F.4 maths........????10點

1. the height of a rectangular box is 15cm. it is known that the volume of the box is V cm3 . and its base a square with the length of each side of x cm.
a) express V in term of x.
V = 15x^2
b)why is V a function of x ?
Since the height is constant, the larger the base area, the bigger will be the volume.
2. the height of trapezium ABCD is (x-1) cm, the lengths of AD and BC are (2x+1)cm and(4x+1) cm respectively.
a.)express the area of trapezium ABCD as a function A[x]
A(x) = (2x +1 + 4x + 1)(x - 1) / 2
= (6x + 2)(x - 1)/2
= (3x + 1)(x - 1) = 3x^2 - 2x - 1
b)if the area of trapezium ABCD is 64 cm2 . find BC-AD
3x^2 - 2x - 1 = 64
3x^2 - 2x - 65 = 0
(3x + 13)(x - 5) = 0
x = 5 or x = -13/3 (rejected)
BC = 4x + 1 = 21
AD = 2x + 1 = 11
BC - AD = 21 - 11 = 10cm