αν m = mg - cv dt (a) Solve this as a linear equation to show that v = mg (1 - e-ct/m). (b) What is the limiting velocity? (c) Find the distance the object has fallen after t seconds.

findthe derivative wer) r+13 dw = ? dr

9. Fill in the blanks AND give reasons for each step of the calculation. Let y = arctan(r+ e). (This could also be written y = tan- (r + e).) We will find its derivative. First rewrite the equation as tan( using the definition of Now apply the method of to get 윤 tan( On the left side of the equation we use the to get: sec ( Now we solve for to get = This shows that arctan(r+ e") %3D If we want to, we can use trigonometry to write the final answer using only the variable r, but for simplicity we'll leave the answer as it is.

Consider that the force of interest, is a function of time, measured in years, and is given by the following expression:  0.05 - 0.0010 t   for  0 < t < 14  0.09          for     t > 14 Hence, find the equivalent constant force of interest per quarter year for the period of t=8 to t=29 years. No tables, only formulas, please