Solve A,B,C,D,E,F, and the problems in the picture

The height in feet of a free falling object t seconds after release is , s(t) = -16t² + v₀t + s_0, where is the height (in feet) at which the object is released, and Vo is the initial velocity (in feet per second). Suppose a coin is dropped from the top of the Empire State Building in New York, which is 1454 feet tall.

A. Determine the position and velocity functions for the coin.

B. Determine the average velocity of the coin on the interval [1, 3].

C. Find the instantaneous velocities when t = 1 and t = 3.

D. At what time is the instantaneous velocity of the coin equal to the average velocity of the coin found in Part B?

E. What is the name of the theorem that says there must be at least one solution to Part D?

F. Find the velocity of the coin just before it hits the ground.

1. Consider the family of curves described by: x2 + xy + ay? = b. Remember to justify your answers. A. Let a =1 and b =7. Find the two x-intercepts. B. Let a =1 and b =7. Using the two points you found in part A, show that the tangents to the curve at these points are parallel, and find the common slope. C. A given curve in the family x2 + xy + ay = b has a tangent line at point (1, 3) with slope -5 What are the values of a and b? 14