finish the following questions:

1. The height y (in feet) of a ball thrown by a child is y=-116x2+4x+3 where x is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child's hand? feet (b) What is the maximum height of the ball? feet (c) How far from the child does the ball strike the ground? feet

2. The Pear company sells pPhones. The cost to manufacture x pPhones is C(x)=-23x2+59000x+20731dollars (this includes overhead costs and production costs for each pPhone). If the company sells x pPhones for the maximum price they can fetch, the revenue function will be R(x)=-29x2+239000x dollars. How many pPhones should the Pear company produce and sell to maximimze profit? (Remember that profit=revenue-cost.) x= 3. A manufacture has been selling 1750 television sets a week at $510 each. A market survey indicates that for each $30 rebate offered to a buyer, the number of sets sold will increase by 300 per week. a) Find the demand function p(x), where x is the number of the television sets sold per week. p(x)= b) How large rebate should the company offer to a buyer, in order to maximize its revenue? $ c) If the weekly cost function is 148750+170x, how should it set the size of the rebate to maximize its profit? $ 4. A baseball team plays in a stadium that holds 56000 spectators. With the ticket price at $9 the average attendance has been 25000. When the price dropped to $6, the average attendance rose to 28000. Assume that attendance is linearly related to ticket price. What ticket price would maximize revenue? $ 5. An fruit grower knows from previous experience and careful data analysis that if the fruit on a specific kind of tree is harvested at this time of year, each tree will yield, on average, 133 pounds, and will sell for $3.5 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 2.5 pounds, while the price per pound will decrease by $0.06. A) How many weeks should the grower wait before harvesting the apples in order to maximize the sales revenue per tree? (Round your answer to the nearest tenth of a week.) Answer: (rounded to the nearest tenth) B) Use your answer in part A to find the actual maximum revenue that can be expected. (Round your answer to the nearest dollar.) Answer: dollars (rounded to the nearest dollar) 6. Given: (q is number of items) Demand function: d(q)=264.6-0.2q2 Supply function: s(q)=0.4q2 Find the equilibrium quantity: items Find the equilibrium price: