SOLUTION: Suppose that x varies directly as z and that y also varies directly as z. (A) does x + y vary directly as as z? (B) does xy vary directly as z? (C) does sqrt(xy) vary directly

Question 828151: Suppose that x varies directly as z and that y also varies directly as z.
(A) does x + y vary directly as as z?
(B) does xy vary directly as z?
(C) does sqrt(xy) vary directly as z? Assume x, y and z are positive.
The answers are yes, no, yes respectively.
I don't really understand why the answer isn't 'yes' for all the questions. I'm thinking that the formula I should work with is z = kxy. Could you please explain to me these answers? Thank you in advance.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Suppose that x varies directly as z and that y also varies directly as z.
(A) does x + y vary directly as as z?
(B) does xy vary directly as z?
(C) does sqrt(xy) vary directly as z? Assume x, y and z are positive.
The answers are yes, no, yes respectively.
I don't really understand why the answer isn't 'yes' for all the questions. I'm thinking that the formula I should work with is z = kxy.
-----------------
For B, xy varies "directly" as z in the sense that when z increases xy increases.
But, since xy is a product it varies as the square of z.
If z is doubled, both x and y are doubled --> xy is 4 times.
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