Question

 X, Y and Z are three quantities such that X varies directly as the square of Y and inversely as the square root of Z.

1. Given that X = 18 when Y = 3 and Z = 4, find X when Y = 6 and Z = 16. 
2. If Y increases by 10% and Z decreases by 19%, find the percentage increase in X. 

Answer 1

1. Given that X = 18 when Y = 3 and Z = 4, find X when Y = 6 and Z = 16. 
   x  ^_r2/_√z
   x ^_kr2/_√z
   when r=3 and z=4, x=18
   18= ^_k32/_√4=18=⁹/₂k
   therefore^{18 ×2}/₉ =4
   EQN × ^_kr2/_√z
   when r=6, and z=16
   = 4(6)²/√16=^{4 ×36}/₄
   =36
2. If Y increases by 10% and Z decreases by 19%, find the percentage increase in X. 
   let x1= ^_xky12/_√z1
   r1¹¹⁰/₁₀₀ r=1.1 r
   z1 = ⁸¹/_100z= 0.81z
   % increase=(^x1-x/_x)100
   k(1.1r)²-  ky² 
   √0.81z    √z
            ky²
           √z
   ky²(1.21-1)×100
   √z    0.9            
        ky2√z
   =310
        9
3. increase in x=34.44%
   A. increase in x=34.44%
   B  4.6 ±0.1 ×10=46 KM ±1 KM
   C   240° ±1° OR S 60 ° W ±2°
   D   122° ±OR S 58° E ±1°
   E   127 ±0.1 ×10=127 ±1 KM