Find the solution to mx''+cx'+kx=f(t), x(0)=0, x'(0)=0 for an arbitrary function f(t), where m> 0, c> 0, k> 0, and c^2-4km> 0 (system is overdamped). write the solution as a definite integral.

An astronaut drops a rock into a crater on the moon. the distance, d(t), in meters, the rock travels after t seconds can be modeled by the function d(t)0.82. what is the average speed, in meters per second, of the rock between 5 and 10 seconds after it was dropped?

1. are the triangles similar and if so why? what is the value of x? show your work.

Consider the graph of the exponential function y=3(2)×