A quantity P varies partly as Q and partly as the square root of Q, given that P=30 when Q=9, and P=14 when Q=16. Find P when Q=36.

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A quantity P varies partly as Q and partly as the square root of Q, given that P=30 when Q=9, and P=14 when Q=16. Find P when Q=36.

1 Answer

anonymous · Answer 1 · 2021-08-13T14:24:28+0000

Let L and K be constants.
P=LQ + K √Q
30 = 9L + √9K
14 = 162 + √16 K
2K + 62 = 20
2K + 8L = 7
-2L = 13
L = ^-13/₂
K + 3(^-13/₂) = 10
K = ¹⁰/₁ + 392 = ⁵⁹/₂
P = ^-13/₂Q = ⁵⁹/₂ √Q
P = ^-13/₂ x 36 + ⁵⁹/₂ x √36
P = -234 + 177 = -57

A quantity P varies partly as Q and partly as the square root of Q, given that P=30 when Q=9, and P=14 when Q=16. Find P when Q=36.

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