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標題:
Mid-year maths
發問:
1a)Write down the three basic operation formulas of logarithms.1b)In 17th century, an astronomer found the distance (d km) between two planets was (1.234x 5.678)^1000 km. Givenlog 1.234=0.0913, log 5.678=0.7541 and log 2,512=0.4,using (a), find the value of d.Give the answer in scientific notation and... 顯示更多 1a)Write down the three basic operation formulas of logarithms. 1b)In 17th century, an astronomer found the distance (d km) between two planets was (1.234x 5.678)^1000 km. Given log 1.234=0.0913, log 5.678=0.7541 and log 2,512=0.4, using (a), find the value of d. Give the answer in scientific notation and correct to 4 sig. fig. 2) The graph of y=f(x) is a quadratic function with x-intercepts -2 and 2, and y-intercept=3. a) If f(x) =ax^2+bx+c, find the values of a,b and c.
最佳解答:
1 a) log(ab) = log(a) + log(b) log(a/b) = log(a) - log(b) nlog(a) = log(a)n b) d = (1.234 x 5.678)1000 log d = log (1.234 x 5.678)1000 log d = 1000 log (1.234 x 5.678) log d = 1000 (log 1.234 + log 5.678) log d = 1000 (0.0913 + 0.7541) log d = 1000 x 0.8454 log d = 845.4 log d = 845 + 0.4 log d = 845 log 10 + log 2.512 log d = log 10845 + log 2.512 log d = log (2.512 x 10845) d = 2.512 x 10845 2) The curve: y = ax2 + bx + c (-2, 0) on the curve: 0 = a(-2)2 + b(-2) + c = 0 4a - 2b + c = 0 ...... (1) (2, 0) on the curve: 0 = a(2)2 + b(2) + c = 0 4a + 2b + c = 0 ...... (2) (0, 3) on the curve: 3 = a(0)2 + b(0) + c c = 3 (1) - (2): -4b = 0 b = 0 Put b = 0 and c = 3 into (2): 4a + 2(0) + (3) = 0 a = -3/4 Ans: a = -3/4, b = 0, c = 3 =
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