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 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. 

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  1. Given that X = 18 when Y = 3 and Z = 4, find X when Y = 6 and Z = 16. 
    x  r2/√z
    kr2/√z
    when r=3 and z=4, x=18
    18= k32/√4=18=9/2k
    therefore18 ×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
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