Hi, I need help on a couple of problems. I'll be having my math mid-terms on the 26th, which is a Friday, and we were told by the teacher that some of the questions appearing in the test would be similar to the problems below. Specifically, I need help on four of them.
1) 1000 copies of a souvenir program will be sold if the price is $50 and that the number of copies sold decreases by 10 for each $1 added to the price. Write a function that determines gross revenue as a function of x. What price yields the largest gross sales revenue and what is the largest gross revenue? How many copies must be sold to yield the maximum gross revenue?
2) A rectangular field is fenced along a river bank, which is not. The material for the fence costs $12 per foot for the side parallel to the river, and while it costs $8 for the two other sides. What are the dimensions of the largest possible rec. field that can be enclosed with a budget of $3600? assume all material would be used up.
3) A waterway whose cross-section is a parabola is being designed for a theme park boat ride. It has a depth of 12ft. and a width of 6ft. at the surface. Rectangular cross-sectioned boats are to be used, and they sink to a depth of 4ft. What should be the proper width of the boat to facilitate easy passage?
[Note: parabola opens upwards]
4) Describe each of the equations in the given non-linear system.
a) (x-3)^2 = 9
-- y + 9
b) (x-3)^2 t y^2 = 4