Theory question 101
Variation(a) If p varies directly as r2 and p = 3.2 when r = 4, find the value of p when r = 6.5
(b) Solve the simultaneous equations x/2 + y/4 = 1; x/3 − y/4 = −1/6
Show the model answer
Model answer
(a) p = kr2: 3.2 = 16k, k = 0.2. p = 0.2 × 6.52 = 8.45.
(b) Add the equations: x/2 + x/3 = 1 − 1/6, so 5x/6 = 5/6 and x = 1.
Then 1/2 + y/4 = 1, y/4 = 1/2, y = 2.
Explanation
Adding removes the y terms because they have opposite signs.