I know these are a lot of questions. So if you can only do some of them that's okay. Thank you so very much in advance for your help.

Find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a sphere with radius 35 cm. The radius is D cm, and the height is D cm. (Type an integer or a decimal. Round to the nearest hundredth as needed.) The volume is D cma. (Type an integer or a decimal. Round to the nearest hundredth as needed.) A particle moves along the parabola y = x in the first quadrant in such a way that its x-coordinate (measured in meters) increases at a steady 25 - m How fast is the angle of inclination 0 of the line joining the particle to the origin changing when x = 2 m? sec The angle of inclination 0 of the line joining the particle to the origin is changing at a rate of rad sec when x = 2 m. (Simplify your answer.)The trough in the gure is to be made to the dimensions shown. Only the angle 9 can be varied. What value of 6 will maximize the trough's volume? The trough has a maximum volume when the value of 6 is :l radians. (Type an exact answer, using 1: as needed.) m3 The height is changing at a rate of Sand falls from a conveyor belt at a rate of 10 . onto the top of a conical pile. The height of the pile is always three-eighths of the base diameter. cm ' _ \"1'" E when the height IS 8 m. How fast are the height and the radius changing when the pile is 8 m high? _ _ (Type an Integer or deCImal. Round to the nearest hundredth.) The radius is changing at a rate of cm . when the height is 8 m. min (Type an integer or decimal. Round to the nearest hundredth.) A hunter is at a point along a river bank. He wants to C get to his cabin, located 4 miles north and 10 miles west. (See figure.) He can travel 6 mph along the 4 river but only 2 mph on the rocky land. How far upriver should he go in order to reach the cabin in H minimum time? 10 The distance that the hunter should walk along the river is approximately mi. (Do not round until the final answer. Then round to the nearest tenth as needed.)in s in A spherical iron ball 12 in. in diameter is coated with a layer of ice of uniform thickness. If the ice melts at a rate of 14- min . how fast is the thickness of The thickness of the ice is decreasing at a rate of min when the ice is 3 in. thick. the ice decreasing when it is 3 in. thick? How fast is the outer surface area of ice decreasing? (Type an exact answer, using it as needed.) in 2 The outer surface area of ice is decreasing at a rate of min - when the ice is 3 in. thick. (Type a simplified fraction.)Next question ft A child ies a kite at a height of 90 ft, the wind carrying the kite horizontally away from the child at a rate of 30 Q. How fast must the child let out the string when the kite is 150 ft away from the child? ft The child must let out the string at a rate of Q when the kite is 150 ft away from the child. (Simplify your answer.) A mailing service places a limit of 102 in. on the combined length and girth of (distance around) a package to be sent parcel post. What dimensions of a rectangular box with square cross-section will contain the largest volume that can be mailed? (Hint: There are two different girths.) The dimensions are x = |Vandy =VA university is trying to determine what price to charge for tickets to football games. At a price of $20 per ticket, attendance averages 40,000 people per game. Every decrease of $2 adds 10,000 people to the average number. Every person at the game spends an average of $4.00 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price? What is the price per ticket? $ What is the average attendance? peopleOn a morning of a day when the sun will pass directly overhead, the shadow of a 69ft building on level ground is 92 it long. At the moment in question, the angle 6 the sun makes with the ground is increasing at the rate of 0.27/min. At what rate is the shadow decreasing? Remember to use radians in your calculations. Express your answer in inches per minute. The shadow is decreasing at inches per minute. (Round to one decimal place as needed.) Next question The voltage V (volts), current I (amperes) and resistance R (ohms) of an electric circuit like the one shown here are related by the equation V= IR. Suppose that V is increasing at a rate of 2 volt/sec, while I is decreasing at the rate of - amp/sec. Let t denote time in seconds. Answer the following questions. R a. What is the value of - dv at ? (Type a simplified fraction.) b. What is the value of ? (Type a simplified fraction.) dR dv c. What equation relates al dt at and ? Choose the correct answer below. O A. dR 1 (dV V al O B. dR V I dt at dt * dt O c. dR 1 R IV O D. dR V dV V al dt at * at at = 1 dt - I dt d. Find the rate at which R is changing when V = 72 volts and 1 = 4 amp. = dR (Type a simplified fraction.) Is R increasing or decreasing? O Decreasing IncreasingFind the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 35 in. by 19 in. by cutting congruent squares from the corners and folding up the sides. Then nd the volume. The dimensions of box of maximum volume are V (Round to the nearest hundredth as needed. Use a comma to separate answers as needed.) The maximum volume is V (Round to the nearest hundredth as needed.)