f.4 maths (functions)

julie

2009-11-06 2:40 am

1) In an experiment, the temperature T of the solution t minutes after adding a substance is given by T=120-(2t-8)^2.
(a) Find the initial temperature of the solution.
(b) How long does it take for the temperature of the solution to attain its maximum? Find its maximum temperature.

2) If a ball is thrown vertically upwards at a speed of 10 m/s, the distance s m of the ball above the ground after t seconds is given by s=-5(t-1)^2+5.
(a) What is the initial distance of the ball above the ground?
(b) How long does the ball take to reach its highest position? How far is it above the ground?

回答 (1)

老爺子

2009-11-06 3:38 am

✔ 最佳答案

1)
(a)
T = 120 - (2t - 8)^2

When t = 0,
T = 120 - (0 - 8)^2 = 56
Hence, the initial temperature of the solution = 56

(b)
T = 120 - (2t - 8)^2

For any real value of t, (2t - 8)^2 ≥ 0
and thus T = 120 - (2t - 8)^2 ≤ 120
The temperature reaches the maximum when (2t - 8)^2 = 0
The maximum temperature = 120
when time = 4 minute

2)
(a)
s = -5(t - 1)^2 + 5

When t = 0,
s = -5(0 - 1)^2 + 5 = 0
The initial distance of the ball above the ground = 0 m

(b)
s = -5(t - 1)^2 + 5

For any real value of t, 5(t - 1)^2 ≥ 0
and thus s = -5(t - 1)^2 + 5 ≤ 5
s reaches the maximum when 5(t - 1)^2 = 0
Time taken by the ball to reach its highest position = 1 second
Distance of the highest position above the ground = 5 m

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