Suppose r varies directly as the square of m, and inversely as s. if r equals 15r=15 when m equals 8m=8 and s equals 4s=4, find r when m equals 16m=16 and s equals 4s=4.

Symbolically,

      k*m^2
r= 
           s

Now replace r with 15 and m with 8.  Calculate the constant of proportionality k:
          k(8)^2
15 =      Solve this for k by dividing both sides of this equation by    
              4

    4                            4
.    We get    * 15 = k, and this simplifies to 60/64 = 15/16.
 8^2                         8^2

Then your function r   is   

      k*m^2      15 *m^2
r=  =
           s           16s

You are to find r when m equals 16 and s equals 4.  This would be:

      k*m^2      15 *m^2               15*16^2       15(16)
r=  =   => r = = = 60 (answer)
           s           16s                      16*4                4

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.