(ii) find, correct to two decimal places, the value of Q when P = 3, m = 15, s = 0.2, k = 4 and r = 10.
a)
(i) To make Q the subject of the formula, we need to isolate Q on one side of the equation.
P = \(\left(\frac{rk}{Q} - ms\right)^{\frac{2}{3}}\)
Take the reciprocal of both sides:
\(\frac{1}{P}\) = \(\frac{Q}{rk}\) - \(\frac{ms}{rk}\)
Add \(\frac{ms}{rk}\) to both sides:
\(\frac{ms}{rk}\) + \(\frac{1}{P}\) = \(\frac{Q}{rk}\)
Multiply both sides by \(\frac{rk}{ms + Prk}\):
Q = \(\frac{rk}{ms + Prk}\)
(ii) Now that we have the formula for Q, we can substitute the given values and calculate:
Q = \(\frac{(10)(4)}{(0.2) + (3)(15)(4)}\)
Q = \(\frac{40}{182}\)
Q = 0.22 (correct to two decimal places)
Therefore, when P = 3, m = 15, s = 0.2, k = 4, and r = 10, Q is approximately equal to 0.22.
b) To find x : y, we can use algebraic manipulation to isolate one of the variables in terms of the other:
\(\frac{x + 2y}{5}\) = x - 2y
Distribute the 5 on the right side of the equation:
\(\frac{x + 2y}{5}\) = x - \(\frac{10y}{5}\)
Simplify:
\(\frac{x + 2y}{5}\) = x - 2y
x + 2y = 5x - 10y
12y = 4x
y = \(\frac{1}{3}\)x
Therefore, x : y is 3 : 1.