中4數1條 - Ans.fyi 參考答案

中4數1條

2007-03-04 6:41 pm

2.The value(in$) of a diamond varies directly as the cube of its weight(in carat).
(a)If the value of a diamond weighting 2carats is $6400, find the value of a diamond weighting 3.5 carats.
(b)If the 2-carat diamond is broken into two pieces of equal weight, what would be the percentage loss in its value?

回答 (1)

用戶121550

2007-03-04 7:11 pm

✔ 最佳答案

Let the value of the diamond be $P and its weight be x carats.
P = kx ^ 3

(a) Put P = 6400 and x = 2.
6400 = k(2) ^ 3
k = 800

So P = 800x ^ 3

When x = 3.5, we have
P = 800(3.5) ^ 3
P = 34300

So the value of a diamond weighing 3.5 carats is $34300.

(b) When x = 1, we have
P = 800(1) ^ 3 = 800

So the value of the 2-carat diamond which is broken into two pieces of equal weight
= $800 * 2 = $1600

The original value of the 2-carat diamond = $6400.

So the percentage loss in its value
= [(6400 - 1600)/6400] * 100%
= 75%

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