Question

If a/b=1/4, where a is a positive integer, which of the following is a possible value of a^2/b?

Answer 1

Let me see

Answer 2

if \[a/b=1/4\] therefore we can solve for what a is \[a=(b)*(1/4)\]

Answer 3

appreciate your time!

Answer 4

so \[a^2 = [(b)*(1/4)]^2 = (b^2)/16\]
so \[(b^2)/16 * 1/b = b/16\]

Answer 5

the question said "which of the following" so there are choices?

Answer 6

Im sorry - the answer choices are, i. 1/4, ii. 1/2, iii. 1 a) none, b) i only, c) i and ii, d) i and iii, and E is i, ii, iii

Answer 7

ok, \[(a/b) = 1/4\] \[a^2/b = (a/b)*a\]

Answer 8

\[a^2/b = (1/4)*(a/b)*b\]

Answer 9

Im a little confused...so what is the answer..?

Answer 10

it is clear that a is value less than b, basically, \[b=4*a\] so \[a^2/4*a=1/4\]=
\[1/4=1/4\]

Answer 11

OK, so when could \[a^2/b\] be equal to 1/2? that would only be when \[a=\sqrt{b/2}\],but b=4a, so can \[a=\sqrt{4a/2}=\sqrt{2a}\]?

Answer 12

Yes it can be

Answer 13

right, if a = 2

Answer 14

can this be equal to 1 ever?

Answer 15

yes.

Answer 16

in the situation you gave me if a=2 it'd be 2=\[\sqrt{4}\]

Answer 17

so 2=2, so it could be "1"?

Answer 18

it would be when \[a=\sqrt{b}\]

Answer 19

so, when \[a=\sqrt{4a}\]

Answer 20

so, when a equals....

Answer 21

you are starting to confuse me...^^;

Answer 22

well, we know \[a/b=1/4\], so, let's check what \[a^2/b\] can equal.
We check out whether \[a^2/b=1/4\], that would be when \[a^2 = (1/4)*b\] which is \[a=\sqrt{(1/4)*b}\], we know that \[b=4*a\], so that holds true is a equals 1

Answer 23

holds true *if* a=1

Answer 24

now, check whether \[a^2/b=1/2\] given that \[b=4*a\]

Answer 25

\[a=\sqrt{(1/2)*b}\] with \[b=4*a\], then \[a=\sqrt{2*a}\] so \[a=2\], so \[a^2/b=1/2\] is possible if \[a=2\]

Answer 26

now for \[a^2/b=1\] if \[a=\sqrt{b}=\sqrt{4a}\] so \[a^2 = 4a\] so \[a=4\]