equation and polynomial

[匿名]

2015-03-20 4:16 am

1.((1-x^2)^n+(1-x)^n)/(1-x)^2n
2.A company purchased 800kg of a material at $40000. The selling price of the
material is restricted to be $50-$90 per kg. A survey showed that if selling price is $90 per kg, the daily sales will be 60kg. The sales will increase by 2kg for each $1
per kg decrease in selling price.(If the decrease in selling price is not a whole
number, the sales will increase in proportion.) There is an extra daily running cost of $800. Let the selling price be $x per kg and the daily profit be $y.
a)show that y = -2x^2+340x-12800
b)solved(max daily profit is $1650 and corresponding selling price is $85)
c)If the material is sold at the price in (b), find the total profit in selling the material.
d)find the total profit if the material is sold at the max. selling price.

更新1:

3.用綜合除法做(-x^3+x^2+36x-50)/(-x+6), quotient = -x^2-5x+6, 正負號調轉, 怎樣辦?

回答 (1)

用戶10012

2015-03-20 4:17 pm

✔ 最佳答案

1. (1 - x^2)^n = (1 + x)^n(1 - x)^n
The expression = [(1 + x)^n(1 - x)^n + (1 - x)^n]/(1 - x)^2n
= [(1 + x)^n + 1]/(1 - x)^n
2.
(a) Let daily sales = s kg. and selling price per kg = x
So s = mx + c
When x = $90, s = 60 kg.
60 = 90m + c .............(1)
When x = $89, s = 62 kg.
62 = 89m + c ............(2)
(2) - (1) we get
2 = -m, so m = - 2.
Sub into (1) 60 = (-2)(90) + c, c = 240
So daily sales,s = - 2x + 240.
Daily income = daily sales x selling price = (-2x + 240)x
Since cost per kg = $40000/80 = $50
So daily material cost = unit cost x daily sales = 50(-2x + 240)
Therefore, daily profit, y = daily income - daily cost
= (-2x + 240)x - 50(-2x + 240) = (-2x + 240)(x - 50)
= -2x^2 + 100x + 240x - 12000
= -2x^2 + 340x - 12000
Including the extra cost of $800
daily profit, y = -2x^2 + 340x - 12800
(b) y = -2(x^2 - 170x) - 12800
= -2[(x - 85)^2 - 85^2] - 12800
= -2(x - 85)^2 + 14450 - 12800
= -2(x - 85)^2 + 1650
So max. daily profit = $1650 when selling price is $85.
(c) When price = $85, daily sales = (-2)(85) + 240 = 70Kg
Profit = daily profit x total materail/70 = 1650 x 800/70 = $18857.
(d) When price at max. = $90, daily sales = (-2)(90) + 240 = 60Kg.
daily profit = -2(90 - 85)^2 + 1650 = 1600
Profit = 1600 x 800/60 = $21333.

2015-03-20 11:59:24 補充：
3. Instead of dividing by (-x + 6), divide (-x^3 + x^2 + 36x - 50) by (x - 6), then multiply the quotient by - 1.

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