Question

A particle is moving along the curve whose equation is (xy^(3))/(1+y^(2))=(375)/(26) Assume that the x-coordinate is increasing at the rate of 10 units/s when the particle is at the point (3,5). (a) At what rate is the y-coordinate of the point changing at that instant? Enter the exact answer. (dy)/(dt)=, unit(s)/(s)

Name: a particle is moving along the curve whose equation is xy31y237526 assume that the x coordinate is increasing at the rate of 10 unitss when the particle is at the point 35 a at what rate is 16786
Uploaded: 2021-10-04T18:07:46-08:00
Duration: 2 min 34 s
Channel: Ma. Theresa Alin
Description: a particle is moving along the curve whose equation is xy31y237526 assume that the x coordinate is increasing at the rate of 10 unitss when the particle is at the point 35 a at what rate is 16786

          A particle is moving along the curve whose equation is
(xy^(3))/(1+y^(2))=(375)/(26)
Assume that the x-coordinate is increasing at the rate of 10 units/s when the particle is at the point (3,5).
(a) At what rate is the y-coordinate of the point changing at that instant?
Enter the exact answer.
(dy)/(dt)=, unit(s)/(s)

Added by Benjamin S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ma. Theresa Alin

10/04/2021

Step 1

Differentiating the equation (xy^3)/(1+y^2) = 375/26 with respect to t, we get: d/dt[(xy^3)/(1+y^2)] = d/dt(375/26) Using the product rule and chain rule, we get: y^3(dx/dt) + 3xy^2(dy/dt)/(1+y^2) - (xy^3(2y(dy/dt)))/(1+y^2)^2 = 0 Simplify the equation: y^3(dx/dt) Show more…

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A particle is moving along the curve whose equation is (xy^(3))/(1+y^(2))=(375)/(26) Assume that the x-coordinate is increasing at the rate of 10 units/s when the particle is at the point (3,5). (a) At what rate is the y-coordinate of the point changing at that instant? Enter the exact answer. (dy)/(dt)=, unit(s)/(s)