急!急!急! 中四數學題

1) c = 6x2 - 360x + 10000

= 6(x2 - 60x) + 10000

= 6(x2 - 60x + 900) + 4600

= 6(x - 30)2 + 4600

Hence when x = 30, min. cost = 4600

2) One square has each side = k cm and the other with each side = (20 - k) cm

Hence their sum of area is:

A = k2 + (20 - k)2

= 2k2 - 40k + 400

= 2(k2 - 20k) + 400

= 2(k2 - 20k + 100) + 200

= 2(k - 10)2 + 200

When k = 10, min. area = 200 cm2

3a) When t = 1, W = 6

-2 + a = 6

a = 8

b) W = -2t2 + 6t

= -2(t2 - 3t)

= -2(t2 - 3t + 2.25) + 4.5

= -2(t - 1.5)2 + 4.5

So the max. reduction of weight should be in 1st or 2nd month

W(1) = 6, W(2) = 4

So max. reduction of the weight is in 1st month

c) -2t2 + 6t >= 0

-2(t - 1.5)2 + 4.5 >= 0

(t - 1.5)2 <= 2.25

t - 1.5 <= 1.5

t <= 3

So Mr. Fat loses weight successfully for 2 months.

d) He gains weight again.