#help-0 | Mathematics | Page 693

next scroll Jul 3, 2021, 3:27 PM

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https://codeforces.com/contest/1542/problem/C this is the problem i'm trying to solve.

Codeforces

Problem - C - Codeforces

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I though there would be a term for that, thanks anyway, i have to think another way now

woeful pulsar Jul 3, 2021, 3:28 PM

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yeah basically the idea is calculating it faster than O(1) each

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hey that's a currently running contest

next scroll Jul 3, 2021, 3:29 PM

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no it's finished

woeful pulsar Jul 3, 2021, 3:29 PM

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oh it's finished

next scroll Jul 3, 2021, 3:29 PM

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yeah just 10-20 min ago

woeful pulsar Jul 3, 2021, 3:29 PM

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very recent one lol

prime badge Jul 3, 2021, 3:32 PM

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it has to be a power of a single prime right?

strong citrus Jul 3, 2021, 3:34 PM

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How are prime numbers used in security fields ?

oak chasm Jul 3, 2021, 3:34 PM

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@next scroll Minimum natural coprime to i. It will be a prime number.

strong citrus Jul 3, 2021, 3:34 PM

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any informative videos related to it?

prime badge Jul 3, 2021, 3:35 PM

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no, it won't be a prime number

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like for 6 it's 4

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it's a power of a prime number

oak chasm Jul 3, 2021, 3:36 PM

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Ahh.

next scroll Jul 3, 2021, 3:36 PM

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i brute forced it, there are no. such as 2,3,4,5,7,8,9,...

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for odd the ans is always 2

prime badge Jul 3, 2021, 3:38 PM

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i bet you don't need it to be very fast, just good enough

lavish cypress Jul 3, 2021, 3:38 PM

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strong citrus How are prime numbers used in security fields ?

One application is RSA. Wikipedia has a good article on it, if you know modular arithmetic.

oak chasm Jul 3, 2021, 3:38 PM

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I bet for even n, f(n) = 2 f(n/2).

woeful pulsar Jul 3, 2021, 3:38 PM

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it seems that f(i) <= 100 for all i up to 10^16

prime badge Jul 3, 2021, 3:38 PM

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I would pick a target f(i), say 4, and generate all numbers that have that f() in order

woeful pulsar Jul 3, 2021, 3:38 PM

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oak chasm I bet for even n, f(n) = 2 f(n/2).

f(4) is 3 which is not 2f(4/2)

prime badge Jul 3, 2021, 3:39 PM

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until n, so you know how many 4s there will be

next scroll Jul 3, 2021, 3:41 PM

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prime badge until n, so you know how many 4s there will be

i was thinking of counting them too, for 2 it is n/2, for 3 it is ... i don't know how to do this part

woeful pulsar Jul 3, 2021, 3:42 PM

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for 3, well it depends on remainder mod 6

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so 2 and 4 mod 6 get counted in

dry thunder Jul 3, 2021, 3:42 PM

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thanks!

woeful pulsar Jul 3, 2021, 3:42 PM

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for 4 it becomes remainder mod 12

dry thunder Jul 3, 2021, 3:42 PM

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its in pascals

strong furnace Jul 3, 2021, 3:45 PM

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if you can get the prime factorization start from 2 and the first missing prime would be it

prime badge Jul 3, 2021, 3:46 PM

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no

strong furnace Jul 3, 2021, 3:46 PM

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why

prime badge Jul 3, 2021, 3:46 PM

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it's not the first missing prime

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it's a power of a prime that's one larger than it already has

strong furnace Jul 3, 2021, 3:47 PM

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how can you disprove what I said ? my argument is the same argument as the sieve thing

oak chasm Jul 3, 2021, 3:48 PM

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f(6) = 4, but 6 is not missing 2.

strong furnace Jul 3, 2021, 3:48 PM

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I misinterpeted the problem my bad

prime badge Jul 3, 2021, 3:49 PM

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ok, so what are first numbers that give 4
6, then 18, 30

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maybe they just go by 12

oak chasm Jul 3, 2021, 3:49 PM

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Let me fire up Haskell.

prime badge Jul 3, 2021, 3:50 PM

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so you just divide n by 12, and that's how many 4s you'll have

oak chasm Jul 3, 2021, 3:51 PM

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First 10 are [6,18,30,42,54,66,78,90,102,114]

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Let me check if that holds for the first million.

alpine sable Jul 3, 2021, 3:52 PM

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how long does it take to finish highschool hw

jagged rapids Jul 3, 2021, 3:52 PM

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oak chasm Let me fire up Haskell.

Teach me, master.

prime badge Jul 3, 2021, 3:52 PM

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oak chasm Let me check if that holds for the first million.

yeah, it's all even numbers that aren't divisible by 4

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nothing more

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uh

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what

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yeah

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no

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so 10 is out because it's not divisible by 3

oak chasm Jul 3, 2021, 3:56 PM

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So, the first million equal to 4 are 12n + 6 for sequential ns.

oak chasm Jul 3, 2021, 3:58 PM

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jagged rapids Teach me, master.

If you insist: ```haskell

let f x = head . filter (\ n -> x mod n /= 0) $ [1 ..]
f 6
4
take 10 . filter ((== 4) . f) $ [1 ..]
[6,18,30,42,54,66,78,90,102,114]
and . take 1000000 . zipWith (==) [6, 18 ..] . filter ((== 4) . f) $ [1 ..]
True

vale wigeon Jul 3, 2021, 3:58 PM

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is that haskell

prime badge Jul 3, 2021, 3:58 PM

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as you go f(5), f(7)... that ~~mutiplier~~ step probably get multiplied by 5 and 7

oak chasm Jul 3, 2021, 3:58 PM

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Yes.

prime badge Jul 3, 2021, 4:02 PM

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no it's 12,12,60,840

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not pretty

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f(2) − numbers not divisible by 2
f(3) − numbers not divisible by 3, but divisble by 2
f(4) − numbers not divisible by 4, but divisble by 2 and 3

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all we need is how to get the distance between numbers from those

oak chasm Jul 3, 2021, 4:09 PM

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Do you mean f(n) = 2 - numbers not divisible by 2?

prime badge Jul 3, 2021, 4:09 PM

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yes

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that

oak chasm Jul 3, 2021, 4:10 PM

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f(x) = n are xs not divisible by n, but divisible by 2 through n - 1.

prime badge Jul 3, 2021, 4:10 PM

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well not really

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maybe

oak chasm Jul 3, 2021, 4:11 PM

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Well, it's the least nondivisor.

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No wait.

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Yeah, it's the least nondivisor, so it can't be divisible by n, but it has to be divisible by all the other numbers before n or else there's a lower nondivisor.

prime badge Jul 3, 2021, 4:12 PM

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okay

next scroll Jul 3, 2021, 4:12 PM

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well it works for 4

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i have to use round(n/12)

prime badge Jul 3, 2021, 4:13 PM

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so if it's divisible by x,y,z,a,b, that's their lcm

next scroll Jul 3, 2021, 4:13 PM

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not floor or ceil

prime badge Jul 3, 2021, 4:15 PM

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if lcm doesn;t grow, you're on f(6) for example, you skip it

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try that

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no, it doesn't add up, why 12,12,60,840

oak chasm Jul 3, 2021, 4:17 PM

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So:

f(2x + 1) = 2
f(2(3x + 1)) = f(2(3x + 2)) = 3
f(6(4x + 1)) = f(6(4x + 2)) = f(6(4x + 3)) = 4

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So how do we combine these into, say f(12x + 6) = 4 for the last line?

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Hmm, that might not be correct.

prime badge Jul 3, 2021, 4:19 PM

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[12,24,36,48,72,84,96,108,132,144] are f() = 7

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it has gaps

oak chasm Jul 3, 2021, 4:21 PM

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f(36) = 5, I think.

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5 doesn't divide 36, but it's less than 7.

prime badge Jul 3, 2021, 4:24 PM

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ok

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fix the program

next scroll Jul 3, 2021, 4:24 PM

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https://codeforces.com/contest/1542/status/C you can see submissions here now

Codeforces

Status - Codeforces Round #729 (Div. 2) - Codeforces

prime badge Jul 3, 2021, 4:24 PM

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no my bad

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that was actually for f() = 5

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sorry

oak chasm Jul 3, 2021, 4:26 PM

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f(2x + 1) = 2
f(6x + 2) = f(6x + 4) = 3
f(12x + 6) = 4

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Found out.

prime badge Jul 3, 2021, 4:27 PM

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well it checks out, the step is lcm, without numbers divisible by n

oak chasm Jul 3, 2021, 4:27 PM

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Right.

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Well, let's see.

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LCM(2, 3, 4) x + all numbers that 2 and 3 divide but 4 doesn't divide.

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12x + 6

prime badge Jul 3, 2021, 4:28 PM

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f() = 7 : [60,120,180,240,300,360,480,540,600,660]

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it skips 420

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and it will skip 840

oak chasm Jul 3, 2021, 4:29 PM

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LCM(2, 3, 4, 5, 6, 7) x + all numbers that 2, 3, 4, 5, 6 divide but 7 doesn't.
420x + 1, 420x + 2, 420x + 3, 420x + 4, 420x + 5, 420x + 6.

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No, that's not right.

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2, 3, 4, 5, 6 divide

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LCM(2, 3, 4, 5, 6) = 60

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420x + 60, 420x + 120, 420x + 180, 420x + 240, 420x + 300, 420x + 360.

prime badge Jul 3, 2021, 4:32 PM

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but for example, [2,4,8,10,14,16,20,22,26,28] is f() =3

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it doesn't have any excluded numbers

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even numbers are alerady not divisible by 3

oak chasm Jul 3, 2021, 4:33 PM

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6x + 6 is excluded.

prime badge Jul 3, 2021, 4:33 PM

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no wait 72 is

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right

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and 6 is right from the start

oak chasm Jul 3, 2021, 4:35 PM

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Looks like you just cross off the x coefficient from the constant terms.

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Let's try f(x) = 7.

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LCM(1 .. 7) = 420. LCM(1 .. 6) = 60.

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420 + 60(1 .. 6)

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f(x) = 2.

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LCM(1 .. 2) = 2. LCM(1 .. 1) = 1.

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2x + 1(1 .. 1).

prime badge Jul 3, 2021, 4:37 PM

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ok, so N / lcm, and then divide that by current f() and subtract

oak chasm Jul 3, 2021, 4:37 PM

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No, just get the two LCMs.

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LCM(1 .. n). LCM(1 .. n - 1).

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LCM(1 .. n) x + LCM(1 .. n - 1) (1 .. n - 1).

prime badge Jul 3, 2021, 4:38 PM

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we don;t need to generate the sequence

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we want the length

oak chasm Jul 3, 2021, 4:38 PM

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The length of what?

prime badge Jul 3, 2021, 4:38 PM

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the length of it, until it reaches n, which is the parameter

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so we divide n by lcm

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and from that, every 7th number will be excluded

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for _ in range(t):
    n = int(input())
    s = 1
    i = 2
    ans = n
    while s <= n:
        ans += n//s
        s = i*s//math.gcd(i,s)
        i += 1
    print(ans%(10**9+7))

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this doesn't subtract hmm

oak chasm Jul 3, 2021, 4:41 PM

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Looks like f(x) = 12 has no xs.

warped phoenix Jul 3, 2021, 4:41 PM

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moshill1

prime badge Jul 3, 2021, 4:41 PM

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12 is not a power of prime

oak chasm Jul 3, 2021, 4:42 PM

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Ahh.

prime badge Jul 3, 2021, 4:42 PM

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same as 6

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i don't get this program

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oh okay

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so like it skips numbers that don;t have xs, one at a time

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and adds 1 for each skip, so eventually it reaches the actual f(x) value

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idk

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some magic

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i just don;t understand why it doesn't need to subtract

oak chasm Jul 3, 2021, 4:54 PM

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Got a more efficient version of f:```haskell
let g x = go 1 2 3 x
where
go a b c x = if x mod a == 0 && x mod b /= 0
then c - 1
else go b (lcm b c) (c + 1) x

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Uses the LCM stuff.

alpine sable Jul 3, 2021, 4:57 PM

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prime badge Jul 3, 2021, 5:00 PM

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[2,3,2,3,2,4,2,3,2,3,2,5,2,3,2] f(x) for x in [1..15]

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all even numbers are at least 3

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the rest are 2

oak chasm Jul 3, 2021, 5:01 PM

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@alpine sable Notice that the second term is the previous first term.

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Sorry, the next first term.

prime badge Jul 3, 2021, 5:01 PM

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all numbers divisible by 6 are a t least 4, the rest are 3

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now i see

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i think

ocean sealBOT Jul 3, 2021, 5:02 PM

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Chai T. Rex

oak chasm Jul 3, 2021, 5:02 PM

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@alpine sable ^

winged citrus Jul 3, 2021, 5:08 PM

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hi

oak chasm Jul 3, 2021, 5:09 PM

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Hello.

winged citrus Jul 3, 2021, 5:10 PM

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i wanted to ask how the identity element of an expression is defined; i tried looking it up but i cant figure it out, maybe im phrasing it wrong? i watched a video on this topic but i cant figure out what's happening here

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what exactly do you do with an identity in this case? do you replace b with it?

ocean sealBOT Jul 3, 2021, 5:11 PM

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Chai T. Rex

oak chasm Jul 3, 2021, 5:11 PM

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So, find some value e such that those equations are true.

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For all values of a.

winged citrus Jul 3, 2021, 5:12 PM

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yes but, how do i put it into the "a*b = a+b=3"? do i replace b with it? wouldnt it just always be 1 otherwise?

oak chasm Jul 3, 2021, 5:12 PM

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isn't multiplication.

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It's a specially-defined operator.

winged citrus Jul 3, 2021, 5:12 PM

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OH

ocean sealBOT Jul 3, 2021, 5:12 PM

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Chai T. Rex

winged citrus Jul 3, 2021, 5:13 PM

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so a * x would be a + x + 3, and if x = -3 then it would still be a

oak chasm Jul 3, 2021, 5:13 PM

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Right.

winged citrus Jul 3, 2021, 5:14 PM

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got it, thanks, i was confused because i thought its multiplication and u need to find values of a and b to solve that equation

oak chasm Jul 3, 2021, 5:14 PM

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No problem.

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@prime badge So, you start n out as 1. You keep track of the LCM of all ns so far as you add 1 to n repeatedly. When the LCM changes, you have a new prime power.

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For each new prime power n, you have a certain number of values in your range of that problem that give f(x) = n.

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You add n times the number of values in the range to the sum.

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You keep doing that until you've covered all the values in the range.

prime badge Jul 3, 2021, 5:39 PM

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it's... hard to comprehend exactly

oak chasm Jul 3, 2021, 5:43 PM

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Well, remember how we got the forms of the inputs that produce a certain prime power output?

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Like LCM(1 .. n) x + LCM(1 .. n - 1) (1 .. n - 1)

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So, for each prime power n, you floor divide the maximum input by LCM(1 .. n) to get the maximum value of x.

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Then you find out what the maximum constant term is with that x such that the expression is less than or equal to the maximum input.

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Like let's say we're at n = 2. Well, LCM(1 .. 2) x + LCM(1 .. 1) (1 .. 1) is just 2x + 1.

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So, let's say the maximum input is 2000.

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floor of 2000/2 is 1000, so x = 1000.

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And then none of the constant terms (1 is the only constant term) work.

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So, we have 999 times the number of constant terms plus 0 extra constant terms.

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So, 2(999 + 0).

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Then we move on to the next prime power, 3.

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LCM(1 .. 3) x + LCM(1 .. 2) (1 .. 2) = 6x + 2 and 6x + 4.

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,calc floor(2000/6)

ocean sealBOT Jul 3, 2021, 5:49 PM

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Result:

oak chasm Jul 3, 2021, 5:49 PM

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So, x = 333.

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,calc 6*333

ocean sealBOT Jul 3, 2021, 5:49 PM

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Result:

oak chasm Jul 3, 2021, 5:49 PM

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So, 6x + 2 works but 6x + 4 doesn't.

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So, 3(333*2 + 1) for a total of 2(999 + 0) + 3(333*2 + 1).

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Then we go on to the next prime power, 5, and so forth.

glacial hedge Jul 3, 2021, 6:19 PM

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ugh

warped phoenix Jul 3, 2021, 6:26 PM

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is that gap at the top of the graph an example of a "hole"?

ancient creek Jul 3, 2021, 6:29 PM

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warped phoenix is that gap at the top of the graph an example of a "hole"?

what's the equation for this graph?

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Or is it not given?

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If it is a continuous function, then this is most likely an error on the "graphing software" side.

alpine sable Jul 3, 2021, 6:44 PM

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69+69

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https://tenor.com/view/lol-northernlion-tiktok-squad-laughing-gif-16360675

Tenor

ancient creek Jul 3, 2021, 6:48 PM

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alpine sable 69+69

opencry

oak chasm Jul 3, 2021, 6:50 PM

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@prime badge https://ideone.com/0WAeAX#stdout

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That's my solution to the original problem.

noble jewel Jul 3, 2021, 6:53 PM

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Hello, is does this proof make sense ?

Question: If U is a subspace of V, what is U + U

Answer: U + U is 2U, therefore 2U contains every vector in U times two (eg. if x in u, then 2x in U + U), but because U is closed under scalar multiplication, 1/2 x also exist, and therefore x is in U + U. This shows that every vector in U also exists in U + U. Therefore U + U = U

blissful musk Jul 3, 2021, 6:55 PM

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i need help, whats 34+35?

vale wigeon Jul 3, 2021, 6:57 PM

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blissful musk i need help, whats 34+35?

if your question can be answered with a calculator, it does not belong here

blissful musk Jul 3, 2021, 6:57 PM

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blink

vale wigeon Jul 3, 2021, 6:57 PM

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and if this was the setup to a joke (which it might've been, given how the answer is sixty-nine) it was not a very good one

noble jewel Jul 3, 2021, 6:57 PM

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I couldn't agree more

blissful musk Jul 3, 2021, 6:58 PM

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im out

ionic jewel Jul 3, 2021, 6:58 PM

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vale wigeon if your question can be answered with a calculator, it does not belong here

okay let's be real Wolfram could answer like half of the problems here with minimal wording changes

noble jewel Jul 3, 2021, 6:59 PM

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😦 Now my question is buried

ionic jewel Jul 3, 2021, 7:00 PM

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noble jewel Hello, is does this proof make sense ? Question: If U is a subspace of V, what...

this is saying that U and U+U span the same thing

oak chasm Jul 3, 2021, 7:00 PM

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I don't think that U + U is 2U. I think it's any vector in U plus any other vector in U.

noble jewel Jul 3, 2021, 7:00 PM

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Ah okay, thank you very much

ionic jewel Jul 3, 2021, 7:00 PM

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the result is still true, but the method would be wrong yes

noble jewel Jul 3, 2021, 7:01 PM

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ionic jewel this is saying that U and U+U span the same thing

I havent learned about span yet, ive been going though the book linear algebra done right and this questions is given before that chapter

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Thanks a lot for the replies tho, I'll keep trying

ocean sealBOT Jul 3, 2021, 7:02 PM

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Chai T. Rex

noble jewel Jul 3, 2021, 7:02 PM

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Ah yes, thanks

ionic jewel Jul 3, 2021, 7:02 PM

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a linear subspace is defined to be closed under addition, so you can use that too

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that's quite literally a property of a linear subspace

noble jewel Jul 3, 2021, 7:03 PM

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I got that U+U is a subset of U since its closed under addition, but thats all i got hahah

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Thanks a lot for the answers btw

wind coyote Jul 3, 2021, 7:08 PM

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Guys i really need help on this what’s-3

ionic jewel Jul 3, 2021, 7:08 PM

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negative three

wind coyote Jul 3, 2021, 7:09 PM

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Thx

verbal gull Jul 3, 2021, 7:09 PM

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https://gyazo.com/eb6d8e405fce4f83cf4e32a57be5e6e3

Gyazo

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trying to figure out this problem

ionic jewel Jul 3, 2021, 7:10 PM

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f'(x) is the slope of f(x)

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as in, when f(x) is decreasing, f'(x) is negative, etc

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f''(x) is the concavity of f(x), or the slope of f'(x)

spring harbor Jul 3, 2021, 7:15 PM

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Is this channel open?

noble jewel Jul 3, 2021, 7:15 PM

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I think it is given that there was no reply

spring harbor Jul 3, 2021, 7:15 PM

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Alright thank you

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Given f(x) and g(x).
The tangent at the point P(a,g(a)) to the graph of g is perpendicular to the tangent at the point Q(1,f(1)) to the graph of f. Determine g(a)

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I found the tangent line of f(x) which is y=x-1 (at point Q(1, f(1))

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So the slope of the perpendicular line is -1

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but I am not sure how to continue

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I got y-g(a) = -x+a

ionic jewel Jul 3, 2021, 7:18 PM

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wait

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these are R2 functions

spring harbor Jul 3, 2021, 7:18 PM

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R2?

ionic jewel Jul 3, 2021, 7:18 PM

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so isn't Q have to be Q(1,f(1))?

spring harbor Jul 3, 2021, 7:19 PM

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oh yeah i meant f(1)

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typo my bad

ionic jewel Jul 3, 2021, 7:19 PM

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okay making sure

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in that case you can find the slope of the tangent at f(1)

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read: f'(1)

spring harbor Jul 3, 2021, 7:19 PM

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i found it

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it is 1

ionic jewel Jul 3, 2021, 7:19 PM

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then find the reciprocal of that slope (for the perpendicular line)

spring harbor Jul 3, 2021, 7:19 PM

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which is -1

ionic jewel Jul 3, 2021, 7:20 PM

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then let g'(a) = -1

spring harbor Jul 3, 2021, 7:20 PM

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yes.

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got that as well

ionic jewel Jul 3, 2021, 7:20 PM

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so what's a?

spring harbor Jul 3, 2021, 7:20 PM

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no clue

ionic jewel Jul 3, 2021, 7:20 PM

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what's g'(a)

spring harbor Jul 3, 2021, 7:20 PM

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i got y-g(a) = -x + a

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oh

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wait

ionic jewel Jul 3, 2021, 7:20 PM

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why is there a y in there

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or an x for that matter

spring harbor Jul 3, 2021, 7:20 PM

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do we set g'(x) equal to -1?

ionic jewel Jul 3, 2021, 7:20 PM

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... yes

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you want the slope of g(x) at the point a to equal -1

spring harbor Jul 3, 2021, 7:21 PM

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oh damn

ionic jewel Jul 3, 2021, 7:21 PM

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g'(a) = -1

spring harbor Jul 3, 2021, 7:21 PM

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so we get 3/2

ionic jewel Jul 3, 2021, 7:21 PM

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solve for a, then solve for g(a)

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then ur done

spring harbor Jul 3, 2021, 7:21 PM

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yeahh i missed something simple

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thank you

ionic jewel Jul 3, 2021, 7:21 PM

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spring harbor i got y-g(a) = -x + a

whatever this thing is is what confused you

spring harbor Jul 3, 2021, 7:22 PM

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this is tangent line equation

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y-f(a) = f'(a)(x-a)

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I thought i had to use this

ionic jewel Jul 3, 2021, 7:22 PM

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you don't care about the line, just the slope, yeah

spring harbor Jul 3, 2021, 7:22 PM

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yeah thanks!

ionic jewel Jul 3, 2021, 7:22 PM

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✅

ivory otter Jul 3, 2021, 7:48 PM

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Hi

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$\frac{\cos^2 x}{\cos^2 x} = 1$

ocean sealBOT Jul 3, 2021, 7:49 PM

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MEOWBRO 父

ivory otter Jul 3, 2021, 7:50 PM

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but what if x is 90 ?

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then its 0

elfin snow Jul 3, 2021, 7:51 PM

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if it is 90 degrees then it becomes 0/0 which is undefined

ivory otter Jul 3, 2021, 7:51 PM

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yes

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but thats a problem if im trying to prove a trigonometric identity

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example:

elfin snow Jul 3, 2021, 7:51 PM

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trig proofs are the general case, you could put that it can not equal certain values

ivory otter Jul 3, 2021, 7:52 PM

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but then the proof would only be true if x != 0

elfin snow Jul 3, 2021, 7:53 PM

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well $x \neq \frac{\pi}{2} + \pi n \ \forall \ n \in \mathbb{Z}$

ivory otter Jul 3, 2021, 7:53 PM

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wait lemme show you instead

ancient creek Jul 3, 2021, 7:53 PM

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ivory otter then its 0

well that is an extraneous solution i believe

ivory otter Jul 3, 2021, 7:54 PM

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ancient creek well that is an extraneous solution i believe

sorry idk what that means lol

elfin snow Jul 3, 2021, 7:54 PM

#

I hate how the quantifiers bunch up with the variables instead of giving them some space like the element symbol

ancient creek Jul 3, 2021, 7:54 PM

#

ivory otter sorry idk what that means lol

"In mathematics, an extraneous solution is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem." - Wikipedia

ivory otter Jul 3, 2021, 7:56 PM

#

ivory otter Jul 3, 2021, 7:57 PM

#

ancient creek "In mathematics, an extraneous solution is a solution, such as that to an equati...

i see, what about the above example i showed then?

ancient creek Jul 3, 2021, 7:57 PM

#

Think of it like this:

y = x

Function is defined at x = 0

It is also true that

y = x * (x/x)

y = (x^2) / x

Now the function is no longer defined at 0??

This contradicts our previous statement, meaning that it actually is defined at 0, and us saying it is undefined at 0 is just an extraneous solution

ivory otter Jul 3, 2021, 7:58 PM

#

this is why i hate maths, always get stuck on the uneccessary/not so important stuff

#

ok so in other words

#

i can just do that

#

to prove trig identities?

ancient creek Jul 3, 2021, 8:00 PM

#

ocean seal **MEOWBRO 父**

Yes, this statement holds true for all values of x

ivory otter Jul 3, 2021, 8:01 PM

#

ok nice

ancient creek Jul 3, 2021, 8:02 PM

#

ivory otter

Suggestion: an easier method would be to multiply both sides by cos^2 (x)

You will get 1 = cos^2 (x) + sin^2 (x)

and we know this is true thanks to the Pythagorean identity

twilit shale Jul 3, 2021, 8:02 PM

#

Hello why is this the answer

#

context cardinal of a = m

#

and x is w/e

#

from book of proof

ivory otter Jul 3, 2021, 8:05 PM

#

ancient creek Suggestion: an easier method would be to multiply both sides by cos^2 (x) You w...

thanks

ancient creek Jul 3, 2021, 8:06 PM

#

np

twilit shale Jul 3, 2021, 8:07 PM

#

nvm i think i got it

#

its m+1 cuz m is the cardinal of a + the void set

tired hamlet Jul 3, 2021, 8:08 PM

#

How would I start this one?

sage jacinth Jul 3, 2021, 8:10 PM

#

tired hamlet How would I start this one?

well if it only has 25% remaining, then you should be able to know how many half lives passed

#

then you can go from there

sly mantle Jul 3, 2021, 8:10 PM

#

twilit shale its m+1 cuz m is the cardinal of a + the void set

that's exactly it

tired hamlet Jul 3, 2021, 8:11 PM

#

sage jacinth well if it only has 25% remaining, then you should be able to know how many half...

Thank you I’m so slow lol

twilit shale Jul 3, 2021, 8:12 PM

#

@sly mantle thanks a lot

glacial hedge Jul 3, 2021, 8:13 PM

#

uhh, I have a sorta stupid question... The answer to this is false right? because theta can be anything and p just has to be 1?

#

r u taking a test?

#

huh usually assignments dont have like a (6 points) (2 points) thing?

velvet forum Jul 3, 2021, 8:14 PM

#

lmao

glacial hedge Jul 3, 2021, 8:17 PM

#

also pretty sure u dont have to justify things on homework till higher level math classes...

#

Lmao he deleted it

tired hamlet Jul 3, 2021, 8:25 PM

#

How would I do this one? Would I plug in each option for t until I get 8000?

sage jacinth Jul 3, 2021, 8:27 PM

#

that isn't really an efficient method especially if you lack a calculator

#

maybe attempt the problem first and see what you get

jagged trout Jul 3, 2021, 8:28 PM

#

I think P = 4000?

tall wing Jul 3, 2021, 8:28 PM

#

is this an examination @tired hamlet

tired hamlet Jul 3, 2021, 8:28 PM

#

No, practice problems

tall wing Jul 3, 2021, 8:28 PM

#

ok

velvet forum Jul 3, 2021, 8:33 PM

#

u just have to plug in the value in yhe formula

#

it asked for double so just plug in 8000 in P

tired hamlet Jul 3, 2021, 8:35 PM

#

I just got that now I’m solving for A=8000

sage jacinth Jul 3, 2021, 8:37 PM

#

just sub then solve for t

velvet forum Jul 3, 2021, 8:37 PM

#

u know n, r, and p

jagged trout Jul 3, 2021, 8:39 PM

#

btw.
$e = \lim_{x \to \infty} (1+\frac{1}{n})^n$

ocean sealBOT Jul 3, 2021, 8:39 PM

#

Moriarty

sage jacinth Jul 3, 2021, 8:40 PM

#

true

velvet forum Jul 3, 2021, 8:41 PM

#

8000 = 4000(1 + (.0075/12)^12t

sage jacinth Jul 3, 2021, 8:41 PM

#

yes now divide then take the log and solve

velvet forum Jul 3, 2021, 8:41 PM

#

I'm actually not sure if it's 12 for monthly compounded but i think so

sage jacinth Jul 3, 2021, 8:41 PM

#

its 12

tired hamlet Jul 3, 2021, 8:41 PM

#

I just did that and I got t=ln2/12ln(12.75/12)

velvet forum Jul 3, 2021, 8:41 PM

#

ok

sage jacinth Jul 3, 2021, 8:42 PM

#

that doesn't look correct

tired hamlet Jul 3, 2021, 8:42 PM

#

Yeah idk what happened

velvet forum Jul 3, 2021, 8:43 PM

#

it should be roughly 92

#

make sure you add more parentheses

#

so you don't get your order of operations mixed up

sage jacinth Jul 3, 2021, 8:44 PM

#

yup

#

i just got that as well

tired hamlet Jul 3, 2021, 8:44 PM

#

I got 0.95 so I think I just messed up my decimals somewhere lol

sage jacinth Jul 3, 2021, 8:44 PM

#

it should be ln(1.000625) instead of ln(1.0625)

tired hamlet Jul 3, 2021, 8:45 PM

#

Ok thx that’s why the decimal was shifted over 2 places

jagged trout Jul 3, 2021, 8:47 PM

#

,w 8000 = 4000 * e^(0.75 * t)

ocean sealBOT Jul 3, 2021, 8:47 PM

#

Results provided by WolframAlpha

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

warped phoenix Jul 3, 2021, 9:02 PM

#

is what i wrote here true?

strong furnace Jul 3, 2021, 9:03 PM

#

first half yes (assuming some defined base) second half no

strong citrus Jul 3, 2021, 9:04 PM

#

warped phoenix is what i wrote here true?

Instead of 3.84 write 3.8416

#

Just to be more exact

fringe yoke Jul 3, 2021, 9:05 PM

#

#

Why is it not A) Residents of the same city

#

For D) I could see how the standard deviation would be lower, so there is less variability in the data and therefore a smaller margin of error, but there is a just data from one specific place

#

you know?

strong furnace Jul 3, 2021, 9:08 PM

#

accurate data - ❎
error less data 💯

#

thats what this sounds like

fringe yoke Jul 3, 2021, 9:08 PM

#

???

strong furnace Jul 3, 2021, 9:09 PM

#

they don't care about how accurate your data represents what you are surveying

#

they just want less deviation

fringe yoke Jul 3, 2021, 9:09 PM

#

I see

warped phoenix Jul 3, 2021, 9:09 PM

#

ancient creek what's the equation for this graph?

sorry i took so long, i dont have the equation but it was either a logarithmic/exponential function so it was going to be continuous if im not mistaken

fringe yoke Jul 3, 2021, 9:09 PM

#

Doesn't less accurate data mean smaller margin of error?

#

Tho

strong furnace Jul 3, 2021, 9:09 PM

#

not necessarily

fringe yoke Jul 3, 2021, 9:09 PM

#

the actual mean will be way different

tired hamlet Jul 3, 2021, 9:10 PM

#

Was the correct answer B?

fringe yoke Jul 3, 2021, 9:10 PM

#

Nope

strong furnace Jul 3, 2021, 9:10 PM

#

has to be D

jagged trout Jul 3, 2021, 9:10 PM

#

@tired hamlet
8000 = 4000 * e^(0.75 * t) | :4000
2 = e^(0.75 * t) | ln
ln(2) = 0.75t | : 0.75
ln(2)/0.75 = t
t ~ 0.924196

So it must be minimum 92 months

strong furnace Jul 3, 2021, 9:10 PM

#

restaurant has variety

fringe yoke Jul 3, 2021, 9:10 PM

#

But listen

strong furnace Jul 3, 2021, 9:10 PM

#

but they go into detail

#

about how school is same

#

daily

fringe yoke Jul 3, 2021, 9:10 PM

#

Sure the standard deviation will be lower in D), but that is a special group of individuals

#

The actual number of vegetables eaten will not be the same as this group

#

Or it will be more different

#

So there is a bigger margin of error

#

despite the low standard deviation

strong furnace Jul 3, 2021, 9:11 PM

#

margin of error is not based on actual data

#

it is based on mean of your own data

fringe yoke Jul 3, 2021, 9:11 PM

#

ohhh

#

really?

#

The margin of error determines the confidence interval

#

And this confidence interval is likely to have the true mean in the interval

strong furnace Jul 3, 2021, 9:12 PM

#

has to do with standard deviation

#

so it has to be same dataset

fringe yoke Jul 3, 2021, 9:12 PM

#

But

#

think about it

lilac snow Jul 3, 2021, 9:13 PM

#

fringe yoke

Haha, SAT practice test?

fringe yoke Jul 3, 2021, 9:13 PM

#

What if this group of students who are on a diet eat 20 vegetables everyday each on average

#

The true national average would probably be like 2 or 3 because they don't care about their health like these diet people

#

Sure if they all follow the same diet

#

they have to each have 20 vegetables everyday

#

it will be a low standard deviation

lilac snow Jul 3, 2021, 9:14 PM

#

jagged trout <@!439563393913978880> 8000 = 4000 * e^(0.75 * t) | :4000 2 = e^(0.75 * t) | ln...

Where did you get e from?

fringe yoke Jul 3, 2021, 9:14 PM

#

but it will be a terrible predictor for actual mean

#

and therefore the interval of confidence will be larger

strong furnace Jul 3, 2021, 9:14 PM

#

but that is not what the problem is talking about by margin of error

#

since it has a definition

fringe yoke Jul 3, 2021, 9:15 PM

#

margin of error defines confidence interval

#

I guess

#

ugh

#

god

strong furnace Jul 3, 2021, 9:15 PM

#

does confidence interval have anything to do with accuracy of your survey?

fringe yoke Jul 3, 2021, 9:15 PM

#

yes

#

Oh wait

#

It's the true mean for that population

#

if he picks the dieters

#

the confidence interval will be the true mean for that specific population

#

not the whole country

#

so if he picks that group

strong furnace Jul 3, 2021, 9:16 PM

#

it has to do with standard deviation and mean of your own dataset

#

yeah

fringe yoke Jul 3, 2021, 9:16 PM

#

I get it

#

If the individual picks the dieting group

#

They will all probably be following the same diet and stuff

#

eating the same amount of regular veggies

#

so there will be a low standard deviation

#

and for the dieters, the mean value from the survey will therefore be an excellent representation of the actual data, so there will be a smaller margin of error

#

And the interval of confidence will be tight around the mean

#

This makes sense I think thantk you Sussy

strong furnace Jul 3, 2021, 9:18 PM

#

fringe yoke and for the dieters, the mean value from the survey will therefore be an excelle...

it is not an excellent representation of the actual data

#

it is just consistent

#

not accurate

fringe yoke Jul 3, 2021, 9:19 PM

#

what do you mean?

#

If you take the dieters

#

they will all be eating a similar amount of veggies everyday

strong furnace Jul 3, 2021, 9:19 PM

#

this dataset does not represent the country's diet practices

#

just that specific group's

fringe yoke Jul 3, 2021, 9:19 PM

#

yeah not the country

#

yeah yeah that's why the answer is D

#

if it were representative of the whole country, the margin of error would be super big

#

but it doesn't talk about that in the question

#

I hope I am understanding this in the right way ://

jagged trout Jul 3, 2021, 9:20 PM

#

@lilac snow $e^x = \lim_{x \to \infty} (1 + \frac{x}{n})^n$

strong furnace Jul 3, 2021, 9:20 PM

#

sounds about right to me

lilac snow Jul 3, 2021, 9:21 PM

#

Oh okay

#

Thank you

fringe yoke Jul 3, 2021, 9:21 PM

#

I will think on this for a bit

ocean sealBOT Jul 3, 2021, 9:21 PM

#

Moriarty

lavish cypress Jul 3, 2021, 9:21 PM

#

fringe yoke if it were representative of the whole country, the margin of error would be sup...

Margin of error depends only on your data, not what it's supposed to be representing.

fringe yoke Jul 3, 2021, 9:21 PM

#

Really?

lilac snow Jul 3, 2021, 9:21 PM

#

Is the proof ofthat simple?

fringe yoke Jul 3, 2021, 9:21 PM

#

Oh wait

alpine sable Jul 3, 2021, 9:21 PM

#

does anyone have any idea about this

fringe yoke Jul 3, 2021, 9:21 PM

#

So if there is a small margin of error

#

But it's a super specific population

#

and you want it to represent something more general

#

what will lower is the percent confidence

#

right?

#

not the margin of error?

#

So we can have a super small margin of error, but we will not be confident at all that the true mean lies within that range

#

It's really weird that it works this way tbh

lavish cypress Jul 3, 2021, 9:22 PM

#

The margin of error would be small, but it would be pretty much meaningless

fringe yoke Jul 3, 2021, 9:22 PM

#

yeah ok

#

Yes that makes so much sense now

#

#

So the answer is D)

#

right?

#

yes

lavish cypress Jul 3, 2021, 9:23 PM

#

Ye

fringe yoke Jul 3, 2021, 9:23 PM

#

it will have mega low % confidence for representing the countries mean veggetable consumption

#

BUt it will be super small margin of error

#

beacuase they all eating similar amounts

#

This is great thanks you

warped phoenix Jul 3, 2021, 9:25 PM

#

@fringe yoke what type of question is that?

#

is it logic?

jagged trout Jul 3, 2021, 9:25 PM

#

lilac snow Is the proof ofthat simple?

https://www.youtube.com/watch?v=2nUJMP_ZnnI

YouTube

blackpenredpen

the fact, again (with a definition of e)

By l'hopital's rule, https://www.youtube.com/watch?v=HM-kwHR4VO4

The other def. of e https://www.youtube.com/watch?v=SxJ7X8vE-f0

I call this limit "the fact" with my students, so we can refer to this easily whenever we need to calculate such limit. ,
Limit as x goes to infinite, (1+a/x)^(bx), using definition of e,
Limit of (1+a/n)^(bn) as ...

▶ Play video

warped phoenix Jul 3, 2021, 9:25 PM

#

cuz doesnt choice D just make more sense than any of the other ones?

strong furnace Jul 3, 2021, 9:27 PM

#

if you are looking for proof of (1+1/x)^(x) as x->inf , it is defined to be e

fringe yoke Jul 3, 2021, 9:27 PM

#

No it's statistics

#

Yeah it made sense to me too

#

But I was confusing percent confidence with confidence interval with margin of error

#

the two are completely different

#

i mean not completely but you get the point

lavish cypress Jul 3, 2021, 9:28 PM

#

I think you also have a misunderstanding of confidence percent

#

But if your sample isn't representative of the population, all the confidence interval and moe stuff is meaningless

neat haven Jul 3, 2021, 9:31 PM

#

Can someone help me understand this?

#

#

Why does x prime = 1?

#

If point p can lie anywhere on the circle, x can range anywhere from 0-1 right?

fringe yoke Jul 3, 2021, 9:32 PM

#

lavish cypress I think you also have a misunderstanding of confidence percent

What do you mean?

#

% confidence in the interval of confidence goes down the less representative your sample is of the general pop.

lavish cypress Jul 3, 2021, 9:34 PM

#

Well I guess that's good enough for SAT.

fringe yoke Jul 3, 2021, 9:34 PM

#

no no

#

tell me more

#

what am I saying wrong

lavish cypress Jul 3, 2021, 9:38 PM

#

If you compute the n% confidence interval of a bunch of random samples, n% of them will contain the population mean. However, the requirement is that these samples are random. Therefore, the confidence interval for a sample consisting of students on a diet is meaningless when you take the population to be Americans.

fringe yoke Jul 3, 2021, 9:39 PM

#

yes

#

Yeah

#

it's meaningless because the % confidence goes down

#

we can't be confident at all that the true mean falls within that interval

jagged trout Jul 3, 2021, 9:41 PM

#

neat haven If point p can lie anywhere on the circle, x can range anywhere from 0-1 right?

What do you mean exactly?

neat haven Jul 3, 2021, 9:47 PM

#

jagged trout What do you mean exactly?

In the highlighted part

#

Point p lies on the outer edge of a unit circle

#

So the x of the point should range from 0-1

#

I’m so confused where the one comes from in the highlighted part

jagged trout Jul 3, 2021, 9:55 PM

#

Maybe because e^(i*x) = cos(x) + i * sin(x)

neat haven Jul 3, 2021, 10:02 PM

#

That seems awfully complex

jagged trout Jul 3, 2021, 10:03 PM

#

neat haven That seems awfully complex

https://www.youtube.com/watch?v=ZPGHuuk2bKw

YouTube

danielwedge

2.71828183: The number e song

A song about an awesome number. Lyrics and a higher quality version available at http://danielwedge.com/esong/

▶ Play video

neat haven Jul 3, 2021, 10:04 PM

#

I think its not talking about the points

#

The line from the origin to the points

#

That makes a bit more sense

#

Whatever

#

I’m just accepting what they say as fact

#

Too difficult

sullen karma Jul 3, 2021, 10:18 PM

#

What’s I then

#

Just tying to figure out how e^i Pi plus 1 = 0

jagged trout Jul 3, 2021, 10:20 PM

#

i^2 = -1

sullen karma Jul 3, 2021, 10:21 PM

#

Ok

#

I googled it it was the square root of -1

#

Or that

jagged trout Jul 3, 2021, 10:25 PM

#

https://www.youtube.com/watch?v=ysVcAYo7UPI

YouTube

Khan Academy

Introduction to i and imaginary numbers | Imaginary and complex num...

Introduction to i and imaginary numbers

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/i_precalc/e/imaginary_unit_powers?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Watch the next lesson: https://www.khanacademy.org/math/precalculus/imaginary_comple...

▶ Play video

sullen karma Jul 3, 2021, 10:25 PM

#

Oh ty

nova shard Jul 3, 2021, 10:39 PM

#

(sorry for the messy work) i included some negatives i feel as though are flawed. did i go through this/approach this right?

Screen_Shot_2021-07-03_at_6.36.22_PM.png

fringe yoke Jul 3, 2021, 10:48 PM

#

#

@nova shard

nova shard Jul 3, 2021, 10:49 PM

#

ohh

#

wait, how did you get (x^2+0x)

#

instead of (x^2-0x)

fringe yoke Jul 3, 2021, 10:50 PM

#

#

-0x = 0x

#

-0 is not a thing btw

#

I mean it is

#

but 0=0

#

you know?

nova shard Jul 3, 2021, 10:50 PM

#

OHH

fringe yoke Jul 3, 2021, 10:50 PM

#

-0 = 0

nova shard Jul 3, 2021, 10:50 PM

#

thanks man lmao

fringe yoke Jul 3, 2021, 10:50 PM

#

-0 = (-1) (0) = 0

#

-0 = -124124124(0) = 0

#

-0 isn't a thing

#

But it doesn't matter

#

That wasn't your mistake

#

btw

nova shard Jul 3, 2021, 10:54 PM

#

oh

#

incredible

fringe yoke Jul 3, 2021, 10:54 PM

#

When doing long division

#

Do what i did]

#

put -( p(x) _

#

-( p(x) )

#

when you subtract

#

In the first line you had 0-(-2x)

#

And you treated it as 0-(2x)

#

Do you understand?

nova shard Jul 3, 2021, 10:56 PM

#

OHH

#

yeah i get it

#

yeah i put 0-(-2x) and ended up with negative 2 completely ignoring the negative for 2x

#

thinkies thanks man

fringe yoke Jul 3, 2021, 11:00 PM

#

Yeah

#

always but a -(what you are subtracting)

#

it makes it more clear

nova shard Jul 3, 2021, 11:01 PM

#

gotcha

#

wait

#

question

#

why-

#

oh

#

nvm

warped phoenix Jul 3, 2021, 11:10 PM

#

For the function $A(t) = 2000e^{0.08t}$

ocean sealBOT Jul 3, 2021, 11:10 PM

#

TheMane3

warped phoenix Jul 3, 2021, 11:11 PM

#

T represent time in years, A represents the future value of the investment, 2000 here is the initial investment, and 0.08 is the interest rate

#

how would I figure out how long in years it would take for the money to double?

ocean sealBOT Jul 3, 2021, 11:12 PM

#

TheMane3

warped phoenix Jul 3, 2021, 11:13 PM

#

what i did was divide both sides by 2000

ocean sealBOT Jul 3, 2021, 11:13 PM

#

TheMane3

warped phoenix Jul 3, 2021, 11:13 PM

#

then i did ln on both sides

ocean sealBOT Jul 3, 2021, 11:14 PM

#

TheMane3

warped phoenix Jul 3, 2021, 11:14 PM

#

and then i divided both sides by 0.08

#

$\frac{ln2} {0.08} = t$

ocean sealBOT Jul 3, 2021, 11:15 PM

#

TheMane3

thorn kindle Jul 3, 2021, 11:38 PM

#

$\frac{f(\infty)-f(-\infty)}{\infty-(-\infty)}$

ocean sealBOT Jul 3, 2021, 11:38 PM

#

AMD

thorn kindle Jul 3, 2021, 11:41 PM

#

Difference quotient over R

rocky cloak Jul 4, 2021, 12:14 AM

#

Is there a name for the following procedure in probability

#

I flip some coins or otherwise observe some binary outcomes

#

I then make a probability distribution of "what would be the probability of this particular outcome given this inherent probability"

#

I then decide what a reasonable range of values for the underlying probability is using the this pdf treating the mode of it as "the mosty likely underlying probability"

noble sinew Jul 4, 2021, 12:21 AM

#

likelihood function and maximum likelihood estimation

rich basin Jul 4, 2021, 12:25 AM

#

Screen_Shot_2021-07-04_at_10.25.30_am.png

#

For (b), i don't get why it is half my answer

#

So i got my answer through grouping the I's together and calling it as one unit, which makes the total word count 8

#

And then i calculate the permutation as 8!

#

,w solve 8!

ocean sealBOT Jul 4, 2021, 12:26 AM

#

Results provided by WolframAlpha

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

rocky cloak Jul 4, 2021, 12:30 AM

#

noble sinew likelihood function and maximum likelihood estimation

oh yeah i suppose its just a single variable fit to some data isnt it

#

thanks!

rich basin Jul 4, 2021, 12:34 AM

#

Woudl anyone be able to help me please?

#

<@&286206848099549185>

alpine sable Jul 4, 2021, 12:43 AM

#

rich basin

8!/2! since there are 2 'n' in 'definition'

rich basin Jul 4, 2021, 12:48 AM

#

@alpine sable How did i not see there is an N

#

Screen_Shot_2021-07-04_at_10.49.12_am.png

#

Also rather confsued with b as wel

#

Nevermind i managed to get that

#

Screen_Shot_2021-07-04_at_10.49.58_am.png

#

Same with b

alpine sable Jul 4, 2021, 12:50 AM

#

Hm

#

I'll let someone take over since my skills aren't that great

rich basin Jul 4, 2021, 12:51 AM

#

so i did 3p2 *8!

#

3 choose 2 for which the singer is next to the drummer

#

and then i made it as if the drummer with the singer are like 1 unit

#

and multiplied by the swapping order

#

The only thing, is that it might cause some duplicates

#

Which is very hard to divide out

noble sinew Jul 4, 2021, 1:03 AM

#

Why 3 choose 2? If we call the drummer A and the two singers B, C then for each position there is either BAC or CAB (so 2 options)

#

Also remember you want all options where they aren’t like that, so your answer will be answer from a) minus ways they can sit together

rich basin Jul 4, 2021, 1:10 AM

#

@noble sinew So you are saying that, because there is an option forexample the particular singer B can sit next to the drummer A, for which the drummer A is sitting next to the singer D, which D is an ordinary singer

noble sinew Jul 4, 2021, 1:11 AM

#

All you care about is if A is between B and C

rich basin Jul 4, 2021, 1:14 AM

#

Okay thanks, but wouldn't my way would work

#

If i'd included the cases when one of particular singers sat next to the drummer

noble sinew Jul 4, 2021, 1:16 AM

#

Why do you care if only 1 sits next to

rich basin Jul 4, 2021, 1:17 AM

#

Well the question is asking the cases for which the two particular singer does not sit next to the drummer

#

So therefore you can have one particular singer sitting next to the drummer and one ordinary one, and it would be fine

#

Do you think, what i did wrong with my way, is that i did not include that

#

I know that your way is more efficient and better. But just want to know if this would still work

#

And that my deduction for why it was wrong was correct?

noble sinew Jul 4, 2021, 1:21 AM

#

Oh

rich basin Jul 4, 2021, 1:22 AM

#

Do you think this would still work?

noble sinew Jul 4, 2021, 1:22 AM

#

Well they don’t have to be a group then so can’t really do it like that so missing a lot of cases

rich basin Jul 4, 2021, 1:23 AM

#

Yeah, i would include the cases for which they are not grouped

#

so case 1: Non grouped + Case 2: 1 particular singer A sitting next to the drummer + Case 3: 1 particular singer B sitting next to the drumer

noble sinew Jul 4, 2021, 1:24 AM

#

Sure can work

rich basin Jul 4, 2021, 1:26 AM

#

And also this would be the last question

#

Screen_Shot_2021-07-04_at_11.26.20_am.png

#

I tried doing it by cases

#

And this kind of looks like a pascal traingle

#

so i did something like 4! + 4C2 * 3! + 4C3 * 2! + 4 + 4C2 * 2

#

if you want i could go into the details why i did that

noble sinew Jul 4, 2021, 1:33 AM

#

Looks fine

ionic jewel Jul 4, 2021, 1:34 AM

#

is this not 16 choose 4

molten jungle Jul 4, 2021, 1:34 AM

#

If ƒ (x) = |5 − 3x| , then ƒ (2) is:
A. ƒ (−1)
B. ƒ(4/3)
C. ƒ (−2)
D. ƒ (0)
E. ƒ (1)

sad

rich basin Jul 4, 2021, 1:34 AM

#

noble sinew Looks fine

But the problem is with the answer, i didn't get the correct answer

#

@noble sinew The answer is 256

noble sinew Jul 4, 2021, 1:42 AM

#

Oh just 4^4 lol

rich basin Jul 4, 2021, 1:43 AM

#

Why is it 4&4

#

4^4, i don't get the intution behind it @noble sinew

white crown Jul 4, 2021, 1:44 AM

#

molten jungle If ƒ (x) = |5 − 3x| , then ƒ (2) is: A. ƒ (−1) B. ƒ(4/3) C. ƒ (−2) D. ƒ (0) E. ƒ...

B. f(4/3)

noble sinew Jul 4, 2021, 1:45 AM

#

Checking for 2 and 3 people that 4^2 and 4^3 is correct is 1 way

rich basin Jul 4, 2021, 1:45 AM

#

The only thing i think I did not cover is that i did not use the 4P3, in which i made the 2 people in one room as one unit

#

But then i'm confused on how i should writing for which there is only 2 people per room

#

I was thinking of something like 4C2 * 4P3 * 3!

#

but that can't be right

#

I think i should just remove the 3!

#

Because the 4P3 already apply the ordering for me

#

That would mean it would be 144

molten jungle Jul 4, 2021, 1:48 AM

#

white crown B. f(4/3)

thank u, could u tell me the procedure HappySmug

rich basin Jul 4, 2021, 1:48 AM

#

That would together bring the total to 180

#

Which is 76 short

white crown Jul 4, 2021, 1:49 AM

#

molten jungle thank u, could u tell me the procedure <:HappySmug:581696724330872838>

f(2)=1, so find which of A-E equal 1 also

rich basin Jul 4, 2021, 1:50 AM

#

Let me see if i add the part when i made both of them 4C2

#

So basically the equation i have right now is 4! + 4C2*4P3 + 4C3 * 2! + 4 + 4C2 * 2

#

which is 192 in total

molten jungle Jul 4, 2021, 1:53 AM

#

white crown f(2)=1, so find which of A-E equal 1 also

but how did u f(2)=1? sorry for being really dumb pleadcry

rich basin Jul 4, 2021, 1:55 AM

#

The problem is that i still am lower than the actual answer

median hound Jul 4, 2021, 2:00 AM

#

yo i need help

#

#

alva is trying to prove congrounecy with two triangles

#

but i don't know how to get said triangles or use a certain congruency law to prove it

#

reply to this with help plz

#

nvm i got it right 🙂

#

but i still dumb with this topic

rich basin Jul 4, 2021, 2:07 AM

#

<@&286206848099549185>

white crown Jul 4, 2021, 2:12 AM

#

molten jungle but how did u f(2)=1? sorry for being really dumb <a:pleadcry:819328960231374968...

f(2)=|5 − 3(2)|=|-1|=1

molten jungle Jul 4, 2021, 2:16 AM

#

white crown f(2)=|5 − 3(2)|=|-1|=1

thank u happypeepo

rich basin Jul 4, 2021, 2:18 AM

#

I am still sad, still have no idea how to get the answer

#

sad

worthy grail Jul 4, 2021, 2:30 AM

#

Hello

#

Does this have a closed form solution for $\tau$?

ocean sealBOT Jul 4, 2021, 2:31 AM

#

fakuivan

worthy grail Jul 4, 2021, 2:59 AM

#

I'm thinking it doesn't, hence why every single symbolic solver I tried fails thonkzoom

turbid beacon Jul 4, 2021, 3:09 AM

#

lets say I have data of how two people rated some N movies from 1-10

#

Cosine Similarity is a good method of finding out how close those two people are right?

#

also should you replace each of the 1-10s with the z-score instead

#

I think this is better but the problem is the numbers are very close and due to the nature of how people score things there are a lot more values in the 7-10 range than 1-6

#

essentially I am asking how would you deal with outliers?

#

would you calculate standard deviation without the outliers and then use that number instead?

#

is there a better server I should be asking this in lmao

late burrow Jul 4, 2021, 4:16 AM

#

Someone help me on Linear equations

#

Mostly Elimination method and Cross Multiplication method

ember lava Jul 4, 2021, 4:26 AM

#

late burrow Mostly Elimination method and Cross Multiplication method

where are you struggling

#

what step do you not understand

glacial hedge Jul 4, 2021, 4:38 AM

#

Anyone know what this question is asking? I know curl of a gradient of a function with continuous 2nd partial derivatives is 0. but that doesnt apply to just the funciton??? Im very confused

lavish cypress Jul 4, 2021, 4:45 AM

#

glacial hedge Anyone know what this question is asking? I know curl of a gradient of a functio...

Divergence of a curl is also 0, and in R³ if it is zero, then the vector field is a curl of another vector field.

unkempt needle Jul 4, 2021, 4:45 AM

#

it's asking : does there exist any vector field F such that curl F = G, and furthermore, F has all continuous second-order derivatives?

glacial hedge Jul 4, 2021, 4:49 AM

#

unkempt needle it's asking : does there exist any vector field F such that curl F = G, and fur...

How would i prove that... instead of reverse engineering the curl of G?

glacial hedge Jul 4, 2021, 4:49 AM

#

lavish cypress Divergence of a curl is also 0, and in R³ if it is zero, then the vector field i...

???????

#

how is this related to divergence

lavish cypress Jul 4, 2021, 4:55 AM

#

If F is a vector field, div(curl(F)) = 0.
If A is a vector field, then div(A) = 0 implies that A = curl(B), where B is another vector field

glacial hedge Jul 4, 2021, 4:56 AM

#

Ohhhhhhhhhhhhhhhhhhhh

#

ty

indigo minnow Jul 4, 2021, 4:57 AM

#

hey

#

how do we find how many 2 multipliers in 30!

glacial hedge Jul 4, 2021, 4:58 AM

#

?

indigo minnow Jul 4, 2021, 4:59 AM

#

yeah thats the question

glacial hedge Jul 4, 2021, 4:59 AM

#

the question doesnt even english properly

indigo minnow Jul 4, 2021, 4:59 AM

#

you gotta learn english man...

glacial hedge Jul 4, 2021, 4:59 AM

#

dude i know english

indigo minnow Jul 4, 2021, 4:59 AM

#

just dont distract people from my question

#

stfu

glacial hedge Jul 4, 2021, 4:59 AM

#

you stfu

#

your question doesnt even make sense

#

Is what im trying to say

indigo minnow Jul 4, 2021, 5:00 AM

#

dude piss off if your question is done

#

my question aint your business

glacial hedge Jul 4, 2021, 5:00 AM

#

im tryn answer ur question...

indigo minnow Jul 4, 2021, 5:00 AM

#

ok let me ask again

#

how many 2 multipliers are there in 50!

#

(fifty factorial)

glacial hedge Jul 4, 2021, 5:01 AM

#

r u asking how many factors of 2 are there in 50!

indigo minnow Jul 4, 2021, 5:02 AM

#

yes

glacial hedge Jul 4, 2021, 5:03 AM

#

well the # of 2 factors in a*b is number of 2 factors in a + number of 2 factors in b

#

so the question is really asking how many factors of 2 are there in 1-50

indigo minnow Jul 4, 2021, 5:03 AM

#

hmm,yes.

glacial hedge Jul 4, 2021, 5:03 AM

#

which is much easier to solve computationally

#

i.e finding all even numbers, and seeing if they are divisible by 4, 8, etc and adding the sums up

indigo minnow Jul 4, 2021, 5:04 AM

#

but there is a short way

#

you divide 50 to 2 continuously

#

add all denominators

#

thats how our teachers solve

#

but I dont know how this works

#

do you know this method?

#

can u prove it

glacial hedge Jul 4, 2021, 5:06 AM

#

Um

#

what exactly does add all denominators mean

indigo minnow Jul 4, 2021, 5:06 AM

#

wait let me send an image

#

just like that

glacial hedge Jul 4, 2021, 5:08 AM

#

uhhh

#

where exactly did your teacher get 25/2 = 16 or 14 ( i cant tell which number it is)

indigo minnow Jul 4, 2021, 5:09 AM

#

its 14

#

you ignore remainders

#

its not just one teacher

glacial hedge Jul 4, 2021, 5:09 AM

#

14*2 = 28

indigo minnow Jul 4, 2021, 5:10 AM

#

all teachers I know did this that way

#

and when I google it

#

I cant find it

glacial hedge Jul 4, 2021, 5:10 AM

#

what class are you taking

indigo minnow Jul 4, 2021, 5:10 AM

#

I dont even know dude education here is fucked up

#

we are learning numbers and factorials

#

ok nevermind lets try another question if you are down

glacial hedge Jul 4, 2021, 5:14 AM

#

yeah sure.

#

i mean your teachers are correct... but their method is... sketchy

indigo minnow Jul 4, 2021, 5:14 AM

#

lmao idk

#

umm nevermind i cant find question xd

#

but thanks for help lol

glacial hedge Jul 4, 2021, 5:15 AM

#

sure...

glacial hedge Jul 4, 2021, 5:16 AM

#

lavish cypress If F is a vector field, div(curl(F)) = 0. If A is a vector field, then div(A) = ...

so the answer is false because the div F = y^2+y^2 which isn't 0

#

?

alpine sable Jul 4, 2021, 5:32 AM

#

pls send ans in dm

#

<@&286206848099549185>

rigid smelt Jul 4, 2021, 5:45 AM

#

please ping helpers after a minimum of 15min

#

you can rewrite 24 as 4*6

#

thats a hint, the rest is for you to figure out

carmine lion Jul 4, 2021, 5:47 AM

#

how do i solve this equation

#

$2\cos{2x}=\tan{\frac{x}{2}}, 0\leq x\leq2\pi$

rigid smelt Jul 4, 2021, 5:49 AM

#

are you sure its tan(x/x)?

ocean sealBOT Jul 4, 2021, 5:49 AM

#

abe

idle trench Jul 4, 2021, 5:50 AM

#

then put it outside of the symbol

#

idk

carmine lion Jul 4, 2021, 5:50 AM

#

bruh

rigid smelt Jul 4, 2021, 5:50 AM

#

ocean seal **abe**

maybe multiply by cos(x/2) on both sides

#

on the condition that cos(x/2) != 0

#

and then apply prod to sum identity

carmine lion Jul 4, 2021, 5:51 AM

#

hmm ok ill try that

rigid smelt Jul 4, 2021, 5:51 AM

#

oh wait

carmine lion Jul 4, 2021, 5:51 AM

#

?

rigid smelt Jul 4, 2021, 5:51 AM

#

actually that might be a terrible idea

carmine lion Jul 4, 2021, 5:51 AM

#

xD

#

i thought about t formula

#

but that got chaotic

#

after i expanded double angle

rigid smelt Jul 4, 2021, 5:52 AM

#

yeah i wouldnt want to apply half angle either

carmine lion Jul 4, 2021, 5:52 AM

#

this was a question meant for a graph intersection (graphical)

#

but i wanted to know how you woud solve this with algebra/trig

idle trench Jul 4, 2021, 5:53 AM

#

how can we just do 4 6

rigid smelt Jul 4, 2021, 5:53 AM

#

math?

idle trench Jul 4, 2021, 5:53 AM

#

ik

#

but ut could be anything

carmine lion Jul 4, 2021, 5:53 AM

#

idle trench how can we just do 4 6

prime factorisation

idle trench Jul 4, 2021, 5:53 AM

#

2 12

rigid smelt Jul 4, 2021, 5:53 AM

#

of course you can do whatever you want

#

but you want to factor it into two numbers that are helpful

carmine lion Jul 4, 2021, 5:53 AM

#

and MOST IMPORTANTLY, looking at the question

#

🥰

carmine lion Jul 4, 2021, 5:56 AM

#

rigid smelt yeah i wouldnt want to apply half angle either

alr

#

how to proceed?

#

i think i've tried all i can think of

rigid smelt Jul 4, 2021, 5:56 AM

#

im still thinking

#

there is probably some nice factorisation we can do here

#

i think algebra might not be possible

#

we are looking at some series expansion here

carmine lion Jul 4, 2021, 5:59 AM

#

what the frick

rigid smelt Jul 4, 2021, 6:00 AM

#

yeah i think if we want to solve it, we would have to approaching it using some sort of series expansion

carmine lion Jul 4, 2021, 6:00 AM

#

lol

#

isn't that Uni level math

rigid smelt Jul 4, 2021, 6:01 AM

#

i guess, not sure how the system is in your country

carmine lion Jul 4, 2021, 6:01 AM

#

australia

rigid smelt Jul 4, 2021, 6:02 AM

#

yeah i think so

carmine lion Jul 4, 2021, 6:03 AM

#

YIKES

#

whoops caps

#

ok ty for offering help tho

rigid smelt Jul 4, 2021, 6:03 AM

#

well thats why sometimes graphs are helpful

carmine lion Jul 4, 2021, 6:03 AM

#

appreciate <3

idle trench Jul 4, 2021, 6:06 AM

#

carmine lion appreciate <3

pale summit Jul 4, 2021, 6:31 AM

#

why do we need left and right hand limits can anyone explain pls?

full wasp Jul 4, 2021, 6:32 AM

#

imagine a jump discontinuity in a function

#

ur gonna get different values if u approach from the left or from the right

#

so

#

its kind of important to make that distinction

#

also in general limits do not exist if the left and right hand limits are not equal

pale summit Jul 4, 2021, 6:37 AM

#

i dont get that

#

i mean can u explain it in easy words

full wasp Jul 4, 2021, 6:39 AM

#

like this function for example

pale summit Jul 4, 2021, 6:39 AM

#

ye i see

#

its discontinious

full wasp Jul 4, 2021, 6:39 AM

#

if u approach x₀ from the left u get a value and it is NOT the same value as if u approach x₀ from the right

pale summit Jul 4, 2021, 6:40 AM

#

so in that case the limit doesnot exist as u said before

#

coz both values not same oh both limits not same

full wasp Jul 4, 2021, 6:43 AM

#

yes

pale summit Jul 4, 2021, 6:44 AM

#

u mean its not a limit

#

as left and right are not the same

full wasp Jul 4, 2021, 6:45 AM

#

yeah because left and right are not the same it is not a limit

#

or rather the limit does not have a value

pale summit Jul 4, 2021, 6:46 AM

#

thanks for the help man

vast bobcat Jul 4, 2021, 6:47 AM

#

A school offers three subjects: Mathematics, Art and Science. At least 80% of students study both Mathematics and Art. At least 80% of students study both Mathematics and Science. Prove that at least 80% of students who study both Art and Science, also study Mathematics.

#

Could someone help with this question please? (ping when you answer)

vast bobcat Jul 4, 2021, 7:22 AM

#

<@&286206848099549185>

woeful pulsar Jul 4, 2021, 7:28 AM

#

vast bobcat A school offers three subjects: Mathematics, Art and Science. At least 80% of st...

Start with some variables
X = proportion of Art Science no Math
Y = proportion of Art Science Math
Z = proportion of Art no Science Math
W = proportion of no Art Science Math

By modelling you should find the following equations
Y+Z >= 0.8
Y+W >= 0.8
X+Y+Z+W <= 1 (disjoint)
Minimise Y/(X+Y).

vast bobcat Jul 4, 2021, 7:29 AM

#

how do I minimise y/(x+y)?

woeful pulsar Jul 4, 2021, 7:30 AM

#

well if you want to show it's >= 0.8, you can also minimise Y-0.8(X+Y) and show this value is always positive

#

and now you have a linear program

#

which you can solve using linear programming methods

vast bobcat Jul 4, 2021, 7:31 AM

#

hmm okay I think I get it now

#

thank you so much! do you mind me pinging you if I need more help on this question?

woeful pulsar Jul 4, 2021, 7:31 AM

#

just ask here ig

#

whoa i didn't expect this was supposed to be a linear programming question lol

#

just using methods i know lol

vast bobcat Jul 4, 2021, 7:32 AM

#

k cool thanks

crystal tapir Jul 4, 2021, 7:34 AM

#

can someone help in this question its Yr 10

#

#

here is the question

#

<@&286206848099549185>

#

help

#

me

woeful pulsar Jul 4, 2021, 7:48 AM

#

crystal tapir can someone help in this question its Yr 10

wait what, the modelling assumptions are weird lol.

but yeah all you need to do is probably find the vertex and plug in the points A, B relative to that

crystal tapir Jul 4, 2021, 7:48 AM

#

can u further explain

#

i am a bit dum

#

soo

woeful pulsar Jul 4, 2021, 7:52 AM

#

firstly, realise the value of x (in terms of p) that would minimise y

woeful pulsar Jul 4, 2021, 7:52 AM

#

crystal tapir can someone help in this question its Yr 10

wait a minute the first 3 parts are missing lol

#

what did you do for them lol

#

typically the question tends to continue on stuff you already have

rich basin Jul 4, 2021, 8:07 AM

#

Screen_Shot_2021-07-04_at_6.07.26_pm.png

#

the equation i had at the end was

#

4! + 4C2*4P3 + 4C3 * 2! + 4 + 4C2 * 2

#

It was the wrong answer

full wasp Jul 4, 2021, 8:14 AM

#

whats the answer

#

if i had to wager a guess id say its like 4⁴ = 256?? im probably wrong cause i suck at combinatorics

rich basin Jul 4, 2021, 8:16 AM

#

yeah

#

that is the answer

#

How did you get to that

full wasp Jul 4, 2021, 8:17 AM

#

basically the first guy can go into any of the four rooms

#

and so can the second guy, and the third guy, and the fourth guy

rich basin Jul 4, 2021, 8:17 AM

#

Yeah

full wasp Jul 4, 2021, 8:17 AM

#

so thats 4 x 4 x 4 x 4

rich basin Jul 4, 2021, 8:18 AM

#

still don't quite get it

#

Because once the first guy can go in. I know the other people can go in as well, but that does not necessary mean that they will go in

#

The answer also has another part with an or

full wasp Jul 4, 2021, 8:19 AM

#

yes but they COULD go in

rich basin Jul 4, 2021, 8:19 AM

#

4^4 or 4 + 48 + 36 + 144 + 24 = 256

full wasp Jul 4, 2021, 8:19 AM

#

the question wants you to consider all possibilities

rich basin Jul 4, 2021, 8:19 AM

#

and my answer is quite similar except the number 48 and 36 is not in mine

#

Which i don't know how the guy even got 48 and 36

full wasp Jul 4, 2021, 8:20 AM

#

i dont know where 4 + 48 + 36 + 144 + 24 comes from ngl

rich basin Jul 4, 2021, 8:20 AM

#

@full wasp Yes but once they get in, there will be less than 4 people to fill in the other rooms

#

I couple explain how i got my solution if you want

full wasp Jul 4, 2021, 8:20 AM

#

sure

rich basin Jul 4, 2021, 8:20 AM

#

So, basically i took this into cases

#

First one which is the 24 in the answer

#

in other words 4!

#

I got 4! from the case, what if only 1 person goes to each of the room

#

and with the second case, what if 2 person goes to 1 room and the rest goes to individual rooms

#

that would be 4C2*4P3

#

4 choose 2 person, and then i made them into one unit and them order them across the 4 rooms

#

which corresponds to 144 in the answer

#

and also the 4, is where everyone goes into one room

#

but then the question here is, how did they get 48 and 36

#

and the equation i have right now is

#

4! + 4C2*4P3 + 4C3 * 2! + 4 + 4C2 * 2
[18:08]

pallid lance Jul 4, 2021, 8:23 AM

#

should be c right?

full wasp Jul 4, 2021, 8:23 AM

#

hhh we are busy

rich basin Jul 4, 2021, 8:24 AM

#

So i got 4C3 from the case when 3 person goes into one room

#

perhaps 4C3 *2 is wrong

full wasp Jul 4, 2021, 8:24 AM

#

im mulling it over

rich basin Jul 4, 2021, 8:24 AM

#

Let me make new calculations

#

Yes i got the 48

#

It is 4C3*4P2

#

4! + 4C2*4P3 + 4C3 *4P2+ 4 + 4C2 * 2
[18:08]

#

And that could possibly mean that 4C2 is wrong as well

#

But this time, i'm rather confused with what i should change the 4C2*2

#

That is the case when they are divided into two rooms

#

Still stuk with the 4C2 * 2 case

full wasp Jul 4, 2021, 8:28 AM

#

i think that way of going about it is more complicated than it needs to be

#

just imagine the first person shows up

#

they can choose any of the 4 rooms so they have 4 choices

#

the second person also has 4 choices

rich basin Jul 4, 2021, 8:29 AM

#

Yeah

full wasp Jul 4, 2021, 8:29 AM

#

and the third and the fourth so the total number of choices they can make is 4 x 4 x 4 x 4

rich basin Jul 4, 2021, 8:29 AM

#

But what about the ordering though

#

I'm think it starting to make sense

#

Just trying to create an image

full wasp Jul 4, 2021, 8:30 AM

#

the ordering is already accounted for in 4 x 4 x 4 x 4

#

like that covers all the ways u could sort the people and shove them into rooms

rich basin Jul 4, 2021, 8:30 AM

#

But I really want to know what i did wrong with my one

#

I just don't want to give up, I want to learn stuff through the hard way

full wasp Jul 4, 2021, 8:31 AM

#

i mean im struggling to see where those numbers come from

rich basin Jul 4, 2021, 8:31 AM

#

I know for sure now that 4C2 * 2 is wrong

#

Because I only accoutned for only 2 rooms

#

But then when I do soemthing like 4C2 * 4P2, i still got the wrong value

#

it is 72

#

However the value is suppose to be 36

#

i mean 36

#

So it is basically half the thing i got for the case when i divide the 4 people

#

into 2 roos

#

I think i'm starting to see why

#

Probably should just focus on the case which I am having trobule with

#

Like, i don't think the other values matter, only this problem is where the issue with my answer derives from

#

Like why is 36 half my answer

#

Would anybody be able to please help me?

full wasp Jul 4, 2021, 8:40 AM

#

i do have a second method but it is a bit counterintuitive

#

so first if u consider treating the people as one large group then you have 4 choices so this is where 4 comes from

rich basin Jul 4, 2021, 8:41 AM

#

But with my one, it is quite similar to the answer. As well as I'm quite close to solving it

#

just need to find a reasoning behind dividing it by 2

#

Like something that must of repeated

full wasp Jul 4, 2021, 8:43 AM

#

i dunno sorry

rich basin Jul 4, 2021, 8:45 AM

#

@crisp iron

#

<@&286206848099549185>

#

I think I start to get what i did wrong

#

it is because I had some duplicates

#

like forexample I would have AB __ CD ___

#

and i hcan have the same thing

dull onyx Jul 4, 2021, 9:35 AM

#

how would i simplify this ><

indigo flint Jul 4, 2021, 9:43 AM

#

What does the the denominator read

dull onyx Jul 4, 2021, 9:44 AM

#

thats a two

prime badge Jul 4, 2021, 9:55 AM

#

rich basin <@&286206848099549185>

the order makes it very complicated

#

because it doesn't matter in which order the room contains 2 specific people

#

it just contains them

#

if it did matter, then it's 7c4 * 4!

#

to go from that to the real answer you'd have to divide by 24 in some cases, by 4 in others, by 6 in others

#

so you think of it as a 4 digit string
1 2 1 4
1 1 1 1
1 1 3 1
just encodes who went where

indigo flint Jul 4, 2021, 10:01 AM

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@dull onyx

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Idk if u can simplify any further

dull onyx Jul 4, 2021, 10:16 AM

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indigo flint <@584909472678412294>

aw thank u!!

urban escarp Jul 4, 2021, 10:17 AM

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can someone assist me with b and c please

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<@&286206848099549185>

ivory otter Jul 4, 2021, 10:28 AM

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Hi

urban escarp Jul 4, 2021, 10:29 AM

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hello

dull onyx Jul 4, 2021, 10:32 AM

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hi again! not sure if this channel is being used or not but… i have the function f(x) = ax^2
and im being asked to find a so the derivative of f at A(2, f(2)) is equal to 4.. literally sorry if this makes no sense in english, its in greek and im having a hard time translating it

rigid smelt Jul 4, 2021, 10:33 AM

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whats the derivative of f(x)?

dull onyx Jul 4, 2021, 10:33 AM

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i found 2xa

rigid smelt Jul 4, 2021, 10:33 AM

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yes derivative of f is f'(x)=2ax

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now plug in the information you have

dull onyx Jul 4, 2021, 10:33 AM

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yup then i found the derivative of 2

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bc it asks for it before it asks for A(2, f(2))

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and i found 4a

rigid smelt Jul 4, 2021, 10:34 AM

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so you want to find a? or do you want to find f(2)?

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ok lets slow down a bit

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you are given:
f(x)=ax^2 and thats all?

dull onyx Jul 4, 2021, 10:35 AM

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it says to find a so the derivative of f at A(2, f(2)) is equal to 4.. translating this from greek is hard asf

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one sec

rigid smelt Jul 4, 2021, 10:36 AM

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is it given that the derivative at x=2 is 4? or is that something you guessed?

dull onyx Jul 4, 2021, 10:36 AM

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also x is an element of R and a is an element of R

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nope it says i should find that so its 4

rigid smelt Jul 4, 2021, 10:37 AM

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ok so its given that f'(2)=4

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and you know that f'(x)=2ax

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can you find a from those two information?

dull onyx Jul 4, 2021, 10:38 AM

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no its kot given