29. Find a point on the graph of so the tangent line to at goes through the origin.
31. Rumor. The percent of a population, , who have heard a rumor by time is often modeled for some positive constant A. Calculate how fast the rumor is spreading, .
In problems 33 – 41, find a function with the given derivative.
Problems 43 – 47 involve parametric equations.
43. At time minutes, robot is at and robot is at .
(a) Where is each robot when and ?
(b) Sketch the path each robot follows during the first minute.
(c) Find the slope of the tangent line, , to the path of each robot at minute.
(d) Find the speed of each robot at minute.
(e) Discuss the motion of a robot which follows the path for 20 minutes.
45. For the parametric graph in Fig. 9, determine whether and are positive, negative or zero when and .
(b) Find , the tangent slope , and speed when and .
(The graph of is called a cycloid and is the path of a light attached to the edge of a rolling wheel with radius ).
49. Describe the path of a robot whose location at time is
(c) Give the parametric equations so the robot will move along the same path as in part (a) but in the opposite direction.
Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-3.6-Some-Applications-of-the-Chain-Rule.pdf
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