variations問題

[匿名]

2010-05-15 7:08 pm

the weight Wg of a crystal ball varies directly as the cube of its radius r cm.
Find the percentage change in the weight of the ball if

A.its radius is decreased to half of its original value
B.its radius is doubled..

更新1:

A shop sells a chemical in the shape of a cube of side x cm .the price of $P of the chemical varies directly as the volume of the cube. If the side of the cube is 15cm, the price is $270.1/Mr Chan wants to purchase the chemical for his laboratory.The budget is $2000.Find the range of the value of x.

回答 (1)

用戶2053

2010-05-15 7:22 pm

✔ 最佳答案

Let the weight be W ,
W = K r^3 , (K is a constant.)
A)its radius is decreased to half of its original value,
% change
= [(K (r/2)^3 - K r^3) / K r^3] x 100%
= {[(r^3)/8 - r^3] / r^3} x 100%
= (1/8 - 1) x 100%
= - 87.5%
B)its radius is doubled.
% change
= [(K(2r)^3 - K r^3) / K r^3] x 100%
= [(8 - 1) / 1] x 100%
= + 700%

2010-05-16 11:39:48 補充：
P = kx^3

270 = k(15)^3

k = 0.08

So

P = 0.08x^3

2000 >= 0.08x^3

25000 >= x^3

29.24 >= x

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