Calculus differentiation problem?
A bug is walking around the circle x^2 + y^2 = 169. At a certain instant the bug is at the point (−5, 12) and its y-coordinate is decreasing at a rate of 3 units per second.
(a) Is the bug traveling the circle in a clockwise direction or a counterclockwise direction?
(b) How fast is its x-coordinate changing at this instant?
Answers
Captain Matticus, LandPiratesInc
x^2 + y^2 = 169 2x * dx/dt + 2y * dy/dt = 0 x * dx/dt + y * dy/dt = 0 x = -5 , y = 12 -5 * dx/dt + 12 * dy/dt = 0 dy/dt = -3 -5 * dx/dt + 12 * (-3) = 0 -5 * dx/dt - 36 = 0 5 * dx/dt + 36 = 0 5 * dx/dt = -36 dx/dt = -36/5 y is decreasing x is decreasing This happens twice: When the bug is walking counter-clockwise and is in the 2nd quadrant or when the bug is walking clockwise and is in the 4th quadrant. (-5 , 12) is in the 2nd quadrant, so it's walking counter-clockwise
ted s
counterclockwise ; 2x [dx/dt] + 2 y [ dy/dt ] = 0 ( - 10 ) [ dx/dt ] + 24 [ - 3 ] = 0 ...solve
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