Question

P varies directly as the cube of Q and inversely as the square root of R

1. Given that P = 35 when Q = 8 and R = 144, find P when Q = 20 and R = 22 
2. If Q decreases by 24% and R increases by 40% find the percentage change in P.

Answer 1

1. P=KQ³
         √R
     35 = K x 8 x 8 x 8
             √144
     35=^512k/₁₂
      K= ¹⁰⁵/₁₂₈
      P =     105Q³
             128√R
      P=   105  x  20³
            128 x √225
        = 105 x 8000m
             128 x 15
         =437.5 

2.  Original value of P =KQ³
                                      √R
new value = K x (0.76Q)³
                        √1.4R
= 0.438976KQ³ 
      1.1832√R
= 0.3710 KQ³
             √R
change = (0.3710 -1) KQ³
                                    √R
0.6290KQ³
        √R
%change = -0.6290 x 100
-62.90%
P has decreased by 62.90%