A particle moves counterclockwise around the ellipse 3×2 + 8y2 = 11. At what rate is the x-coordinate changing when the particle passes the

Question

A particle moves counterclockwise around the ellipse 3×2 + 8y2 = 11. At what rate is the x-coordinate changing when the particle passes the point (1, 1) if its y-coordinate is increasing at a rate of 8 ft/s?

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Josie 2 weeks 2021-09-13T12:44:30+00:00 1 Answer 0

Answers ( )

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    2021-09-13T12:46:23+00:00

    Answer:

    D(x) /dt  =  – 21,33 ft/s

    Step-by-step explanation:

    We have an equation, in which both  x  and  y coodinates are function of t, then we take derivatives on both sides of the equation to obtain

    3*x²   +  8*y²  =  11

    6* x * D(x) /dt  +  16* y * D(y)/dt  = 0

    6* x * D(x) /dt   =  –  16* y * D(y)/dt       (1)

    Now from problem statement we know:

    D(y) /dt  = 8 ft/s

    And we are loking for D(x)/dt  = ?? when particle passes the point ( 1,1)

    x = 1      y  =  1

    Plugging these values in equaton (1)

    6* x * D(x) /dt   =  –  16* y * D(y)/dt  

    6* D(x) /dt  = – 16* 8

    D(x) /dt  =  – 128 /6      ⇒    D(x) /dt  =  – 21,33 ft/s

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