[shut tartan]

so 60 divide by 61 is .9836065574

[plucky crow]

dafuq

[shut tartan]

if i round it to the nearest tenth of a percent its

1

[glacial hedge]

@plucky crow ?

[plucky crow]

multicalc

how old r u

[glacial hedge]

14

[night owl]

First we need the Pythagorean theorem.
I'll be assuming you understand its proof.

Imagine a right hand triangle with a hypotenuse of length 1 and a corner with angle z.
The opposite and adjacent sides to our corner will be of lengths sin(z) and cos(z) respectively.
The reason for this is because sin(z) is equal to the opposite side divided by the hypotenuse. But since our triangle has it equal 1, it is equivalent to doing nothing.
The same applies for cos(z) with the adjacent side.

Now by combining what we just learned with the Pythagorean theorem, we derive the following equation.
sin(z)^2+cos(z)^2=1
Just visualize the triangle I described and apply the theorem to it.

With that formula we can now derive a general equation for solving for sin(z) when we're given cos(z)=x
sin(z)=±sqrt(1-cos(z)^2)

With this we can now determine sin(z)
sin(z)=±sqrt(1-cos(z)^2)=±sqrt(1-(1/2)^2)=±sqrt(3/4)=±sqrt(3)/2

The only answer out of your options matching the answer is the 3rd option.

[plucky crow]

oh it must be weird notation then

ive never seen this stuff in my life

[glacial hedge]

oh

whoops

i snipped the wrong problem

xD

[plucky crow]

never seen this stuff in ma life

what country r u in

[glacial hedge]

wait did you take multi variable calc?

[plucky crow]

dont think so

[glacial hedge]

oh thats probably why

[shut tartan]

The probability of rolling the same digit with each die is 1/4.

The probability of rolling a number less than 5 is 1/7.

The odds against rolling a number less than 7 is 7:5.

The odds in favour of rolling a 10 is 1:13.

do u know the true statements in this question

its rolling two dice

[strong furnace]

introduce a new parameter and translate this problem in terms of that new parameter ?

[glacial hedge]

it wants you to do it via lagrangian multipliers

[shut tartan]

what are the true statements

[dire spindle]

Can someone help me find the surface area

[edgy drum]

how does this work?

${{4x+5}/{2x-3}} => {2 + {11/{2x-3}}}

,,(4x+5)/(2x-3) => {2 + {11/({2x-3})}}

[ocean seal]

pizzaparty

[edgy drum]

not sure how to make this stack the quotients

[gray isle]

long division or clever manipulation

[edgy drum]

been trying to get this worked out, but cant

[gray isle]

consider that 2*(2x-3) = 4x - 6
and then do -6 + 6 on the numerator

[edgy drum]

def clever

is that how i need to get rid of the two x's?

the real problem is this

it's example (a) here

i can't really "bring" the denominator over the inequality, because I'm not sure if its positive or negative, right?

or is that allowed?

like -(2x-3) < 4x+5

or can i assume 2x-3 is a positive value?

[gray isle]

you can consider both cases

[woven pollen]

you get two cases

oh, that's too big. I'll work on it

[edgy drum]

yeah but the value 2x-3 is positive or negative depending on the value of x

[gray isle]

one where (2x-3) is pos and the other case where it's neg

[edgy drum]

hm

so i can say -(2x-3) < 4x+5

for the left side?

the other way is just eliminating the 2 x's with the long division thing

[gray isle]

you'd need to state whether you're considering (2x-3) to be positive or negative for that case

[woven pollen]

I think you are not dividing by a negative number so the sign won't flip, you are multiplying. Is that is?

[edgy drum]

multiplying by negative flips the inequality

and I can't be sure whether 2x-3 is positive or negative

@gray isle , is the original solution just intuition, or is that reduction always possible?

[dire spindle]

This is how you do it

[edgy drum]

ah you squared it

so it's always positive

clever

[gray isle]

the division itself doesn't give the full solution

but helps simplify things

[edgy drum]

i think the square trick is the easiest way. that keeps it at 2 cases and guarantees positive

[woven pollen]

that's cool.

[edgy drum]

galaxy brain

did you write that on paper and take a photo?

or is there a program for that?

[dire spindle]

I have an ipad

[woven pollen]

ipad

[edgy drum]

i have ipad too, did you send this to your pc and attach it that way - or just do it all through ipad?

just wondering for future questions

[dire spindle]

I just screenshotted it and sent it on discord

[edgy drum]

cool tyty

notability?

[dire spindle]

Goodnotes

[edgy drum]

is that better, i saw both

notability wants me to spend another $3 to get text -> math

does goodnotes give that for free?

[winter rampart]

please!

[undone rain]

Not sure if the method Im thinking of is right but try using pythogoras on the multiple triangles

U know 44 + 11 is the hypothenuse

[glacial hedge]

@winter rampart use the geometric mean theorem where n = sqrt(44*11) = 22

[woven pollen]

I don't know that Theorem. (heads to wiki)

[glacial hedge]

@woven pollen you could also use the similar triangles

(I think)

[woven pollen]

i've forgottent hat

[glacial hedge]

right

[edgy drum]

having issues with this one

same one

[glacial hedge]

there's the right triangle similarity theorem xD

[edgy drum]

the left and right side conflict

[glacial hedge]

@edgy drum what is the problem?

or orgininal equation

[edgy drum]

the (a)

we were chatting about it above

i got four solutions, and some of them conflict

like x > 3/2 and x < 3/2

[gray isle]

you want to determine where they intstersect

[edgy drum]

how can it be both greater and less than 3/2?

[gray isle]

ploting them on a number line may help

[edgy drum]

the solution in the book looks like this

that first step doesnt make sense to me though

[gray isle]

1 sec

[edgy drum]

np

[woven pollen]

That's it graph.

[gray isle]

the work you've done so far is fine

[woven pollen]

y = (4x+5)(2x-3)

[edgy drum]

the screenshot i took isnt wrong?

[gray isle]

you just need to find the intersection of your solution for each case

[edgy drum]

sorry it's been like 10 years since i've done math. What term do i google to figure out how to do that?

[gray isle]

you can consider graphing the solutions for each case on a number line

and then determine where they overlap

actually the right case is a bit off
it should be x<3/2 AND x>-4
which simplifies to -4 < x < 3/2

[edgy drum]

yeah i have both of those

my screenshot plot doesnt want to send

[dire spindle]

Are you saying how can x be less than -1/3 and greater than 3/2 at the same time?

[edgy drum]

i asking how it can be less than and greater than 3/2

[gray isle]

it can't both be greater and less than 3/2

[dire spindle]

Who said it was less than and greater than 3/2

[gray isle]

it'd be one or the other

[edgy drum]

i cant send my screenshot for some reason, but that's what my work says

[dire spindle]

Did you look at my screenshot

[edgy drum]

yah

oh i screwed up the signs

i think

on the LHS

[dire spindle]

Hold on

[gray isle]

consider what graphing them on the number line yields

[dire spindle]

What is this lhs and rhs business

[gray isle]

the left and right cases overlap at the part between the red dashed lines

i.e. where
-4 < x < -1/3

which is the solution to the whole inequality

[dire spindle]

Oh ok

[edgy drum]

i'm concerned more about the 3/2 thing

i dont think i screwed up the signs right?

0 < (2x-3)(6x+2)

[gray isle]

the work you did is more or less fine

[dire spindle]

So I’m assuming they overlap at -4<x<-1/3

[gray isle]

the right case is a bit off
the solution for that case should be x<3/2 AND x>-4, instead of 'comma' which implies OR

[dire spindle]

Yeah you haven’t done anything wrong

[edgy drum]

the 3/2 thing is really confusing me

[dire spindle]

You’re just thinking about the problem wrong

When it says a<x<b

That doesn’t mean that x is greater than a and less than b

What it’s actually saying is

For all x values in that range, the original inequality holds true

So in this case

For the left one

[edgy drum]

i get that much

[dire spindle]

Yeah so for the right one

The x values above 3/2 satisfies it

And for the left one

[gray isle]

the 3/2 thing is really confusing me
just means that x can't both be simultaneously greater or less than 3/2 (which is trivial)
it'd be one or the other

[dire spindle]

The x values below 3/2 satisfies it

Since there is no range that is greater than 3/2 and less than 3/2 (obviously)

You don’t need to include it

[edgy drum]

so will i always get 2 "incoherent" values in problems like this?

or is this a special case?

[dire spindle]

There are no incoherent values

There is only one range that is the solution

[dire spindle]

Which is this

Because that’s the only range that both of the inequalities are true in

In other words

Out of all possible x values

[edgy drum]

so there could have been two ranges

[dire spindle]

Only values -4<x<-1/3 plugged into both inequalities will return true

Yeah there could’ve been

[edgy drum]

sorry, another noob question. How are you taking screenshots?

do i need to say "hey siri"?

[gray isle]

winkey + shift + S

[edgy drum]

on the ipad

[gray isle]

nfi, i don't use apple

[dire spindle]

Just press the Lock button and the volume up button simulataneosly

Simultaneously

[edgy drum]

yeah im on linux and got this ipad to do my notes on

[dire spindle]

Do you program?

[edgy drum]

yeah

hmm that doesnt do it

oh well ill use siri

[dire spindle]

Hold on

Does your ipad have a home button

[edgy drum]

i do haskell and i'm learning math to build up to category theory

yeah

[dire spindle]

Try lock button and home button at the same time

[edgy drum]

that was it

[dire spindle]

Anyways do you understand the problem?

[edgy drum]

i still am confused about how this problem can produce the 3/2 issue - but i'll get over it

because those arent valid values of x

but i graphed it and i see the range of x's

for some reason discord doesnt want to accept my screenshot

it just says "compressing files"

this is the book I'm working through

https://www.amazon.com/Mathematics-Physicists-Manchester-Physics-Martin/dp/0470660228

i looked through like 5-6 and this one looked the best

[gray isle]

its not really an issue

[edgy drum]

there are mistakes in it though

found 2 in the first section already

[gray isle]

if you know the distinctions between or/and , union/intersection

[edgy drum]

i see

i dont know how much this text goes into set theory

thanks for all the help though

really learned a lot

the square denominator trick is nice

[woven pollen]

I was looking at your screen shot sent @8:01 and that is also a good explanation?

Where you do the long division.

[gray isle]

the solution in the book is quite nice too

[edgy drum]

yeah i cannot figure out how to get there

with the book solution

[woven pollen]

The long division?

[edgy drum]

whatever method the author used

like if i have (bx+c)/(nx +d)

and getting rid of one of the x's

[gray isle]

mostly division

[edgy drum]

is there a formal name for this kind of reduction?

that i could google

and find some example problems

[gray isle]

polynomial long division

[edgy drum]

ok

[gray isle]

but there are tricks for simpler things like i showed earlier

without having to go through setting that up ^

[edgy drum]

you just intuited it, right?

[gray isle]

yeh

[edgy drum]

my math is so rusty i'm going to need to rely on formalisms like what tensor showed

for a while

[fervent gull]

hello

can i ask here

i wrote some formulas i need to know if im wrong

Fg = m.g

Fn = Fg*sin(a)

Ft = Fg cos (a)

can someone tell me if thats wrong?

[woven pollen]

Fn is the cosine in this case.

[fervent gull]

thank you for correcting me

[south notch]

Hey so I am confused on how I am supposed to answer this, I know I have to figure out if there is a nonremovable/removable. Its functions of continuity. I am just confused on how I can do this. Thank you for the help!

[civic crypt]

@south notch So you know all but 7) ?

[south notch]

Sorry I do not understand how to any of them. I've been looking at my notes for a bit and I just don't know how to relate the limits to the graph given to me. @civic crypt

[ruby parcel]

could anyone help me with understanding quadratic equations, im really struggling with how to properly setup the square roots, if you would be able to hop in a vc id appreciazte it

[lost violet]

How can i show that If ${a_n} \rightarrow a $ then ${a_{n-1}}_{n=2}$ converges to $a$

[ocean seal]

alef0

[civic crypt]

Do you know what is limit?

[heady crest]

https://www.youtube.com/watch?v=Y7sqB1e4RBI

[heady crest]

what are you trying to understand? completing the square? https://www.youtube.com/watch?v=xGOQYTo9AKY

[woven pollen]

I think you just write again what you

've written with n=2.

[glass lichen]

they're the exact same sequences, one's just re-indexed

[woven pollen]

It's the base case, right?

[glass lichen]

$$a_1 , a_2, a_3, ...$$ vs $$a_{2-1},a_{3-1},a_{4-1},...$$

[ocean seal]

Mosh

[lost violet]

@glass lichen Yes, thats what i was thinking thank you!

[lost violet]

yes

what about if ${a_{n-1}}_{n=1}$

[ocean seal]

alef0

[glass lichen]

It's the same in the infinite limit

since the 2nd term and onwards to n-> inf will be the same as {a_n}

[shut tartan]

When rolling the dice, the outcome is expressed as a sum of the two dice. For example, if after you rolled the dice, and one die was a 3 and the other was a 4, you will have rolled a 7.

Select all of the TRUE statements below. There may be more than one.

Question 3 options:

The probability of rolling the same digit with each die is 1/4.

The probability of rolling a number less than 5 is 1/7.

The odds against rolling a number less than 7 is 7:5.

The odds in favour of rolling a 10 is 1:13.

WHAT ARE THE TRUE STATEMENTS

[lost violet]

And how can i prove it? i know that $\forall \epsilon > 0$ $\exists N_0$ such that for all $n>N_0$ then
$|a_n -a |< \epsilon$ but how can i prove that $|a_{n-1} - a|<\epsilon?$

[ocean seal]

alef0

[tawny lion]

what happens when the function approaches -2 from the right?

[south notch]

It infinitly gets closer to -2 but never gets to it. Wouldn't that mean that there is no limit as x approaches from the right @tawny lion

[tawny lion]

no because it's not a question of whether it gets to it

it's a question of what it approaches

[gusty torrent]

(sorry I'll take my question to a different place)

[south notch]

Okay so it approaches -2 then?

[tawny lion]

now, for 3 for example, what do you see?

no

it approaches positive infinity

look at the picture

[south notch]

Ah okay, I think I understand that

[tawny lion]

tell me what you see for 3)

in this case it D.N.E because the one sided limits approach negative and positive infinities

[south notch]

It doesn't reach -2\

[tawny lion]

yes

they approach different values

[south notch]

Ah okay, and for it to reach the limit of -2 the + and - need to be the same right

[tawny lion]

yup exactly correct

so let's say they both approached positive infinity, then the limit would exist

because they would both approach the same value

[south notch]

Okay that makes a lot of sense thanks.

[tawny lion]

no prob

[south notch]

I have one more question too, what would happen for number 6

[tawny lion]

this is for evaluating limits

it's very useful

if you've done l'hopital's rule you'll know there is another way of determining it

for 6?

[south notch]

Yeah Im confused by 6, as there is a dot in the middle

[tawny lion]

well you have two one-sided limits, and the function approaches the same value

that just means it's defined

[south notch]

Okay so that would mean that the limit would be defined at x = 4

[tawny lion]

it's defined, but that's not the limit

which is why the function is not continuous

[south notch]

Okay, I think I understand now. Thank you

[tawny lion]

no problem

[south notch]

I appreciate it a lot thanks

[tawny lion]

👍

[alpine sable]

Help, what is my desmos doing wrong?
https://www.desmos.com/calculator/xgpnmpeoxk

I'm trying to get the point of intersection between the blue and red lines.

They are drawn dynamically between points (h1, k1) and (h2, k2)

I need help finding out how to find the point of intersection using a formula

[fringe lantern]

yo how can i do this question

does anyone know

i cant figure it out i tried like 5 times

i wrong place

[alpine sable]

Here is my question, as moodman solved his problem in another channel.
However, mine is still open ;-;

[heady crest]

do you know the points or the equations of the graphs?

or are you supposed to read the points off the graph

[alpine sable]

I know the equations

I am allowed to use the equations, but only some ppoints

I only know about two points => (h1, k1) and (h2, k2)
I know two lines:
0y=x-2 and y=k2-k1/h2-h1+(k1-k2-k1/h2-h1*h1)

I can also pick out numbers from the lines

[heady crest]

https://www.youtube.com/watch?v=R0bGxNzgL2o

[jovial aurora]

Is it ok if I ask a question about excel that's sort of related to math?

[heady crest]

yes

[jovial aurora]

Is there a "formula" to output the greatest integer value n such that f(n) < [some value] or a defined function?

[heady crest]

wolframalpha.com can do things like that for you

it's kinda hard to answer without knowing the specifics

[jovial aurora]

It's for a statistics project,
say, if you wanted the greatest integer output for n^2 < 104

Tried googling it, buy couldn't find anything that comes close

[heady crest]

only way i can think is to calculate each one and then compare them and find the biggest one

[alpine sable]

10.19803899999999..?
from
n^2=104
n=10.whatever
n < 10.whatever

[jovial aurora]

wait

I can just inverse it and round down

[heady crest]

i'm pretty sure excel has a function to see if something's an integer

and yeah what obscured said, that's a faster way of doing it instead of doing every number

then you just have to cut off the decimals, which i know excel can do

so it's 10

[heady crest]

so yeah the funciton would be something like cutOffDecimals(sqrt(104))

[jovial aurora]

facepalm
Okay, the inverting and rounding down seemed to be the exact thing I'd been looking for 30 minutes

[heady crest]

lol ❤️

i know the feeling

[dense spoke]

am i supposed to deduce what the function is?

and i really cant tell what P' is measuring, how is it relevant?

[heady crest]

have you done derivatives yet?

[dense spoke]

yes

[heady crest]

p' is the rate of change of the mosequito population

so how fast the population is increasing

[dense spoke]

oh shit im a dumbass

so 8*107

and then add that to the initial population

[heady crest]

yeah i think that's right

[dense spoke]

ur a god

it worked

thx

[heady crest]

lol ❤️

[glacial pier]

Can I get help

[heady crest]

i have no way of knowing if i can help without seeing what you need help with

[lost violet]

is this true?

[vague coral]

that's basically the definition of induction

If i'm not wrong

[lost violet]

mm right I had not noticed that it looks like definition of induction

[cobalt eagle]

I NEED HELP LIKE RN

ANYONE REALLY GOOD AT MATH

[vague coral]

just ask

[cobalt eagle]

like im doing assignment due in 16 min and have no idea how to do it i needa stream

[karmic spade]

just ask your question here

[charred flint]

QUICK

[karmic spade]

or be fast on streaming :V

[cobalt eagle]

k im in vc

i cant stream wtf

how do i determine whether its reflection on y axis or x axis through a chart

[karmic spade]

end of unit retest

[cobalt eagle]

shhhhhh

thats what im confused on

i aced the other parts

[karmic spade]

sorry if this is for a test you arent gonna get help here

[cobalt eagle]

damn it

[heady crest]

easiest way is to do a sketch

[umbral pulsar]

Can somebody help me with this.
$$\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+.....\ =\ ?$$

[ocean seal]

Chaitanya

[cobalt eagle]

i mean i got like 9 minutes cause my parents put a time limit on interenet and the test closes at 12

so i cant do it in morning

[karmic spade]

its one of the rules of this server that people are not supposed to cheat for you

im pretty sure you shouldnt be asking here

[cobalt eagle]

fair enough

its pretty crucial

[umbral pulsar]

Can somebody help?

[charred flint]

@umbral pulsar do you know the formula for 1+2+3+...+n?

[umbral pulsar]

yes n(n+1)/2

[karmic spade]

so i guess this is the sum of 2/(n(n+1) for all integers n from 1 to infinity

[heady crest]

https://www.quora.com/What-is-the-value-of-1-1-%2B-1-1%2B2-%2B-1-1%2B2%2B3-%2B-1-1%2B2%2B3%2B-n?share=1

[charred flint]

oh wait this is a telescope problem

[karmic spade]

which is 2 * sum of 1/(n^2 + n) for integers n from 1 to infinity

[vague coral]

$\sum_{n=1}^{\infty} \frac{2}{n(n+1)}$

[umbral pulsar]

oh thnx

[charred flint]

if you do partial fraction decomposition it'll all work out

[umbral pulsar]

I got it

[ocean seal]

Herels

[charred flint]

it's so weird how this has a nice answer but 2/n^2 doesn't

[karmic spade]

thanks, i dont know latex xP

[umbral pulsar]

$1-\frac{1}{n+1}$

[ocean seal]

Chaitanya

[umbral pulsar]

n->∞

[bold mantle]

What does that wired sideways M thing mean?

[umbral pulsar]

@charred flint ans is 1?

[charred flint]

2

[vague coral]

?

[slender forge]

It’s a summation

[bold mantle]

Whats that

[umbral pulsar]

is this correct?

[bold mantle]

Summation

[charred flint]

no it should be 1/n - 1/(n+1)

er all that times 2

[slender forge]

U plug in all number from 1 to infinity and add them up basically

[umbral pulsar]

ohhhhhh

silly mistake

LOL

[charred flint]

lol yea

[umbral pulsar]

thnx

[glacial hedge]

@cobalt eagle thta cheating but ill help

xD

[karmic spade]

wait how do you get the sum of an infinite series again (given that such a sum exists)
i thought there was some calculus way of doing it

[glacial hedge]

uhh

[karmic spade]

all i can remember is determining if it converges or not

[glacial hedge]

you can onlyfind sume of a telesoping or geometric series

[charred flint]

^

[slender forge]

^

[vague coral]

^

[glacial hedge]

bruhv

[charred flint]

telescoping is mostly taught in math competitions though

[hazy nebula]

There r multiple methods

[bold mantle]

@charred flint what r u taking for math rn

[charred flint]

I'm done with math

😎

[bold mantle]

Oh cool

[ancient chasm]

can someone help with complex functions?

[vague coral]

#real-complex-analysis

[slender forge]

What was ur last math u took? @charred flint

[glacial hedge]

@charred flint what classes did you take

[bold mantle]

Must be nice to have majored in all ur math classes

[vague coral]

math is useless

🗿

[charred flint]

uh maybe algebraic topology and representation theory were the highest math

[bold mantle]

Why

[covert breach]

exactly

[bold mantle]

Lucky

[hazy nebula]

Nope

[vague coral]

We do it because we love it

[bold mantle]

I wanna know math

[vague coral]

Maths is magic

[glacial hedge]

just like you 😆

[hazy nebula]

You ever heard of finance?

[hazy nebula]

What maths is included in that?

[vague coral]

yes and ?

[slender forge]

Cool basically just starting my math journey compared to u. I just finished calc 3 and linear algebra and prob stats

[vague coral]

probability and other stats shit

[bold mantle]

Whats the fundamental counting principle, my math teacher says it all the time but I didn't really pay attention when he told us what it is so idk whay is it

[vague coral]

I'm talking about real maths, not apply maths

[hazy nebula]

You would love probability once you know how much it helps you in financial markets

[charred flint]

oh that principle is super important

[vague coral]

I hate probabilities with passion

[hazy nebula]

:/ what's real maths

[hazy nebula]

Lmao

[glacial hedge]

lmao

[charred flint]

it's like if there are 3 entrees and 4 side dishes you can make 3*4=12 dishes total

[slender forge]

U would hate prob stats then

[umbral pulsar]

Don't underestimate the power of MATH. Computers could not have been made if Math was useless. (Alan Turing)

[bold mantle]

Whats the fundamental counting principle

[glacial hedge]

NO WAY

[hazy nebula]

Oh in that maths useless for us

[charred flint]

@bold mantle what I just said

[hazy nebula]

XD

[charred flint]

basically if there's an AND in a counting problem, you multiply the numbers

[umbral pulsar]

if there is OR we have to add

[slender forge]

But also remember to subtract the extra for the ors

[bold mantle]

@charred flint you have a fair 2 sided coin and a 8 sides 1-8 dice. What's the probability (p) that you will land heads, then a 3 on ur first go, and heads, then a 7 on ur second go.

[slender forge]

P(aorb)=P(a)+p(b)-p(aandb)

[hazy nebula]

Just multiply all 4 probabilities as they r independent events

[vague coral]

$P(A \cup B) = P(A) + P(B) -P(A \cap B)$

[ocean seal]

Herels

[slender forge]

I really need to learn the commands for that bot

[cobalt eagle]

Can someone explain calculus to Mr in baby words

Me

[vague coral]

calculus are useful for physics

[cobalt eagle]

Sick

[bold mantle]

What about
7c3
7! / c! (7-3)

I think I did that wrong

[hazy nebula]

:/ who is asking qn first of all lol

[slender forge]

7c3= 7!/(4!3!)

[bold mantle]

7x6x5x4x3x2

I don't understand the "(4!3!)"

[slender forge]

That’s 4! Times 3!

[vague coral]

$\begin{pmatrix} 7 \ 3 \end{pmatrix} = \frac{7!}{3!(7-3)!}$

[hazy nebula]

.

[slender forge]

Thank you

[ocean seal]

Herels

[slender forge]

That is very cool I needa learn that

[bold mantle]

That's what I recognize

Can I get a brief inteo to pre calculus

Nvm

What are quadratics

[vague coral]

$ax^2 + bx +c$

[ocean seal]

Herels

[slender forge]

X^(2)

[bold mantle]

What does that mean
How do I solve it

[vague coral]

with a different of 0

[slender forge]

Any function with power of 2

[vague coral]

why do you want to solve it

[bold mantle]

Idk

[slender forge]

U can factor or use quadratic formula

Usually use quadratic formula if can’t factor

[bold mantle]

Ur talking Greek to me

[glacial hedge]

look up the quadratic formula (i think its part of algebra 1)

[bold mantle]

Ok

b±√(b²-4ac))/(2a

[slender forge]

That can be used for any quadratic equation to find its zeros

[glacial hedge]

yep

both complex and real

[tidal badge]

is this free?

[vague coral]

yes

[tidal badge]

i have a series question

[dark crypt]

https://gyazo.com/63cf590137c3a1e76e3bf6cfb8d38c69

[dark crypt]

2(d)

[tidal badge]

heres my attempt

[dark crypt]

thats difficult

[vague coral]

you can start by expanding

[tidal badge]

I dont see how the n^2 - 19 comes out of all positive values?

[vague coral]

maybe you did a mistake

[tidal badge]

no i did the question twice

[vague coral]

[tidal badge]

look at the working though, it makes no sense for the answer to contain a negative unless the final quadratic factorises as such

but.. it doesNt

[vague coral]

thats what I'm doing

The work looks clean

i dont know what is wrong

[tidal badge]

me neither

there aren't any worked solutions either so idk

[north fulcrum]

When determining range such as in this example, do i read the graph from bottom to top, so (-inf,-1]

[charred flint]

@north fulcrum yes

[alpine sable]

i cant determine what the answer of this would be, no one can help me either apparently.

<@&286206848099549185>

[charred flint]

@alpine sable question seems broken lol

if it was a polynomial it'd be degree at least 5

[alpine sable]

ok whatever ill just go with not

question has caused me too many problems

[gray isle]

5 is at least 3

but question options are pretty bad

[alpine sable]

so its either 1 or not?

A or not?

[gray isle]

yeh

probs A is better in context

[north fulcrum]

How do I find part C? This isnt a test/quiz, its review for practice. I got it wrong the first time around and I'm still stumped.

[alpine sable]

okay well, if i dont pass this quiz ill do A next time cause i cant go back thanks though

[gray isle]

it satisfy the properties of a polynomial

and i guess their choice of number is based on the amount of roots

[karmic spade]

yeah i was about it say it sounds like A

[gray isle]

at least 5 is at least 3, so A would still be valid

[north fulcrum]

Do I plug the number of years 2007-1987 = 20 into my slope intercept form, and solve?

That's what I've gathered so far.

[solar tapir]

Any statistician online?

I have a doubt about hypothesis building

But it's not numerical

[pale night]

I'm not a statistician but I recent finished a course on statistics, what is confusing you about hypothesis building?

[solar tapir]

OK, it's the following

There's a problem where a man makes a statement about the profit levels of some economic sectors. He says that the profit of every sector, on average, is positive

[alpine sable]

can someone please explain how
tan-¹(cot x)
=> tan-¹ tan(π/2 -x)

[solar tapir]

Channel busy

@pale night Here it comes

The situation is modelled as a Bernoulli rv, and the parameter will be p

When profit > 0, the rv=1

So, we have this discussion

I say let's use this hypothesis set for every sector

$H_0: p \leq 0, : H_1: p>0$

[ocean seal]

Max Hetfield

[solar tapir]

My friend says

Get the point estimator p for every sector

Let's say we get

0.5, -0.43, 0.2

for 3 sectors

Then the hypothesis should be

Sector 1: $H_0: p \leq 0, : H_1: p>0$

[ocean seal]

Max Hetfield

[solar tapir]

Sector 2: $H_0: p \geq 0, : H_1: p<0$

[ocean seal]

Max Hetfield

[solar tapir]

Sector 3: $H_0: p \leq 0, : H_1: p>0$

[ocean seal]

Max Hetfield

[solar tapir]

Who is right?

[glacial hedge]

i mean it could be a polynomial

whoop

[pale night]

Ok i'm a little confused is rv the standard deviation?

[solar tapir]

No, it's random variable

[pale night]

It really depends what your testing for

and that is a little unclear from what you've given me

To me I'd say H naught is > 0, H1 <= 0, sorry i haven't used this system enough to understand how to to Tex yet

if you are test a case where the hypthosis is true

that is if we are testing the specified mean and standard deviation are true proposed by the man

if we are testing the other way around then you are correct in your initial assessment

does any of that make sense

[solar tapir]

No, tbh

Hypothesis testing is not symetrical

So there's a difference

[pale night]

it isn't?

[solar tapir]

No, of course not

You cannot switch alternative and null

<@&286206848099549185>

[pale night]

perhaps i misunderstood the central limit theorem then

[solar tapir]

No, it's nothing about CLT, it's about errors in hypothesis testing

That's why you can't switch

[pale night]

Ok, from the course I just took the instructor was switching them back and forth.

Depending on the test

But I'm curious why, based on differing criteria it wouldn't make sense to switch them. Maybe someone will answer that

[solar tapir]

Because if you fail to reject the null hypothesis, you may be using a test with low power

And one cannot conclude that the null cannot be rejected without taking that into account

[pale night]

Ok, I see what I'm missing on this

Just a second

[solar tapir]

<@&286206848099549185>

[pale night]

The key was the fact that it was a Bernoulli Random Variable

In which case you would be correct

[alpine sable]

So what was it?

Yours?

[pale night]

honestly the bernoulli random variable of 1 indicates success, whatever that means, again I think my initial assessment was correct. Since you specified in the original problem when profit > 0, rv = 1 to me that is H0>0, H1<=0. Good luck, I'm going to bed.

[indigo crown]

hello, I need help with 13b

I know it relates to a circle, but I'm stuck with how I can continue onwards

[vague coral]

regroup the terms in x and the terms in y

[indigo crown]

yes i am doing that

[vague coral]

so I guess you know what doing after this

[indigo crown]

e.g. I have x^2 - 10x

no no

Idk what to do after that

[vague coral]

canonical form

[indigo crown]

what's that?

[vague coral]

wait, I think you dont have the same word as we call it in french

yea english isnt my first language

[indigo crown]

that's okay 🙂

[vague coral]

Basically you need to find something in this form :

[indigo crown]

so I've got x^2 -2(5)x

but idk how to go on

[vague coral]

example

damn that picture missed a step

Well I'll do it myself

$x^2 - 10x = (x-5)^2 -5^2 = (x-5)^2 - 25$

[ocean seal]

Herels

[vague coral]

are u still there ?

[indigo crown]

i don't get it

how did u get (x-5)^2?

[vague coral]

try to read this, that's the process

[indigo crown]

what is that called?

[vague coral]

I dont know the name in english

[indigo crown]

could u send me a link pls?

[vague coral]

all my link are in french

you still want them ?

[indigo crown]

that's ok 🙂

yes pls

[vague coral]

https://homeomath2.imingo.net/polysec.htm#:~:text=3 formes courantes pour un,apparaît qu'une seule fois.

[indigo crown]

what's this method called?

[vague coral]

again I dont know his name in english

but in french : Forme canonique

Forme canonique d'un polynôme du second degré

[indigo crown]

ok thank you!

[ionic jewel]

completing the square

[indigo crown]

yeah I got it now, thank you!

[spare summit]

completing the square

[spare summit]

that is correct

[alpine sable]

Missing parenthesis

)

In the first line at the end

[carmine lion]

Consider $y=1+\ln{2x}$:$\ \$
Find $m$, such that $y=mx+2$ is a tangent to the curve

[ocean seal]

abe

[carmine lion]

heres what i've tried so far

i know that if you're given a point $P(x_1,y_1)$

[ocean seal]

abe

[carmine lion]

then, you find the derivative as a function, then substitute x_1 to get the gradient of the tangent

then write the equation of the tangent in point-gradient form

$y-y_1=m(x-x_1)$

[ocean seal]

abe

[carmine lion]

if i compare the equations

$y=mx+2 \ $ and $y=m(x-x_1)+y_1$

[ocean seal]

abe

abe

[carmine lion]

i've probably gone wrong already somewhere

[ocean seal]

abe

[carmine lion]

This is the question again

https://cdn.discordapp.com/attachments/490557019623915520/853190924934709288/473221703418511360.png

[alpine sable]

m=dy/dx=1/x

[carmine lion]

yes i know

[golden pollen]

Question 26c) I dont understand how to get to the quadratic

[alpine sable]

(1/x)x+2 = 1+ln(2x)

1. find x

2. sub x into m

[carmine lion]

wait

why are you equating

[alpine sable]

because its tangent

well so we can find m

[tribal geyser]

Hey guys why does the answer say there is no solution for this

I got 2pi as one

[carmine lion]

omg

this chaannel is occupied

im so confused

i don't understand

<@&286206848099549185>

[rigid smelt]

the tangent line and the original curve meets at one point, you can call that point (a,b)

if you plug in a into the derivative, you get the slope

now plug that slope into your equation

and plug in the point (a,b) to see if anythign cancels out

[carmine lion]

which equation

the y=mx+2

right

[rigid smelt]

which one do you think

does y=1+ln(2x) has anything to do with slopes?

[carmine lion]

no

u there?

waler

[rigid smelt]

yes

i think you know for sure which one to plug it in

just tell me what you get after pluggin in the slope and the point

[carmine lion]

$m=\frac{b-2}{a}$

[ocean seal]

abe

[carmine lion]

$y-b=m(x-a)$

[ocean seal]

abe

[carmine lion]

or am i using wrong eqn

[rigid smelt]

this is definitely wrong

[rigid smelt]

and this is not what i meant

how do you find the slope of the tangent line at a point (a,b)?

oops wrong channel

[carmine lion]

when $x=a$, $\frac{d}{dx}a=\frac{1}{a}$, $b=1+\ln{2a}$

[ocean seal]

abe

[rigid smelt]

yes

the slope is 1/a

so plug it in the tangent line equation

and then you also know that the tangent goes thru (a,b)

so plug in a and b into x and y

[alpine sable]

i am in class 4

where to study

[rigid smelt]

something will cancel out

[carmine lion]

$y-b=\frac{1}{a}(x-a)$

[rigid smelt]

no thats not what i meant y plugging in

[carmine lion]

oh

[rigid smelt]

and why is the d/dx there?

that doesnt mean anything

i just told you that the slope is 1/a

[ocean seal]

abe

[rigid smelt]

plug 1/a into y=mx + 2

and then plug (a,b) into that

[carmine lion]

b=3?

[rigid smelt]

yes

now you know b=3

plug it back into the original curve

to find a

since the curve also goes thru (a,b)

[carmine lion]

a=e^2/2 ?

[rigid smelt]

so whats the slope?

[carmine lion]

2/e^2

[rigid smelt]

yes

[carmine lion]

hmm ok

so thats the approach

ty

[south oak]

What i do

here

[topaz wedge]

How many 1/4 teaspoons equals 1/4 tablespoons?

[rigid smelt]

try converting tablespoons into teaspoons

[alpine sable]

I know that all the permutations of n
letters are n!, but I need only these that are not cyclic permutations of each other; for example: abc→bca→cab is distinct from acb→cba→bac. The number of them is (n−1)!, right? Can anyone recommend some literature and/or algorithm on how to generate them?

[gentle flame]

I think looking into circular permutations might help

[prime badge]

that didn't work

or was that right, i don't know anymore

because it does make (n-1)! permutations

abcd → acbd, acdb, adcb, adbc, abdc, abcd

but it's just "a" plus all permutations of "bcd", so it's not that probably

[blissful igloo]

[prime badge]

does that make sense?

it's just all permutations with one fixed letter, first one for convenience

[pallid lance]

pls anyone can help me with cos(4x) - sin(4x) = 1 step by step

[alpine sable]

Ok, thanks for the help, I was typing in google "cycling" in google instead of "circular", so I wasn't getting the right results (even if later found some sources that call them like that): and on what you will get will depend on the symmetry of the group of permutations (need to read more about Burnside's lemma). Thanks for the help

[glass lichen]

have you tried posting the entire question?

"help with random equation" means nothing

[pallid lance]

find x in cos(4x) - sin(4x) = 1 on range or 0,2pi

[sudden crater]

Any idea how to do the twelfth one?

[icy trail]

you'll need to put the whole thing in terms of either cos or sin, do you remeber your trig identities that relate cos and sin?

you'll end up solving it like a quadratic in terms of either cos or sin

[golden bridge]

are people using this channel ?

if not can someone help me with these 2 questions

[icy trail]

4(z - 2) = (2+i)(3+zi)
4z - 8 = 6 + 2zi + 3i - z
5z - 2zi = 14 + 3i

(5-2i) z = (14 + 3i)

@golden bridge

[golden bridge]

!

Thank you!

Its not the exact answer but now I know what to do

you're missing 1 step

but thank you so muchhh

@icy trail if you are free can you solve this as well

[icy trail]

yes aha ik

z - 3 = 2iz - 2
z - 2iz = 1
(1 - 2i ) z = 1
and again u can solve for z from there

[golden bridge]

lmao I just realized how easy this question is but I keep forgetting about the last part so I never got the answer

thank you so much

[pine lake]

Nice

Can someone help me with this

[gentle flame]

Note that the diagonal of the square is a diameter of the circle

Can you use that information somehow?

[past bramble]

yes

You have the value that connects the square and the circle

6 is not the diameter

this is 6

[subtle nebula]

pythagorean theorem

hypotenuse is the diameter

yes

sqrt(72)

8.48528137424

thats ur diameter

uhh

square root of that is

sec

[subtle nebula]

this is ur diabeter

bruh

the formula is

a squared + b squared = c squared

square root of 72 is ur hypotenuse and diameter

im not clicking that

[subtle nebula]

this is the formula for circumference

radius is diameter / 2

8.48528137424 half this

...

c^2

means sqrt(a^2 + b^2)

8.48528137424 is ur hypotenuse and diameter

what grade are u in

anyways

well

anyways

im g9 too

anyways

8.48528137424

half that (based onthe formula of circumference)

then multiply it to pi

and 2

thats ur circumference

want me to do it for u?

@shadow tundra

BRO

72 is not ur hypotenuse.............

[subtle nebula]

this is ur hypotenuse

yes.

sqrt of 72 is ur hypotenuse

@shadow tundra

i got the answer now

...

i told u

ok

lemme see

quick

why did u multiply it

its addition

k

quick i gtg soon

yes

[subtle nebula]

see

but thats not the answer yet

@shadow tundra

multiply that to 2 and pi

what

quick

bro

[pine lake]

bruh

u didnt solve this

photomath did

[subtle nebula]

half

ok whatever

i gtg

...

study basic maths

uknowwhatim just gonna spoonfeed u

@shadow tundra

bye

26.657297629

[subtle nebula]

this is the answer

[pine lake]

okden

[alpine sable]

I'm just going to check out this question...

[gleaming warren]

How is this wrong

[vale wigeon]

$(-7)^2 \neq -(7^2)$

[ocean seal]

Ann

[gleaming warren]

how

[vale wigeon]

$(-7)^2 = (-7) \times (-7) = 49 \ -(7^2) = -(7 \times 7) = -49$

[ocean seal]

Ann

[gleaming warren]

ohhhhh

so which on should i do

$(-7)^2 or -(7^2)$

[ocean seal]

TheGameBot

[vale wigeon]

you had it all correct at the third line from the bottom

it's when you replaced 9^2 + (-7)^2 with 81 - 49 instead of 81 + 49 that you fucked up

[gleaming warren]

oh i get it

-7 * -7 = 49

[vale wigeon]

that's what i said, yes.

[gleaming warren]

right?

ok thankyou

[alpine sable]

Yeah, negatives can be tricky sometimes, always be weary

[gleaming warren]

lol yes

[quartz stone]

How would I choose x, y, z matrix here, given a, d, g such a^2 + d^2 + g^2 = 1 such that the matrix has det 1? I want to use it to represent rotation.

I'm guessing this will be useful, but have no clue how quaternions work

Because if q is a unit then the matrix should have determinant one and also be orthogonal

function spring (xS, yS, zS)
  [x, y, z] = sphere (100);
  colormap (winter);
  surfl (0.25 * x + xS, 0.25 * y + yS , 0.25 * z + zS);
  shading interp;
  hold on;
  t = 0:0.1:100;
  mag = sqrt(xS^2 + yS^2 + zS^2); 
  a = xS / mag;
  d = yS / mag;
  g = zS / mag;
  coords = [sin(t) * 0.25; cos(t) * 0.25;  0.01 * t  * mag];
  plot3 (sin(t) * 0.25, cos(t) * 0.25,  0.01 * t) 
  plot3 (
    [d^2 - a * g + g^2, - d, a] * coords,
    [- d * (a + g), a - g, d] * coords, 
    [a^2 + d^2 - a * g, d, g] * coords);
  axis equal;
  title ("Simulation of Spring", "fontsize", 20);
  # hold off; 
endfunction  
``` here's what I'm doing

I believe I could do it by doing smth like [sin(t) * 0.25 * 1/det(m); cos(t) * 0.25 * 1/det(m); 0.01 * t * mag], which I could convert into a matrix (change of basis) but I feel like that's somewhat ugly

I may just go with that tbf, but if anyone knows a better way to draw a sphere with a spring attached to it, please tell me

[gleaming warren]

<@&286206848099549185> I have test tommoroe

[quartz stone]

I'm willing to help you, but please don't ping helpers instantly

Hi 🙂

[gleaming warren]

Ok

Srry

Hi

[quartz stone]

So are you calculating the length of a line?

[gleaming warren]

Yes

[quartz stone]

Do you know the coordinates of the ends of the line?

[gleaming warren]

No

Maybe

I'll send question

[quartz stone]

Ah ok

[gleaming warren]

Q.2 part 5

[quartz stone]

ok so imagine it on a graph

[gleaming warren]

ok

[quartz sage]

I have 82 friends. As I leave high school, I’m down to 56 friends. Where did my friends go. Why did they leave. Why did they not come back into contact with me?

(A friend wanted me to ask this)

[quartz stone]

I'm drawing the graph for this

@gleaming warren does this look right?

Wait Q is 2

Oh wait it was 1

Ye

[gleaming warren]

nobody knows

its a mystery you have to solve with scooby and the gang

[quartz stone]

Do you understand what the question wants?

[gleaming warren]

The distance

[quartz stone]

Ok so where are P and Q?

[gleaming warren]

q is on y axis and p is on x axis

[quartz stone]

Ye

So you want the green line on that graph i made right?

[gleaming warren]

yes

[quartz stone]

Do you know the pythagorean theorem?

[gleaming warren]

yes $(hyp)^2 = (perpendicular)^2 + (base)^2$

[ocean seal]

TheGameBot

[quartz stone]

So you could do it for the green line?

[gleaming warren]

it is a right angle triangle so yes

(it has become one after adding the line)

[quartz stone]

ye

So $c^2 = (\sqrt{2})^2 + 1^2$

[ocean seal]

TrueBoxGuy

[quartz stone]

What's c?

[gleaming warren]

yes

isnt it supposed to be d?

for distance

[quartz stone]

Yes if you're doing coordinate geo

[gleaming warren]

i am doing that

[quartz stone]

ye

[quartz stone]

And in general the formula, if you have $(x_1, y_1)$ and $(x_2, y_2)$ is $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, but the order of $x_1$ and $x_2$ doesn't matter because square of a negative is the same