Please help, thanks!

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)√AB

Answer 1

a)

 

A = aC and B = bC where a and b are constants

 

Then

 

A + B = aC + bC = (a + b)C where a + b = constant

 

b)

 

A - B = aC - bC = (a - b)C where a - b = constant

 

c)

 

√(AB) = √(aCbC) = √(ab) √(C²) = √(ab) C where √(ab) = constant