3Q about maths!!!

1) If x units of rubbish bin are produced and sold. The cost function (in $) isC(x) = 400 + 8x ,and the selling price is $12 for one unit.

(a) How many units will result in break-even?
400 + 8x = 12x
4x = 400
x = 100
(b) How many items must be produced to make a profit of $200?
12x - (400 + 8x) = 200
12x - 400 - 8x = 200
4x = 600
x = 150


2) (a) The 4th term of an arithmetic sequence is 22, and the 7th term is 37.Find the 10th term of the sequence.
a + 3d = 22 ------ (1)
a + 6d = 37 ------ (2)
(2) - (1), 3d = 15
d = 5

(b) Find the sum of the infinite geometric series 3-(3/5)+(3/25)-(3/125)+...
a = 3
r = -(3/5)/3 = -1/5
sum = 3/(1 - (-1/5)) = 5/2

3) The rectangular top-side of a table has an area of 180 cm2 and its length is 3 cm longer than its width. What is the width and length of the table top?
length = l
width = l - 3
l(l - 3) = 180
l^2 - 3l - 180 = 0
(l - 15)(l + 12) = 0
l = 15
w = 12