(拯救文科生)問數 - Ans.fyi 參考答案

(拯救文科生)問數

2007-04-04 8:27 pm

The area of a paper bookmark is A cm^2 and its perimeter is P cm. Its is known that A is the sum of two parts,one part varies as P and the other part varies as the square of P.
When P =24,A=36 and when P=18 ,A=9.

1) The best-selling paper bookmark has an area of 54cm^2 . Find the perimeter of this bookmark =)

show step pls .

Ans=27cm

回答 (1)

myisland8132

2007-04-04 8:36 pm

✔ 最佳答案

Answer
Since A is the sum of two parts,one part varies as P and the other part varies as the square of P.
So we can let
A=KP+MP^2 (where K and M are constants)
From P =24,A=36 and when P=18 ,A=9.
We have
36=24K+576M...(1)
9=18K+324M...(2)
(2)*(-4)+(1)
0=-48K-720M
K=-15M
sub into 2
9=18(-15M)+324M
54M=9
M=1/6
Then K=-5/2
A=(-5/2)P+(1/6)P^2
The best-selling paper bookmark has an area of 54cm^2
(-5/2)P+(1/6)P^2=54
-15P+P^2=324
P^2-15P-324=0
(P+12)(P-27)=0
P=-12 (rejected) or 27
So, the perimeter of this bookmark is 27 cm

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