Please help me with the following questions.

1.

The given figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 34 units long. (a) Express the y-coordinate of P in terms of x. (Hint: Write an equation for the line AB.) (b) Express the area of the rectangle in terms of x. (c) What is the largest area the rectangle can have, and what are its dimensions? P(x,?) A -17 X 17 (a) The expression for the y-coordinate of P is (Type an expression using x as the variable.)Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 2. 2 2 V=cubic units (Round to two decimal places as needed.)A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface area is 10 times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed at 12000 cubic units and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction. The radius of the cylindrical base (and of the hemisphere) is |ft. (Round to the nearest tenth as needed.)A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where shoul boat be landed in order to arrive at a town 15 miles down the shore from P in the least time? The boat should be landed miles down the shore from P. (Type an exact answer.)A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface area is 7 times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed at 18000 cubic units and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction. The radius of the cylindrical base (and of the hemisphere) is ft. (Round to the nearest tenth as needed.)