中四程度數學求解~!

Cagalli

2011-08-12 2:19 am

只有3條,煩請連步驟

1) If f(x) = x+(1/x) , find the value of [f(x)]^2 -f(x^2)

2) y varies directly as√x.(←這是開方x)
a) find the percentage change in y if x is increased by 10%.
b) when x=25,y=10.find y when x=64.

3) The speed of an electric train is measured as 6 km/min, correct to nearest P km/min,the percentage error in this measurement is 5/3%.
a) find the value of P
b) can the true speed of the train be 370 km/h?explain.

回答 (1)

用戶10012

2011-08-13 12:41 am

✔ 最佳答案

1.[ f(x)]^2 = (x + 1/x)^2 = x^2 + 1/x^2 + 2
f(x^2) = x^2 + 1/x^2. So their difference = 2.
2.
a) Original value of y = y
Original value of x = x
New value of x = x(1 + 10%) = 1.1x
So new value of y = y sqrt (1.1x)/sqrt x = y sqrt 1.1 = 1.0488y
So % change in y = (1.0488y - y)/y x 100% 0.0488 x 100% 4.88%.
b) 10/sqrt 25 = y/sqrt 64 = constant, k.
10/5 = y/8, so y = 2 x 8 = 16.
3. Scale interval = P, so max. error = P/2.
% error = max. error/measured value
so 5/3 % = (P/2)/6 x 100 %
5/3 = 100P/12
P = 60/300 = 1/5 = 0.2 km/min.
So upper limit of speed = 6 + max. error = 6 + P/2 = 6.1 km/min.
= 6.1 x 60 km/hr. = 366 km/hr.
Therefore true speed cannot be 370 km/hr.

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