Please solve with explanation

1) The radius of a spherical balloon increases at a rate of 1 mm/sec. How fast is the surface 1) area increasing when the radius is 10mm? (Note: The surface area S of a sphere of radius r is S = 4mr2.) Enter just a real number (no approximations, no units or words). 2) Mr. Smith is 6 ft tall and walks at a constant rate of 2 ft/sec toward a street light that is 10 ft 2 ) above the ground. At what rate is the length of his shadow changing when he is 6 ft from the base of the pole that supports the light? Enter just an integer (no units). Solve the problem. 3) Given the revenue and cost functions R(x) = 34x - 0.7x2 and C(x) =3x + 13, where x is the daily 3) production, find the rate of change of profit with respect to time when x = 15 units and dx dt = 4 units per day. A) $103/day B) $118.4/day C) $40/day D) $52/day 4) A piece of land is shaped like a right triangle. Two people start at the right angle at the same time, 4) and walk at the same speed along different legs of the triangle while spraying the land. If the area covered is changing at 3 m2/sec, how fast are the people moving when they are 3 m from the right angle? (Round approximations to two decimal places.) A) 3.00 m/sec B) 2.00 m/sec C) 0.50 m/sec D) 1.00 m/sec 5) A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping at 5) the constant rate of 4 ft/s, how fast is the bottom of the ladder moving along the ground when the bottom is 5 ft from the wall? A) 9.6 ft/s B) 10.4 ft/s C) 2.4 ft/s D) 0.80 ft/s Solve the problem. Round your answer, if appropriate. 6) One airplane is approaching an airport from the north at 151 km/hr. A second airplane approaches 6) from the east at 203 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 26 km away from the airport and the westbound plane is 15 km from the airport. A) -232 km/hr B) -116 km/hr C) -464 km/hr D) -348 km/hr 7) The radius of a right circular cylinder is increasing at the rate of 10 in./sec, while the height is 7) decreasing at the rate of 5 in./sec. At what rate is the volume of the cylinder changing when the radius is 6 in. and the height is 12 in.? A) 1260rt in.3/sec B) 540n in.3/sec C) -210 in.3/sec D) 540 in.3/sec 8) The volume of a sphere is increasing at a rate of 2 cm3/sec. Find the rate of change of its surface 8) area when its volume is - cm3. (Do not round your answer.) A) 2 cm2/sec B) = cm2/sec C) 4n cm2/sec D) 1 cm2/sec 9) Water is being drained from a container which has the shape of an inverted right circular cone. The 9) container has a radius of 3.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 3.00 inches deep, the surface level is falling at a rate of 1.7 in./sec. Find the rate at which water is being drained from the container. A) 22.4 in.3s B) 25.0 in.3/s C) 17.3 in.3/s D) 16.5 in.3/s 10) A man 6 ft tall walks at a rate of 6 ft/sec away from a lamppost that is 18 ft high. At what rate is the 10) length of his shadow changing when he is 30 ft away from the lamppost? (Do not round your answer) A) 3 ft/sec B) ~ ft/sec C) > ft/sec D) 30 ft/sec