Science:Math Exam Resources/Courses/MATH104/December 2010/Question 01 (j)
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Question 01 (j) 

A racing car travels along the ellipse where x and y are measured in kilometers. When the car is at the point (1,2), the xcoordinate of the point is changing at the rate of 3 kilometers per minute. How fast is the ycoordinate changing at that moment? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Here x and y are functions of time, so we have the implicit relation 
Hint 2 

Use implicit differentiation! 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We have that and we want to find dy/dt when x=1, y=2 and dx/dt=3. Therefore, we implicitly differentiate and isolate for dy/dt, We then sub in x=1, y=2, and dx/dt=3 to get that and so we conclude that the ycoordinate is changing at 3/4 kilometers per minute at that moment. 