#help-0 | Mathematics | Page 688

gray isle Jun 30, 2021, 1:07 AM

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for the exact reason mentioned above

woven flume Jun 30, 2021, 1:07 AM

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oh wait

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its positive

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is that it?

oak chasm Jun 30, 2021, 1:07 AM

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(-1)^4 = 1, so yes.

gray isle Jun 30, 2021, 1:07 AM

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Also 2 * 4 isn't 16

woven flume Jun 30, 2021, 1:08 AM

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yeah that was my confusion

gray isle Jun 30, 2021, 1:08 AM

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It looks like you wrote an 8 first, which would've been correct

woven flume Jun 30, 2021, 1:08 AM

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but then I don't get x^4

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I get x^2

gray isle Jun 30, 2021, 1:08 AM

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But then you crossed it out and replaced it with 16

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Ur stuffing up another one of your exponent laws

woven flume Jun 30, 2021, 1:09 AM

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yeah...

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this is the question

gray isle Jun 30, 2021, 1:10 AM

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$\frac{a^m}{a^n} = a^{m -n} \neq a^{\frac mn}$

ocean sealBOT Jun 30, 2021, 1:10 AM

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ℝamonov

gray isle Jun 30, 2021, 1:11 AM

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$\frac{x^8}{x^4} = x^{8 -4} \neq a^{\frac 84}$

ocean sealBOT Jun 30, 2021, 1:11 AM

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ℝamonov

woven flume Jun 30, 2021, 1:12 AM

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OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOH

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thank you

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I think this is it

gray isle Jun 30, 2021, 1:19 AM

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notation can be improved a bit,
= signs are used inappropriately in the first half of the work

woven flume Jun 30, 2021, 1:20 AM

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should I use therefores instead?

gray isle Jun 30, 2021, 1:20 AM

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would be better if you introduced
**kx^4 = **

woven flume Jun 30, 2021, 1:20 AM

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how can I improve that

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wdym by kx^4 ?

gray isle Jun 30, 2021, 1:22 AM

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woven flume Jun 30, 2021, 1:22 AM

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ah

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sure

void reef Jun 30, 2021, 1:25 AM

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anyone good with probabilities ?

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how do I reach that value?

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the teacher didn't put the formula

lavish cypress Jun 30, 2021, 1:26 AM

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Calculate P(Y = 1) and P(Y = 0), add them up, and subtract the sum from 1

vestal warren Jun 30, 2021, 1:28 AM

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hello, I need help with this problem

void reef Jun 30, 2021, 1:28 AM

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how?

jagged imp Jun 30, 2021, 1:45 AM

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integrate twice to find y

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you have enough information to determine both constants of integration as you introduce them

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remembering that the slope of the tangent line at x=a is y'(a)

jagged imp Jun 30, 2021, 1:46 AM

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void reef how?

using the binomial probability formula or a calculator that can do it

ionic jewel Jun 30, 2021, 1:48 AM

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yeah use the pmf

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do you know the pmf for the binomial distribution?

void reef Jun 30, 2021, 1:50 AM

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no

jagged imp Jun 30, 2021, 1:50 AM

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do you know the formula for binomial probabilities?

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cause the pmf is just a fancy way of saying that

void reef Jun 30, 2021, 1:52 AM

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no I don't know either

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any good videos on that?

ionic jewel Jun 30, 2021, 1:52 AM

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it's just a formula you memorize it

void reef Jun 30, 2021, 1:52 AM

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I procrastinated and started studying way too late

ionic jewel Jun 30, 2021, 1:52 AM

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you could look up a derivation but I'm sure it's not that nice

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well actually it's probably pretty simple, you don't need any calc for discrete prob functions

void reef Jun 30, 2021, 1:53 AM

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could you also identify

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what's going on here?

full wasp Jun 30, 2021, 1:53 AM

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huh what language is that

void reef Jun 30, 2021, 1:54 AM

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it's portuguese

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it's to check if sales are over 2000

ionic jewel Jun 30, 2021, 1:54 AM

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i can't read Portuguese but looks like calculations for mean and variance

void reef Jun 30, 2021, 1:54 AM

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i'm not sure how the teacher solved it

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yes

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it uses mean and variance

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idk what she does after having both values tho

ionic jewel Jun 30, 2021, 1:54 AM

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what kind of distribution is it?

void reef Jun 30, 2021, 1:55 AM

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normal

ionic jewel Jun 30, 2021, 1:55 AM

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then it's just using the formula

full wasp Jun 30, 2021, 1:55 AM

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if you have the mean and variance then u can evaluate probabilities

ionic jewel Jun 30, 2021, 1:55 AM

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,w normal distribution (1900, 500), P(X>= 2000)

ocean sealBOT Jun 30, 2021, 1:55 AM

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Results provided by WolframAlpha

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

void reef Jun 30, 2021, 1:55 AM

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this?

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,w normal distribution (1900, 2500), P(X>= 2000)

ocean sealBOT Jun 30, 2021, 1:56 AM

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Results provided by WolframAlpha

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

void reef Jun 30, 2021, 1:56 AM

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hmm

ionic jewel Jun 30, 2021, 1:56 AM

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no

void reef Jun 30, 2021, 1:56 AM

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values don't match

ionic jewel Jun 30, 2021, 1:56 AM

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Wolfram uses SD as their other normal argument

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not variance

void reef Jun 30, 2021, 1:57 AM

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still doesn't match tho

ionic jewel Jun 30, 2021, 1:57 AM

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so you have to take the square root of your variance to get standard deviation

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yes I agree

void reef Jun 30, 2021, 1:57 AM

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teacher got 0,02

ionic jewel Jun 30, 2021, 1:57 AM

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i guess that means it's not a normal distribution

void reef Jun 30, 2021, 1:57 AM

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it says it's normal

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on the exercise

full wasp Jun 30, 2021, 1:57 AM

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perhaps your teacher has messed something up

ionic jewel Jun 30, 2021, 1:58 AM

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yeah looks wrong, I'd trust wolfram

void reef Jun 30, 2021, 1:58 AM

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4.1 Calculate the probability that, on a given day, the value of sales for traditional trade exceeds that of department stores.
4.2 The factory will set a target of 2000€ of sales per week. What is the probability of reaching this goal? (Consider 1 week = 5 working days.```

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Can you confirm?

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It's ex 4.2

ionic jewel Jun 30, 2021, 2:00 AM

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their answer is just wrong

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mean of 1900 and var of 2500 intuitively doesn't make P(x>=2000) that low of a nunber

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they much have been solving for something else, or messed up

void reef Jun 30, 2021, 2:00 AM

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sqr root of 2500 is 50

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,w normal distribution (1900, 50), P(X>= 2000)

ionic jewel Jun 30, 2021, 2:01 AM

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A_keka

ocean sealBOT Jun 30, 2021, 2:01 AM

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Results provided by WolframAlpha

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

ionic jewel Jun 30, 2021, 2:01 AM

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ah yes

void reef Jun 30, 2021, 2:01 AM

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gives the value now

ionic jewel Jun 30, 2021, 2:01 AM

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so my mental math is slacking

void reef Jun 30, 2021, 2:01 AM

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you did 500

ionic jewel Jun 30, 2021, 2:01 AM

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got it

void reef Jun 30, 2021, 2:01 AM

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xd

ionic jewel Jun 30, 2021, 2:01 AM

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thanks lol

void reef Jun 30, 2021, 2:01 AM

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yea nice

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Y_ThumbsUp

full wasp Jun 30, 2021, 2:01 AM

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well fwiw i didnt notice that either

void reef Jun 30, 2021, 2:01 AM

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exam is in 6 hours

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we can't use wolfram tho

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sadKEK

ionic jewel Jun 30, 2021, 2:02 AM

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is it open note?

full wasp Jun 30, 2021, 2:02 AM

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as long as u can do it on ur GDC or whatever youll be fine

void reef Jun 30, 2021, 2:02 AM

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we can take papers

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with notes

ionic jewel Jun 30, 2021, 2:02 AM

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if you don't know the formulas and you don't have a way to use them you fail

void reef Jun 30, 2021, 2:02 AM

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yes

ionic jewel Jun 30, 2021, 2:02 AM

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okay

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get the PDF and CDF of all relevent distributions

void reef Jun 30, 2021, 2:02 AM

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is this the formula?

ionic jewel Jun 30, 2021, 2:02 AM

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that's the PDF yes

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you may want the CDF as well

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well

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the CDF is ugly

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but you might need calculus then

void reef Jun 30, 2021, 2:03 AM

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hmm well technically the notes is the PDF the teacher gives so this is all we have to use

full wasp Jun 30, 2021, 2:03 AM

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do u get to use a calculator

void reef Jun 30, 2021, 2:03 AM

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when i said open note is because we can write

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she won't check

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but jesus_shrug

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yes

alpine sable Jun 30, 2021, 2:03 AM

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https://study.com/academy/course/honors-geometry-textbook.html

void reef Jun 30, 2021, 2:03 AM

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scientific

alpine sable Jun 30, 2021, 2:04 AM

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is this a good resource

void reef Jun 30, 2021, 2:04 AM

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graphic calculator i mean

full wasp Jun 30, 2021, 2:04 AM

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most graphic calculators can do normal PDF and CDF

void reef Jun 30, 2021, 2:04 AM

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how

full wasp Jun 30, 2021, 2:04 AM

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depends on your model

void reef Jun 30, 2021, 2:04 AM

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casio fx-CG 20

full wasp Jun 30, 2021, 2:05 AM

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ive never even seen one of those before uhhh you might need to check your manual

void reef Jun 30, 2021, 2:06 AM

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aight

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does this look close to it?

full wasp Jun 30, 2021, 2:07 AM

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yeah

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does it give you the answer

void reef Jun 30, 2021, 2:07 AM

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p=1.0798e-03

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i don't think this is right

full wasp Jun 30, 2021, 2:07 AM

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ok wait nvm

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u need to use normal CSF

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CDF

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instead of PDF

void reef Jun 30, 2021, 2:09 AM

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what do you mean?

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i don't know the acronyms in english

full wasp Jun 30, 2021, 2:09 AM

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you see how here it said P.D

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u should be able to find another option that says Normal C.D

void reef Jun 30, 2021, 2:10 AM

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this?

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p = 0.977

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hm

full wasp Jun 30, 2021, 2:11 AM

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well youve just calculated P(X ≤ 2000)

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you want P(X ≥ 2000)

void reef Jun 30, 2021, 2:11 AM

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i thought

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since i put in upper

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it meant bigger than 2000

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is my logic wrong?

full wasp Jun 30, 2021, 2:12 AM

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what lower and upper means is it calculates P(lower ≤ X ≤ upper)

void reef Jun 30, 2021, 2:12 AM

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I can't do lower: 2000 upper: 0

full wasp Jun 30, 2021, 2:13 AM

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yeah because P(2000 ≤ X ≤ 0) is nonsense

void reef Jun 30, 2021, 2:13 AM

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btw if I seem dumb is because it's 3am and ive been studying for 10hours

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so im a bit slow atm

warped phoenix Jun 30, 2021, 2:13 AM

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real quick question, are trigonometric functions considered algebra II content?

full wasp Jun 30, 2021, 2:14 AM

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u want to set lower to 2000 and then upper to some number like 3000

void reef Jun 30, 2021, 2:14 AM

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thanks

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it worked

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i'll try doing 4.1 with the calculator too

full wasp Jun 30, 2021, 2:15 AM

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after like 5 standard deviations from the mean the probabilities are almost zero

void reef Jun 30, 2021, 2:15 AM

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it's 0.22

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can you tell me the diff between Npd and Ncd?

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I didn't understand that part

full wasp Jun 30, 2021, 2:16 AM

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Npd calculates the probability of a single value

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Ncd calculates the probability of a range of values

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thats why Ncd makes you specify a lower and upper number because itll find the probability of all values between the lower and upper number

void reef Jun 30, 2021, 2:17 AM

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oh aight

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makes sense

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i'm so tired

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that I tried taking a screenshot

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in my calculator..

full wasp Jun 30, 2021, 2:18 AM

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u should sleep before your test like

void reef Jun 30, 2021, 2:18 AM

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i did it like this for the 4.1

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gave the correct value

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thanks

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i didn't know the calculator could do this

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thanks

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eh.. I'm not gonna sleep
im pulling an all nighter

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way too behind on the things

full wasp Jun 30, 2021, 2:20 AM

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your teacher shouldve told u about this like
no sane person with a GDC is going to be out here trying to calculate 1/√2πσ² etc.

void reef Jun 30, 2021, 2:20 AM

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imma be honest

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im in college

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with covid most classes were online

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online classes are very hard to not skip

full wasp Jun 30, 2021, 2:21 AM

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rip

warped phoenix Jun 30, 2021, 2:21 AM

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Hey guys, for $x(x^2 + x - 2) = 0$, I got x = 0, x = 1, and x = 1, does that mean there are only 2 roots, 0 and 1?

ocean sealBOT Jun 30, 2021, 2:21 AM

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TheMane3

void reef Jun 30, 2021, 2:22 AM

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what

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how did you do that?

full wasp Jun 30, 2021, 2:22 AM

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warped phoenix Hey guys, for $x(x^2 + x - 2) = 0$, I got x = 0, x = 1, and x = 1, does that mea...

im pretty sure theres more than 2 distinct roots

void reef Jun 30, 2021, 2:22 AM

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so I can also solve this

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with my calculator, right?

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it's poison something

full wasp Jun 30, 2021, 2:23 AM

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the calculator should have a poisson CDF

void reef Jun 30, 2021, 2:23 AM

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I should use CDF here?

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yea im using tat one

full wasp Jun 30, 2021, 2:24 AM

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hold on isnt that a binomial distribution

void reef Jun 30, 2021, 2:25 AM

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oh yea

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you're right

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nice

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it gave me the correct value

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thanks lollipop

woven pollen Jun 30, 2021, 2:26 AM

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ocean seal **TheMane3**

it's -2, 0, 1

void reef Jun 30, 2021, 2:26 AM

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https://tenor.com/view/quby-dance-cute-pentol-gif-18406660

Tenor

full wasp Jun 30, 2021, 2:26 AM

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aw thats nice

void reef Jun 30, 2021, 2:26 AM

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learning more from you

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than from my teacher

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in her defense i attended very few classes

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i gotta memorize where to use each of the distributions tho

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still not sure

full wasp Jun 30, 2021, 2:27 AM

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sometimes itll say in the question

void reef Jun 30, 2021, 2:28 AM

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3.1. Present the variable that models the above situation, indicating its distribution and parameter(s).```

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in this one it didn't

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how do you figure it's poisson?

full wasp Jun 30, 2021, 2:29 AM

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poisson distribution takes one parameter, which is the expected value

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here u only have one parameter and its the expected number of soaps the equipment can process (per minute)

void reef Jun 30, 2021, 2:30 AM

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oh aight

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makes sense

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can the calculator do intervals of confidence?

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idk whats the name in english

full wasp Jun 30, 2021, 2:35 AM

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maybe, im not sure

void reef Jun 30, 2021, 2:42 AM

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Could you please try to me explain me this one Lollipop?

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The question is to calculate the confidence interval for Homen (h) at 95%

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but i don't understand anything going on

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here's the table

full wasp Jun 30, 2021, 2:44 AM

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sorry uhh i havent learnt about confidence intervals

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someone else is gonna have to help. im just as lost as you are

woven pollen Jun 30, 2021, 2:45 AM

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void reef The question is to calculate the confidence interval for Homen (h) at 95%

Do you think this data is "normally" distributed? If so, use the standard error for a normal and the 95% CI number from the normal table. I'm sure you have a formula. This is classic material.

void reef Jun 30, 2021, 2:45 AM

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oh

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I get it

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Kinda

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Thanks

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I'll check that out

full wasp Jun 30, 2021, 2:48 AM

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yeah idk maybe this will help https://www.statisticshowto.com/probability-and-statistics/confidence-interval/#CISample lol

vague iris Jun 30, 2021, 2:48 AM

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What is the value of 12 ÷ 2 (5 – 2) = ?

2 or 18?

viral patio Jun 30, 2021, 2:52 AM

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vague iris What is the value of 12 ÷ 2 (5 – 2) = ? 2 or 18?

based on bodmas/bidmas/birdmas/pemdas (different places call it different things), you do brackets first, then indices/exponents, then multiplication/division (from left to right), then addition/subtraction (from left to right)
follow that, we get:
12 ÷ 2 (5 – 2)
= 12 ÷ 2 * 3
= 6 * 3
= 18

split ridge Jun 30, 2021, 2:57 AM

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help me pls

Screen_Shot_2021-06-29_at_10.57.34_PM.png

undone dock Jun 30, 2021, 3:02 AM

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sin=opposite/hypotenuse
cos=adjacent/hypotenuse
tan=opposite/adjacent

split ridge Jun 30, 2021, 3:03 AM

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so is it going to be 2

undone dock Jun 30, 2021, 3:04 AM

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Look at which side is opposite to angleA

split ridge Jun 30, 2021, 3:04 AM

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angle b

undone dock Jun 30, 2021, 3:04 AM

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Side not angle

split ridge Jun 30, 2021, 3:05 AM

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C

undone dock Jun 30, 2021, 3:06 AM

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What's the side length of the side that's opposite to AngleA I mean

split ridge Jun 30, 2021, 3:06 AM

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idk

undone dock Jun 30, 2021, 3:07 AM

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Think about this

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And just fill in the gaps

split ridge Jun 30, 2021, 3:09 AM

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thx

void reef Jun 30, 2021, 3:19 AM

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woven pollen Do you think this data is "normally" distributed? If so, use the standard erro...

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i understood everything

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except the yellow part

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what's that z?

slim elbow Jun 30, 2021, 3:22 AM

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Can a problem like this can be solved without LCM? If so, will the answer be different?

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,rotate

ocean sealBOT Jun 30, 2021, 3:23 AM

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flat gust Jun 30, 2021, 3:31 AM

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Ummm im pretty sure you need the lcm so that you can actually add or minus them.

alpine sable Jun 30, 2021, 3:53 AM

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help pls

full wasp Jun 30, 2021, 3:55 AM

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me when the differential equation

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well you have h'(t) = 1.4t + 5 so how would u go about finding h(t)

alpine sable Jun 30, 2021, 3:56 AM

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huh

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o

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yes

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antiderivative

full wasp Jun 30, 2021, 3:57 AM

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yes and then use the boundary condition to find the value of c

alpine sable Jun 30, 2021, 4:00 AM

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full wasp yes and then use the boundary condition to find the value of c

so itd be .7x^2+5x+15 right?

full wasp Jun 30, 2021, 4:00 AM

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i think so

alpine sable Jun 30, 2021, 4:00 AM

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ok thank you

woven pollen Jun 30, 2021, 4:04 AM

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void reef what's that z?

In your case z=1.96. And this is what you multiply the Standard Error by to get your confidence interval, at the 95% level. Different levels of confidence (e.g. 90%) will have a different z value. Most of us have memorized the 1.96 for z, because 95% confident intervals are so commonly used.

warped phoenix Jun 30, 2021, 4:09 AM

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@full wasp wdym theres more than 3 distinct roots

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i did the math wrong?

full wasp Jun 30, 2021, 4:10 AM

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originally you said there were two distinct roots

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if u look at it harder theres actually three distinct roots

warped phoenix Jun 30, 2021, 4:14 AM

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yeah i screwed up the math sorry

dull onyx Jun 30, 2021, 4:14 AM

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hello… i have to check if a decimal part of a number is equal to 0,5 or above but im not sure how i can do it in a program.. like how the hell would i check that

warped phoenix Jun 30, 2021, 4:14 AM

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btw, is the left side of the x axis called negative x?

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@full wasp

full wasp Jun 30, 2021, 4:15 AM

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yeah its the negative x axis

warped phoenix Jun 30, 2021, 4:15 AM

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ok awesome, ty!

lean niche Jun 30, 2021, 4:17 AM

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Hello

tall bough Jun 30, 2021, 4:22 AM

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1+1

strong knot Jun 30, 2021, 4:23 AM

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tall bough 1+1

3

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full wasp Jun 30, 2021, 4:24 AM

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no its 6+4i

muted portal Jun 30, 2021, 4:24 AM

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How do I find "b" in this piece wise function problem? I've looked up several ways and can't seem to find a way how people got "b" in their equation.

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@ me if you answer

full wasp Jun 30, 2021, 4:25 AM

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well the line segments have to line up @muted portal

muted portal Jun 30, 2021, 4:25 AM

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What do you mean by that?

full wasp Jun 30, 2021, 4:26 AM

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im assuming this is uhh

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the taxing system where higher brackets are taxed more

muted portal Jun 30, 2021, 4:26 AM

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Yes

lean niche Jun 30, 2021, 4:28 AM

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so..if i ask any q, u guys will help me ?

full wasp Jun 30, 2021, 4:29 AM

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ok hold on i need to think about this

flat apex Jun 30, 2021, 4:30 AM

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lean niche so..if i ask any q, u guys will help me ?

Yes in a channel that's not in use

full wasp Jun 30, 2021, 4:30 AM

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ok so i graphed the first part of the function

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basically if u look at it theres a break in the graph at x = 22000

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so what u have to do is set the value of "b" such that these two line segements line up

muted portal Jun 30, 2021, 4:32 AM

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Oh ok, so without the graph, how would I find "b"?

flat apex Jun 30, 2021, 4:32 AM

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B is the y-intercept no?

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In a y=mx+b function

muted portal Jun 30, 2021, 4:33 AM

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Yes

full wasp Jun 30, 2021, 4:33 AM

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well if you approach x = 22000 from the left side you have 22000 * 0.09 = some number

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but if you approach x = 22000 from the right side you have 22000 * 0.16 = some other number

muted portal Jun 30, 2021, 4:34 AM

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Ok I get what you're saying. So both of those values subtracted by each other, the 2nd equation being the 1st number?

full wasp Jun 30, 2021, 4:35 AM

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yeah what you want is 22000 * 0.16 + b = 22000 * 0.09

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and solve for b

muted portal Jun 30, 2021, 4:35 AM

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👍 Thank you so much

full wasp Jun 30, 2021, 4:35 AM

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the same goes for the other ranges of x, basically u just dont want any breaks in the graph

civic elbow Jun 30, 2021, 4:54 AM

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wait I am a little confused on a trig question can someone help? I know it is 51.08 but I wanna know the steps

untold sequoia Jun 30, 2021, 4:55 AM

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tan20=opposite/adjacent

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opposite=48tan20

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hypotenuse^2=adjacent^2+opposite^2=48^2+(48tan20)^2

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@civic elbow

civic elbow Jun 30, 2021, 4:58 AM

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So ik the opposite is 17.47

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I wanna know just without the opposite how I can find the hypotenuse with cos

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so cos(20)=48/y?

untold sequoia Jun 30, 2021, 4:59 AM

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civic elbow so cos(20)=48/y?

yep

civic elbow Jun 30, 2021, 5:00 AM

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Ya then you can multiply 9

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then divide cos(20)

untold sequoia Jun 30, 2021, 5:00 AM

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wt?

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why did you multiply with 9?

civic elbow Jun 30, 2021, 5:03 AM

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eh just to move y on the left side

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that is what our teachers told us to do

twin haven Jun 30, 2021, 5:30 AM

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start with numerator

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then change of base

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did you get that @tired hamlet ?

tired hamlet Jun 30, 2021, 5:37 AM

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No wdym

twin haven Jun 30, 2021, 5:37 AM

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is it a test?

tired hamlet Jun 30, 2021, 5:39 AM

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No homework

vale wigeon Jun 30, 2021, 5:40 AM

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log(23)? where are you getting 23 from

twin haven Jun 30, 2021, 5:41 AM

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nope jb8

tired hamlet Jun 30, 2021, 5:41 AM

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Oh wrong problem lol I was looking at a different one on my screen

karmic zodiac Jun 30, 2021, 5:44 AM

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Hey, can someone explain why πR2 - πr2 = π(R2- r2)

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Like, not the meaning of the formula or anything, just the algebra stuff

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πR² - πr² = π(R²- r²)
Where did the second π go?

tired hamlet Jun 30, 2021, 5:46 AM

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It gets distributed to the (R2-r2)

robust spindle Jun 30, 2021, 5:47 AM

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karmic zodiac πR² - πr² = π(R²- r²) Where did the second π go?

distributive law, the pi is common in both terms

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its like A * (B - C) = AB - AC

tired hamlet Jun 30, 2021, 5:48 AM

#

It’s πr2 and π-r2

karmic zodiac Jun 30, 2021, 5:49 AM

#

OHHHHH

#

Ok ok ty

#

I bugged for a second

#

Thank you both :)

alpine sable Jun 30, 2021, 6:45 AM

#

is -1 - x the same as x - 1?

muted portal Jun 30, 2021, 6:49 AM

#

alpine sable is -1 - x the same as x - 1?

No

#

-1-x =/= x-1

#

Because the x on the left side is negative

#

and the other is positive, therefore, it's not a true statement

cobalt coyote Jun 30, 2021, 6:56 AM

#

Doesn't sinc function is an acceptable wave function

royal magnet Jun 30, 2021, 7:08 AM

#

#

can somebody help

ionic jewel Jun 30, 2021, 7:09 AM

#

i wouldn't recommend taking your pictures while ur jumping out of a train

jagged imp Jun 30, 2021, 7:09 AM

#

can you take a worse picture next time

royal magnet Jun 30, 2021, 7:09 AM

#

no like i can type it too

#

i need help

#

in that sum

ionic jewel Jun 30, 2021, 7:09 AM

#

we literally cannot read it

royal magnet Jun 30, 2021, 7:10 AM

#

its (36a^8) ^-1/2 (125a^15) ^1/3

#

this is the sum

thorn kindle Jun 30, 2021, 7:10 AM

#

It's not a sum

#

That is a product

ionic jewel Jun 30, 2021, 7:11 AM

#

okay fantastic, distribute the exponents then simplify

royal magnet Jun 30, 2021, 7:11 AM

#

ik

#

sry

#

can u help tho

thorn kindle Jun 30, 2021, 7:11 AM

#

Think about it

#

What is (a^b)^c

royal magnet Jun 30, 2021, 7:11 AM

#

the power

royal magnet Jun 30, 2021, 7:12 AM

#

ionic jewel okay fantastic, distribute the exponents then simplify

how i tried it and i got a very long number

thorn kindle Jun 30, 2021, 7:12 AM

#

What is (5^2)^3

royal magnet Jun 30, 2021, 7:12 AM

#

like 2 is the power of 5 and 3 is the power of both

#

i need help

#

fast

#

somebody

#

??

ocean sealBOT Jun 30, 2021, 7:19 AM

#

Result:

onyx chasm Jun 30, 2021, 7:21 AM

#

royal magnet the power

Simplify (a^b)^c

alpine sable Jun 30, 2021, 7:23 AM

#

What is vanishing Ricci curvature?

royal magnet Jun 30, 2021, 7:25 AM

#

onyx chasm Simplify (a^b)^c

how

onyx chasm Jun 30, 2021, 7:26 AM

#

Such that theres only 1 exponential

spiral solar Jun 30, 2021, 7:30 AM

#

(a^b)^c = (a)^bc

rich basin Jun 30, 2021, 7:35 AM

#

Screen_Shot_2021-06-30_at_5.35.31_pm.png

#

why does it only include 3 answers and not all 5

#

my bad

#

i got a similar issue with another question

jagged imp Jun 30, 2021, 7:36 AM

#

,w solve sin^2(x)=1-cosx on [-pi,pi]

ocean sealBOT Jun 30, 2021, 7:36 AM

#

Results provided by WolframAlpha

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jagged imp Jun 30, 2021, 7:36 AM

#

looks like theres only 3 solns

rich basin Jun 30, 2021, 7:39 AM

#

Screen_Shot_2021-06-30_at_5.39.12_pm.png

#

same range

#

,w solve cos(2x)=sinx on [-pi,pi]

ocean sealBOT Jun 30, 2021, 7:40 AM

#

Results provided by WolframAlpha

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rich basin Jun 30, 2021, 7:41 AM

#

but wouldn't -pi/6 work s well

jagged imp Jun 30, 2021, 7:42 AM

#

1/2=-1/2?

#

lhs is 1/2 and rhs is -1/2

#

seems to not work imo

small holly Jun 30, 2021, 8:20 AM

#

royal magnet how

do you still need help?

obtuse valve Jun 30, 2021, 9:21 AM

#

can someone help me ?

#

Yakınsaktır mean converges

#

Iraksaktır mean diverges

#

how can i find that series function

placid zinc Jun 30, 2021, 9:48 AM

#

The answers should give a pretty solid hint - What's the taylor series of ln(1 + x)? Your book may have it

#

@obtuse valve

obtuse valve Jun 30, 2021, 9:48 AM

#

i dont have

#

how did u find

placid zinc Jun 30, 2021, 9:50 AM

#

You can find it by hand too, or Google if you're feeling lazy

#

Or Wolfram Alpha is a good tool

#

,w Taylor series ln(1 - x)

ocean sealBOT Jun 30, 2021, 9:51 AM

#

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

placid zinc Jun 30, 2021, 9:51 AM

#

I changed my mind I care more about ln(1 - x)

#

Looks pretty familiar

dire patrol Jun 30, 2021, 9:56 AM

#

obtuse valve Jun 30, 2021, 9:56 AM

#

thx

dire patrol Jun 30, 2021, 9:56 AM

#

anyone know how to do this

#

all i know is v max is when x is at centre

#

im a bit stuck

placid zinc Jun 30, 2021, 9:58 AM

#

Allowed to use calculus?

dire patrol Jun 30, 2021, 10:00 AM

#

ye

#

ofc

placid zinc Jun 30, 2021, 10:00 AM

#

So the equation describing the motion can be:
s(t) = asin(bt)

dire patrol Jun 30, 2021, 10:01 AM

#

s(t) = a sin(bt+ alpha) ?

#

or no

placid zinc Jun 30, 2021, 10:01 AM

#

The only thing the alpha would change is the start time. As you'll see when you start taking derivatives, it doesn't matter anyway

dire patrol Jun 30, 2021, 10:02 AM

#

OHHH

#

wait hold on

#

ok ok

#

so do we not consider it at the start

#

if it doesnt say anything in the question

placid zinc Jun 30, 2021, 10:02 AM

#

More like, we can make our life simpler by just letting it start at the midpoint

dire patrol Jun 30, 2021, 10:02 AM

#

alright

#

ok ok

#

would we derive s(t) twice

#

to get acceleration ?

placid zinc Jun 30, 2021, 10:03 AM

#

Yeye

dire patrol Jun 30, 2021, 10:03 AM

#

-n^2 x ?

#

im not sujre what to do with max velocity and max accel tho

placid zinc Jun 30, 2021, 10:03 AM

#

Then that would tell you what a and b are

dire patrol Jun 30, 2021, 10:03 AM

#

is max accel when velocity is 0?

placid zinc Jun 30, 2021, 10:04 AM

#

Yes

#

Wait no haha

dire patrol Jun 30, 2021, 10:04 AM

#

oh >

#

wait i think its the other way raound isnt it

placid zinc Jun 30, 2021, 10:04 AM

#

Other way around. Max accel is when a'(t) = 0

dire patrol Jun 30, 2021, 10:04 AM

#

ye

obtuse valve Jun 30, 2021, 10:04 AM

#

,w Taylor series 1/2-2x

ocean sealBOT Jun 30, 2021, 10:04 AM

#

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

placid zinc Jun 30, 2021, 10:05 AM

#

Mind you, the maximum of abcos(bx) doesn't need an algebraic proof. The max is when cos = 1

dire patrol Jun 30, 2021, 10:05 AM

#

wait ok ok

#

ill try derive twice see where i get

#

wait

#

actually

#

how do u know it starts at sin

#

because it could start at cos

#

it doesnt say anything in the question

placid zinc Jun 30, 2021, 10:06 AM

#

That's the same idea as the alpha

dire patrol Jun 30, 2021, 10:06 AM

#

about the initial condition

placid zinc Jun 30, 2021, 10:06 AM

#

We have control of the start time, so start at the simplest possible time

dire patrol Jun 30, 2021, 10:06 AM

#

ok now i am confused ahah

placid zinc Jun 30, 2021, 10:07 AM

#

All we care about is the simple harmonic motion (motion is a sinudoid)

So let it be any sinusoid. We'll choose the easiest one to work with.

#

Yeah you could make it cos(bx + 1) but ehh.

alpine sable Jun 30, 2021, 10:08 AM

#

Kaynex, is it alright if I ask a question next after this?

dire patrol Jun 30, 2021, 10:08 AM

#

wait

placid zinc Jun 30, 2021, 10:08 AM

#

Ping me in a different channel I'll help there

dire patrol Jun 30, 2021, 10:08 AM

#

it doesnt even make sense

#

cause we have displacement in terms of time

#

if i want vmax dont i need like velocity in terms of displacement

#

like v^2=n^2(a^2-x^2) ?

placid zinc Jun 30, 2021, 10:09 AM

#

Nah vmax is just a velocity

#

Ignore the time and place it happens

#

I suppose I already know in advance that in asin(bt + alpha)

a and b change the velocity and acceleration

alpha does not

#

If you're wary of this, it isn't a big deal to include it

dire patrol Jun 30, 2021, 10:10 AM

#

ok so what do i do after finding x dot

#

idk what to sub in

placid zinc Jun 30, 2021, 10:10 AM

#

v(t) = absin(bt + α)

#

That is maximized when sin = 1. So the max actually is just ab

#

Gives us ab = 3

dire patrol Jun 30, 2021, 10:11 AM

#

OHH

#

WAIT I HAVE IT

#

thank u

#

i got it all g

alpine sable Jun 30, 2021, 10:12 AM

#

good job

placid zinc Jun 30, 2021, 10:12 AM

#

Happy to help. Feel free to ask if you have any other questions.

bitter yew Jun 30, 2021, 10:18 AM

#

can someone help with this?

dull onyx Jun 30, 2021, 10:20 AM

#

how would i find the derivative of f(x) = x^2 e^-2x

#

is it (f g)’

#

and then the derivative of e^f(x)?

glass lichen Jun 30, 2021, 10:22 AM

#

dull onyx is it (f g)’

it's a product so yeah, use product rule

dull onyx Jun 30, 2021, 10:23 AM

#

ah okay thank u

#

getting into monotonic functions and im hella confused

tribal geyser Jun 30, 2021, 10:24 AM

#

Can someone pls help with 5) b and c

#

I don’t get what it means

glass lichen Jun 30, 2021, 10:25 AM

#

negative definite means the function is never non-negative

#

f(x)<0 for all x

tribal geyser Jun 30, 2021, 10:26 AM

#

Ohh and positive means it’s always positive?

glass lichen Jun 30, 2021, 10:26 AM

#

yes

tribal geyser Jun 30, 2021, 10:26 AM

#

Sorry could u help with another question

#

glass lichen Jun 30, 2021, 10:27 AM

#

make it into a quadratic, then use discriminant

tribal geyser Jun 30, 2021, 10:27 AM

#

I did

#

I’ll show u

#

#

Is that right so far?

#

@glass lichen

#

And then I thought to do p^2-4(x+1)

glass lichen Jun 30, 2021, 10:30 AM

#

no

tribal geyser Jun 30, 2021, 10:30 AM

#

Oh

glass lichen Jun 30, 2021, 10:31 AM

#

$x^2-(p-1)x+1=0$

ocean sealBOT Jun 30, 2021, 10:31 AM

#

Mosh

tribal geyser Jun 30, 2021, 10:33 AM

#

If I do the discriminate for that it would be p^2-2p-3

#

Um sorry the channel is taken

dull onyx Jun 30, 2021, 10:34 AM

#

yep sorry just saw!!

glass lichen Jun 30, 2021, 10:34 AM

#

$(-(p-1))^2-4(1)(1)\geq 0$

ocean sealBOT Jun 30, 2021, 10:34 AM

#

Mosh

tribal geyser Jun 30, 2021, 10:34 AM

#

Yes

glass lichen Jun 30, 2021, 10:34 AM

#

so just solve that inequality

tribal geyser Jun 30, 2021, 10:35 AM

#

I did but I got p^2-2p-3

glass lichen Jun 30, 2021, 10:35 AM

#

yeah looks right

tribal geyser Jun 30, 2021, 10:35 AM

#

So shouldn’t it be x less than or equal to -1 or x is greater than or equal to 3

#

I mean p

glass lichen Jun 30, 2021, 10:36 AM

#

yes

tribal geyser Jun 30, 2021, 10:36 AM

#

Ahh okay thanks

glass lichen Jun 30, 2021, 10:36 AM

#

$p\in (-\infty , -1]\cup[3,\infty )$

ocean sealBOT Jun 30, 2021, 10:36 AM

#

Mosh

dull onyx Jun 30, 2021, 10:38 AM

#

i don’t understand how the -x got factored ㅠㅠ

#

(sorry if ur not finished^^)

shell widget Jun 30, 2021, 10:39 AM

#

-x = 2x - 3x

#

As to why they chose 2 and -3, that's because when we multiply 2 and -3, we get -6(the term without any x)

dull onyx Jun 30, 2021, 10:40 AM

#

Ohhh

#

thank u i was so lost

tribal geyser Jun 30, 2021, 10:42 AM

#

Hey guys how can an angle be bigger than 270 but less than 180

#

Is there a typo or am I just blind

shell widget Jun 30, 2021, 10:43 AM

#

it says less than 270 and bigger than 180

tribal geyser Jun 30, 2021, 10:43 AM

#

Or I am blind

#

Whoops thank you

crisp sleet Jun 30, 2021, 10:45 AM

#

How do i verify

#

Its 1a)

shell widget Jun 30, 2021, 10:50 AM

#

@crisp sleet You can find f(1). Then find f'(x) and show that it's > 0 and so for all x>=1, we have f(x) >= f(1)

#

For the other part, you should know that x^2 / (1 + x^2 ) < 1 for all x

#

since the denominator is larger than the numerator

inland agate Jun 30, 2021, 11:20 AM

#

i need help with differential equations

#

specifically with modelling problems

glass lichen Jun 30, 2021, 11:21 AM

#

inland agate i need help with differential equations

again, dont ask to ask

dire patrol Jun 30, 2021, 11:34 AM

#

#

how do i do this

#

im new to this concept

#

so im lost

#

i know F= m times a

vale wigeon Jun 30, 2021, 11:38 AM

#

you have a force which varies with time

#

you're told that F varies linearly from t=0 to t=20 and that F(0) = 20 and F(20) = 0

#

it does not actually matter that this time-dependent quantity is a force, as far as part a goes

dire patrol Jun 30, 2021, 11:39 AM

#

ok so where should i start

#

@vale wigeon

vale wigeon Jun 30, 2021, 11:42 AM

#

you are told that $F(t) = at + b$ for some constants $a$ and $b$

ocean sealBOT Jun 30, 2021, 11:42 AM

#

Ann

dire patrol Jun 30, 2021, 11:42 AM

#

wait what

#

where did this come from

vale wigeon Jun 30, 2021, 11:42 AM

#

a force that decreases uniformly

#

i.e. decreases at a constant rate

dire patrol Jun 30, 2021, 11:42 AM

#

oh

vale wigeon Jun 30, 2021, 11:42 AM

#

i.e. is linear as a function of time

dire patrol Jun 30, 2021, 11:44 AM

#

ohh okj

#

ye i got it now thanks

#

sory but i dont know how to do part b aswell ahah

#

#

@vale wigeon

#

how would i do part b

vale wigeon Jun 30, 2021, 11:50 AM

#

this is where F = ma comes in

#

you have found that $F(t) = 20 - t$, right?

ocean sealBOT Jun 30, 2021, 11:51 AM

#

Ann

dire patrol Jun 30, 2021, 11:51 AM

#

yes

vale wigeon Jun 30, 2021, 11:51 AM

#

and you know that the particle has a mass of 10 kg

#

thus you know its acceleration for $0 \leq t \leq 20$ is described by $a(t) = 2 - 0.1t$

ocean sealBOT Jun 30, 2021, 11:51 AM

#

Ann

dire patrol Jun 30, 2021, 11:52 AM

#

wait what

#

i am confused how u got to that step

#

OH WAIT

#

nah i get it

#

ok ok

vale wigeon Jun 30, 2021, 11:55 AM

#

so you need to find v(20)

dire patrol Jun 30, 2021, 11:55 AM

#

i integrated

vale wigeon Jun 30, 2021, 11:55 AM

#

knowing that v' = a, and v(0) = 0

dire patrol Jun 30, 2021, 11:57 AM

#

right ok i got it

#

sory to bother but how do i do c @vale wigeon

#

i tried integrating velocity

#

then let x=0 but i got t=60

#

when answer is t=5

vale wigeon Jun 30, 2021, 12:05 PM

#

what did you get for the velocity at t=20?

dire patrol Jun 30, 2021, 12:05 PM

#

20ms^-1

vale wigeon Jun 30, 2021, 12:06 PM

#

20 m/s, ok

#

gonna take your word for that

#

now we have a force of 40N slowing our particle down

#

remember our particle has a mass of 10 kg

#

what is the deceleration of the particle?

dire patrol Jun 30, 2021, 12:07 PM

#

wait

#

do i put it into the formula

#

f=ma

#

-40=10a?

#

im not sure

vale wigeon Jun 30, 2021, 12:10 PM

#

F = ma yes.

#

you should get a deceleration of 4 m/s^2.

dire patrol Jun 30, 2021, 12:10 PM

#

yes

#

ok where am i meant to use that now

#

wait

#

do i let f=0
?

#

wait nvm

vale wigeon Jun 30, 2021, 12:17 PM

#

your particle starts out with a velocity of 20 m/s and is decelerating at 4 m/s^2; how long does it take before the particle is at rest?

rich basin Jun 30, 2021, 12:18 PM

#

,w solve 3 tan(2θ) = 2tan(θ) on [-pi,pi]

ocean sealBOT Jun 30, 2021, 12:18 PM

#

Results provided by WolframAlpha

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dire patrol Jun 30, 2021, 12:19 PM

#

i not sure

#

what to sub it into'

vale wigeon Jun 30, 2021, 12:20 PM

#

you're overthinking it woa

rich basin Jun 30, 2021, 12:33 PM

#

,w solve sin x = cos x on [0, 2pi]

ocean sealBOT Jun 30, 2021, 12:33 PM

#

Results provided by WolframAlpha

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glass lichen Jun 30, 2021, 12:38 PM

#

rich basin ,w solve sin x = cos x on [0, 2pi]

#bots or just use regular wolfram...

#

if you dont have a question, dont use the help channel

loud pagoda Jun 30, 2021, 12:54 PM

#

Prove that f is continuous if for all monotonic sequences (x_n) converging to x_0 we have lim f(x_n) = f(x_0)
I tried using the theorem that all sequences have monotonic subsequences, and that f(x_n) is a sequence that is a subsequnce of some other sequence f(x_k). Now, f(x_k) is bounded because its monotonic subsequence converges. I am unable to show lim f(x_k) = lim f(x_n)

#

Kindly ping me if you reply

#

<@&286206848099549185>

woeful pulsar Jun 30, 2021, 1:25 PM

#

loud pagoda Prove that f is continuous if for all monotonic sequences (x_n) converging to x_...

all [converging] sequences have a monotonic subsequence
So you shown that a subsequence converges to f(x_0). However, the other elements are kinda in the way. Is there a better way to perhaps rearrange the sequence to get rid of the non-monotonic bits?

#

or use epsilon delta

nova anvil Jun 30, 2021, 1:40 PM

#

a contrapositive argument works well here right, suppose f is not continuous on x_0, then you can construct this sequence inductively which doesnt converge to f(x0) even though x_n -> x0

#

by shrinking the delta balls

loud pagoda Jun 30, 2021, 1:42 PM

#

Hey wdym by construct a sequence inductively?

nova anvil Jun 30, 2021, 1:45 PM

#

loud pagoda Hey wdym by construct a sequence inductively?

if it was not continuous at x_0 then theres an epsilon ball around f(x_0) so that for all delta ball no matter how small around x_0, the image of the ball through f will contain points outside the epsilon ball

#

so pick a ball of radius 1, find a point in that ball that gets mapped outside epsilon ball, then another point from ball of radius 1/2 mapping outside ep-ball around f(x_0), and so on..., creating a sequence x_n converging to x_0

loud pagoda Jun 30, 2021, 1:47 PM

#

Oh right!!

#

Got it thx

pale haven Jun 30, 2021, 1:49 PM

#

hullo guys
 If the degree of accuracy is not specified in the question, and if the
answer is not exact, give the answer to three significant figures. Give
answers in degrees to one decimal place
what is meant by this. It was on my exam paper

#

a past paper

nova anvil Jun 30, 2021, 1:50 PM

#

for example for non-angle answers if you got sqrt(2) as your answer then write 1.41. and if your answer is some angle then you write it in degree form to 1 d.p.

#

wait nvm

#

ignore the first part since sqrt(2) is exact i guess

pale haven Jun 30, 2021, 1:51 PM

#

what is meant by exact in this context?

nova anvil Jun 30, 2021, 1:51 PM

#

yea I'm not sure

quartz stone Jun 30, 2021, 1:52 PM

#

It probably means not algebraic, although that even may be too far

#

With my exams, the maximum you'd go to before putting your answer to 3dp is probably: using fractions; using pi; using surds

alpine sable Jun 30, 2021, 1:53 PM

#

quartz stone Jun 30, 2021, 1:54 PM

#

So if you have a sin / arcsin in there, they probably want dp

quartz stone Jun 30, 2021, 1:54 PM

#

alpine sable

u doing calculus?

alpine sable Jun 30, 2021, 1:55 PM

#

yes

#

i dont know how to do this at all lol

quartz stone Jun 30, 2021, 1:56 PM

#

I mean they probably want you to assume you're making a rectangle

#

Altho u could be cheeky.

alpine sable Jun 30, 2021, 1:57 PM

#

no i fr dont know how to answer that

#

im literally asking my classmates about it xd

quartz stone Jun 30, 2021, 1:57 PM

#

I'll check if rectangle is the best case but if we assume this (this is what they usually do), then you have the following setup:

alpine sable Jun 30, 2021, 1:58 PM

#

Btw it notes that its a rectangle yes

#

graceful sierra Jun 30, 2021, 1:58 PM

#

alpine sable no i fr dont know how to answer that

Find the Area expression and differentiate it and equate it to zero

alpine sable Jun 30, 2021, 1:58 PM

#

still not sure how to get the area expression xd like i literally need someone to explain it to me D:

quartz stone Jun 30, 2021, 1:58 PM

#

I can

#

I'm making a drawing

alpine sable Jun 30, 2021, 1:58 PM

#

okay

quartz stone Jun 30, 2021, 2:00 PM

#

#

This is your house and rope, right?

alpine sable Jun 30, 2021, 2:00 PM

#

okay

graceful sierra Jun 30, 2021, 2:00 PM

#

alpine sable still not sure how to get the area expression xd like i literally need someone t...

thats ^

quartz stone Jun 30, 2021, 2:00 PM

#

And it says that you have 90 metres of rope

#

So what can you say about a and b?

graceful sierra Jun 30, 2021, 2:00 PM

#

alpine sable okay

When does a rectangle have maximum area?

alpine sable Jun 30, 2021, 2:01 PM

#

uh so

#

wait so you have only?

quartz stone Jun 30, 2021, 2:01 PM

#

alpine sable wait so you have **only**?

only 90 metres of rope?

alpine sable Jun 30, 2021, 2:01 PM

#

wait

#

oh

#

yeah

#

you do only have 90

#

so basically you distribute it to both A and B?

quartz stone Jun 30, 2021, 2:02 PM

#

Yes

#

You want to figure that out

alpine sable Jun 30, 2021, 2:03 PM

#

Ok so what do I do is

#

Divide? ok im not sure how you're going to do that

quartz stone Jun 30, 2021, 2:04 PM

#

You need to use calculus, but first, is it possible to make an expression for the area of the rectangle just given side a?

#

As in, knowing side a, can you find out side b

alpine sable Jun 30, 2021, 2:04 PM

#

quartz stone You need to use calculus, but first, is it possible to make an expression for th...

no

quartz stone Jun 30, 2021, 2:05 PM

#

alpine sable no

why not?

alpine sable Jun 30, 2021, 2:05 PM

#

because if you did, side a will be using all of the rope?

#

🤷

quartz stone Jun 30, 2021, 2:06 PM

#

alpine sable because if you did, side a will be using all of the rope?

What I mean, is if you know how long side a is, do you know how long side b is?

#

For any configuration of the rectangle

alpine sable Jun 30, 2021, 2:07 PM

#

I don't think you do, side b will be longer than that because that would be a square?

#

wait let me clarify that

quartz stone Jun 30, 2021, 2:07 PM

#

You know that there are 90 metres of rope

alpine sable Jun 30, 2021, 2:08 PM

#

yes

quartz stone Jun 30, 2021, 2:08 PM

#

So can you say anything about the sum of the rope used in all the sides?

alpine sable Jun 30, 2021, 2:08 PM

#

ohhhhhh

#

I am not sure on how to find the sum of the rope of all sides, is there some sort of formula to know?

quartz stone Jun 30, 2021, 2:08 PM

#

quartz stone

use this picture

#

smth + smth + smth = 90 metres

alpine sable Jun 30, 2021, 2:09 PM

#

I can't possibly divide it to 3 because that would be a square

graceful sierra Jun 30, 2021, 2:09 PM

#

alpine sable I can't possibly divide it to 3 because that would be a square

man.

quartz stone Jun 30, 2021, 2:09 PM

#

a and b are different / don't have to be the same

alpine sable Jun 30, 2021, 2:09 PM

#

I dont know

#

XD

quartz stone Jun 30, 2021, 2:10 PM

#

What is the perimeter of the red lines?

graceful sierra Jun 30, 2021, 2:10 PM

#

see the pic,, and relate a and b , and the length of the rope

alpine sable Jun 30, 2021, 2:11 PM

#

okay let me think

#

45 = b,
22.5 = a?

#

ok help me im dumb

graceful sierra Jun 30, 2021, 2:13 PM

#

NO

alpine sable Jun 30, 2021, 2:13 PM

#

LOL

graceful sierra Jun 30, 2021, 2:13 PM

#

I mean that is wrong

quartz stone Jun 30, 2021, 2:13 PM

#

Have you done algebra?

alpine sable Jun 30, 2021, 2:13 PM

#

i never learned anything since online classes happened

graceful sierra Jun 30, 2021, 2:14 PM

#

The general expression bro.

quartz stone Jun 30, 2021, 2:14 PM

#

I mean it would be a kind thing to give the answer, but at the same time, it's going to be useful for jezreel in the future to know maths

alpine sable Jun 30, 2021, 2:14 PM

#

ouef

quartz stone Jun 30, 2021, 2:15 PM

#

alpine sable i never learned anything since online classes happened

Have you ever seen expressions like a + b = 10, or been asked to solve for a in a^2 + 5a - 10 = 0 ?

alpine sable Jun 30, 2021, 2:15 PM

#

i used to xd

quartz stone Jun 30, 2021, 2:15 PM

#

ok so that's good

alpine sable Jun 30, 2021, 2:15 PM

#

but like i dont even like math so i forgot either ways

quartz stone Jun 30, 2021, 2:15 PM

#

😦

alpine sable Jun 30, 2021, 2:15 PM

#

meme

#

XZD

quartz stone Jun 30, 2021, 2:15 PM

#

xd

graceful sierra Jun 30, 2021, 2:15 PM

#

So see the pic jezreel

quartz stone Jun 30, 2021, 2:15 PM

#

Do you know how to find the perimeter of a shape?

alpine sable Jun 30, 2021, 2:15 PM

#

im literally googling 💀

#

XD

#

n o

quartz stone Jun 30, 2021, 2:16 PM

#

#

What's the perimeter of this shape?

alpine sable Jun 30, 2021, 2:16 PM

#

14 + 8?

#

idk

quartz stone Jun 30, 2021, 2:16 PM

#

Ok epic

alpine sable Jun 30, 2021, 2:16 PM

#

xd

graceful sierra Jun 30, 2021, 2:17 PM

#

quartz stone

Enough man.

quartz stone Jun 30, 2021, 2:17 PM

#

quartz stone

now do it for this shape, but remember that the house isn't part of the rope

alpine sable Jun 30, 2021, 2:17 PM

#

but like the thing is how could you do it with 3 sides tho idk

quartz stone Jun 30, 2021, 2:17 PM

#

alpine sable but like the thing is how could you do it with 3 sides tho idk

you add up each side

quartz stone Jun 30, 2021, 2:17 PM

#

graceful sierra Enough man.

wdym?

alpine sable Jun 30, 2021, 2:17 PM

#

i mean like if i said

#

30

#

its going to be a square right? im not sure

graceful sierra Jun 30, 2021, 2:18 PM

#

I mean say the expression already... He will probably not get the expr by himself . but next time he'll use this thing

alpine sable Jun 30, 2021, 2:18 PM

#

XD

quartz stone Jun 30, 2021, 2:18 PM

#

Ah ok

#

2a + b = 90

#

does this make sense?

alpine sable Jun 30, 2021, 2:18 PM

#

a

#

yes

#

no

#

yes and no

quartz stone Jun 30, 2021, 2:18 PM

#

So the rope is 90 metres

graceful sierra Jun 30, 2021, 2:18 PM

#

a + a+ b = fence length

quartz stone Jun 30, 2021, 2:18 PM

#

And you have the sides a, a, and b in the fence

alpine sable Jun 30, 2021, 2:18 PM

#

ok

quartz stone Jun 30, 2021, 2:19 PM

#

graceful sierra I mean say the expression already... He will probably not get the expr by himsel...

thanks for ur tip

alpine sable Jun 30, 2021, 2:19 PM

#

zoomEyes

graceful sierra Jun 30, 2021, 2:19 PM

#

You get it?

#

@alpine sable

alpine sable Jun 30, 2021, 2:19 PM

#

but how are you going to distribute it at all 💀

graceful sierra Jun 30, 2021, 2:20 PM

#

see the drawing once.

quartz stone Jun 30, 2021, 2:20 PM

#

Calculus 👀

graceful sierra Jun 30, 2021, 2:20 PM

#

alpine sable but how are you going to distribute it at all 💀

We are not finished yet

quartz stone Jun 30, 2021, 2:20 PM

#

The area of the rectangle is a * b, right?

alpine sable Jun 30, 2021, 2:20 PM

#

ok

quartz stone Jun 30, 2021, 2:20 PM

#

quartz stone `2a + b = 90`

And you can define b in terms of a

#

What is b, in terms of a?

alpine sable Jun 30, 2021, 2:21 PM

#

45? idf

#

kms

quartz stone Jun 30, 2021, 2:21 PM

#

It's an algebraic expression, not a number

alpine sable Jun 30, 2021, 2:21 PM

#

heh

quartz stone Jun 30, 2021, 2:21 PM

#

quartz stone `2a + b = 90`

Rearrange this to get b

graceful sierra Jun 30, 2021, 2:22 PM

#

alpine sable 45? idf

we havent found a and b yet .. how come you say 45?

alpine sable Jun 30, 2021, 2:22 PM

#

2a - 90 = b?

#

XD

quartz stone Jun 30, 2021, 2:22 PM

#

EPIC

#

So you know b = 2a - 90

#

So can you define the area of the rectangle, a * b, using just a

alpine sable Jun 30, 2021, 2:23 PM

#

um

quartz stone Jun 30, 2021, 2:23 PM

#

given that b is the same thing as 2a - 90

alpine sable Jun 30, 2021, 2:23 PM

#

okay

quartz stone Jun 30, 2021, 2:23 PM

#

u can do it?

alpine sable Jun 30, 2021, 2:24 PM

#

a * 2a - 90? idfk

quartz stone Jun 30, 2021, 2:24 PM

#

ye

#

a * (2a - 90)

#

brackets are useful just for order of operations

alpine sable Jun 30, 2021, 2:24 PM

#

ijay

#

*okay

#

a * (2a - 90)

quartz stone Jun 30, 2021, 2:25 PM

#

Wait

#

90 - 2a

alpine sable Jun 30, 2021, 2:25 PM

#

88a?

#

xd

quartz stone Jun 30, 2021, 2:25 PM

#

alpine sable 2a - 90 = b?

This should be 90 - 2a, sorry

#

Does that make sense?

alpine sable Jun 30, 2021, 2:25 PM

#

because 90 is bigger than 2? idk

quartz stone Jun 30, 2021, 2:25 PM

#

But you were pretty close

quartz stone Jun 30, 2021, 2:26 PM

#

alpine sable because 90 is bigger than 2? idk

You do the same thing to both sides of the equation, because if both sides are equal, if you do the same thing to them, they'll still be equal

alpine sable Jun 30, 2021, 2:26 PM

#

okay

quartz stone Jun 30, 2021, 2:26 PM

#

2a + b = 90
Subtract 2a from both sides
2a + b - 2a = 90 - 2a
b = 90 - 2a

alpine sable Jun 30, 2021, 2:27 PM

#

why did it become - 2a

quartz stone Jun 30, 2021, 2:27 PM

#

alpine sable why did it become - 2a

why did i choose -2a?

alpine sable Jun 30, 2021, 2:27 PM

#

because its the opposite side?

quartz stone Jun 30, 2021, 2:27 PM

#

We add -2a to both sides, because if we do the same thing to both sides, the equation is still true

alpine sable Jun 30, 2021, 2:28 PM

#

ohh

quartz stone Jun 30, 2021, 2:28 PM

#

So you see on the graph

#

There's a point where the area is maximum, right?

alpine sable Jun 30, 2021, 2:29 PM

#

uh

quartz stone Jun 30, 2021, 2:30 PM

#

As in there's a value of a where you have the greatest area

alpine sable Jun 30, 2021, 2:30 PM

#

yes yes

#

like the peak?

quartz stone Jun 30, 2021, 2:30 PM

#

Yes

alpine sable Jun 30, 2021, 2:30 PM

#

ok

quartz stone Jun 30, 2021, 2:30 PM

#

Exactly

#

So you use calculus to find this peak

alpine sable Jun 30, 2021, 2:30 PM

#

yeah my dumb ass doesnt know what calculus to use here xd

quartz stone Jun 30, 2021, 2:31 PM

#

Firstly, a(90-2a) = 90a - 2a^2

#

(I mean this equation you don't even need calculus, but they probably want you to use it )

alpine sable Jun 30, 2021, 2:31 PM

#

yea its calculus

#

the subject

quartz stone Jun 30, 2021, 2:31 PM

#

ye

quartz stone Jun 30, 2021, 2:31 PM

#

quartz stone Firstly, `a(90-2a) = 90a - 2a^2`

Does this make sense?

alpine sable Jun 30, 2021, 2:32 PM

#

not really

#

like theres a lot of things that just came there randomly lol

quartz stone Jun 30, 2021, 2:32 PM

#

a * (90-2a) = a * 90 - a * 2a = 90a - 2a^2

alpine sable Jun 30, 2021, 2:33 PM

#

ok ok

#

got it

quartz stone Jun 30, 2021, 2:33 PM

#

do you know how to take derivatives?

alpine sable Jun 30, 2021, 2:33 PM

#

a

#

:dead:

quartz stone Jun 30, 2021, 2:33 PM

#

$\frac{\mathrm{d}}{\mathrm{d}x}$

alpine sable Jun 30, 2021, 2:33 PM

#

nop

#

i saw it but no

ocean sealBOT Jun 30, 2021, 2:33 PM

#

TrueBoxGuy

alpine sable Jun 30, 2021, 2:34 PM

#

yes that

#

i saw that xd

quartz stone Jun 30, 2021, 2:34 PM

#

you don't know at all?

alpine sable Jun 30, 2021, 2:34 PM

#

nao

quartz stone Jun 30, 2021, 2:34 PM

#

$\frac{\mathrm{d}}{\mathrm{d}a} 90a - 2a^2$

#

Ok

ocean sealBOT Jun 30, 2021, 2:34 PM

#

TrueBoxGuy

quartz stone Jun 30, 2021, 2:35 PM

#

Basically, each term between + and -, you take the derivative of, and the derivative of $a$ is $1$ and the derivative of $a^2$ is $2a$

ocean sealBOT Jun 30, 2021, 2:35 PM

#

TrueBoxGuy

alpine sable Jun 30, 2021, 2:35 PM

#

oh no

#

xd

quartz stone Jun 30, 2021, 2:35 PM

#

derivative of 9 * smth is 9 * derivative of smth

#

Ok so try these ones:

#

Derivative of $5a$

ocean sealBOT Jun 30, 2021, 2:36 PM

#

TrueBoxGuy

quartz stone Jun 30, 2021, 2:36 PM

#

Derivative of $5a + a^2$

ocean sealBOT Jun 30, 2021, 2:36 PM

#

TrueBoxGuy

quartz stone Jun 30, 2021, 2:36 PM

#

Can u do those ones?

graceful sierra Jun 30, 2021, 2:37 PM

#

Oh man.. still going on?

alpine sable Jun 30, 2021, 2:37 PM

#

uhh

#

XD

#

i dont even know what is going on

graceful sierra Jun 30, 2021, 2:37 PM

#

Dont you know differential calculus? 🙂

alpine sable Jun 30, 2021, 2:38 PM

#

i said i literally know nothing

#

because online school sucks

#

asz

graceful sierra Jun 30, 2021, 2:38 PM

#

How do you expect to do the problem then? 🙂

alpine sable Jun 30, 2021, 2:38 PM

#

nothing

#

im hopeless

quartz stone Jun 30, 2021, 2:38 PM

#

graceful sierra How do you expect to do the problem then? 🙂

tru that

alpine sable Jun 30, 2021, 2:38 PM

#

when it comes to math 🙂

quartz stone Jun 30, 2021, 2:38 PM

#

Maybe Khan academy or another site will help

#

But later

graceful sierra Jun 30, 2021, 2:39 PM

#

You want the solution?

quartz stone Jun 30, 2021, 2:39 PM

#

It you want to catch up on what you missed

alpine sable Jun 30, 2021, 2:39 PM

#

im just doing this because the deadline of all of my requirements is just until now at 12:00 am XD

quartz stone Jun 30, 2021, 2:39 PM

#

Ye perhaps we do this step

alpine sable Jun 30, 2021, 2:39 PM

#

and my dumb ass doesnt know how to answer it 💀

quartz stone Jun 30, 2021, 2:40 PM

#

ocean seal **TrueBoxGuy**

Answer is 90 - 4a

#

You then solve for 90 - 4a = 0 to get a

#

You can calculate b using that

#

And then a * b is the area

alpine sable Jun 30, 2021, 2:41 PM

#

ok i will just

#

calculate

#

xd

#

r

graceful sierra Jun 30, 2021, 2:41 PM

#

refer this:

#

glass lichen Jun 30, 2021, 2:42 PM

#

quartz stone $\frac{\mathrm{d}}{\mathrm{d}a} 90a - 2a^2$

\dv{a}

quartz stone Jun 30, 2021, 2:42 PM

#

glass lichen \dv{a}

Cute thanks

alpine sable Jun 30, 2021, 2:45 PM

#

thank you for teaching me guys, and im sorry that i literally dont know anything

#

^not really but

quartz stone Jun 30, 2021, 2:45 PM

#

alpine sable thank you for teaching me guys, and im sorry that i literally dont know anything

You should have the answer there 🙂

alpine sable Jun 30, 2021, 2:45 PM

#

yea

quartz stone Jun 30, 2021, 2:46 PM

#

a = 45/2, b = 45, area = 45 * 45/2

#

You're doing linear algebra or smth else?

sweet meadow Jun 30, 2021, 2:50 PM

#

May I ask a Korean high school math problem?

#

The area is calculus.

quartz stone Jun 30, 2021, 2:50 PM

#

Perhaps in another channel (BurnedGalaxy has asked a question)

sweet meadow Jun 30, 2021, 2:50 PM

#

ah sry

quartz stone Jun 30, 2021, 2:52 PM

#

sweet meadow ah sry

i will try to answer if u ask in another channel, but can't guarantee i'll be able to 🙂 (

nova shard Jun 30, 2021, 2:57 PM

#

is this right?

Screen_Shot_2021-06-30_at_10.55.38_AM.png

vocal drum Jun 30, 2021, 2:58 PM

#

exscuse me but can someone explain to me what I5I notation means |5 − 8| − |2 − 5|

nova shard Jun 30, 2021, 2:59 PM

#

nova shard is this right?

i got it by doing 2^2 - 2 - 1 which equals 1, and -1^2 - -1 -1 which equals -1. since the "formula" goes x_f - x_i, I plugged in the values, which leaves me with 1--1..

graceful sierra Jun 30, 2021, 3:00 PM

#

nova shard is this right?

right

nova shard Jun 30, 2021, 3:00 PM

#

im am idiot

#

but i was left with 1--1

#

which is 2

#

not 0

rigid smelt Jun 30, 2021, 3:00 PM

#

f(-1) isnt -1

#

but anyway

#

you can also notice that the secant line (that goes thru f(-1) and f(2)) is parallel to the x axis

#

which means that the average change is 0

nova shard Jun 30, 2021, 3:01 PM

#

rigid smelt f(-1) isnt -1

angerysad

#

i just did the math wrong

#

welp

#

thanks lads

graceful sierra Jun 30, 2021, 3:03 PM

#

nova shard <:angerysad:602329540131553290>

You can also differentiate and match the x with the interval

pseudo grotto Jun 30, 2021, 3:05 PM

#

use euclid's division lemma to show that the square of any positive integer is not of the form 5m + 2, 5m + 3

#

can anyone help me with this?

warped phoenix Jun 30, 2021, 3:13 PM

#

Hey guys how is a interval sometimes positive and sometimes negative?

lavish cypress Jun 30, 2021, 3:15 PM

#

pseudo grotto use euclid's division lemma to show that the square of any positive integer is n...

You can just consider numbers of the form 5a + b for b = 0, 1, 2, 3, 4

pseudo grotto Jun 30, 2021, 3:22 PM

#

lavish cypress You can just consider numbers of the form 5a + b for b = 0, 1, 2, 3, 4

thats it?

lavish cypress Jun 30, 2021, 3:23 PM

#

Well you have to square them and show that none of the cases result in a number of the form 5a + 2 or 5a + 3

pseudo grotto Jun 30, 2021, 3:24 PM

#

MAN I AM SO SILLY

#

NEWUOFNEWOFEWONFEWO

#

THANKS DUDE

lavish cypress Jun 30, 2021, 3:32 PM

#

Np

twilit ibex Jun 30, 2021, 3:35 PM

#

What is so special about 5, that so many primes stem from its branch if you make an inverse of the Collatz conjecture?

#

Not looking for a specific answer, just some thoughts some of you more experienced mathematicians may have on it.

#

<@&286206848099549185>

glass lichen Jun 30, 2021, 3:35 PM

#

twilit ibex <@&286206848099549185>

#❓how-to-get-help

twilit ibex Jun 30, 2021, 3:35 PM

#

Yes?

#

What are you alluding to?

glass lichen Jun 30, 2021, 3:36 PM

#

The fact you broke a rule

twilit ibex Jun 30, 2021, 3:36 PM

#

Yes, but which?

#

It is unoccuppied and I asked a question?

glass lichen Jun 30, 2021, 3:36 PM

#

and pinged helpers right away... given I responded to the helper ping

twilit ibex Jun 30, 2021, 3:37 PM

#

Oh

#

Sorry, didn't see the one about 15 minutes.

#

But do you perhaps have any thoughts?

glass lichen Jun 30, 2021, 3:37 PM

#

5 is just a number like 3 or pi

#

I have no clue what you mean by its branch

twilit ibex Jun 30, 2021, 3:39 PM

#

Okay, so you know of the Collatz conjecture right?

f(x) = {x/2 \in \doubleZ divide by 2 if x\2 \notIn \doubleZ multiply by 3 and minus 1 }

sage summit Jun 30, 2021, 3:39 PM

#

well every collatz trajectory that ends at 1 and that is not from 16,8,4,2 or 1 either goes through 5 or through 32

#

I am not aware of any result about the asymptotic proportion of the numbers that go through 5 or 32

twilit ibex Jun 30, 2021, 3:40 PM

#

Has this been proven or is this just observational?

sage summit Jun 30, 2021, 3:40 PM

#

not even that it actually exists

twilit ibex Jun 30, 2021, 3:41 PM

#

Also, what does "asymptotic proportion" mean thonk

sage summit Jun 30, 2021, 3:43 PM

#

I think asymptotic density might be more correct

#

the asymptotic density of a subset A of the positive integers is limit of 1/n * size of A intersected with {1...n}

#

the limit may or may not exist

#

your observation that there are more numbers that go through 5 than 32, could be turned into a more precise mathematical statement saying that the set of numbers that goes through 5 has asymptotic density > 1/2

#

but who knows if that's true

twilit ibex Jun 30, 2021, 3:47 PM

#

ahh...

#

Didn't think about that. In fact, I had heard about the zeta function, but I didn't know its connection to primes.

#

This is actually very interresting...

sage summit Jun 30, 2021, 3:48 PM

#

that's uuuh pretty irrelevant to collatz

twilit ibex Jun 30, 2021, 3:48 PM

#

Yeah, but at this point I don't care so much about proving the actual conjecture. I just like figuring out what makes it go like it does

#

or what it tells us about numbers

sage summit Jun 30, 2021, 3:49 PM

#

ah well I am sad to admit that I have found absolutely nothing of worth when I thought about those questions

twilit ibex Jun 30, 2021, 3:49 PM

#

For example, if each new odd integer in the inverse function is a branch, and the even number it stems from is its stem.

You can figure out what number the next branch will have by summing up the branch with its stem.

#

Really?

#

I mean, I haven't started uni yet so I might just be fascinated by all maths. But I've found some very cool patterns

#

Its very simple, because 3 is the lowest non-even prime and 2 is in half of every number. So there are a lot of intuitive discoveries or what you might call them.

#

but back to the original question.

Do, again, have any idea why 5 is so comparatively special?

So far the only thing I've found is that 5 is the very first branch, except for 3 itself.

sage summit Jun 30, 2021, 3:54 PM

#

it just so happens that besides the 1-2-4 cycle, the only ways to get there is 5 -> 16 -> 8 -> ... or 32 -> 16 -> 8 -> ... and that 5 or 32 split is the first one

#

the first one of many splits

twilit ibex Jun 30, 2021, 3:57 PM

#

Oh,

But 32 isn't a split.

1 -> 2 -> 4 -> 8 -> 16 ->32
*5 -> 10->20....
*3......

Literally all numbers will have to pass through either. But there are no primes on the first branch.

I am thinking more of the intrinsic properties of 5.

Like 3 + 2 = 5, which are the denominators (I assume there is another name for that?) of the function.

Or 5 = 1 + 2^2, which looks a bit like a complex number.

sage summit Jun 30, 2021, 3:58 PM

#

then replace all of my 32 with 16

twilit ibex Jun 30, 2021, 3:58 PM

#

Wait

sage summit Jun 30, 2021, 3:58 PM

#

why do you think there are no primes on 32's branch

twilit ibex Jun 30, 2021, 3:59 PM

#

So... More numbers pass through 5, than any of the branches that have a stem in the original 1->2->4 branch...?

#

Well, if every odd number denotes a new branch, and the even number it came from a stem.

Then the first branch is just 1*2^n, which as you might recognize will only contain even numbers.

#

but was my first question correct?

sage summit Jun 30, 2021, 4:00 PM

#

but it still has lots of splits

twilit ibex Jun 30, 2021, 4:00 PM

#

Because that would be very weird

#

Yes, but they are new branches

#

You see, in the inverse function, if you get an odd number twice you will reach 1

sage summit Jun 30, 2021, 4:00 PM

#

there are still primes that won't go through 5

twilit ibex Jun 30, 2021, 4:00 PM

#

Yes

#

There are

#

but did you say that more will go through 5 than not?

#

That would be quite interesting

sage summit Jun 30, 2021, 4:01 PM

#

yes I said that we can observe something like that

twilit ibex Jun 30, 2021, 4:01 PM

#

Wow

sage summit Jun 30, 2021, 4:01 PM

#

but I can't actually prove it

twilit ibex Jun 30, 2021, 4:01 PM

#

Nono

#

Do you have any papers or data of some sort?

sage summit Jun 30, 2021, 4:01 PM

#

nope