SOLUTION: A bug is moving along the right side of the parabola y = x^2 at a rate such that its distance from the origin is increasing at 3 cm/min. At what rates are the x and y coordinates o

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: A bug is moving along the right side of the parabola y = x^2 at a rate such that its distance from the origin is increasing at 3 cm/min. At what rates are the x and y coordinates o      Log On


   

Question 1099809: A bug is moving along the right side of the parabola y = x^2 at a rate such that its distance from the origin is increasing at 3 cm/min. At what rates are the x and y coordinates of the bug increasing when the bug is at the point (6,36)? Please state the x coordinate and the y coordinate.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
V=sqrt%28%28dx%2Fdt%29%5E2%2B%28dy%2Fdt%29%5E2%29
sqrt%28%28dx%2Fdt%29%5E2%2B%28dy%2Fdt%29%5E2%29=3
%28dx%2Fdt%29%5E2%2B%28dy%2Fdt%29%5E2=9
and
y=x%5E2
dy%2Fdt=2x%2A%28dx%2Fdt%29
Substituting,
%28dx%2Fdt%29%5E2%2B%282x%2A%28dx%2Fdt%29%29%5E2=9
%28dx%2Fdt%29%5E2%2B4x%5E2%28dx%2Fdt%29%5E2=9
%28dx%2Fdt%29%5E2%281%2B4x%5E2%29=9
%28dx%2Fdt%29%5E2=9%2F%281%2B4x%5E2%29
So when x=6,
%28dx%2Fdt%29%5E2=9%2F%281%2B4%286%29%5E2%29
%28dx%2Fdt%29%5E2=9%2F%281%2B4%2836%29%29
%28dx%2Fdt%29%5E2=9%2F%281%2B144%29
%28dx%2Fdt%29%5E2=9%2F145
dx%2Fdt=3%2Fsqrt%28145%29cm%2Fmin
So then from above,
dy%2Fdt=2x%28dx%2Fdt%29
dy%2Fdt=2%286%29%289%2Fsqrt%28145%29%29
dy%2Fdt=108%2Fsqrt%28145%29cm%2Fmin