Question 1155352

Let a be directly proportional to m and n^2​, and inversely proportional to y^3. If a=4 when m=9​, n=4​, and y=2​, find a when m=8​, n=3​, and y=5.
<pre>{{{matrix(1,3, a, "=", kmn^2/y^3)}}}
{{{matrix(1,3, 4, "=", k(9)(4^2)/2^3)}}} ------ Substituting {{{matrix(4,3, 4, for, a, 9, for, m, 4, for, n, 2, for, y)}}}
{{{matrix(5,3, 4, "=", k(9)(16)/8, 4, "=", k(9)2cross((16))/cross(8), 4, "=", 18k, 4/18, "=", k, 2/9, "=", k)}}}

{{{matrix(1,3, a, "=", kmn^2/y^3)}}} 
{{{matrix(1,3, a, "=", (2/9)(8)(3^2)/5^3)}}} ------ Substituting {{{matrix(4,3, 2/9, for, k, 8, for, m, 3, for, n, 5, for, y)}}}
{{{matrix(3,3, a, "=", (2/9)(8)(9)/125, 
a, "=", 2(8)/125,
a, "=", highlight(16/125))}}}</pre>