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Unformatted text preview: with coordinates (0, 0, 5). (a) Show that the position vector b of the balloon at time t is given by x 0 10.8 b = y = 0 + t 14.4 . z 5 0 (6) At time t = 0, a helicopter goes to deliver a message to the balloon. The position vector h of the helicopter at time t is given by x 49 – 48 y = 32 + t – 24 h= z 0 6 (b) (i) Write down the coordinates of the starting position of the helicopter. (ii) Find the speed of the helicopter. (4) (c) The helicopter reaches the balloon at point R. (i) Find the time the helicopter takes to reach the balloon. (ii) Find the coordinates of R. (5) (Total 15 marks) 519 763. The polynomial f(x) = x3 + 3x2 +ax + b leaves the same remainder when divided by (x – 2) as when divided by (x +1). Find the value of a. (Total 6 marks) 764. The displacement s metres of a moving body B from a fixed point O at time t seconds is given by s = 50t – 10t2 + 1000. (a) Find the velocity of B in m s–1. (b) Find its maximum displacement from O. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (Total 6 marks) 520 765. A test marked out of 100 is written by 800 students. The cumulative frequency graph for the marks is given below. 800 700 600 Number of candidates 500 400 300 200 100 10 20 30 40 50 60 70 80 90 100 Mark 521 (a) Write down the number of students who scored 40 marks or less on the test. (b) The middle 50 % of test results lie between marks a and b, where a < b. Find a and b. ..................................................................................................................................... .......................................................................................
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