The lower edge of a 4 foot tall painting is 4 feet above your eye level (see picture below for the idea, but be aware it's not drawn to scale). I / DD /' .5 4ft '3. /\\9 ,,-\" 4ft ,9 .u At what distance should you stand from the wall so your viewing angle of the painting is maximized? _t Give your answer accurate to at least 2 decimal places You want to get from a point A on the straight shore of the beach to a buoy which is 59 meters out in the water from a point B on the shore. B is 70 meters from you down the shore. If you can swim at a speed of 3 meters per second and run at a speed of 5 meters per second, at what point along the shore, x meters from B, should you stop running and start swimming if you want to reach the buoy in the least time possible? f\\Buoy 70m Find a formula for the time spent in terms of a: T0\") = Find the value for a: that will minimize the total time spent running and swimming. A small house was built on an island off a perfectly straight shoreline. The point B on the shoreline that is closest to the island is exactly 5 miles from the island. Eight miles east of B is the closest source of fresh water to the island. A pipeline is to be built from the island to the source of fresh water by laying pipe underwater in a straight line from the island to a point Q on the shoreline between B and the water source, and then laying pipe on land along the shoreline from Q to the source. It costs 8000 dollars per mile to lay the pipe under the water and 5000 dollars per mile to lay pipe on land. How far east of B should Q be located in order to minimize the total construction costs? D 3 undergrggg Find a formula for the cost of laying the pipe in terms of :1: 0(3) _ Find the value for a: that will minimize the total cost. U.S. postal regulations state that the sum of the length and girth (distance around) of a package must be no more than 108 inches (see below). girth length Find the dimensions of the acceptable box that has the largest volume if the end of the box is a rectangle that is 3 times as long as it is wide. Be sure you can do this with calculus. The largest possible volume is cubic inches. Find the point on the curve 3; = 1/51: + 6 which is closest to the point (6, O).