#help-0 | Mathematics | Page 576

raw inlet Apr 23, 2021, 2:06 AM

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if anyone could help on b)

ionic jewel Apr 23, 2021, 2:06 AM

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#old-network physics server

vale wigeon Apr 23, 2021, 2:07 AM

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no. your root starts out as sqrt(n^2-i^2)

kindred shard Apr 23, 2021, 2:29 AM

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Can some1 help pls

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with #2 pls

undone copper Apr 23, 2021, 3:05 AM

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kindred shard

(3x)^2 -2^2

cold mica Apr 23, 2021, 3:23 AM

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any one know how to solve this integral with the given two suggested integrals - i tried u = 2r/a as a substitution but i don't think my solution is correct

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C is just some constant

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main problem is if i use u = 2r/a for the e^-u i don't know how to handle the 1/r term infront

daring rapids Apr 23, 2021, 3:26 AM

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Someone please help

cold mica Apr 23, 2021, 3:26 AM

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-_-

spring harbor Apr 23, 2021, 3:26 AM

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@daring rapids move to some other channel

daring rapids Apr 23, 2021, 3:26 AM

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Oh sorry

spring harbor Apr 23, 2021, 3:27 AM

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@cold mica maybe you can rewrite u=2r/a to r that way you can just put it in 1/r and get rid of it

cold mica Apr 23, 2021, 3:27 AM

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well solving that for r gives r = au/2 but 1/r then means the integral has 2/(au)

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which means i have 1/u e^-u (once i take out the constants)

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which is not quite right

spring harbor Apr 23, 2021, 3:30 AM

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mm not sure I don’t have pen and paper on me right now, maybe you could partial integrate it though

cold mica Apr 23, 2021, 3:30 AM

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thats beyond the level im at so i dont think thats going to be the solution

spring harbor Apr 23, 2021, 3:33 AM

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Ok you can just rewrite your function if that’s the case

cold mica Apr 23, 2021, 3:34 AM

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what do you mean

spring harbor Apr 23, 2021, 3:34 AM

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e^(-2r/a) = ... * ...

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I’ll let you think about it first

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Keep in mind that the 2 and a are constants, so if you have e^constant you can move it out

cold mica Apr 23, 2021, 3:34 AM

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well thats = e^(-r/a)*e^(-r/a)

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but not sure if thats what you meant

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r is not a constant don't forget

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thats the subject of the integral

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unless you mean factor out e^(2/a0)

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leaving just e^-r

spring harbor Apr 23, 2021, 3:37 AM

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Yeah that was my initial plan but it doesn’t work nvm

cold mica Apr 23, 2021, 3:37 AM

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tho im not seeing it still since i have one in the denominator and one in the numerator

spring harbor Apr 23, 2021, 3:40 AM

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Wait

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Did you forget to change the dr part?

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since you get du = 2/a dr

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Or dr = 2/a du

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This is a constant you can move it out

cold mica Apr 23, 2021, 3:41 AM

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no i didnt forget that

spring harbor Apr 23, 2021, 3:42 AM

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Then where’s the problem

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What did you exactly get?

cold mica Apr 23, 2021, 3:42 AM

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well it doesn't remove 1/u e^-u

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when i need u e^-u

normal spoke Apr 23, 2021, 3:45 AM

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Given the density d of particles, what's the average distance between two particles?

spring harbor Apr 23, 2021, 3:45 AM

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Channel taken

normal spoke Apr 23, 2021, 3:45 AM

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ah

cold mica Apr 23, 2021, 3:46 AM

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i might've solved it @spring harbor

spring harbor Apr 23, 2021, 3:46 AM

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What did you do?

cold mica Apr 23, 2021, 3:46 AM

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i think i calculated the integrand wrong

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i think it was meant to be e^-2/ra

spring harbor Apr 23, 2021, 3:47 AM

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So the question was wrong?

cold mica Apr 23, 2021, 3:47 AM

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possibly but not sure yet still checking it all

spring harbor Apr 23, 2021, 3:47 AM

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Alright that’s possible then

cerulean glade Apr 23, 2021, 3:54 AM

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ik this is a math server but can someone help me with history?

alpine sable Apr 23, 2021, 3:58 AM

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ik this is a math server
ok starting off well
but
oh no
can someone help me with history

alpine sable Apr 23, 2021, 3:59 AM

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cerulean glade ik this is a math server but can someone help me with history?

The help channels are solely for help with math, so feel free to post your question. Asking whether you can ask a question or if anyone knows about some specific topic is unnecessary, so please try to avoid questions of that nature.
nope you'll have to find a different server

lost geyser Apr 23, 2021, 4:05 AM

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my assumption is that
part a the displacement = 10 meters
part b professor buske is 10 meters away from his mailbox

severe silo Apr 23, 2021, 4:15 AM

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B= {multiple of 5 from 1 to 50}

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Is {0, 50} a proper subset of B?

ionic jewel Apr 23, 2021, 4:16 AM

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lost geyser my assumption is that part a the displacement = 10 meters part b professor busk...

i get 7.5 for 1

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negative

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then i get -2.5m for the second

gleaming granite Apr 23, 2021, 4:18 AM

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ionic jewel i get 7.5 for 1

same for both

ionic jewel Apr 23, 2021, 4:19 AM

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severe silo Is {0, 50} a proper subset of B?

do you think you know?

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tell us what you have and we can say if it's right

severe silo Apr 23, 2021, 4:19 AM

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I think it's false

lost geyser Apr 23, 2021, 4:20 AM

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@ionic jewel how did you get 7.5 for part a

ionic jewel Apr 23, 2021, 4:20 AM

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integral from 2 to 4

ionic jewel Apr 23, 2021, 4:20 AM

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severe silo I think it's false

it is false, but do you know why?

severe silo Apr 23, 2021, 4:21 AM

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My guess is that it's because B is from 1 to 50 not 0 to 50

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I'm still very confused with this topic so I'm not sure

ionic jewel Apr 23, 2021, 4:21 AM

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that's right

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i assume you know why that matters, but exactly

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it would be true if it was 0 to 50

severe silo Apr 23, 2021, 4:23 AM

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Thanks @ionic jewel

rancid fern Apr 23, 2021, 4:23 AM

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so if i have 5000 of something andsell it for 6500$, for 250 of it i pay 75$ how much profit would i get

ionic jewel Apr 23, 2021, 4:23 AM

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what

woeful pulsar Apr 23, 2021, 4:23 AM

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rancid fern so if i have 5000 of something andsell it for 6500$, for 250 of it i pay 75$ how...

???

ocean sealBOT Apr 23, 2021, 4:23 AM

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number 1 crip gangster

woeful pulsar Apr 23, 2021, 4:24 AM

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can you phrase it more clearly?

lost geyser Apr 23, 2021, 4:24 AM

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they're paying 75 dollars for 250 units of something and they sold 5000 units of this soemthing for 6500 dollars

ionic jewel Apr 23, 2021, 4:24 AM

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or post the original problem

lost geyser Apr 23, 2021, 4:24 AM

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is what it sounds like

rancid fern Apr 23, 2021, 4:24 AM

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exactly

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how much profit would i get

woeful pulsar Apr 23, 2021, 4:24 AM

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rancid fern how much profit would i get

post the original problem

ionic jewel Apr 23, 2021, 4:25 AM

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you don't have 5000 units of it how did you sell that much?

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as written it's 6500-75 with magic units appearing somewhere

woeful pulsar Apr 23, 2021, 4:26 AM

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So your cost price for 250 units is $75 and your sales price for 5000 units is $6500... and you want the profit for selling 5000 units?

vale wigeon Apr 23, 2021, 4:26 AM

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woeful pulsar can you phrase it more clearly?

this is a useless question to ask on this server

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nobody ever has any clearer wordings

woeful pulsar Apr 23, 2021, 4:26 AM

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ikr

lost geyser Apr 23, 2021, 4:26 AM

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ionic jewel then i get -2.5m for the second

also how did you get -2.5 for part b, i understand you found the area for part a on the interval [2, 4], but idk how you got part b at all

ionic jewel Apr 23, 2021, 4:26 AM

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i did integral from 0 to 4 lol

lost geyser Apr 23, 2021, 4:27 AM

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would that even work... ?

ionic jewel Apr 23, 2021, 4:27 AM

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why not

rancid fern Apr 23, 2021, 4:27 AM

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so look i buy 250 apples for 75 dollars

ionic jewel Apr 23, 2021, 4:27 AM

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you could make a lot of apple sauce with that

rancid fern Apr 23, 2021, 4:27 AM

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and then i buy 5000 apples and sell them for 6500 how much profit would i get

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this is so confusing i know

alpine sable Apr 23, 2021, 4:28 AM

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ugley

ionic jewel Apr 23, 2021, 4:28 AM

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you made it worse but i understand what you mean

woeful pulsar Apr 23, 2021, 4:28 AM

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How much money does it take to buy 5000 apples?

ionic jewel Apr 23, 2021, 4:28 AM

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so you need to buy 5000 apples at a price of $75/250apples

rancid fern Apr 23, 2021, 4:28 AM

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yes

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exactly

ionic jewel Apr 23, 2021, 4:29 AM

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woeful pulsar How much money does it take to buy 5000 apples?

well starting with this is good

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how much to buy the apples?

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i love magic the gathering

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oh bye

stone scroll Apr 23, 2021, 4:30 AM

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Can I ask for help

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It's physics but just the same, need to be computed lol

lost geyser Apr 23, 2021, 4:38 AM

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how to find part b
delta x_k = 6 though right

woeful pulsar Apr 23, 2021, 4:45 AM

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lost geyser how to find part b delta x_k = 6 though right

yeah, now look at x_k*

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the first one is at?

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the picture divides it quite regularly

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but it's not very standard

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it's not a left sum or right sum

lost geyser Apr 23, 2021, 4:46 AM

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first one is at x = 14 and then from there it adds 6

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but i dont know how to develop a formula for it

woeful pulsar Apr 23, 2021, 4:47 AM

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lost geyser but i dont know how to develop a formula for it

it's an arithmetic progression, right?

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when k=1, we want 14

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continue...?

lost geyser Apr 23, 2021, 4:47 AM

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k = 2 we want 20

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i cant find a working formula where
10 + x = 14
10 + 2(x) = 20
10 + 3(x) = 26

woeful pulsar Apr 23, 2021, 4:51 AM

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lost geyser i cant find a working formula where 10 + x = 14 10 + 2(x) = 20 10 + 3(x) = 26

because it's not 10

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try starting with something other than 10?

lost geyser Apr 23, 2021, 4:51 AM

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oh can we do that

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okay so 8 + 6k

stiff valve Apr 23, 2021, 5:00 AM

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A product in a shop is reduced in price by 20%. At this reduced price the shopkeeper makes only 4% profit. What percentage profit (to the nearest whole percent) does the shopkeeper make at its normal selling price?
How do i form an equation for this?

woeful pulsar Apr 23, 2021, 5:01 AM

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stiff valve A product in a shop is reduced in price by 20%. At this reduced price the shopke...

hmm actually this is quite conceptual

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but you can say the cost price is c

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and see what happens

oak chasm Apr 23, 2021, 5:38 AM

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@alpine sable OK, what two sides do you have, relative to the known angle?

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You have the opposite and hypotenuse.

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You correctly picked sine.

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So, write the equation.

ocean sealBOT Apr 23, 2021, 5:39 AM

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Chai T. Rex

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Chai T. Rex

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Chai T. Rex

oak chasm Apr 23, 2021, 5:41 AM

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No.

ocean sealBOT Apr 23, 2021, 5:41 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 5:41 AM

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What do you get as the new equation?

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No.

ocean sealBOT Apr 23, 2021, 5:42 AM

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Chai T. Rex

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Chai T. Rex

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Chai T. Rex

oak chasm Apr 23, 2021, 5:43 AM

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Right.

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What is that?

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OK, now simplify.

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Right.

ocean sealBOT Apr 23, 2021, 5:44 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 5:45 AM

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What's the left side?

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Of the equation.

hollow atlas Apr 23, 2021, 5:46 AM

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bro

oak chasm Apr 23, 2021, 5:46 AM

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No, that's the right.

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What's the other side?

ocean sealBOT Apr 23, 2021, 5:46 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 5:46 AM

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That's the equation we started with.

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What's the left side?

ocean sealBOT Apr 23, 2021, 5:47 AM

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Chai T. Rex

hollow atlas Apr 23, 2021, 5:47 AM

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correct

ocean sealBOT Apr 23, 2021, 5:48 AM

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Chai T. Rex

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Chai T. Rex

steel scaffold Apr 23, 2021, 5:48 AM

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ocean sealBOT Apr 23, 2021, 5:48 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 5:49 AM

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Right, so what's the left side after you do that?

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What's the right side?

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No, without doing the calculation.

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What does the right side turn into?

ocean sealBOT Apr 23, 2021, 5:51 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 5:51 AM

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What's the right side divided by it?

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No, that's not it.

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What's the right side?

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No, that's after you try to change it.

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What did it start as?

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Right, and then what did it become?

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Right, so let's go from there.

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Right.

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Divide by means you put what you're dividing by on the bottom.

ocean sealBOT Apr 23, 2021, 5:54 AM

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Chai T. Rex

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Chai T. Rex

oak chasm Apr 23, 2021, 5:54 AM

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Yeah, you were.

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OK, so use your calculator now.

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Yes, that's right.

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So, that's x.

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What's the next digit after that?

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OK, so the next digit is 9, which is 5 or higher, so you go up one.

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61.82.

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You're right.

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You're welcome.

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It means arctangent.

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Arctangent undoes tangent.

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So, which sides do you have relative to the angle they're looking for?

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No, probably not.

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OK, so let's do the equation.

ocean sealBOT Apr 23, 2021, 6:00 AM

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Chai T. Rex

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Chai T. Rex

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Chai T. Rex

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Chai T. Rex

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Chai T. Rex

$\tan^{-1}(\tan(x^{\circ})) = \tan^{-1}(\frac{23}{31})$

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Chai T. Rex

oak chasm Apr 23, 2021, 6:03 AM

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OK, so we simplify the left and get:

ocean sealBOT Apr 23, 2021, 6:04 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 6:05 AM

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No, look at your answers.

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No, don't put it in your calculator.

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Look at your four choices.

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One of them matches our last equation.

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Right.

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Well, write down the equations.

ocean sealBOT Apr 23, 2021, 6:13 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 6:14 AM

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No, that's the first answer.

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Cosine is CAH, right?

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What's the adjacent side length?

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What's the hypotenuse?

ocean sealBOT Apr 23, 2021, 6:15 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 6:15 AM

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The first answer doesn't match what it should be.

ocean sealBOT Apr 23, 2021, 6:16 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 6:16 AM

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The correct equation, I mean.

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That's the answer.

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I'm asking you for the correct equation.

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Sine is SOH, right?

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What's the opposite of B?

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No, the opposite side length.

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Which side is 25?

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Right, so it's not the opposite side.

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What's the opposite side length?

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What does adjacent mean?

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No, what does adjacent mean?

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Right, the leg next to the angle.

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What does opposite mean?

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Right, the leg across from the angle.

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What does hypotenuse mean?

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Right, or the side across from the right angle.

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No, it's not always diagonal.

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But it's always the side across from the right angle.

ocean sealBOT Apr 23, 2021, 6:22 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 6:23 AM

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Which of SOH CAH TOA is for sine?

ocean sealBOT Apr 23, 2021, 6:23 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 6:24 AM

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OK, what's the opposite side from B?

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What does opposite mean?

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What side is across from angle B?

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That's next to B.

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Right.

ocean sealBOT Apr 23, 2021, 6:26 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 6:27 AM

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What's SOH stand for?

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What's the opposite side from angle B?

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What are the two sides next to B?

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OK, so write the triangle on paper with the letters and the numbers and the right angle symbol.

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Let me know when you've done it.

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Have you drawn the triangle on paper?

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OK, look at the triangle on your screen.

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We're going to find opposites.

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First, we'll find the opposite of angle A.

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What sides are next to angle A?

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Cover those sides up with your fingers.

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What side is still showing?

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Right, so that's the opposite side of angle A.

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Let's find the opposite side of angle B.

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What are the two sides next to angle B?

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OK, cover those sides up with your fingers.

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What's the side you can still see?

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Right.

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Let's do the opposite of angle C.

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What are the two sides next to C?

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Right, cover those up. What's left?

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Right. That's how you find the opposite side of an angle.

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OK, so what's the opposite of angle B?

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Right, what's the hypotenuse?

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OK, look at the right angle.

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What's the opposite side of the right angle?

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OK, how do we find the opposite side with fingers?

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No, cover up the sides next to the angle.

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What sides are next to the right angle?

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Where's the right angle symbol?

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Right, so C.

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What side is opposite the right angle?

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Right, so that's the hypotenuse.

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So, let's do $\sin(B)$

ocean sealBOT Apr 23, 2021, 6:37 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 6:37 AM

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SOH CAH or TOA?

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OK, so what's the opposite side of B?

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What's the hypotenuse?

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OK, which angle is the right angle?

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Which angle has the right angle symbol next to it?

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OK, which angle is the right angle?

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OK, what sides are next to C?

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OK, cover them up. What's left?

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Right, so what's the hypotenuse?

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Right.

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So, what's the opposite side of B?

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What's the hypotenuse?

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No.

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What angle is the right angle?

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What side is opposite angle C?

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What's the hypotenuse?

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So, what's the opposite side of B?

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What's the hypotenuse?

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What's opposite over hypotenuse?

ocean sealBOT Apr 23, 2021, 6:41 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 6:42 AM

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Does that match the answer?

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OK, so that answer is wrong.

ocean sealBOT Apr 23, 2021, 6:42 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 6:42 AM

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Is that SOH CAH or TOA?

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OK, now there's a trick.

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C is the right angle, right?

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How many degrees is a right angle?

ocean sealBOT Apr 23, 2021, 6:44 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 6:44 AM

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Right.

ocean sealBOT Apr 23, 2021, 6:44 AM

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Chai T. Rex

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Chai T. Rex

oak chasm Apr 23, 2021, 6:45 AM

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Is B the right angle?

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OK, so we can't just use our calculator.

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Is cosine SOH CAH or TOA?

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What side is adjacent to B?

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What's the hypotenuse?

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What letter is the right angle?

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What side is opposite from the right angle?

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That's the hypotenuse.

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Now, if 25 is the hypotenuse, it can't be the adjacent side, since that's a leg.

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So, what's the adjacent leg to B?

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What sides are next to B?

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Cover up the hypotenuse.

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OK, cover up the opposite and hypotenuse.

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Actually, let's do it this way.

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Let's find adjacent sides.

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Angle A. What sides are next to angle A?

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Which one is shorter?

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That's the adjacent side.

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Angle B. What sides are next to angle B?

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Which side is shorter?

vestal hollow Apr 23, 2021, 7:08 AM

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How do I compute this limit? Isn't it infinity?? But according to calculators it's -pi/40...

limit as x -> -inf of (1/20)arctan(5x/4)

oak chasm Apr 23, 2021, 7:12 AM

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@vestal hollow Well, you can move the constant out.

vestal hollow Apr 23, 2021, 7:12 AM

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Yes, so lim x->-inf arctan(5x/4) should be -pi/2, which Google confirms. But I don't get how :( something about turning arctan into tan and then into sinx/cosx?

ocean sealBOT Apr 23, 2021, 7:13 AM

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Chai T. Rex

$\lim_{x \to -\infty} \frac{1}{20} \arctan\left(\frac{5x}{4}\right)$

vestal hollow Apr 23, 2021, 7:13 AM

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Yup!

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That exactly

ocean sealBOT Apr 23, 2021, 7:13 AM

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Chai T. Rex

gray isle Apr 23, 2021, 7:13 AM

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consider the range of arctan and how the tan function looks
and/or properties of tan and arctan in general

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and the limit should be clear

vestal hollow Apr 23, 2021, 7:15 AM

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I see that it does approach a finite limit, but that's it :( how am I supposed to arrive at -pi/40 mathematically?

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I didn't realize it was -pi/40 from the graph

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But I did see that it went to a finite limit

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Just not how

ocean sealBOT Apr 23, 2021, 7:16 AM

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Chai T. Rex

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Chai T. Rex

vestal hollow Apr 23, 2021, 7:17 AM

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Undefined

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Oh

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approach

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xd

oak chasm Apr 23, 2021, 7:17 AM

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Sure, but the limit.

vestal hollow Apr 23, 2021, 7:17 AM

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Sorry

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Infinity

oak chasm Apr 23, 2021, 7:17 AM

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Almost.

vestal hollow Apr 23, 2021, 7:17 AM

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Oops again

oak chasm Apr 23, 2021, 7:17 AM

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Tangent is the slope of the angle.

vestal hollow Apr 23, 2021, 7:18 AM

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I'm sorry?

ocean sealBOT Apr 23, 2021, 7:18 AM

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Chai T. Rex

oak chasm Apr 23, 2021, 7:18 AM

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It becomes larger and larger negative values.

vestal hollow Apr 23, 2021, 7:18 AM

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I don't understand, I'm sorry :(

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Wait

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I plotted

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Omg I'm sorry

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Doesn't the limit not exist?

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As we approach from the left, we get positive infinity

oak chasm Apr 23, 2021, 7:19 AM

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Right.

vestal hollow Apr 23, 2021, 7:19 AM

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From the right we get negative infinity

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Gotchya

oak chasm Apr 23, 2021, 7:20 AM

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Hmm.

gray isle Apr 23, 2021, 7:21 AM

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the range of arctan is (-pi/2 , pi/2)

vestal hollow Apr 23, 2021, 7:21 AM

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Oh

oak chasm Apr 23, 2021, 7:21 AM

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Ahh, yes.

vestal hollow Apr 23, 2021, 7:22 AM

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So it should obviously approach -pi/2

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As we approach infinity

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negative

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brain is fried sorry, thank you both for being patient with me

oak chasm Apr 23, 2021, 7:22 AM

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No problem.

vestal hollow Apr 23, 2021, 7:22 AM

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Okay yeah I get it now, thanks

waxen pendant Apr 23, 2021, 7:32 AM

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hey

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help me solve 29 please

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I broke up the (-3)^(n-1)

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which gave me

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-3^n * -3^-1

vale wigeon Apr 23, 2021, 7:33 AM

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parentheses around the -3.

waxen pendant Apr 23, 2021, 7:33 AM

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all over 4^n

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ohh shit whats going on ann

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I have another test how are u doing

vale wigeon Apr 23, 2021, 7:34 AM

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this is a geometric series. do you know how to calculate the sum of a geometric series?

waxen pendant Apr 23, 2021, 7:34 AM

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a/1-r

vale wigeon Apr 23, 2021, 7:34 AM

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parentheses.

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a/(1-r)

waxen pendant Apr 23, 2021, 7:34 AM

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yes

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so I got

vale wigeon Apr 23, 2021, 7:34 AM

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what is your first term and what is your ratio

waxen pendant Apr 23, 2021, 7:34 AM

#

(-1/3)/(1--(3/4)

vale wigeon Apr 23, 2021, 7:35 AM

#

the value of $\frac{(-3)^{n-1}}{4^n}$ at $n=1$ is not $-\frac13$.

ocean sealBOT Apr 23, 2021, 7:35 AM

#

Ann

waxen pendant Apr 23, 2021, 7:36 AM

#

so ur saying the first term is not -1/3

#

-(1/3)

echo python Apr 23, 2021, 7:37 AM

#

how would I solve this equation p * (1 - p) = 0.1224?

gray isle Apr 23, 2021, 7:38 AM

#

yes, its not -1/3. how did you get -1/3?

waxen pendant Apr 23, 2021, 7:38 AM

#

-3^-1

gray isle Apr 23, 2021, 7:39 AM

#

where did that come from?

waxen pendant Apr 23, 2021, 7:39 AM

#

can we go in a voice channel please

#

But if not okay

#

so I broke up

#

(-3)^(n-1)

#

which is

gray isle Apr 23, 2021, 7:40 AM

#

you're over complicating this

waxen pendant Apr 23, 2021, 7:40 AM

#

-3^n*-3^-1

gray isle Apr 23, 2021, 7:40 AM

#

PARENS

#

to get the first term
simply sub n=1 into your summand

waxen pendant Apr 23, 2021, 7:41 AM

#

why would u substiture n=1

gray isle Apr 23, 2021, 7:41 AM

#

because the index of your series starts at n=1

waxen pendant Apr 23, 2021, 7:43 AM

#

gray isle Apr 23, 2021, 7:43 AM

#

PARENS PARENS PARENS

waxen pendant Apr 23, 2021, 7:44 AM

#

PARENS

ocean sealBOT Apr 23, 2021, 7:44 AM

#

Chai T. Rex

#

Chai T. Rex

gray isle Apr 23, 2021, 7:45 AM

#

this does not mean the first term is -1/3

waxen pendant Apr 23, 2021, 7:45 AM

#

a/(1-r)

#

a is the first term ?

gray isle Apr 23, 2021, 7:46 AM

#

yes, a would represent the first term

waxen pendant Apr 23, 2021, 7:46 AM

#

I see my mistake im used to just plugging in the number outside

#

but that usually works because the other number is to the power of n-1

#

is in reality it is (-1/3)*(-3/4)

#

okay thank you guys so much

lost geyser Apr 23, 2021, 7:52 AM

#

steel scaffold Apr 23, 2021, 8:19 AM

#

is my method correct?
18) If x⊗y = (xy)^(1/2) then what is the value of (3⊗48)⊗9 ?
(3⊗48) = sqrt(144) = 12
(12⊗9) = sqrt(108) = 10.39230485
(12⊗9) = 6sqrt(3)

ionic jewel Apr 23, 2021, 8:20 AM

#

steel scaffold is my method correct? 18) If x⊗y = (xy)^(1/2) then what is the value of (3⊗48)⊗9...

the idea is right, i didn't check the actual numbers

willow bluff Apr 23, 2021, 8:25 AM

#

#

Someone please dm me and help🥶

hasty hound Apr 23, 2021, 8:34 AM

#

,rotate

ocean sealBOT Apr 23, 2021, 8:34 AM

#

rich basin Apr 23, 2021, 8:54 AM

#

Screen_Shot_2021-04-23_at_6.53.47_pm.png

#

Would anyone be able to please help me

#

Screen_Shot_2021-04-23_at_6.54.47_pm.png

rich basin Apr 23, 2021, 9:20 AM

#

I need help with c

sullen nova Apr 23, 2021, 9:23 AM

#

yo

#

can someone explain me this?

#

#

<@&286206848099549185>

rich basin Apr 23, 2021, 9:31 AM

#

@sullen nova Would you be able to help me, looks like you are ahead in the exponential part

sullen nova Apr 23, 2021, 9:35 AM

#

show me ur ans on A and B

#

@rich basin

rich basin Apr 23, 2021, 9:35 AM

#

Screen_Shot_2021-04-23_at_7.35.41_pm.png

#

So this is how far in it that I have

#

I derived the slope at the point -1/2,2 1/4 in the function

#

which the equation for the tangent at that point is y=3x+15/4

#

and I have the normal tangent that collides with point B the equation being y=(x+5)/2

#

And since I know these equations, how can I find the angle

#

for c

#

I'm just brainstorming some ideas

sullen nova Apr 23, 2021, 9:54 AM

#

how do you get this?

#

y=3x+15/4

#

@rich basin

rich basin Apr 23, 2021, 10:09 AM

#

I got y =3x+15/4 through finding the derivative at the point of -1/2 in the parabola

shell widget Apr 23, 2021, 10:10 AM

#

@sullen nova dy/dx = -ay, rearranging, we have dy/y = -a dx, integrating both sides, we get ln(y) = -ax + k, which is just e^(-ax + k) = y, which is just y = e^(-ax) * e^k

sullen nova Apr 23, 2021, 10:10 AM

#

this is the formula to find an angle made between 2 lines

shell widget Apr 23, 2021, 10:10 AM

#

e^k is just a constant, so let it be A

#

so you get y = Ae^(-ax)

rich basin Apr 23, 2021, 10:10 AM

#

I still didn't get it correctly

#

this is not the soluton

#

the answer for that is 45 degrees. But got it incorrect

sullen nova Apr 23, 2021, 10:11 AM

#

so you got 45 deg?

rich basin Apr 23, 2021, 10:11 AM

#

No

#

So when i evaluate it into tan() = 1

#

I got 0.78

#

The answer is 45 degrees, but don't know how to get to there

sullen nova Apr 23, 2021, 10:13 AM

#

,w tan^-1(abs((3-1/2)/(1+3(1/2))))

ocean sealBOT Apr 23, 2021, 10:15 AM

#

Results provided by WolframAlpha

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

rich basin Apr 23, 2021, 10:15 AM

#

Yeah that is what I got

sullen nova Apr 23, 2021, 10:15 AM

#

and it is in radian

#

turn it into degreee

#

it will be 45

rich basin Apr 23, 2021, 10:15 AM

#

Oh yeah, I'm in radian mode

#

Oh nice, thanks. But where did you get that formula from

fluid valley Apr 23, 2021, 10:17 AM

#

hi guys !!!

#

how can i produce this sequence ?

#

1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1,…

vale wigeon Apr 23, 2021, 10:20 AM

#

are you looking for an explicit formula or something?

#

am i understanding correctly that this sequence consists of steadily lengthening runs of ones and zeros?

sullen nova Apr 23, 2021, 10:21 AM

#

hmm

vale wigeon Apr 23, 2021, 10:22 AM

#

so it goes with 4 ones then 4 zeros then 5 ones then 5 zeros and so on

#

is my understanding correct? @fluid valley

sullen nova Apr 23, 2021, 10:24 AM

#

something to do with the sin funciton

fluid valley Apr 23, 2021, 10:24 AM

#

vale wigeon is my understanding correct? <@807250841341394975>

yea exactly!!!

vale wigeon Apr 23, 2021, 10:25 AM

#

uh huh

#

give me a moment...

fluid valley Apr 23, 2021, 10:25 AM

#

ok !!!

vale wigeon Apr 23, 2021, 10:28 AM

#

i think i got it

#

$a_n = \begin{cases} 1 & n \leq \mathrm{round}(\sqrt{n})^2 \ 0 & n > \mathrm{round}(\sqrt{n})^2 \end{cases}$

ocean sealBOT Apr 23, 2021, 10:30 AM

#

Ann

vale wigeon Apr 23, 2021, 10:30 AM

#

where round(x) is the function which rounds x up or down to the nearest integer, whichever is closer; for consistency you can say that it rounds half-integers (like 6.5 or 1.5 or 123.5) upward, but it doesn't matter here since sqrt(n) is never a half-integer

#

@fluid valley there you go

fluid valley Apr 23, 2021, 10:32 AM

#

wow amazing !!! how did u figure it out ?

vale wigeon Apr 23, 2021, 10:33 AM

#

i noticed that the last 1 in every run was at a position that is a perfect square

#

that is, the 1-runs ended at positions 1, 4, 9, 16, 25 and so on

robust fjord Apr 23, 2021, 10:33 AM

#

doesnt $\operatorname{round}(\sqrt{n+1})-\operatorname{floor}(\sqrt{n})$ also work?

ocean sealBOT Apr 23, 2021, 10:33 AM

#

Obstacle

vale wigeon Apr 23, 2021, 10:33 AM

#

does it?

#

lemme take a look

#

looks like it does! but it's shifted by 1 relative to my solution

fluid valley Apr 23, 2021, 10:35 AM

#

since it is sequence question there are a lot of solutions to it

thanks alot Ann

sullen nova Apr 23, 2021, 10:38 AM

#

first 100

#

[1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]

#

algorithm

oak chasm Apr 23, 2021, 10:38 AM

#

Start with index 1.

sullen nova Apr 23, 2021, 10:38 AM

#

def gen(n):
n = n + 1
... res = []
... for i in range(n):
... if i <= round(math.sqrt(i))**2:
... res.append(1)
... else:
... res.append(0)
... return res

oak chasm Apr 23, 2021, 10:38 AM

#

Note the extra 1 in front.

sullen nova Apr 23, 2021, 10:39 AM

#

fixed

vale wigeon Apr 23, 2021, 10:39 AM

#

you can make code blocks like this

#

```
code goes here
multiple lines possible
```

oak chasm Apr 23, 2021, 10:40 AM

#

Yeah,

```python
code
code
```

For syntax highlighting.

vale wigeon Apr 23, 2021, 10:40 AM

#

def gen(n):
     n = n + 1
     res = []
     for i in range(n):
             if i <= round(math.sqrt(i))**2:
                     res.append(1)
             else:
                     res.append(0)
     return res

oak chasm Apr 23, 2021, 10:40 AM

#

I think that still starts with 0, though, so it has an extra leading 1.

#

How do you get the range to start with 1?

vale wigeon Apr 23, 2021, 10:41 AM

#

range(1,n+1)?

sullen nova Apr 23, 2021, 10:41 AM

#

yes

oak chasm Apr 23, 2021, 10:41 AM

#

def gen(n):
     res = []
     for i in range(1, n + 1):
             if i <= round(math.sqrt(i))**2:
                     res.append(1)
             else:
                     res.append(0)
     return res

sullen nova Apr 23, 2021, 10:49 AM

#

i believe we can also use pascal for this

vale wigeon Apr 23, 2021, 10:49 AM

#

you can write an algorithm in basically any language for this

#

even brainfuck if youre so inclined

sullen nova Apr 23, 2021, 10:50 AM

#

not pascal as a language

#

the pascal formual

vale wigeon Apr 23, 2021, 10:50 AM

#

the what now

vestal needle Apr 23, 2021, 11:13 AM

#

could I get some help with this?

shell widget Apr 23, 2021, 11:19 AM

#

whats question 22

limber ledge Apr 23, 2021, 11:20 AM

#

good morning

vestal needle Apr 23, 2021, 11:20 AM

#

#

this

shell widget Apr 23, 2021, 11:20 AM

#

ok so try to use part a

vestal needle Apr 23, 2021, 11:21 AM

#

hmmmm

#

so something like $z=\dfrac{1}{\bar{z}}$?

ocean sealBOT Apr 23, 2021, 11:22 AM

#

Mani

elfin ibex Apr 23, 2021, 11:30 AM

#

this chat aint occupied

#

hey anyone know how to start this?

#

vestal needle Apr 23, 2021, 11:32 AM

#

@elfin ibex what do u need help with? simplify it?

elfin ibex Apr 23, 2021, 11:32 AM

#

yeah ^^

vestal needle Apr 23, 2021, 11:32 AM

#

do u know how to simplify surds?

elfin ibex Apr 23, 2021, 11:32 AM

#

surds?

vestal needle Apr 23, 2021, 11:32 AM

#

$sqrt{a}$

ocean sealBOT Apr 23, 2021, 11:32 AM

#

Mani

vale wigeon Apr 23, 2021, 11:32 AM

#

$\sqrt{a}$

ocean sealBOT Apr 23, 2021, 11:32 AM

#

Ann

vale wigeon Apr 23, 2021, 11:32 AM

#

roots

elfin ibex Apr 23, 2021, 11:32 AM

#

yeah

vestal needle Apr 23, 2021, 11:32 AM

#

damn

elfin ibex Apr 23, 2021, 11:33 AM

#

i just dont know how to find the prime factor thing

vale wigeon Apr 23, 2021, 11:33 AM

#

factor 45 and 80

#

what's giving you trouble w/ doing that?

elfin ibex Apr 23, 2021, 11:33 AM

#

idk..

#

i just dont know how

#

like how do u find it easier

vale wigeon Apr 23, 2021, 11:33 AM

#

do you know how to factor numbers in general

vestal needle Apr 23, 2021, 11:33 AM

#

@elfin ibex are there any perfect squares that 45 and 80 are divisible by?

elfin ibex Apr 23, 2021, 11:34 AM

#

i just keep putting random numbers into my calculator

elfin ibex Apr 23, 2021, 11:34 AM

#

vestal needle <@!561978974230544408> are there any perfect squares that 45 and 80 are divisibl...

5

#

wait

vale wigeon Apr 23, 2021, 11:34 AM

#

5 is not a perfect square

vestal needle Apr 23, 2021, 11:34 AM

#

^

vale wigeon Apr 23, 2021, 11:34 AM

#

but 45 is divisible by 5

#

and 80 is also divisible by 5, by coincidence

#

45 = 3 * 3 * 5 and 80 = 2 * 2 * 2 * 2 * 5

#

these are the prime factorizations

#

look up "how to factor numbers into primes"

elfin ibex Apr 23, 2021, 11:35 AM

#

but 3 isnt a perfect square

#

niether is 2 or 5 ;-;

vestal needle Apr 23, 2021, 11:35 AM

#

thats the prime factorisation of 45 and 80

#

then you can break up the square root

vale wigeon Apr 23, 2021, 11:36 AM

#

2, 3 and 5 are primes

#

but i can also write this as

#

$\sqrt{45} = \sqrt{3^2 \cdot 5}$

ocean sealBOT Apr 23, 2021, 11:36 AM

#

Ann

vale wigeon Apr 23, 2021, 11:36 AM

#

and $\sqrt{80} = \sqrt{4^2 \cdot 5}$

ocean sealBOT Apr 23, 2021, 11:36 AM

#

Ann

elfin ibex Apr 23, 2021, 11:36 AM

#

vale wigeon 5 is not a perfect square

;-;

vestal needle Apr 23, 2021, 11:37 AM

#

@elfin ibex to simplify surds look for perfect squares that the number inside the surd is divisible by

elfin ibex Apr 23, 2021, 11:37 AM

#

but what perfect square is 45 divisible by

vestal needle Apr 23, 2021, 11:38 AM

#

9

elfin ibex Apr 23, 2021, 11:38 AM

#

ohh

#

so what do i do next?

vestal needle Apr 23, 2021, 11:38 AM

#

elfin ibex Apr 23, 2021, 11:38 AM

#

vestal needle Apr 23, 2021, 11:38 AM

#

here read this

#

$2\sqrt{45}-\dfrac{1}{2}\sqrt{80}=2\sqrt{9\times 5}-\dfrac{1}{2}\sqrt{16\times 5}$

ocean sealBOT Apr 23, 2021, 11:40 AM

#

Mani

graceful lance Apr 23, 2021, 11:40 AM

#

vestal needle Apr 23, 2021, 11:40 AM

#

and then you can take split the surd and the perfect square using the rule that $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$

ocean sealBOT Apr 23, 2021, 11:40 AM

#

Mani

elfin ibex Apr 23, 2021, 11:40 AM

#

okay.....

vestal needle Apr 23, 2021, 11:41 AM

#

you should probably watch a video on youtube on how to simplify surds

elfin ibex Apr 23, 2021, 11:41 AM

#

i tried

#

they didnt help

vestal needle Apr 23, 2021, 11:42 AM

#

https://www.youtube.com/watch?v=YPcKs1OV-X0

YouTube

Eddie Woo

Simplifying Surds (1 of 2: Squares vs. square roots)

More resources available at www.misterwootube.com

▶ Play video

#

here

elfin ibex Apr 23, 2021, 11:43 AM

#

@~~@

#

idk what surds are

#

im just here to simplify a square root

#

vestal needle Apr 23, 2021, 11:44 AM

#

square root are surds

elfin ibex Apr 23, 2021, 11:44 AM

#

alr for this eqution

vestal needle Apr 23, 2021, 11:44 AM

#

square root is the symbol

elfin ibex Apr 23, 2021, 11:44 AM

#

would a perfect square

#

be

#

9

#

for 90

vestal needle Apr 23, 2021, 11:45 AM

#

for which number?

#

yes

#

correct

elfin ibex Apr 23, 2021, 11:45 AM

#

for 10 what would it be?

vestal needle Apr 23, 2021, 11:45 AM

#

is 10 divisible by a perfect square?

elfin ibex Apr 23, 2021, 11:45 AM

#

no

vestal needle Apr 23, 2021, 11:45 AM

#

then its already simplified

elfin ibex Apr 23, 2021, 11:45 AM

#

oh

vestal needle Apr 23, 2021, 11:46 AM

#

you cant simplify $\sqrt{10}$ further

elfin ibex Apr 23, 2021, 11:46 AM

#

i always thought u had to keep dividing until u cant anymore

ocean sealBOT Apr 23, 2021, 11:46 AM

#

Mani

elfin ibex Apr 23, 2021, 11:46 AM

#

like 10/2

#

5

vestal needle Apr 23, 2021, 11:46 AM

#

na

elfin ibex Apr 23, 2021, 11:46 AM

#

okay thanks

vestal needle Apr 23, 2021, 11:46 AM

#

nws

elfin ibex Apr 23, 2021, 11:47 AM

#

so

#

now that i got 10 and 9

#

what do i do?

vestal needle Apr 23, 2021, 11:49 AM

#

so now you can rewrite it as $-6\sqrt{10}+5\sqrt{90}=-6\sqrt{10}+5\sqrt{9\times 10}=-6\sqrt{10}+5\sqrt{9}\times\sqrt{10}$

ocean sealBOT Apr 23, 2021, 11:49 AM

#

Mani

elfin ibex Apr 23, 2021, 11:49 AM

#

oh

#

thats simplified then?

#

i thought it was 3 numbers

vestal needle Apr 23, 2021, 11:50 AM

#

whats $\sqrt{9}$?

ocean sealBOT Apr 23, 2021, 11:50 AM

#

Mani

elfin ibex Apr 23, 2021, 11:50 AM

#

3

vestal needle Apr 23, 2021, 11:50 AM

#

yes

#

so you can write it as 3

#

and then simplify further

elfin ibex Apr 23, 2021, 11:51 AM

#

im gonna go die

vestal needle Apr 23, 2021, 11:51 AM

#

if u still dont get it, then u should watch a video on youtube and try to understand it properly

graceful lance Apr 23, 2021, 11:54 AM

#

#

the (iv) one

alpine sable Apr 23, 2021, 12:04 PM

#

graceful lance

still need help?

#

im not sure if this is the way

#

but i can try

elfin ibex Apr 23, 2021, 12:05 PM

#

@alpine sable can u help me with this

alpine sable Apr 23, 2021, 12:05 PM

#

uh sure

#

i will try my best!

elfin ibex Apr 23, 2021, 12:06 PM

#

can i dm u?

graceful lance Apr 23, 2021, 12:06 PM

#

alpine sable still need help?

yea

elfin ibex Apr 23, 2021, 12:06 PM

#

oh

alpine sable Apr 23, 2021, 12:07 PM

#

graceful lance yea

okay so the new polynomial can be represented in the form (x-(a-b))(x-(a+b))

#

right?

alpine sable Apr 23, 2021, 12:07 PM

#

elfin ibex can i dm u?

sure

graceful lance Apr 23, 2021, 12:08 PM

#

alpine sable okay so the new polynomial can be represented in the form (x-(a-b))(x-(a+b))

k[x^2 - (alpha + beta) + alpha Beta]

alpine sable Apr 23, 2021, 12:10 PM

#

graceful lance k[x^2 - (alpha + beta) + alpha Beta]

whats the k doing there?

graceful lance Apr 23, 2021, 12:10 PM

#

alpine sable whats the k doing there?

k = constant

alpine sable Apr 23, 2021, 12:12 PM

#

okay, but so just replace the values of alpha and beta

#

you should be good to go

little nebula Apr 23, 2021, 12:58 PM

#

https://gyazo.com/58f319841afda5e6f3d5516b2fa4422e

Gyazo

#

can someone help me with my exit ticket?

#

plugging in no work

vale wigeon Apr 23, 2021, 12:59 PM

#

exit ticket?

#

is that like a test? or is it not timed / open-book

#

also, i see you've selected choice A. was that intentional or random?

alpine sable Apr 23, 2021, 1:00 PM

#

two different definitons given for h(x)

#

but luckily this won't affect the answer

alpine sable Apr 23, 2021, 1:01 PM

#

little nebula https://gyazo.com/58f319841afda5e6f3d5516b2fa4422e

use the formula for average rate of change for all the intervals

#

keep in mind the average rate of change of a line over any interval is equal to the slope

little nebula Apr 23, 2021, 1:02 PM

#

ok

#

@alpine sable i think its A

#

it was the graph being different no wonder yi couldnt solve it

vestal hollow Apr 23, 2021, 1:04 PM

#

Oops my bad

alpine sable Apr 23, 2021, 1:05 PM

#

little nebula <@456226577798135808> i think its A

yeah that'd be correct

little nebula Apr 23, 2021, 1:05 PM

#

yeah i c how to do it

#

it was just written wrong

alpine sable Apr 23, 2021, 1:06 PM

#

worldly pike Apr 23, 2021, 1:06 PM

#

#

Simplify ?

limpid spade Apr 23, 2021, 1:14 PM

#

simplify tanxsinx first

wild shard Apr 23, 2021, 1:24 PM

#

worldly pike

its secx

#

tanx and sinx make sinx^2 / cosx

#

then find a common denom

#

get sinx^2 / cosx + cos^2 / cosx

#

that simplifies to 1/cosx

vale tundra Apr 23, 2021, 1:26 PM

#

Can anyone help

#

Part b

#

.-.

sullen nova Apr 23, 2021, 1:30 PM

#

hello

vale tundra Apr 23, 2021, 1:30 PM

#

Wait

sullen nova Apr 23, 2021, 1:32 PM

#

vale tundra Can anyone help

10,-20 and 20,10

#

pls halp

#

#

<@&286206848099549185>

vale tundra Apr 23, 2021, 1:33 PM

#

sullen nova 10,-20 and 20,10

wrong

#

Pls i am still stuck

#

Dont post over me

alpine sable Apr 23, 2021, 1:34 PM

#

any free to help

vale tundra Apr 23, 2021, 1:34 PM

#

sullen nova Apr 23, 2021, 1:35 PM

#

i thin k I know

vale tundra Apr 23, 2021, 1:35 PM

#

Hmm can you try to explain?

sullen nova Apr 23, 2021, 1:35 PM

#

I am checking my notes

vale tundra Apr 23, 2021, 1:37 PM

#

Oki take your time

alpine sable Apr 23, 2021, 1:38 PM

#

How do u solve sin(x)=cos(x/2)

vale tundra Apr 23, 2021, 1:38 PM

#

alpine sable How do u solve sin(x)=cos(x/2)

This is occupied

sullen nova Apr 23, 2021, 1:42 PM

#

what is the line equation on the second part of the graph?

vale tundra Apr 23, 2021, 1:43 PM

#

Solving

#

y=3/4x-5

vale tundra Apr 23, 2021, 1:44 PM

#

sullen nova what is the line equation on the second part of the graph?

Here

#

Used point 40,25 and 20,10

vale tundra Apr 23, 2021, 1:48 PM

#

vale tundra

<@&286206848099549185>

#

anyone?

sullen nova Apr 23, 2021, 1:56 PM

#

vale tundra

try 10,-400

upbeat oxide Apr 23, 2021, 1:57 PM

#

what is this evaluated?

sullen nova Apr 23, 2021, 1:58 PM

#

@vale tundra

nocturne wolf Apr 23, 2021, 1:58 PM

#

#

I need help, not sure if its 65 or 92

vale tundra Apr 23, 2021, 1:58 PM

#

sullen nova try 10,-400

I have one try left

#

I dont know if i should risk it

sullen nova Apr 23, 2021, 1:59 PM

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don't

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I am not sure

vale tundra Apr 23, 2021, 2:00 PM

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I will post at another time i think

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sullen nova Apr 23, 2021, 2:05 PM

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my best guess is (10,-50)

indigo jetty Apr 23, 2021, 2:06 PM

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how did you get the answers for the critical points?

nocturne wolf Apr 23, 2021, 2:07 PM

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I need help

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sullen nova Apr 23, 2021, 2:16 PM

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@vale tundra Trust me

woeful remnant Apr 23, 2021, 2:16 PM

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Hey everyone, the average tweet takes 10-15 seconds to type.. if a user joined Twitter in 2009 and has 70,000 tweets, how would you calculate the approx amount of time the user has spent on Twitter in total?

sullen nova Apr 23, 2021, 2:16 PM

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I am 90% sure

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(10,-50)

vale tundra Apr 23, 2021, 2:19 PM

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sullen nova (10,-50)

Omg itss right

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How did you do it????

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I have been stuck on this for forever

sullen nova Apr 23, 2021, 2:19 PM

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how did you get the part (a) right?

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if you know (a) it's not hard to do (b)

vale tundra Apr 23, 2021, 2:20 PM

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sullen nova how did you get the part (a) right?

I did it like a week ago

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I dont remember tbh

sullen nova Apr 23, 2021, 2:21 PM

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btw do you know how to do integral?

vale tundra Apr 23, 2021, 2:22 PM

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sullen nova btw do you know how to do integral?

Yes

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@sullen nova How about 20

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Hmm

ocean carbon Apr 23, 2021, 2:35 PM

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Does anyone know how I am supposed to predict the velocity of a bullet moving from one starting vector to an ending vector, given a static speed value and a gravity value?

alpine sable Apr 23, 2021, 2:38 PM

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Okay so i have this question on a mock exam paper that has rlly stumped me:

Two similar solids have base areas of 47cm2 and 199cm2. The volume of the smaller solid is 350cm3, calculate the volume of the larger solid.

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How would I go about solving this?

sullen nova Apr 23, 2021, 2:39 PM

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@vale tundra (20,-75)

sullen nova Apr 23, 2021, 2:40 PM

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ocean carbon Does anyone know how I am supposed to predict the velocity of a bullet moving fr...

use equation of motion

alpine sable Apr 23, 2021, 2:40 PM

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anyone free to help me with some problems

sullen nova Apr 23, 2021, 2:40 PM

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alpine sable Okay so i have this question on a mock exam paper that has rlly stumped me: Tw...

what type of solid is this

ocean carbon Apr 23, 2021, 2:41 PM

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sullen nova use equation of motion

wuld that be able to give me a velocity vector

alpine sable Apr 23, 2021, 2:41 PM

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Uhh

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I dont know what kind of solid it is

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It looks to be like, halfway between a pentagonal prism and a trapezoid?

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Hold on

sullen nova Apr 23, 2021, 2:44 PM

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ocean carbon wuld that be able to give me a velocity vector

ye

ocean carbon Apr 23, 2021, 2:44 PM

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To get the distance of two vectors, could I just add them together and then get the Length of the new vector

alpine sable Apr 23, 2021, 2:45 PM

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Ugh images take forever to sent with my internet

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Just gonna delete that because I forgot to crop it

merry nova Apr 23, 2021, 2:46 PM

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the length of the sum of two vectors is not necessarily equal to the sum of the lengths of the vectors

sullen nova Apr 23, 2021, 2:46 PM

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ocean carbon To get the distance of two vectors, could I just add them together and then get ...

starting vector and ending vector are just angles

alpine sable Apr 23, 2021, 2:49 PM

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merry nova Apr 23, 2021, 2:51 PM

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so we need two facts:

if you scale a 2 dimensional figure by a scale factor k, the area changes by a factor of k^2
if you scale a 3 dimensional figure by a scale factor k, the volume changes by a factor of k^3

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we are given the these two figures are similar, so one must have been formed by scaling the other

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in particular the two bases are also similar

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assume the scale factor is k

alpine sable Apr 23, 2021, 2:52 PM

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that makes sense

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lemme just

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nvm Idk how to calculate the scale factor of 2d shapes

merry nova Apr 23, 2021, 2:53 PM

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so write an equation relating the two areas

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(area of base on left)*(k^2)=(area of base on right)

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then solve

alpine sable Apr 23, 2021, 2:54 PM

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so l*k^2=r?

merry nova Apr 23, 2021, 2:54 PM

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what is r and I?

alpine sable Apr 23, 2021, 2:54 PM

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left and right

merry nova Apr 23, 2021, 2:54 PM

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yes

alpine sable Apr 23, 2021, 2:54 PM

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ok...

vale tundra Apr 23, 2021, 2:55 PM

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sullen nova <@!664964995498508288> (20,-75)

That is right

alpine sable Apr 23, 2021, 2:55 PM

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so to make k^2 the subject id need to add r to both sides, and divide by k^2?

vale tundra Apr 23, 2021, 2:55 PM

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Thank you so much

merry nova Apr 23, 2021, 2:55 PM

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47k^2=199

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divide by 47

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then take the square root

alpine sable Apr 23, 2021, 2:55 PM

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ohh that makes more sense

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199/47 is 4.234, sqrt(4.234)= 2.057

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thats k, so that means k^3=8.712

merry nova Apr 23, 2021, 2:57 PM

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yes

alpine sable Apr 23, 2021, 2:57 PM

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which is the scale factor for the volume

merry nova Apr 23, 2021, 2:57 PM

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yep

alpine sable Apr 23, 2021, 2:57 PM

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350*8.712= 3049.305

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NICE

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tyvm

vale tundra Apr 23, 2021, 2:58 PM

#

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Anyone?

alpine sable Apr 23, 2021, 2:58 PM

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that is far beyond my area of knowledge lmao

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shut

merry nova Apr 23, 2021, 3:00 PM

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where did you get -30

vale tundra Apr 23, 2021, 3:00 PM

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merry nova where did you get -30

I guessed

merry nova Apr 23, 2021, 3:01 PM

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do you know why you got the x coord to be 4

vale tundra Apr 23, 2021, 3:01 PM

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merry nova do you know why you got the x coord to be 4

Yes

merry nova Apr 23, 2021, 3:01 PM

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cool

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$G(t)=G(0)+\int_{0}^{t}G'(s)ds$

ocean sealBOT Apr 23, 2021, 3:02 PM

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AAAAAAAAAAAAAAAAAAAA

merry nova Apr 23, 2021, 3:02 PM

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so plug in t=4 and compute

vale tundra Apr 23, 2021, 3:02 PM

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Ohhh

merry nova Apr 23, 2021, 3:02 PM

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btw this comes from rearranging

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$\int_0^t G'(s) ds = G(t)-G(0)$

ocean sealBOT Apr 23, 2021, 3:03 PM

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AAAAAAAAAAAAAAAAAAAA

vale tundra Apr 23, 2021, 3:04 PM

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So i need to find G(4)

merry nova Apr 23, 2021, 3:04 PM

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yes

vale tundra Apr 23, 2021, 3:05 PM

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-8+ 1/2*-4x2

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For the f

merry nova Apr 23, 2021, 3:06 PM

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for the integral part yes

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you also need to add in the initial condition

vale tundra Apr 23, 2021, 3:07 PM

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so 18

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Ayyyy

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Thank you

stable dune Apr 23, 2021, 3:09 PM

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im not sure about this could you help me?

alpine sable Apr 23, 2021, 3:10 PM

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a^2 + b^2 = c^2

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With C being the hypotenuse, and A being the length

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To work out b, you need to work out c^2, and take a^2 from it

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@stable dune

stable dune Apr 23, 2021, 3:13 PM

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so

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5^2 + b^2=13^2

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25+b^2=169

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but how can i figure out b^2 now

alpine sable Apr 23, 2021, 3:15 PM

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Take 25 fro 169

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And that gives you b^2

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Then take the square root of that number and you have your answer

stable dune Apr 23, 2021, 3:17 PM

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ah okay'

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i subtracted 169 and 25

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i got 144

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now doing the square root

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i got 12

alpine sable Apr 23, 2021, 3:17 PM

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I have that number burned into my memory lmao

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12*12 = 144

stable dune Apr 23, 2021, 3:17 PM

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lmao

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right

alpine sable Apr 23, 2021, 3:17 PM

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Your answer is 12

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So C

stable dune Apr 23, 2021, 3:18 PM

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what about this

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a^2+b^2=c^2

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right?

alpine sable Apr 23, 2021, 3:18 PM

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Well, this is just worded differently

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The base of the house is 6ft, which means the base of the triangle is 3ft

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The hypotenuse is 5ft

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Just plug those into the formula, just like before

stable dune Apr 23, 2021, 3:19 PM

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hm

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6^2+3^2=5^2?

alpine sable Apr 23, 2021, 3:20 PM

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No

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3^2 + b^2 = 5^2

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You are solving for B

stable dune Apr 23, 2021, 3:20 PM

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ah but whats 6?

alpine sable Apr 23, 2021, 3:20 PM

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Okay

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The house is made up of two right angle triangles

stable dune Apr 23, 2021, 3:20 PM

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right

alpine sable Apr 23, 2021, 3:20 PM

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The problem tells us that the base of the entire house is 6ft

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Which means the base of both triangles is 3ft

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Considering that the hypotenuse is equal for both, and they share the same height

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And as you are trying to find the height, you need to use 3ft instead of 6ft

stable dune Apr 23, 2021, 3:22 PM

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ohhh

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4?

alpine sable Apr 23, 2021, 3:23 PM

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Idk, you are the one working it out

stable dune Apr 23, 2021, 3:24 PM

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thats what i got after figuring out i got 14

alpine sable Apr 23, 2021, 3:24 PM

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Does anyone have any idea how Im supposed to go about solving this question?

stable dune Apr 23, 2021, 3:24 PM

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square root of 14 is is 4

young pier Apr 23, 2021, 3:24 PM

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lol

alpine sable Apr 23, 2021, 3:24 PM

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No, its not

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Square root of 16 is 4, but not the sqrt of 14

velvet pelican Apr 23, 2021, 3:25 PM

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alpine sable Does anyone have any idea how Im supposed to go about solving this question?

Do you know the circle theorems required?

alpine sable Apr 23, 2021, 3:25 PM

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Nope

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Not for finding y, at least

velvet pelican Apr 23, 2021, 3:26 PM

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Have you heard of circle theorems?

alpine sable Apr 23, 2021, 3:26 PM

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I can find x if I have y

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Yes, I have

velvet pelican Apr 23, 2021, 3:26 PM

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You can find x using the cyclic quadrilateral one

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then use the angle at the centre theorem

alpine sable Apr 23, 2021, 3:26 PM

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Ohhhh

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That makes much more sense

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But id need to know BAD and DCB for that

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Wouldnt I?

velvet pelican Apr 23, 2021, 3:27 PM

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What does the cyclic quadrilateral theorem say?

alpine sable Apr 23, 2021, 3:28 PM

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Wait no

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Just remembered

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ADC + ABC = 18P

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180*

velvet pelican Apr 23, 2021, 3:28 PM

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Yes

alpine sable Apr 23, 2021, 3:28 PM

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I remember now

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Thanks

velvet pelican Apr 23, 2021, 3:28 PM

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Welcome

halcyon cloud Apr 23, 2021, 3:31 PM

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can anyone help me with this, its not a test

alpine sable Apr 23, 2021, 3:35 PM

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A) is simple trigonometry, just scroll up and ive already explained how to do it

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B) i actually suck at trigonometry so I couldnt tell you

stable dune Apr 23, 2021, 3:39 PM

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im not sure ab this

rigid gyro Apr 23, 2021, 3:40 PM

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I know how to do

stable dune Apr 23, 2021, 3:40 PM

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can you explain

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ik its a^2+b^2=c^2

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but is it 10^2+b^2=26^2?

rigid gyro Apr 23, 2021, 3:41 PM

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Yeah so c is always the longest side

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Yes

glass solstice Apr 23, 2021, 3:41 PM

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uhh

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i have a question

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Screen_Shot_2021-04-23_at_11.41.11_AM.png

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how do i do this

rigid gyro Apr 23, 2021, 3:41 PM

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Oh that

glass solstice Apr 23, 2021, 3:41 PM

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yeah

rigid gyro Apr 23, 2021, 3:42 PM

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I forget how to do that

glass solstice Apr 23, 2021, 3:42 PM

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oh

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dont i subsitute n for 10

rough spear Apr 23, 2021, 3:43 PM

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I think I can help

glass solstice Apr 23, 2021, 3:43 PM

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and then do av9*3

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oh

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great

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bc im stuck

rough spear Apr 23, 2021, 3:43 PM

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a_1 is 10

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you substitute n for the other terms

glass solstice Apr 23, 2021, 3:43 PM

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oh

rough spear Apr 23, 2021, 3:43 PM

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so a_2 will be the second term

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a_3 third

glass solstice Apr 23, 2021, 3:44 PM

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ohh

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so for n it would be the term

rough spear Apr 23, 2021, 3:44 PM

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so to find the second term

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yes

glass solstice Apr 23, 2021, 3:44 PM

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ohh

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and u subtract 1

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bc its the formula

rough spear Apr 23, 2021, 3:44 PM

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$a_2=a_{2-1}×3$

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yes

stable dune Apr 23, 2021, 3:44 PM

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halcyon cloud Apr 23, 2021, 3:45 PM

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can anyone help me with this

ocean sealBOT Apr 23, 2021, 3:45 PM

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nintendo

halcyon cloud Apr 23, 2021, 3:45 PM

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glass solstice Apr 23, 2021, 3:45 PM

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thanks

rough spear Apr 23, 2021, 3:45 PM

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no big

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@halcyon cloud what have you tried

halcyon cloud Apr 23, 2021, 3:45 PM

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wym

stable dune Apr 23, 2021, 3:45 PM

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stable dune

a^2+b^2=c^2 but wouldnt it be 100^2+b^2=130^2?

rough spear Apr 23, 2021, 3:45 PM

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like what has been your attempt so far in getting the solution

halcyon cloud Apr 23, 2021, 3:46 PM

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not much ive been absent for the past few classes and im not sure where to start

rough spear Apr 23, 2021, 3:46 PM

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I see

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do you know the Pythagoras theorem

halcyon cloud Apr 23, 2021, 3:46 PM

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yh

rough spear Apr 23, 2021, 3:46 PM

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hyp²=adj²+opp²

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that's what you use for a

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do you know what side we're looking for here?

halcyon cloud Apr 23, 2021, 3:47 PM

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so im solving for hypotenuse right

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the longest side?

vast ether Apr 23, 2021, 3:47 PM

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halcyon cloud

Still need help solving this?

rough spear Apr 23, 2021, 3:48 PM

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no

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you have the longest side

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halcyon cloud Apr 23, 2021, 3:48 PM

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yea @vast ether

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oh

rough spear Apr 23, 2021, 3:48 PM

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the part the ladder touches the building

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to the ground

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that distance

halcyon cloud Apr 23, 2021, 3:48 PM

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so how would i solve for that

rough spear Apr 23, 2021, 3:49 PM

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since you have the hypotenuse and the adjacent you just plug in the values for Pythagoras

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then change the subject formula to find the opposite

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since that's what we're looking for here

halcyon cloud Apr 23, 2021, 3:49 PM

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so hyp - adj = opp

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thats what im doing right

rough spear Apr 23, 2021, 3:50 PM

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yes

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don't forget the square

halcyon cloud Apr 23, 2021, 3:50 PM

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ok so isnt that 5 squared?

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wait

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im doing 10^2 - 5^2?

rough spear Apr 23, 2021, 3:51 PM

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10²=5²+opp²
10²-5²=opp²

vast ether Apr 23, 2021, 3:52 PM

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halcyon cloud Apr 23, 2021, 3:52 PM

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so 5√3 radical

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so what abt the values?

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wait i have an idea

vast ether Apr 23, 2021, 3:54 PM

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If you need help with part b lmk

halcyon cloud Apr 23, 2021, 3:55 PM

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ye i need help

vast ether Apr 23, 2021, 3:55 PM

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halcyon cloud so what abt the values?

They are just labels basically

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Do you know how to use trigonometric ratios?

halcyon cloud Apr 23, 2021, 3:57 PM

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looks good?

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@vast ether

alpine sable Apr 23, 2021, 4:00 PM

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yo tiggle u tryna copy me?

vast ether Apr 23, 2021, 4:01 PM

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halcyon cloud

Not quite. Remember Soh Cah Toa

vast ether Apr 23, 2021, 4:01 PM

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alpine sable yo tiggle u tryna copy me?

Who are you imposter?

alpine sable Apr 23, 2021, 4:01 PM

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i think u are the imposter

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im SPONGEBOB

halcyon cloud Apr 23, 2021, 4:02 PM

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i dont know what to do honestly @vast ether

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and theres other questions

vast ether Apr 23, 2021, 4:03 PM

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Stop twerkin' my square booty

vast ether Apr 23, 2021, 4:03 PM

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halcyon cloud i dont know what to do honestly <@!296676313484361728>

Ok let me do some writing

alpine sable Apr 23, 2021, 4:03 PM

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yo tiggle yk who we hate

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vast ether Apr 23, 2021, 4:04 PM

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D: Doodlebob