Growth in sales would not continue 1 total 11 marks

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Unformatted text preview: rve y = 2x3 + ax2 + bx – 9 at the point (1,7). Find the values of a and b. Working: Answers: ………………………………………….. (Total 3 marks) 365. A continuous random variable X has probability density function 4 f ( x) = π (1 + x 2 ) , for 0 ≤ x ≤ 1, 0, elsewhere Find E(X). Working: Answers: ………………………………………….. (Total 3 marks) 254 1 366. The matrix 1 – 3 –2 –k 5 – 3 –13 is singular. Find the values of k. k Working: Answers: ………………………………………….. (Total 3 marks) 367. Consider the function y = tan x – 8 sin x. dy . dx (a) Find (b) Find the value of cos x for which dy = 0. dx Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 255 368. Find the values of x for which 5 – 3x ≤ x + 1. Working: Answers: ………………………………………….. (Total 3 marks) 369. Consider the tangent to the curve y = x3 + 4x2 + x – 6. (a) Find the equation of this tangent at the point where x = –1. (b) Find the coordinates of the point where this tangent meets the curve again. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 3 marks) 256 370. A point P(x, x2) lies on the curve y = x2. Calculate the minimum distance from the point 1 A 2, – to the point P . 2 Working: Answers: ………………………………………….. (Total 3 marks) 371. Point A(3, 0, –2) lies on the line r = 3i – 2k + λ(2i – 2j + k), where λ is a real parameter. Find the coordinates of one point which is 6 units from A, and on the line. Working: Answers: ………………………………………….. (Total 3 marks) 257 372. Let θ be the angle between the unit vectors a and b, where 0 < θ < π. Express |a – b| in terms of 1 sin θ . 2 Working: Answers: ………………………………………….. (Total 3 marks) 373. How many four-digit numbers are there which contain at least one digit 3? Working: Answers: ………………………………………….. (Total 3 marks) 258 1 . After visiting two 3 shops in succession, he finds he has left his umbrella in one of them. What is the probability that he left his umbrella in the second shop? 374. The probability that a man leaves his umbrella in any shop he visits is Working: Answers: ………………………………………….. (Total 3 marks) 375. A sample of radioactive material decays at a rate which is proportional to the amount of material present in the sample. Find the half-life of the material if 50 grams decay to 48 grams in 10 years. Working: Answers: ………………………………………….. (Total 3 marks) 259 376. Find the area enclosed by the curves y = 2 and y = e3, given that –3 ≤ x ≤ 3. 2 1+ x Working: Answers: ………………………………………...
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