Prove that each of the following is directly proportional to C.

Question

If A is directly proportional to C and B is directly proportional to C, prove that each of the following is directly proportional to C.

a)     A + B

b)     A -  B

c)     square root of AB   

Answer 1

A=kC

B=jC

A+B= kC +jC = (k+j)C k+j is a constant, so A+B = mC where m=k+j

A-B = kC-jC = (k-j)C k-j is a constant, so A-B = nC where n=k-j

sqrAB = sqrAsqrB = sqrkCsqrjC = sqrkjC

square both ends

sqrAB^2 = sqrkjC^2

AB = kjC kj is a constant,

AB =pC where p =kj, a constant