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一些數學問題想請解答
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Compound Inequalities:1. Radio stations A and B are 100km apart. The broadcast ranges of station A and station B are 45 km and 30km respectively. Tommy is driving from station A to station B at 50km/h, After travelling t minutes from station A, Tommy cannot hear any broadcasting from station A or station B. Find... 顯示更多 Compound Inequalities: 1. Radio stations A and B are 100km apart. The broadcast ranges of station A and station B are 45 km and 30km respectively. Tommy is driving from station A to station B at 50km/h, After travelling t minutes from station A, Tommy cannot hear any broadcasting from station A or station B. Find the range of the possible values of t. 2.A painter can choose to be paid in any one of the following three ways: (A) $1000, plus $60 per hour (B) $1500, plus $40 per hour (C) $80 per hour Suppose a job takes n hours. Find the range of the possible values of n such the at the painter will earn most money by choosing (A). 3.John is now x years old. Andy is 4 years younger than John, while Peter is 3 years older than John. 7 years ago, their total age was less than 29. 4 years later, their total age will be greater than 56. Find the possible value of x if x is an integer. 拜托解一解。
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最佳解答:
1. After t minutes: Distance between the car and station A = 50 × (t/60) = 5t/6 km Distance between the car and station B = [100 - (5t/6)] km = (600 - 5t)/6 km 5t/6 > 45 and (600 - 5t)/6 > 30 5t > 270 and 600 - 5t > 180 t > 54 and -5t > -420 t > 54 and t 1500 + 40n and 1000 + 60n > 80n 20n > 500 and 1000 > 20n n > 25 and 50 > n Hence, 25 56) (x - 7) + (x - 4 - 7) + (x + 3 - 7) 56 3x - 22 56 3x 45 x 15 15
其他解答:
時間有限, 暫只做第三題。 John 現在 x 歲, Andy 比 John 年輕 4 歲, 而 Peter 比 John 年長 3 歲。 七年前, 他們的歲數總和小於 29。四年後, 他們的歲數總和大於 56。 若 x 是整數, 找出 x 的可能值。 解答: Andy's age now = x - 4 Peter's age now = x + 3 2015-02-09 18:54:58 補充： 7 years ago: John's age = x - 7 Andy's age = x - 4 - 7 = x - 11 Peter's age = x + 3 - 7 = x - 4 (x - 7) + (x - 11) + (x - 4) 56 3x + 11 > 56 3x > 45 x > 15 Therefore, from x 15 and x is an integer, we must have x = 16.
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