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11條10分 a______________________
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(12) 42x+1 = 5 (2x + 1) log 4 = log 5 2x + 1 = 1.161 x = 0.080 (13) log3 (2x + a) = 2 2x + a = 9 x = (9 - a)/2 (14) log2 (2x + 1) + log2 (x - 3) = 2 log2 [(2x + 1)(x - 3)] = 2 2x2 - 5x - 3 = 4 2x2 - 5x - 7 = 0 (2x - 7)(x + 2) = 0 x = 7/2 or -2 (rejected) since 2x + 1 500 2000 x 1.05n > 2500 1.05n > 1.25 n log 1.05 > log 1.25 n > 4.6 So n = 5 (19) Let the original sound intesity be I, then the new intensity be I', so: 10 log I' - 10 log I = 20 log (I'/I) = 2 I'/I = 100 (20) 10 log (I/10-12) = 103 log (I/10-12) = 10.3 I = 0.02 (ans = A) (21) From the given, we can see that the function can be expressed as: y = a(x - 1)2 - 1 where a is a constant. Sub x = -1, we have y = 1 and hence: 1 = 4a - 1 a = 1/2 So, y = (x - 1)2/2 - 1 = x2/2 - x - 1/2 (22) Let the numbers be x and x + 3, so: x2 + (x + 3)2 is at minimum. x2 + (x + 3)2 = 2x2 + 6x + 9 = 2(x2 + 3x) + 9 So when x = -3/2, the sum is minimum and 2 nos. are -3/2 and 3/2.
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