6. f(θ) = 4 cos2 θ – 3 sin2 θ (a) Show that f(θ) = 1/2 + 7/2 Cos 2θ (b) Hence, using calculus, find the exact value of ∫ θf(θ) dθ
Given that l1 and l2 meet at the point C, find
(a) the coordinates of C.
The point A is the point on l1 where λ = 0 and the point B is the point on l2 where μ = –1.
(b) Find the size of the angle ACB. Give your answer in degrees to 2 decimal places.
(c) Hence, or otherwise, find the area of the triangle ABC.
Figure 2 shows a cylindrical water tank. The diameter of a circular cross-section of the tank
is 6 m. Water is flowing into the tank at a constant rate of 0.48πm3min-1. At time t minutes,
the depth of the water in the tank is h metres. There is a tap at a point T at the bottom of the
tank. When the tap is open, water leaves the tank at a rate of 0.6πh m3min-1.
(a) Show that t minutes after the tap has been opened
75 dh/dt = (4 - 5h)
When t = 0, h = 0.2
(b) Find the value of t when h = 0.5