Math Homework

1.         Write the following equations in the standard form Ax + By = C

            i. Slope = 2, containing point (-4, 1)

            ii. Slope  , containing the point (3, 1)

            iii. Containing points (-1, 2) and (1, 3)

2.         Determine whether the given pair of lines are parallel, coincident, or intersecting.

            i. L: x + y = 10 and M: 3x + 3y = 6

            ii. L: 2x + y = 4 and M: 2x – y = 8

            iii. L = -x + y = 2 and M: 2x – 2y = -4

3.         The cost of renting a bus is $450 per week, plus a charge of $0.28 per mile driven.             Write an equation that relates cost C for a weekly rental in which the bus is driven

            x miles.

4.         If a manufacturer produces items at a daily cost of $0.65 and sells for $1.15. The

            daily operational overhead is $300. What is the break-even point?              
 

5.         a. If people in Tula were willing and above to buy 10 smart phones when the price             was $300 each, and 20 smart phones when the price was $100, derive the demand

            curve P_D(Q) for smart phones.

                        The two given points are (10, 300) and (20, 100).

                        The slope of the line between the two points is:

                        The equation of the line has the form:

                        Substituting the point (10, 300) and solving for b gives:

                        The demand curve is then:

            b. If vendors in Tula were willing and able to sell 10 smart phones when the price was 300 and 40 smart phones when the price was $2100, derive the supply curve,

            P_S(Q) for smart phones.

            c. Determine equilibrium price and quantity for smart phones in Tula.

1.         Solve the following using an appropriate method:

            i.                    
 

            ii.

            iii.

           
             iv.      

            v.

            vi.

            vii.

            viii.             

2.         The product of two consecutive numbers is 240. What are the numbers?                 

3.         Two numbers differ by 12. Their product is 133. What are the numbers?

4.         The price p and quantity x sold of a certain product obey the demand curve

              , 0 ≤ x ≤ 300

            i. Express the revenue, R, as a function of x.

            ii. What is the revenue if 100 units are sold?

            iii. What quantity x will maximize revenue? What is the maximum revenue?

            iv. What price should the company charge to maximize revenue?                    

5.         A clothing store sells gloves for $50 per pair. The store averages sales of 90 pairs    each week. The store owner’s past experience leads him to believe that for each

            $2 increase in the price of the gloves, one less pair would be sold each week.

            What price would result in $5100 weekly sales?