idk im completely lost would u guys please help me with me hw

If a closed tin can with a volume of 16π in3 is to be in the form of a right circular cylinder, what is the radius if its surface area is a minimum?

A 15 foot ladder is leaning against a wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 ft/sec. Find the rate at which the area of the triangle is changing when the base of the ladder is 9 ft from the wall.

A wire 4 ft long is to be cut into two pieces. One piece is bent into a circle and the other into a square. What would the length of the side of the square need to be if the sum of the areas is a maximum?

A boat is pulled by means of a winch on a dock 12 feet above the deck of the boat. The winch pulls in the rope at a rate of 4 ft/sec. What is the speed of the boat when there are 13 feet of rope out?

A man 6 feet tall walks at a rate of 5 ft/sec away from a light that is 15 feet above the ground. When he is 10 feet from the base of the light, at what rate is the tip of his shadow moving?

A right circular cylinder has a diameter of 12 in. and a height of 12 in. If water is flowing in at the rate of 4π in3 per minute, find the rate of change of the height when the height is 4 in.

A piece of wire 20 in. long is cut into two pieces, and each piece is bent into the shape of a square. What should the lengths of the two pieces be if the sum of the areas of the two squares is a minimum?

A rectangular field is to be fenced off on three sides with the fourth side being the bank of a river. If the cost of the fence is $8 per foot for the two ends and $12 per foot for the side parallel to the river, what are the dimensions of the largest rectangle that can be enclosed with $3840 worth of fence?

Two cars, one going due east at 25 m/sec and the second going due south at 50/3 m/sec are traveling toward the intersection of the two roads they are driving on. At what rate are the two cars approaching each other at the instant when the first car is 200 m and the second car is 150 m from the intersection?

A man 6 feet tall walks at a rate of 5 ft/sec away from a light that is 15 feet above the ground. When he is 10 feet from the base of the light, at what rate is the length of his shadow changing?

A particle moves along thex-axis, with its positionxgiven byx(t) =t− cost. At which of the following times is the velocity of the particle equal to 0?

A point moves along thex-axis, with its position,x, at timet> 0 given by

x(t) =t3 − 12t2 + 45t− 50.

For which of the following values oftis the point momentarily at rest (motionless)?