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Q2. (a) Solve for x in the following equation: (10)

(7x + 1)/(x - 2) - (4x - 1)/(x + 2) = 7

(b) Makes the subject of the following formula: (6)

T = R/π (1/h - 1/s)

Q3. (a) Solve the following system of equations for x, y and z: (9)

2x - y + z = 9

3x + 2y -3z = 16

5x - y + 2z = 25

(b) A rectangular steel plate, of area 12 m², has its length 1.4 m greater than its breadth.

Calculate the dimensions of the plate, correct to two decimal places. (7)

Q4. Solve for x in EACH of the following equations:

(a) 5x – 2 = 32x + 1                 (8)

(b) ln((3 - x)/(2 - x)) = 0.8               (8)

Q7. (a) The daily profit, P pounds, of a small oil refinery is given by:

P = 80x - 0.2x², where x is the number of barrels of oil refined.

Calculate EACH of the following:

(i) the number of barrels to be refined to maximise the profit; (6)

(ii) the maximum profit. (2)

(b) Given: T = 3 + 4sin θ - 2cos θ

(i) Determine the value of dT/dθ when θ = 5π/6 radians    (4)

(ii) Solve dT/dθ = 0 for θ in the range π/2 ≤ θ ≤ π           (4)

Q8. A small ship has a forepeak bulkhead as shown in Fig Q8.

The equations of the deck and hull with respect to an origin 0 are:

Deck: y = 0.36 – 0.04x²

Hull: y = 0.4x² – 3.6

Determine the area of the bulkhead. (16)