Give the value of α to 3 decimal places.
(b) Hence write down the minimum value of 7 cos x – 24 sin x.
(c) Solve, for 0 ≤ x < 2π, the equation
7 cos x – 24 sin x = 10
giving your answers to 2 decimal places.
1 (a) Trigonometry
as a single fraction in its simplest form.
f(x) = (4x -1)/[2(x -1)] - 3/[2(x - 1)(2x - 1)] - 2, x > 1
(b) show that f(x) = 3/(2x -1)
(c) Hence differentiate f(x) and find f'(2).
2 cos 2θ = 1 – 2 sin θ
in the interval 0 ≤ θ < 360°.
θ = 20 + Ae-kt ,
where A and k are positive constants.
Given that the initial temperature of the tea was 90°C,
(a) find the value of A.
The tea takes 5 minutes to decrease in temperature from 90°C to 55°C.
(b) Show that k = 1/5 ln2.
(c) Find the rate at which the temperature of the tea is decreasing at the instant when t = 10. Give your answer, in °C per minute, to 3 decimal places.4(a)
f(x) = (8 - x)ln x , x > 0
The curve cuts the x-axis at the points A and B and has a maximum turning point at Q, as shown in Figure 1.
(a) Write down the coordinates of A and the coordinates of B.
(b) Find f'(x)
(c) Show that the x-coordinate of Q lies between 3.5 and 3.6
(d) Show that the x-coordinate of Q is the solution ofx = 8/(1 + ln x)
(e) Taking x0 = 3.55, find the values of x1, x2 and x3.
Give your answers to 3 decimal places. 5(a)
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