SOLUTION: a point moves on the parabola y^2=16x in such a way that the rate of change of the abscissa is always 3 units/sec. how fast is the ordinate changing when the abscissa is 1 unit?

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Question 1202345: a point moves on the parabola y^2=16x in such a way that the rate of change of the abscissa is always 3 units/sec. how fast is the ordinate changing when the abscissa is 1 unit?
Answer by ikleyn(52898)   (Show Source): You can put this solution on YOUR website!
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a point moves on the parabola y^2=16x in such a way that the rate of change of the abscissa
is always 3 units/sec. how fast is the ordinate changing when the abscissa is 1 unit?
~~~~~~~~~~~~~~~~~~~~ 

The point  (x,y)  moves  x = x(t),  y = y(t)  along the parabola 

    y^2 = 16x      (1)

in such a way that the rate of change of the abscissa  always is  = 3 units/sec.

        They want you find    at x = 1.


It is easy.  Take the derivatives respective the time "t" of the equation (1).  You will get

     = ,    (2)


At x= 1, y^2 = 16, from equation (1).  So, substitute in (2) y = +/-  = +/- 4,   = 3, as it is given.  You will get

    2*(+/-4)* = ,

which gives you

     = +/- 6.



ANSWER.  Under given conditions,   = +/- 6.

         It means that when the point (x,y) moves on the upper branch y =  ,   = 6 at x= 1.
                       When the point (x,y) moves on the lower branch y = ,  = -6 at x= 1.

Solved.



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