# Briefly Compare and Contrast the Concepts of Needs Wants and Demands Essay

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MAT1106 Tutorial 2 1. Determine whether the following pairs of lines are coincident, parallel, perpendicular or intersecting . a) c) 2. 2x + y = 3 and 6x + 3y = 9 3x – 4y = 5 and x + y = 3 b) d) x – 2y = 4 and – 4x + 8y = 16 7x + 5y = – 2 and 5x – 7y = 9 Find the point of intersection for the given pairs of lines. a) 3x + 2y = 4 and x – 5y = 7 b) 3x – 5y = –11 and 5x + y = 19 3. Find the equation of the line parallel to 4x + y = 5 and passing through the point ( 8 , – 1 ) Find the equation of the line containing ( – 2 , 5 ) and perpendicular to the line containing the points ( 2 , 8 ) and ( 5 , – 1 ). Find an equation of the line perpendicular to the line 6x – 2y = – 5 and containing the point ( – 1 , – 2 ). 4. 5. Applications 1. Theatre Attendance The Star Theater wants to know whether the majority of its patrons are adults or children. During a week in July, 2600 tickets were sold, and the receipts totaled \$16440. The adult admission is \$8 and the children’s admission is \$4. How many adult patrons were there? Mixture Problem One solution is 20% acid and another is 12% acid. How many cubic centimetres of each solution should be mixed to obtain 100 cubic centimetres of a solution that is 15% acid? Cost and Revenue A manufacturer sells a product at \$8.35 per unit, selling all produced. The fixed cost is \$2116 and the variable cost is \$7.20 per unit. At what level of production will a) there be a profit of \$4600? b) there be a loss of \$1150? c) the break even point occur? 2. 3. Answers 1)a) 2)a) 3) 4) 5) Coincident (2,–1) 4x + y = 31 x – 3y = – 17 x + 3y = – 7 b) b) Parallel (3,4) c) Intersecting d) Perpendicular Applications 1) 2) 3)a) 1510 adults 37.5 cm3 5840 ; b) 62.5 cm3 840 c) 1840 Produced by Yong San Loo