1.) A 20 foot long pole leans against a wall. The bottom is 12 feet from the wall. How much farther should the bottom be pulled away from the wall so that the top moves the same amount down the wall? 2.) A rectangular field will be fenced on all four sides. Fencing for the north and south sides costs $8 per foot and fencing for the other two sides costs $9 per foot. What is the maximum area that can be enclosed for $4800?

3.) Find the dimensions of the rectangular box with a square base and no top that has a volume of 70000 cubic centimeters and the smallest possible surface area. Round your answer to the nearest hundredth of centimeter.

4.) If you borrow $600 from a credit union at 8% annual interest and $350 from a bank at 19% annual interest, what is the effective annual interest rate (that is, what single rate of interest on $950 would result in the same total amount of interest)? (Round your answer to one decimal place.)

5.) A cylindrical waste container with no top, a diameter of at least 2 feet, and a volume of 45 cubic feet is to be constructed. What should its radius be if the smallest possible amount of material is to be used to construct it?

6.) A cylindrical can of volume 51 cubic inches is to be designed. For convenient handling, the can must be at least 5 inches high and 2 inches in diameter. If the cost of materials is 5 cents per square inch for the top and bottom of the can, and 3 cents per square inch for its height, what dimensions should be used to minimize the cost of making the can?

7.) A certain type of fencing comes in rigid 20-foot-long segments. Four uncut segments are used to fence in a garden on the side of a building, as shown in the figure. What value of x will result in a garden of the largest possible area? Round your answer to the nearest foot?

8.) A rectangle is to be inscribed in a semicircle of radius 6. What is the largest possible area of such a rectangle? [Hint: The width of the rectangle is the second coordinate of the point P (why?), and P is on the top half of the circle x² + y² = 36.

9.) Find the point on the graph of the equation that is closest to the point (0, 1) and has positive coordinates. (Hint:The distance from the point (x,y) on the graph to (0, 1) is expressyin terms ofx.)

Please show your work on everything.