# 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.

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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.

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