Each month, College of Science alumni have the opportunity to test their skills and solve a current science student exam question. These questions are posed in the monthly College of Science newsletter, Discovery Monthly. The very first Science Question of the Month was featured in the 2022 alumni magazine Discovery. The question, provided by mathematics professor Charlie Nazemian, was pulled from a Math 181 exam.
Question
A particle is moving along the curve whose equation is: xy3/1+y2 = 8/5
Assume that the x-coordinate is increasing at the rate of 6 feet/sec when the particle is at the point (1, 2). At what rate is y-coordinate changing at that instant, and is it rising or falling?
Solution
This is a related rate problem.
- Given dx/dt = 6 ft/sec, when x =1 and y = 2.
- We take implicit differentiation from both of: (xy3)/(1+y2) = 8/5
- 5xy3 = 8 + 8y2
- 5[(dx/dt)y3 + 3xy2(dy/dt)] = 0 + 16y(dy/dt)
- After simplifications and substitutions for dx/dt = 6 , x = 1 and y = 2, we can solve for dy/dt.
- Answer: dy/dt = -60/7 ft/sec, the negative answer means that it is falling at that moment.
September's Winner
September's winner was Michael Jennings. He submitted the correct answer first. Congratulations, Michael Jennings!
Jennings, class of ’86 B.S. (Physics), ’98 M.S. (Physics), ‘07 Ph.D. (Educational Leadership), answered the Math 181 exam question correctly.
Jennings grew up in Reno and Sparks "when they were separate cities. That is to say, I grew up in Reno when the Convention Center was one of the last buildings in town and you could feed horses right off Kietzke Lane," Jennings said.
Jennings worked for the Washoe County School District as a high school dean, a math teacher and a computer literacy teacher. He also worked for the Nevada System of Higher Education as a physics instructor, and after that decided to become "semi-retired." Jennings spends his "semi-retired" time traveling, enjoying what the beautiful Truckee Meadows has to offer and numerous hobbies.
