Please help me with this, they're all application of derivatives questions.

Assume that a rectangle with sides x and y is expanding with time. Let y = 2x and t) : 3t + 1. What is the formula for the rate of change of the area with respect to time? 0 : 12(3t+ 1) 0 2 (3t + 1) 0 : 12(3t 1) o :4(3t1) The volume of a sphere is expanding where r = 2t. What is the rate of ohenge in volume with respect to time? The volume of a sphere is V : gm\"? 0 g : 163??2 0 g : 32w2 0 %:8m2 0 g = urn-rt2 Assume that a rectangle with sides x and y is changing with time. Let y = 2x and 113(t) : t2. What is the rate of change of the area at time t = 2? 0%:30 dA_ 05410 dA_ 0536 o:64 Assume that an airplane is flying toward you at a constant height h = 1 mile and at a speed at = -20 miles/hr. h X When the plane is 2 miles away, what is the rate of change of 0? tan (0) = O ad = 4 degrees/second O de = 6 degrees/second O = -6 degrees/second O = -4 degrees/secondGiven the triangle shown with base b and height h: Assume that b + h = 25; what formula will maximize the area of the triangle? Note: x2 - 62 X 4 + h2 h O A= 25b 2 O A= 25 + O A = 25b b 2 O A= 25For the following diagram: If the area of the inner region A = (:1: 1)(y 1) = 100, what equation will minimize the total area TA : my? The area of a rectangle is A = bh. Given the perimeter of the rectangle is 2b + 2h = 32, what dimensions maximize the area of the rectangle? O b = 8, h = 8 b = 10, h = 10 O b = 9, h = 7 O b=8,h=6 Given the right triangle shown where x + y = 10, what is the maximum area for the triangle? A=12.5 O A=13.5 David is building a play area for his kids. They are learning their shapes and he wants it to be an isosceles triangle with base b and height h. He is restricted to dimensions such that b + h = 25. What is the maximum area of the triangle? b O A: 86.125 0 A: 79.5 Q A: 78.125 0 A: 67.5 Jill is building a right triangular shelf which will t into the corner of a room. The shelf has sides x and y where x + y = 10. What is the largest area possible for the shelf given the constraints? 2 Y I O A=9.5 A=1'l.5 O A=12.5 O A: 13.5 Kim throws a ball against a wall at time t = 0. At time t = 1, it hits the wall and then at time t = 2 it is back where it started. If the average speed of the ball is 10 miles per hour, can you apply the MVT to show that the baseball must be traveling at 10 miles! hr at some point between [0,2]? Jon received his math grade for algebra. His class average over 10 tests is 89. Can you use the MVT to show that Jon must have received an 89 on one of the 10 tests? Let f(x) = x3 3x. Use Rolle's Theorem to find all the values c in the interval [, .5 such that f '{c) = O. \fThe temperature of coffee in a large urn fluctuates as coffee is dispensed and more coffee is added. The temperature measured in degrees Fahrenheit is modeled by the function f(t) = 140 + 10 sin(t) where t is measured in minutes. What is the instantaneous rate of change at t = 2 minutes