If P varies jointly as q, r and s - assume this is in direct proportion, then P ∠qrs so P = kqrs where k is a constant.
70 = k x 7 x 5 x 4 = 140k : k = 140/70 = 0.5
When q = 2, r = 15 and s = 7 then,
P = 0.5 x 2 x 15 x 7 = 105
f = 54
Find an equation of variation where y varies directly as x. One pair of values is y = 80 when x = 40
If P varies directly with q, r and s then P = kqrs, where k is a constant. As 70 = k x 7 x 5 x 4 = 140k : k = 70/140 = 1/2 The equation of joint variation is P = ½qrs.
40
y = -5
a = 0.8
f = 54
x = 75
Find an equation of variation where y varies directly as x. One pair of values is y = 80 when x = 40
If P varies directly with q, r and s then P = kqrs, where k is a constant. As 70 = k x 7 x 5 x 4 = 140k : k = 70/140 = 1/2 The equation of joint variation is P = ½qrs.
As x ∝ yz2 then x = kyz2 where k is a constant. Substituting the given figures, 40 = k*20*22 = 80k Then k = ½ and the formula is, x = ½yz2 So, x = ½ * 30 *32 = 135
57
40
y = -5
80
3
What is y? Fx varies with x, but y could be anything.