help-26

[wintry coyote]

yes it was

thank you

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[placid veldt]

Fab

Np

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[wicked burrow]

this is relating to estimators in statistics. in this example, they're showing an estimator for difference of probabilities of two samples that are binomially distributed. I just have a question about the formula for the variance. is there a reason why the - sign is removed when they split up the variance into two separate variances, or should i just close my eyes and follow the formula?

[pastel salmon]

variance of the difference is the sum of the variances, , that is known fact, since, when you take constant ou tof the variance, you square it, so (-1)^ 2 = 1

[wicked burrow]

ah ok thanks :)

[pastel salmon]

yvw)

[wicked burrow]

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[raven latch]

m

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[grand sinew]

I'm sort of embarrassed because I feel like I should know this Can someone explain why square rooting everything doesn't work at all?

[grand sinew]

I know that it doesn't work I just don't know why.

[worthy storm]

what did you get when you square rooted everything

show the equation

[worthy storm]

yea the problem is this:

what is the square root of (-1)^2

it's not -1

so if your x-3 or x+2 are negative then the square roots are wrong

[grand sinew]

That makes a lot of sense

Thank you

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[balmy bolt]

i get lim n>inifnity e^cosn - e

but how would i evaluate cosn at infinity

[icy sky]

you dont

[spiral slate]

looks like you can do a u sub

[icy sky]

the limit is dne

[spiral slate]

and that

[balmy bolt]

oh it diverges

ok thanks

[leaden furnace]

@icy sky did you try to solve it?

[icy sky]

yes

[leaden furnace]

Ok

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[trim jasper]

Find the number of ways to distribute 21 identical oranges among 3 children such that all of them get atleast 2

[trim jasper]

What method can i use, other than partition and multinomial theorem

[last scroll]

Hmm

21 - (3*2) = 15

15 choose 3 = 455?

Maybe?

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[opal ocean]

Can I get help with this question I dont see how to write an equation and find the period and stuff thank you

[royal glacier]

Is this for speficic lecture or class?

[opal ocean]

No just textbook trig

[royal glacier]

So it's trig question alr

do you know any trig functions that looks similar

[opal ocean]

yes I know its csc

but they all are supposed to have specific periods to them

[trim jasper]

they also moved it

[royal glacier]

what is period of csc(x)?

[opal ocean]

2pi

[royal glacier]

what is period in image?

[trim jasper]

a graph from one point to another which will repeat itself again and again

[opal ocean]

i dont know

would it be 2pi/1

[trim jasper]

oh i thought u were op, mb

[royal glacier]

I personally think period as how far it needs for graph to repeat itself

or f(x+period)=f(x)

[trim jasper]

yes

[opal ocean]

how

so it would be 2pi/3

[royal glacier]

blue part is repeatdd as yellow right?

[opal ocean]

yes

those 2 on the right

the first 2

I found the period but now im trying to find the stretch

[royal glacier]

you mean stretch csc(x) to make it same period as image?

[opal ocean]

actually it would be 2pi/2

yes

if its stretch idk

[royal glacier]

you're right

for stretch

you can solve this question only thinking stretch not with period IMO

[opal ocean]

yes

i dont know how to find that though

[royal glacier]

Do you have an idea on how much you would need to stretch it?

Like ratio of csc(x) and the one on image

[opal ocean]

i put y=csc(pix)-1 into wolfram alpha and it looks similar but its saying its wrong

[royal glacier]

you can get help with the fact that $\csc{x}\le -1 or 1\le \csc{x}$

[thorny flame]

Dri111

[royal glacier]

for the function in image $f(x), f(x)\le -4~or~0\le f(x)$

[thorny flame]

Dri111

[opal ocean]

I dont understand

[royal glacier]

Or, you can set the function in image as $n\csc{\pi x}+m$ form

[thorny flame]

Dri111

[royal glacier]

and use the point that graph goes through to find n&m

like (1/2,0) and (3/2,-4)

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[real basin]

anyone free to help me out on this one :3

[exotic carbon]

if |x| < y then -y < x < y

are you aware about this?

[real basin]

logically yes

dont think we've covered it specifically tho

[exotic carbon]

okay

so could you apply this into the equation?

[real basin]

could you do it with x-2?

and do like -1< x-2 < 1

[craggy haven]

yep!

[real basin]

im attempting to figure out how to factor that out of 2x^2 -3x -2 rn

i think its

(x-2)(2x+1)?

so then

i already know the value of x-2

[craggy haven]

you know a range for it yes

[real basin]

how would i go about incorporating 2x+1 though?

would i like

solve for a range of x itself?

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@real basin Has your question been resolved?

[real basin]

D:

:p

[real basin]

if anyone who sees this could let me know it’d be greatly appreciated bc i have to go to sleep😕

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[glossy wave]

Why is it important that the exp function is continuous

[clear crescent]

That guarantees that you can interchange the limit

[thorny flame]

ℝ ⊇ Mikkel ∉ 𝐵(ℝ)

[glossy wave]

Right

[glossy wave]

Is it to do with sequential continuity

<@&286206848099549185>

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[ancient trellis]

How do i start ? Q3a

[woven creek]

use half angle formula to find tan(b/2

[ancient trellis]

Like these?

[ivory sorrel]

,rotate

[topaz sinew]

@ancient trellis Has your question been resolved?

[velvet sparrow]

Is the answer 47/12?

[ancient trellis]

Yeah

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[velvet lance]

is this correct?

[frigid blade]

y can be -3 or 11

is that what you are answering

[velvet lance]

yes

just wanna double check

[frigid blade]

testing right now

[surreal sand]

im getting -3

[frigid blade]

could be -1 as well?

[surreal sand]

and 11

yet

[velvet lance]

im prettys ure theres 2 answers

[surreal sand]

yea

[velvet lance]

mhm

[surreal sand]

-3 and 11

mhm

[velvet lance]

kk thx

[velvet lance]

thx :D

[surreal sand]

: D

[velvet lance]

wait XDDD

i got it wrong

[surreal sand]

uh

[velvet lance]

apparently its -11

XD

[surreal sand]

oh yeah -3 and -11

[velvet lance]

XD om

[surreal sand]

my bad i forgot about the negative sign too

[velvet lance]

XD k

ash

[surreal sand]

ash

[velvet lance]

XD

[gritty flume]

Gel yaliyim

[velvet lance]

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[gritty flume]

yağlı yağlı

[frigid blade]

if y was -3

then wouldnt area be 9 squ

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[topaz sinew]

@neon iron Has your question been resolved?

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@neon iron Has your question been resolved?

[neon iron]

<@&286206848099549185>

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[sweet shard]

What don't you get

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[rose fjord]

im having trouble figuring out where to start

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[rose fjord]

<@&286206848099549185>

if i let ad=bc and just plug in some values is that enough?

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@rose fjord Has your question been resolved?

[twilit ferry]

You can approach it from them definition ad-bc=0 , for the first question, think about what being a multiple of each other means in terms of the ratio of a:c and b:d

The second question should be similar

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[neon iron]

7b+2 right?

Since 7*4=28

[ornate magnet]

!status

[topaz sinew]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[ornate magnet]

@neon iron

[neon iron]

Sorry

So 7a+b should be a tens?

<@&286206848099549185>

??

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[upbeat linden]

how do i solve this

[marble yew]

you could try substituting one equation into the other

[upbeat linden]

huh

[marble yew]

like you can change the first equation to say x=-5-3y right?

[upbeat linden]

OH

0k then

i

basially subed into the net

other

then

i didnt know what to dop

i jkust had a polynomial

[marble yew]

yeah sub x=-5-3y into the second one

you get a quadratic right?

[upbeat linden]

thas wehat i did

yuea

yea

[marble yew]

then you can use the quadratic formula to solve it if it doesnt have nice values

[upbeat linden]

nice values?

huh

[marble yew]

like easily factorised values

like you can spot how to factorise x^2-2x-3 pretty easily right

find 2 numbers that add to give -2 and multiply to give -3

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[trim tundra]

can anyone solve this. Thank you

and what is the answer

[desert junco]

A^-1 = adjA/det(A) so A(adjA) = A * det(A) * A^-1 = I * det(A) so 6

[trim tundra]

thank you

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[patent hollow]

how do i differentiate that

pleaseee help

[restive inlet]

follow waht i recommnded

chain rule one stage at a time

[patent hollow]

yeah so i tried with the other one can u check if it’s right please

[restive inlet]

you showed this earlier, i said it was dodgy

you posted something after that, that was correct

[patent hollow]

wait so this is right?

[restive inlet]

no

[patent hollow]

oh

[restive inlet]

that's pretty much what you just posted

you posted something else

with radical form

[patent hollow]

i did?

[restive inlet]

oh, nvm, that was someone else giving away solutions (which they shouldn't do)

lets go back

can you show how you did questions 1 and 2?
i'll be easier to use something you did as reference

how did you differentiate
$$(x^2+4)^6$$

[thorny flame]

ℝαμΩℕωⅤ

[ivory sorrel]

Honestly I'd use logrithmatic differentitation here

[restive inlet]

are you still there?

[patent hollow]

yeah sorry

[restive inlet]

read my message above

[restive inlet]

,rotate

[restive inlet]

note that for a,b)
you that after applying power rule
you multiplied by the derivative of the inside

[patent hollow]

yes

[restive inlet]

$$\sqrt{\red{x^2 + \cbrt{x^3+1}}}$$
the inside here is the whole red part.

[thorny flame]

ℝαμΩℕωⅤ

[patent hollow]

ok

so then?

[restive inlet]

apply power rule for the sqrt on the outside, then multiply by the derivative of the red,
leaving that as d/dx (red) for now (don't differentiate this yet)

looking more carefully, the notation in your a,b is off

[patent hollow]

why is it off

also when i differentiate the inside do i use the chain rule

[restive inlet]

for a) either have
$$\begin{aligned} y &= (x^2 + 4)^6 \
\dv{y}{x} &= 6(x^2+4)^5(2x) \end{aligned}$$
or
$$\begin{aligned} \dv{x} (x^2+4)^6 = 6(x^2+4)^5(2x) \end{aligned}$$

[thorny flame]

ℝαμΩℕωⅤ

[restive inlet]

you'll need it again, but don't worry about that for now

[patent hollow]

ok thanks

[restive inlet]

focus on the first application of chain rule

worry about the rules required to differentiate that afterwards

[patent hollow]

yeah so i did the first but

[restive inlet]

you had a similar notation issue for b)

[patent hollow]

but idk how to differentiate the inside of the bracket now

[restive inlet]

using b) as an example, what i'm trying to get you to do is instead of trying to jump to the end result directly, is something like:
$$\dv{x} \cbrt{\red{x^3-2x-2}} = \frac13 (x^3 -2x - 2)^{-\frac23} \cdot \dv{x}(\red{x^3-2x-2})$$

[thorny flame]

ℝαμΩℕωⅤ

[restive inlet]

can you write what you have so far for c)

[restive inlet]

,rotate

[restive inlet]

now focus on differentiating

and you didn't fix the notation issue above

d/dx is the deriviative operation, that itself shouldn't be set equal to stuff

that applied to the original function gives the derivative

or starting with y, dy/dx will be the derivative

[patent hollow]

ok i fixed it now

[restive inlet]

you can differentiate each term individually and then you'll apply power-chain rule again for the cube root (which notation aside, you were able to do in part b)

[patent hollow]

i differentiate that inside ok cool

is that right now

[restive inlet]

you made a mistake with the derivative of x^3 + 1 at the very end

its not 3x

[patent hollow]

oops 3x^2

[restive inlet]

then yeh

[patent hollow]

TAUNKS

THANKS

[restive inlet]

convert that to radical notation if desired

[patent hollow]

thank you so much for your help

really thank y

up

.close

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[velvet pecan]

i forgot about limits

it should be the top one right?

since limit is used to find the value that is close to x

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[cobalt wagon]

Would it be more accurate say that the equation y = mx + b is not of a line, but of the points in that line?

[frigid blade]

the points make the line though

[split cloak]

Like put infinity points

And you get line

[cobalt wagon]

I'm talking about accuracy here guys

[split cloak]

Ig both are correct

[cobalt wagon]

yes but it'd be more accurate, wouldn't it?

[coral jackal]

no because there is an infinite numbner of points

because between for example 1 and 2, in terms of integers there is only 1 or 2, but there is an infinite number of decimal or fractional numbers in there

[cobalt wagon]

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[inner drum]

dose ln(anything1) - ln(anything2) = ln(anything1/anything2)

.close

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[neon iron]

can somebody explain me polar co-ordinates ?

[reef fjord]

https://tutorial.math.lamar.edu/classes/calcii/polarcoordinates.aspx This link has a pretty good explaination

[neon iron]

hmm okay

thanks

.close

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[mild fractal]

,tex $\int \frac{x + 4}{5x + 5} \dd x$

[thorny flame]

@mild fractal

[mild fractal]

I don’t know where to start

[abstract wadi]

x+4 = (x+1) + 3

Split the integral.

[mild fractal]

Ohhh okay

,tex $\int \frac{x + 1 + 3}{5(x + 1)} \dd x$

[thorny flame]

@mild fractal

[mild fractal]

,tex $ \frac{\int \frac{x + 1 + 3}{x + 1} \dd x}{5}$

[thorny flame]

@mild fractal

[abstract wadi]

Really? That's how you'd write it? Come on there has to be a better way, don't you think?

[mild fractal]

Ye

,tex $\frac{1}{5} \int \frac{x + 1 + 3}{x + 1} \ddx$

[thorny flame]

@mild fractal

$\frac{1}{5} \int \frac{x + 1 + 3}{x + 1} \ddx$
```Compilation error:```! Undefined control sequence.
l.49 ...ac{1}{5} \int \frac{x + 1 + 3}{x + 1} \ddx
                                                  $
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2023/texmf-var/fonts/map/pdftex/updmap/pdftex.map}{/usr/l```

[abstract wadi]

[\f15 \int \frac{x + 1 + 3}{x + 1} \dd x]

[thorny flame]

! What the hell am I doing here?

[mild fractal]

,tex $\frac{1}{5} \int \left( 1 + \frac{3}{x+1} \right) \dd x $

[thorny flame]

@mild fractal

[mild fractal]

,tex $$\frac{1}{5} \left( \int 1 \dd x + \int \frac{3}{x+1} \dd x \right)$$

[abstract wadi]

Times?

Are you sure?

[thorny flame]

@mild fractal

[mild fractal]

Oops

,tex $$ \frac{1}{5} \left( x + 3 \ln(x + 1) \right) $$

[thorny flame]

@mild fractal

[mild fractal]

,tex $$\frac{x + 3\ln(x + 1)}{5}$$

[thorny flame]

@mild fractal

[mild fractal]

Would this be correct?

[abstract wadi]

I'd personally write ln|x+1|

[mild fractal]

Oh right

,tex $$\frac{x + 3\ln(|x + 1)|}{5} + C$$

[thorny flame]

@mild fractal

[mild fractal]

Also forgot the C

[abstract wadi]

yeah

[mild fractal]

Okay, thanks for the help!

.close

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[abstract wadi]

(could have done this for yourself)

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[spring rune]

yo i need help with a proof

[junior chasm]

show ur working and question

[clear lodge]

!show

[topaz sinew]

Show your work, and if possible, explain where you are stuck.

[spring rune]

1203027735308406835

how do i link the message

it;s in the help forum

[junior chasm]

https://media.discordapp.net/attachments/1203027735308406835/1203027735488893028/Screenshot202024-02-0220at2000.png?ex=65cf99e3&is=65bd24e3&hm=7dd908095363c4b64c5e5b569930dad8477d11ff50a323a5986e5b51e1c5d859&=&format=webp&quality=lossless

[spring rune]

yes

the solution image got funky when i exported it

[topaz sinew]

@spring rune Has your question been resolved?

[spring rune]

hello?

here's my proposed solution

[clear lodge]

I dont think you can take the derivative on both sides on the first assumption.
The convergent integral between a and b of any function is a number, and thus f(b)-f(a) on any function would be 0, which would mean that for every function with a convergent integral the endpoints would have the same y-value, which is clearly false

for example. Let's take f(x) = x;
F(x) = (x^2)/2
F(1) = 1/2
F(0) = 0
f(1) = 1
f(0) = 0
f(1) - f(0) = 1

[spring rune]

oh ok that makes sense thanks!

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[spring rune]

@clear lodge does this work?

[clear lodge]

that's unreadable

[spring rune]

open in new tab

here you go

[topaz sinew]

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@spring rune Has your question been resolved?

[spring rune]

<@&286206848099549185>

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[thorn niche]

If b/a = 2/3, c/b = 3/4, how much is (a+b+c)/(a-b-c)
From a/b/c = 6/4/3, follows a = 6k, b = 4k and c = 3k

how tf does this answer make any sense

[placid crater]

https://tenor.com/view/choco_fish-gif-25946991

[chilly walrus]

which part do you not get?

a : b = 3 : 2 = 6 : 4
b : c = 4 : 3
combining, a : b : c = 6 : 4 : 3

[thorn niche]

why is a 6 and not 3

[chilly walrus]

2/3 is the same thing as 4/6

[chilly walrus]

similarly, you couldn't have combined these terms like that if you left it at 3 : 2

this is because the 4 from b : c needs to go with the 4 in a : b

to get the 4 in a : b, you need to multiply both numerator and denominator of the ratio by 2

therefore the 3 becomes a 6

[thorn niche]

thanks

i didnt notice b is different

[chilly walrus]

if you are done, type ".close"

[thorn niche]

.close

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[clear pike]

could someone help me with this one

[chilly walrus]

try drawing a diagram

specifically of the circle being in one of the corners in the square

[clear pike]

does this have to be accurate?

[chilly walrus]

no

[rigid ivy]

As accurate as whatever would help you understand the problem

[chilly walrus]

pretty much yeah

just note that the circles diameter is 1.8 cm while the square's side length is 2 cm

[rigid ivy]

(I prefer 18mm and 20mm, personally)

[clear pike]

hmmm

now that i think about it

you have 2mm of 'tolerance' vertically to move the circle about horizontally

and the same vertically

so 2x2 = 4 mm^2?

[chilly walrus]

yep

[chilly walrus]

that's your answer

[clear pike]

cheers

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[visual leaf]

Ok what the actual hell are these calculations???

[visual leaf]

I feel like Im being gaslit

Since when was ln|sec(0)| equal to 5ln2???

sec(0) is 1 no??
So ln|sec(0)| should be 0

What the fuck is happening???

[pulsar coyote]

u right

[craggy haven]

it should be 0 and it is 0

[placid veldt]

^^

[visual leaf]

Bruhhhhhh

Ok wait one sec lemee check the final answer for the whole integral with a calculator

Ok so this does work

[visual leaf]

But idk how this gets to 5ln2

Wiat nvm

This part equals 5ln(2)

So mymathlab glitch then nice

[visual leaf]

Imma go report this lmaoo

.close

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[neon iron]

soo

[topaz sinew]

Please don't occupy multiple help channels.

[neon iron]

i need help

[alpine mist]

first, close one of your rooms

second, what's the actual question?

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

dont yell at me

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[sweet shard]

No one's yelling. Just follow the rules

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[lunar stump]

hang on

is it possible to find the value of 2 missing degree values in law of sine

or is that not possible

[mild fractal]

as long as you have any of:

the ratio of an angle's sine and the angle's opposite side

the value of at least two angle degrees

there might be more, but these are the ones that i know

[mild fractal]

in this case, you seem to have the first condition available

[lunar stump]

this is the equation

,rc

so i have the condiiton for "ratio of an angle's sine and the angle's opposite side"?

with sin(48.16)/112.63

?

[ivory wave]

!msgdel

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[lunar stump]

oh

ok

ty

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@keen skiff Has your question been resolved?

[keen skiff]

<@&286206848099549185>

[compact holly]

If this is just producing the binary sum, then you would just subtract the two base 10 numbers (102 - 59 = 43) and convert it to binary. So, you would convert it to 00101011.

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[topaz sinew]

@trim tundra Has your question been resolved?

[outer portal]

|a x b| = |a| |b| |sin angle|
|a * b| = |a| |b| |cos angle|
you know |a * b|, |a|, and |b|, use this to figure out what |cos angle| is, then what |sin angle| is and then to find |a x b|

[trim tundra]

@outer portal

is this correct?

[outer portal]

yes, good job

[trim tundra]

thank you @outer portal

[outer portal]

np

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[leaden mortar]

Last part for the second picture

[leaden mortar]

(As soon as possible please. I hope that doesn't come off as rude 🥹 ...)

[worthy storm]

looks like you need to make exactly one sale during the first 7 interviews, and a sale in the 8th interview

[trim jasper]

why wont it be failure^6 * success^2

[trim jasper]

would that be different than what i said?

[worthy storm]

seems to imply a specific ordering?

[trim jasper]

hm

[worthy storm]

that would be the probability of say:
FFFFFFSS

[trim jasper]

but wouldnt that still mean multiplying them?

[worthy storm]

but there are other possibilities

[trim jasper]

SFFFFFFS

[worthy storm]

FFFFFSFS

etc

[trim jasper]

i see

how does that change the answer tho, can you elaborate a bit more

[worthy storm]

each one of those has the probability f^6 s^2 where f = p(fail) and s = p(succ)

you need to count them all and add their probabilities

[trim jasper]

what if i said, 6! ways to arrange first sale and 6 fails

and then theres just one way to multiply by second sale

[worthy storm]

it's not 6! ways, it's 7 ways

to arrange the first sale and 6 fails

[trim jasper]

ah

[worthy storm]

first sale goes in any of the 7 slots

[trim jasper]

i see what i did

[worthy storm]

fails go everywhere else

[trim jasper]

yes yes

[worthy storm]

you counted the fails as distinguishable

[trim jasper]

i mixed two concepts

[trim jasper]

whereas i should have done 7c1

[worthy storm]

yea

[leaden mortar]

okay I'm reading all whay y'all said

I stepped out to take out the trash

Okay for the second picture (the sales) would I have to find the total number of possible orderings for the 2 sales and 6 non-sales then multiply that by the product of sale^2*non-sale^6?

Wait...

would it be nPr(8,2)sale^2**non-sale^6 or
nCr(8,2)**sale^2non-sale^6

(I can't get the product sign in without changing it to italics)

And what's for the first picture?

[trim jasper]

no

basically

in the first part you need one sales and 6 fails

so you need 7c1 sales and the remaining fails

and well the last one is a sale so

[trim jasper]

if you do 8c2, you could pick both the sales in the first 7

which is not what we want

[leaden mortar]

so
$nCr(7, 1) * s * n_s^6$

[thorny flame]

nakles

[leaden mortar]

?

No?

:(

[topaz sinew]

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@leaden mortar Has your question been resolved?

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@leaden mortar Has your question been resolved?

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[mortal junco]

I'm new to this concept called "Probability of Combined Events"
I find it hard because I can never understand what the question asks
I am not going to send one question because i get most questions wrong as a whole
In my chapter it talks about the Addition Rule and the Multiplication Rule, Mutually Exclusive events and Non-mutually exclusive events
Is there a source that can explain this to me easily? I don't understand which question uses multiplication rule and which uses addition (I can somewhat understand mutually and non-mutually exclusive events)

[valid marsh]

How does it define combined events?

[valid marsh]

When two things are mutually exclusive, you can add their probabilities

[mortal junco]

The combined events are the combination of two or more events
in an outcome.

Kamal chooses two marbles randomly from a box which contains four red marbles, three yellow marbles and one green marble. The first marble returned to the box before the second marble is chosen.

what does this mean

4 + 3 + 1

so 1/8 * 1/8 ?

[valid marsh]

That is the number of marbles in the box

[valid marsh]

What are you calculating it for?

[mortal junco]

the probablity that two yellow marbles are chosen

[valid marsh]

Oh

[valid marsh]

No, this is not the probability that two yellow marbles are chosen

[mortal junco]

hmmm

[valid marsh]

because you have 3/8 chance of choosing a yellow marble

[mortal junco]

so is the answer just 3/8?

[valid marsh]

No

[valid marsh]

It would be 3/8 * 3/8

Can you see why?

[mortal junco]

yes but i dont understand

if we pick two yellow marbles

from 1 box with 8 marbles

[valid marsh]

You first have a 3/8 chance of getting a yellow marble

[mortal junco]

ok i almost got it

oh continue

[valid marsh]

Then you put whatever you got back in

So then you pick another one

still 3/8 chance

and these events are independent

so you multiply

[mortal junco]

why does it have to multiply?

[valid marsh]

to get 3/8 * 3/8

[mortal junco]

and not use addition?

[valid marsh]

Consider another example

There are two coins in a box, one black and one white

Pick one

You have 1/2 chance of getting the white one

Put it back

and pick again

1/2 chance again

of getting the white one

so getting the white one twice in a row has probability 1/2 * 1/2

but if you were adding, it would be 1

which means it must happen

[mortal junco]

ohh

so when is addition rule ever used?

[valid marsh]

that’s one way to see why it isn’t adding

another way to see it is because there are 4 possibilities: both black, black then white, white then black, or both white

[valid marsh]

When you’re calculating the probability of getting a green marble or a yellow one

The marble can’t be both green and yellow

[mortal junco]

for example?

[valid marsh]

When you’re calculating the probability of getting a green marble or a yellow one

It would be 3/8 + 1/8

= 4/8

because there are 3 yellow and 1 green marbles

[mortal junco]

so additon rule is when you want to find the probablity to get two things?

so if we had 1 black, 1 white and 1 green

and we wanted to know how to get 1 black and 1 white

[valid marsh]

More like two mutually exclusive events

[mortal junco]

it would be 1/3 + 1/3

[mortal junco]

wait so we were talking about indepdent just now

what makes something mutually exclusive

or non-mutually exclusive

[valid marsh]

Because multiplication is for independent events, and addition is for mutually exclusive events

[valid marsh]

Mutually exclusive events can’t both happen

[valid marsh]

Non-mutually exclusive events can both happen

[mortal junco]

so that means i cant take 2 white balls from a box with 1 white ball?

[mortal junco]

i see

[valid marsh]

You can if you put it back

[mortal junco]

what would be an example of a mutually exlcusive event then

[valid marsh]

Day and night

[valid marsh]

“Mutually exclusive” refers to two events

Like how you don’t say a number is equal

you say a number is equal to another number

[mortal junco]

so if there was a question regarding day and night what would it look like?

[valid marsh]

What is the probability of it being day or night

[mortal junco]

1/2...?

[valid marsh]

Then you can add the probabilities of it being day, and of it being night

[valid marsh]

It is always day or night

(either day or night)

[mortal junco]

im starting to understand

so that means if there were 4 day-night things

sun, moon, x and y

[valid marsh]

What

[mortal junco]

then the probability for x and y

would be 1/4 + 1/4?

[valid marsh]

No

[mortal junco]

this is tricky 🤔

[valid marsh]

x and y aren’t events, they don’t have probabilities

Things don’t have probabilities

Events do

[mortal junco]

i see

i think i understand a bit more

the addition rule is a bit tricky but i think i can get a hang of it

thank you for your help

[valid marsh]

Take this as an example: if there is a box with only one marble, which is yellow, then the probability of getting the yellow marble from that box is 1

But it may not be the same if you get it from some other box

So the probability is not a feature of the thing

It is a feature of the situation

[valid marsh]

You can try some more questions, and if you don’t understand them, then you can come to these channels for help

[mortal junco]

okiee

[mortal junco]

got it

so popular questions would use the multiplication rule

[valid marsh]

Some of them use the addition rule too

For example, take this question:

How many ways are there to choose 5 people from 3 men and 4 women, where at least 1 man and 1 woman must be chosen?

[mortal junco]

1/7 + 1/7?

[valid marsh]

If you read the question again, notice that we aren’t looking for probability

Instead, we’re looking for the number of ways to choose those 5 people

[mortal junco]

so how would we find it?

[valid marsh]

Split into cases

The possible choices are:

1 man and 4 women

2 men and 3 women

3 men and 2 women

4 men and 1 women

Notice these are all mutually exclusive

So, you would need to use the addition rule

by the way, do you know n choose k notation?

[mortal junco]

nope

[valid marsh]

Oh

[mortal junco]

u mean permutations and combinations?

[valid marsh]

Yes

[mortal junco]

oop

ye

but for some reason my syllabus split it into different subjects

there's the probability we talked about in maths

and permutations in additonal maths

and i am weak at both 🥹

[valid marsh]

Permutations and combinations are related to probability

[mortal junco]

ye

It's just in different subjects for me

so i try to focus on the other probablity

[topaz sinew]

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[dusty cargo]

Thats a word question

But im guessing you highlighted it in black

Still not related with math

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[celest fjord]

pls anyone tell me what to do in this

i dont understand the question

[regal mural]

Volume of the cylinder is equal to the volume of the rectangular tank

,tex $ pir^2 h = lb*h $

[thorny flame]

Nalla Manithan

[regal mural]

,tex $ \pi 0.7^2 h = 50440.21 $

[thorny flame]

Nalla Manithan

[regal mural]

we can substitute the value of h as speed x time

,tex $ \pi 0.7^2 (15000t) = 5044*0.21 $

[thorny flame]

Nalla Manithan

[regal mural]

@celest fjord are you from tamilnadu

[celest fjord]

no

himachal

[regal mural]

India ??

[celest fjord]

himachal is in india...

[regal mural]

didn't saw your message

[celest fjord]

ohk

thx for help

[regal mural]

did you got the answe

[celest fjord]

hmm

2hrs

[regal mural]

i had this question last year

[celest fjord]

ohk

grade studying in?

[regal mural]

now 11th

[celest fjord]

hmm

im in 10th

[regal mural]

that's why i asked whether u r from tamilnadu

[celest fjord]

oh

btw thats for help

imma close this

.close

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[neon iron]

This is a group

Does 8 mean here it has only 8 elements in it and is finite?

[odd pagoda]

Z_8 has 8 elements, yes

[neon iron]

1 more question which has been confusing me

The 8 under the +

What does that mean?

[odd pagoda]

that the addition is in Z_8

instead of eg the normal addition in Z or R

[neon iron]

Thanks

.close

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[calm prawn]

Hi, Im stuck on this matrix question

[calm prawn]

Ill use another server

[fair thorn]

lmao both got pinned

XD

[calm prawn]

.close

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[fair thorn]

@neon iron type your question now

so what's your question

20/12 times 8

assuming you walk at a constant rate

!done

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[fair thorn]

are... you testing me?

that's not what this server is for

what?

area?

how would there be a formula for a rhombus-

for area yea i think so iirc

diagonal 1 length times diagonal 2 length divided by 2

nah i gotchu

if done type .close

dude i cant help you with stuff like that

thats a whole subject

please don't ask questions like that here

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[neon iron]

for parametric eqns, does v have to be paralle

parallel

[neon iron]

because i kinda saw the eqn of a line as choosing a fixed point and an arbitrary point, haveing a vector point to the fixed point

and then finding the vector from the fixed point to arbitrary point

so that its like

i guess this is technically more accurate

am i over complicating this

is L just parallel to v meaning that they just go in the same direction

like did they just find the length of the line and then say its v is parallel since its literally equal to the length of the line

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

@neon iron Has your question been resolved?

[weary pier]

You are definitely overcomplicating this by a lot, I could do those exercises sleeping and still I am not sure about what aee you saying. Anyway being parallel just means that they go in the same direction, (wtf is the length of the line btw… it’s infinite😂 )

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[lament fractal]

can somone pls check my work and tell me if my answer is correct

[ivory sorrel]

,rotate

[long beacon]

i would suggest dont cut it completely , rest looks fine

[fair thorn]

one thing

you missed an a^2

[long beacon]

did he?

[fair thorn]

yep

numerator u'v

u' = a, v = x^3 - a

while simplifying

and he missed a minus sign

in uv'

[long beacon]

oh in the second last line yeah

[fair thorn]

yep

apart from that seems okay

[lament fractal]

oh i see

thank u

[fair thorn]

np

!done

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[lament fractal]

.close

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[hot iris]

Hey honestly not sure where to start

[hot iris]

I understand what a contour plot is supposed to be

But I am not sure how z works into it

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@hot iris Has your question been resolved?

[hot iris]

<@&286206848099549185>

[grave yarrow]

Contour plot shows you all the points (x,y) such that g(x,y) is a particular constant value of z

[hot iris]

.close

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[spiral mural]

why pin??

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[fair dagger]

These numbers are the solutions to the equation z^n=m (n and m are real)
Find n and m

[fair dagger]

I know that n is 6 because there are 6 solutions
And I tried that for m?

I know that if m was 64 so there were real solutions and because there are no real solutions it means that the answer has to be -64 but it doesn't sound like a proper answer
Any way I can find m algebraically?

[worthy storm]

just take z_1 to the 6th power

or do the same with any of the z_2, z_3, etc

z_1 to the 6th power is not 64, so m can't be 64

[fair dagger]

but again it's just saying "it's not 64 so it must be -64" and i do not know if they will accept it

[worthy storm]

why must it be -64, you have to explain this

just do the calculation

[fair dagger]

which I ask how to do it

[worthy storm]

(2 cis(30))^6 = 2^6 (cis(30))^6

you know 2^6 is 64

what is (cis(30))^6

[fair dagger]

It was weird looking so I though it's not -1

Oh wait tf am I doing

I raised it the 64th power instead of 6th

Yea yea of course it's -1

Omg I am so stupid

thx

.close

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[inner drum]

find the locus place where OE and BC are colliding (P)

(t,k) = (Px,Py)

BA y = (6/8)x + 6

I don't know how could this help

how do I make a connection between (t,k) and what I got with

<@&286206848099549185>

<@&286206848099549185>

[keen hinge]

do you have original task?

[inner drum]

yes but this is in a languge you won't understand

you need to find the yBC = yEO point which is P

but the locus

[topaz sinew]

@inner drum Has your question been resolved?

[inner drum]

<@&286206848099549185>

[topaz sinew]

@inner drum Has your question been resolved?

[noble laurel]

!15mins

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[inner drum]

.close

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[ancient solstice]

I don't understand what's wrong with my answer. I followed an example that was relatively the same, but it's not working

[mint crescent]

Note that t/2 is in the second quadrant

[ancient solstice]

oh god I forgot about that

let me fix it real quick

Okay there we go, it was -1/3 in the end

Thank you for the notice

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[iron dawn]

compute the scalar-surface integral f Ds:
double integral g x^2zdS where G is the cylinder (including the top and bottom) x^2 + y^2 = 4, 0 <= z <= 3

[topaz sinew]

Please don't occupy multiple help channels.

[iron dawn]

<@&286206848099549185>

[charred hearth]

.15min

Idk how to do it

.15m

Basically don't ping helpers until you've been waiting 15 minutes @iron dawn

[acoustic pecan]

use ! not .

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[glass dock]

Anybody got tips on how to start? Thx

,rccw

[noble laurel]

<@&268886789983436800>

[urban grove]

@last cypress please read #❓how-to-get-help and stop typing in other people's channels

[topaz sinew]

@glass dock Has your question been resolved?

[glass dock]

I tried something else but I overcomplicated I think haha

,rccw

[glass dock]

<@&286206848099549185>

[glass dock]

<@&286206848099549185>

[sonic escarp]

if they are at equal intervals on a striaight line, what does this mean for e.g. the y-coordinates? -26 -> 1 -> g -> 55?

[glass dock]

The difference between each coordinate is 27?

[sonic escarp]

yes

[glass dock]

So I do the same thing for the x coordinates?

[sonic escarp]

yes

[glass dock]

Ok thx

Ok I got it now, e=-117, g=28, h=39

Tysm have a great day!

.close