A ball is dropped from a 200 foot cliff. If gravity is 32 ft/sec2, find the position function of the ball at time t. Using t^2 for t2.

Find the derivative

A duck's flight is given by the following expression: y = x^2 + x + 4. X and y are coordinates of its flight. When x = 2, the duck takes a hit and thereafter its flight follows the trajectory of a tangent line. What is the coordinate when x=4.

A light is placed on the tip of a windmill blade to protect planes from crashing into them. The windmill's center is 400 ft above the ground and the blades of the windmill are 180 feet long. The windmill rotates in the counter-clockwise direction and completes one full revolution every 10 seconds starting from the 3 o'clcok position. Define the function f that represents the light's distance above the ground in terms of the amount of time in seconds, t, since the windmill started rotating. Determine the equation of the midline for the function f. Graph the function using Desmos to check your answer. Assume y=f(t). Determine the amplitude of the function f. Graph the function using Desmos to check your answer.\ Determine the period of the function f. Graph the function using Desmos to check your answer.

Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis and a tangent line to the graph of f = (x + 1)-². Area =

Is the derivative 15?

Simplify (5x'y+)3

Find dt