The cost($C) of holding a mini-concert is the sum of 3 parts. The first part is a constant of $2000, the second part varies directly as the number of participants(x), the third part varies directly as the square of the number of prativipants.
The cost is$3000 when there are 100 participants and the cost is $2750 when there are 150 participants.
a) Express C in terms of x.
b)find the cost when there are 20participants.
c)Find the number of participants when the cost is $2960
variations (10 marks) 急
2007-06-19 4:31 am
回答 (2)
2007-06-19 4:43 am
✔ 最佳答案
a. Let C = 2000 + k1x + k2x² , where k1 and k2 are constants.When x = 100, C = 3000
i.e. 3000 = 2000 + k1(100) + k2(100)²
1000 = 100k1 + 10 000k2
10 = k1 + 100k2 ───── (1)
When x = 150, C = 2750
i.e. 2750 = 2000 + k1(150) + k2(150)²
750 = 150k1 + 22 500k2
5 = k1 + 150k2 ───── (2)
(2) - (1):
-5 = 50k2
k2 = -1/10
So, 5 = k1 + 150(-1/10)
k1 = 20
So, C = 2000 + 20x - x²/10
b. When there are 20 participants, i.e. x = 20
So, C = 2000 + 20(20) - (20)²/10
C = 2000 + 400 - 40
C = 2360
So, the cost is $2360.
c. When the cost is $2960, i.e. C = 2960
So, 2960 = 2000 + 20x - x²/10
960 = 20x - x²/10
x² - 200x + 9600 = 0
(x - 80)(x - 120) = 0
x = 80 or 120
So, the number of participants are 80 or 120.
參考: Myself~~~
2007-06-19 4:46 am
a)C=2000+aX+bX^ (^=square)
b)when cost is 3000 and 2750
3000=2000+a100+b100^ ----1
2750=2000+a150+b150^ ----2
1-2:
4500=3000+a150+b15000 ----1X1.5
2750=2000+a150+b22500 ----2
==>
1800=1000+7500b
b= 0.1067
a= -0.667
c) cost =2960
C=2000+aX+bX^
2960=2000 -0.667X + 0.1067X^
0.1067X^ - 0.667X -960 =0
X=98
b)when cost is 3000 and 2750
3000=2000+a100+b100^ ----1
2750=2000+a150+b150^ ----2
1-2:
4500=3000+a150+b15000 ----1X1.5
2750=2000+a150+b22500 ----2
==>
1800=1000+7500b
b= 0.1067
a= -0.667
c) cost =2960
C=2000+aX+bX^
2960=2000 -0.667X + 0.1067X^
0.1067X^ - 0.667X -960 =0
X=98
參考: me
收錄日期: 2021-04-13 00:38:21
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