Math 3 questions

2012-09-18 11:55 pm

1. How to solve ln x +ln(x-1)=1
2. A mass is oscillating on the end of a spring. The distance, , of the mass from its equilibrium point is given by the formula y=7z cos(16piewt)
where is in centimeters, is time in seconds, and and are positive constants.
How many oscillations are completed in 1 second?
3.The monthly charge for a waste collection service is 1070 dollars for 100 kg of waste and 1670 dollars for 160 kg of waste.
Find a linear model for the cost,C, of waste collection as a function of the number of kilograms,w.
C=?

回答 (1)

micatkie

2012-09-19 12:56 am

✔ 最佳答案

1.
ln x + ln (x - 1) = 1
ln [x(x - 1)] = ln e
x(x - 1) = e
x² - x - e = 0
x = {1 ± √[(-1)² - 4(1)(-e)]}/2
x = [1 + √(1 + 4e)]/2 or x = [1 - √(1 + 4e)]/2 (rejected)

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2.
Something has been missing in the question :
" ...... The distance, ? , ...... where ? is in centimeters, ? is time in seconds, and ? are positive constants......"

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3.
Put C = hw + k
where h and k are constant.

When w = 100, C = 1070 :
1070 = h(100) + k
100h + k = 1070 ...... (1)

When w = 160, C = 1670 :
1670 = h(160) + k
160h + k = 1670 ...... (2)

(1) - (2) :
60h = 600
h = 10

Put h = 10 into (1) :
100(10) + k = 1070
k = 70

Hence, C = 10w + 70

參考: micatkie

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