Figure 1 above shows an athlete's forearm holding a steel ball. The forearm is supported by a contraction of the biceps muscle, which causes a torque around the elbow. Assuming that the tension
in the biceps acts along the vertical direction given by gravity and the centre of gravity of the forearm
is half of L. What tension must the biceps muscle exert to hold the forearm at the position shown?
Sketch and label your free body diagram. (Let L = 33.5 cm, d = 3.8 cm, mass of steel ball = 280 g, mass
of the forearm = 2,5 kg)
(5 marks)

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit