Answer:
[tex]r=8[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y=kx[/tex]
In this problem
Let
[tex]y=m[/tex]
[tex]x=r^{2}[/tex]
substitute
[tex]m=kr^{2}[/tex]
Find the value of k
For [tex]r=2, m=14[/tex]
[tex]14=k(2^{2})[/tex]
[tex]14=4k[/tex]
[tex]k=14/4[/tex] ----> constant of proportionality
the equation is equal to
[tex]m=(14/4)r^{2}[/tex]
Find the value of r when m=224
substitute in the equation and solve for r
[tex]224=(14/4)r^{2}[/tex]
[tex]r^{2}=224*4/14[/tex]
[tex]r^{2}=64[/tex]
[tex]r=8[/tex]
