SOLUTION: 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

Algebra ->  Proportions  -> Lessons -> SOLUTION: 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      Log On


   

Question 1079225: 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 by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A=u%2AC
B=v%2AC
where u and v are constants.
So then,
A%2BB=u%2AC%2Bv%2AC=C%28u%2Bv%29
Directly proportional to C.
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A%2BB=u%2AC-v%2AC=C%28u-v%29
Directly proportional to C.
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sqrt%28AB%29=sqrt%28u%2AC%2Av%2AC%29=sqrt%28uv%2AC%5E2%29=sqrt%28uv%29%2AC
Directly proportional to C.