SOLUTION: Dear Math tutor, p varies directly as the square root of q. p=8 when q=25 Find p when q =100 what does varies directly mean? Thank you Best Wishes, Nats

Question 787050: Dear Math tutor,
p varies directly as the square root of q.
p=8 when q=25
Find p when q =100
what does varies directly mean?
Thank you
Best Wishes,
Nats
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
"varies directly" means "if x increases, y will increase".
The way to express that algebraically is x = ky.
"k" is call the constant of variation.
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Your Problem::
p varies directly as the square root of q.
p = k*sqrt(q)
------
Solve for "k" using "p=8 when q=25"
8 = k*sqrt(25)
8 = k*5
k = 8/5
------
Equation:
p = (8/5)sqrt(q)
-------
Find p when q =100
p = (8/5)*sqrt(100)
p = 16
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Cheers,
Stan H.
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