Math 170 – 22: Extra Credit Opportunity Due: Tuesday, July 12 Each problem is worth between 0 and 5 points (so there is a maximum number of 20 points possible). I will add ¼ of your total number of points to your overall grade in the course. Thus you can earn 5 points toward your overall grade (that is half a letter grade). To earn all 5 points for a problem, you must have the correct answer and sufficient support worked out in a clear and concise manner. Partial credit can be earned for significant progress toward a complete and accurate solution. A correct answer with little or no support will not get many points. You may use any source you wish, but you need to write up the solutions on your own before turning in the work. Do each problem on a separate sheet of paper. Turn in a clear and concise write up for each problem and clearly indicate your final answer. 1. A set of 24 duplexes (so 48 units) was sold to a new owner. The previous owner charged $700 per month for rent and had all 48 units occupied. The new owner started raising the rent so as to increase the amount of money made each month. When the price was raised to $750 a month, there were only 47 units occupied. When the price was raised to $800 each month, two of the units were empty. Let x = the number of $50 rent increases the new owner makes. Give an equation for the monthly rental income for the new owner – assuming the pattern for number of units occupied continues in the fashion of the first two increases, and find the maximum monthly rental income the new owner can achieve. What is the monthly rent at this point? 2. Two carts, A and B, are connected by a rope 39 feet long that passes over a pulley P that is 12 feet above the ground. The point on the ground (Q) directly beneath the pulley is between the two carts. Cart A is being pulled away from Q at a rate of 2 feet per second. How fast is cart B moving towards Q at the instant when cart A is 5 feet from Q? P z 12 x y B A Q 3. Worldwide quarterly sales of a certain cell phone is approximately n = −x + 156 million phones when the price is $x per phone. Suppose it costs the company $40 to manufacture each phone. What price should be charged per phone to maximize quarterly profit? What is this maximum value of profit? €
4. For a certain engine, a 7-­‐inch connecting rod is fastened to a crank of radius 3 inches. The crankshaft rotates counterclockwise at a constant rate of 200 revolutions per minute. Find the velocity of the piston when θ = π3 . Recall the law of cosines: c 2 = a2 + b2 −2abcosθ €