Question

If m is directly proportional to r^3, and m=1/12 when r=1/2, what is the value of m when r=3/2?

Answer 1

@Directrix

Answer 2

@Directrix

Answer 3

mk=r^3 for some number k
let m = 1/12 and r = 1/2
k/12 = 1/8
k = 12/8 = 3/4
so
(3/4)m=r^3
let r = (3/2)
(3/4)m = (3/2)^3 = 27/8
(3/4)m = 27/8
m = (4/3)(27/8) = 4(9/8) = 9/2

Answer 4

@zzr0ck3r

Why would the initial equation not be the following:

m=kr^3 for some number k

I'm confused on that.

Answer 5

well its just a number so m=kr^3 would just be m(1/k) = r^3 just l = 1/k and we have
ml=r^3

Answer 6

does direct proportion mean integer?

Answer 7

What about this:

m* (1/k) =r^3 for some number k

Would that be correct?

Answer 8

I think, but k is just a number so no reason to right 1/k. just call that k.

Answer 9

write*

Answer 10

Neither of your answers are on the answer choices

Answer 11

Plus, I don't know the answer

Answer 12

@sakigirl That's what mathematics is all about - getting answers not the first time around but sometime around. Cogitation is everything. :)

Answer 13

Haha, that's very true

Answer 14

woops
mk=r^3 for some number k
let m = 1/12 and r = 1/2
k/12 = 1/8
k = 12/8 = 3/2 NOT (3/4)
so
m(3/2) = r^3
let r = (3/2)
m(3/2) = 27/8
m = (2/3)(27/8) = 2(9/8) = 9/4
is 9/4 a choice?

Answer 15

Yes!

Answer 16

if not try the other way lol
m = k * r^3
let m = 1/12 and r = 1/2

1/12 = k * 1/8
k = 2/3
r = 3/2
m = (2/3)(27/8) = 9/4
so it does not matter if we do m = kr^3 or mk=r^3 @Directrix I guess that makes sense....I guess lol

Answer 17

Well, I started out this way:

r^3 * 1/12 = m * (3/2)^3

(1/2)^3 * (1/12) = m * (3/2)^3

1/8 * 1/12 = m * 27/8

1/8 * 1/12 * 8/27 = m

At that point, m went off track.

I did not account for the constant of proportionality.

Answer 18

ahh