F.4 math---inequalities5

用戶36732

2009-12-27 2:07 am

The speed of a solar-powered toy car is V cm/s and the length of its solar panel is L cm, where 5<=L<=25. V is a function of L. It is known that V is the sum of two parts, one part varies as L and the other part varies as the square of L. When L=10, V=30 and when L=15, V=75.

(a) Express V in terms of L.

(b) Find the range of values of L when V>=30.

回答 (1)

用戶9112

2009-12-27 2:31 am

✔ 最佳答案

(a) V = kL + cL^2 where k and c are proportional constants
When L = 10, V = 30, 30 = 10k + 100c ... (1)
When L = 15, V = 75, 75 = 15k + 225c ... (2)
(1) => 3 = k + 10c
k = 3 - 10c ... (3)
Sub into (2), 75 = 15(3 - 10c) + 225c
75 = 45 - 150c + 225c
30 = 75c
c = 2/5
Sub into (3), k = 3 - 10(2/5) = -1
Therefore V = -L + (2/5)L^2
(b) When V >= 30,
-L + (2/5)L^2 >= 30
-5L + 2L^2 >= 150
2L^2 - 5L - 150 >= 0
(L - 10)(2L + 15) >= 0
L >= 10 or L <= -15/2
Since 5 <= L <= 25, therefore 10 <= L <= 25

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