# Mobile Phone Company

Topics: Mobile phone, Mobile network operator, Telephone company Pages: 2 (540 words) Published: October 11, 2012
DEPARTMENT OF MATHEMATICS NAME: Chen Haiwei Student Id: 42416302 FACULTY OF SCIENCE

MATH123 S212 Mathematics 123 Tutorial Week 3

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MATH123 Mathematics 123 S212 2012 Tutorial Week 3
1. Simplify each of the following expressions, to obtain equivalent expressions, and reducing the complexity of denominators wherever possible. Show all your steps. In each case, identify any special values of the variables where the original form may diﬀer in value from the simpliﬁed form (including the possibility of being undeﬁned). 1 1 + x + 3y x − 3y 4x2 − 9 x2 − 1 (b) × x+1 4x + 6 x2 − 1 1 (c) ÷ 1+ 2x x (a) 2. Simplify: (a) 3x − 4 x+5 − 3x + 2 2x − 3 (c) (d) 5 3 + x x (x + 1) (x − y) (x + y) − x2 y2 2 2

(d)

25x2 − 4 x+3 × −5 x2 − 9 5x − 2 3 1 2 (e) + − x (x + 2) x2 − 2x x2 − 4 1 1 (f) 2 + 2 x + xy y + xy

a b c + + (b) ab bc ac

3. Factorise each of the following expressions using laws of squares and cubes as necessary: (a) x4 − x2 (b) x6 − y 6 (c) x6 − y 3 (d) x3 y − xy 3 (e) x4 y + xy 4 (f) x2 − y 2 − 7x + 7y

4. Simplify each of the following expressions, showing all your steps. (a) (b) (c) 1 2 3 + 2 − 2 x (x + 2) x − 2x x − 4 y 2xy x − − x − y x + y x2 − y 2 x − 1 / (y − x) y (d) (x + h) − x2 h 1 1 − x+h x (e) h 3 (x + h) − x3 (f) h 2

5. Which pairs of lines in the following list are parallel? Which are perpendicular? (a) 3x + 5y = 2 (b) 5x − 3y = 1 (c) 5x + 3y = 13 (d) 10x − 6y = 9 (e) y = 0.6x + 2

6. (a) The Wonderful Mobile Phone Company charges \$70 per month, and calls cost \$0.50 per minute. If I use my phone for x minutes in a month, write down an expression for the total cost in terms of x. (b) Repeat the previous part for the Fantastic Mobile Phone Company, which charges \$20 per month and \$1 per minute. (c) Plot both graphs on the same axes and hence ﬁnd the call time per month which gives...