1. Suppose y partly varies directly as x^2 and partly varies directly as x-5. When x=6 , y =28 , wnen x=8 ,y=40.
a)express y in terms of x
b)find the value of x when y=25
c)find the minimum value of y
2.The cost of making a wooden sphere varies directly as its volume and the cost of painting varies directly as its surface area. the total cost $c of making and painting a wooden sphere of radius 1m is $200 and that of a sphere of radius 2m is $1120.
a)express c in terms of r
b) a company orders a wooden sphere of radius 2.5m for decoration. find the total cost of making and painting the sphere.
c)the manufacturer of wooden spheres reduces the cost of making by10% and the cost of painting by 5% . what is the overall % change in total cost of amking painting a sphere of radius 2.5m?
最後 我想問下6000x-2x^2點變成-2(x-150)^2+45000
thx!!!!
(急)VARIATIONS 數學
2011-11-22 2:42 am
回答 (1)
2011-11-22 3:55 am
✔ 最佳答案
1.a)
y = k1x² + k2(x - 5) where k1 and k2are constant.
When x = 6 , y = 28 :
28 = k1(6)² + k2(6 - 5)
36k1 + k2 = 28
108k1 + 3k2 = 84 ...... [1]
when x = 8 ,y = 40 :
40 = k1(8)² + k2(8 - 5)
64k1 + 3k2 = 40 ...... [2]
[1] - [2] :
44k1 = 44
k1 = 1
Put k1 = 4 into [2] :
64(1) + 3k2 = 40
3k2 = -24
k2 = -8
Hence, y =x² - 8(x - 5)
or y = x² - 8x + 40
b)
When y = 25 :
25 = x² - 8x + 40
x² - 8x + 15 = 0
(x - 3)(x - 5) = 0
x = 3 or x = 5
c)
y = x² - 8x + 40
y = (x² - 8x + 4²) + 40 - 4²
y = (x - 4)² + 24
For all real values of x, (x - 4)² ≥0
Hence, y = (x - 4)² + 24 ≥ 24
The minimum value of y = 24
2.
a)
c = constant1*(4/3)πr³ + constant2*(4πr²)
Hence, c = k1r³ + k2r² where k1 and k2are constant.
When r = 1, c = 200 :
200 = k1(1)³ + k2(1)²
k1 + k2 = 200 ...... [1]
When r = 2, c = 1120 :
1120 = k1(2)³ + k2(2)²
8k1 + 4k2 = 1120
2k1 + k2 = 280 ...... [2]
[2] - [1] :
k1 = 80
Put k1 = 80 into [1] :
80 + k2 = 200
k2 = 120
Hence, c = 80r³ + 120r²
b)
When r = 2.5 :
c = 80(2.5)³ + 120(2.5)²
c = 2000
Total cost = $2000
c)
New total cost
= 80(2.5)³(1 - 10%) + 120(2.5)²(1 - 5%)
= 1837.5
Overall % change in total cost
= [(1837.5 - 2000)/2000] * 100%
= -8.125%
6000x - 2x² 點變成 -2(x - 150)² + 45000
應是 6000x - 2x² 之誤。
600x - 2x²
= -2(x² - 300x)
= -2[x² - 2*150*x + 150²] + 2*150²
= -2(x- 150)² + 45000
2011-11-21 20:08:14 補充：
最後一問應是 600x - 2x² 之誤。
參考: Tsui, Tsui
收錄日期: 2021-04-13 18:22:18
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