calculus

posted by .

Can someone tell me how to do this type of problem? A particle moves along the curve y=sqrt(1+x^3). As it reaches the point (2,3) the y coorindate is increasing at a rate os 4cm/s. How fast is the x coordinate of the point changing at that instant?

  • calculus -

    Differentiate both sides with respect to t:
    dy/dt = d(sqrt(1+x^3))/dx * dx/dt
    =(3x²/(2sqrt(1+x³)))*dx/dt

    So given x=2,y=3 and dy/dt=3 cm/s
    substitute in formula above to solve for dx/dt.

    I get dx/dt=2.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    I need help setting up this problem: A particle moves along the curve y=sqr(1+x^3). As it reaches the point (2,3) the y-cordinate is increasing at a rate of 4cm/s. How fast is the x-coordinate of the point changing at that instant. …
  2. college calculus

    1) each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square is 16 cm^2?
  3. calculus

    A particle moves along the curve y=square sqrt 1+x^3. As it reaches the point (2,3), the y-coordinate is increasing ata a rate of 4cm/s. How fast is the x-coordinate of the point changing at that instant?
  4. calculus

    A particle is moving along the curve below. y = sqrt(x) As the particle passes through the point (4,2), its x-coordinate increases at a rate of 4 cm/s. How fast is the distance from the particle to the origin changing at this instant?
  5. math

    a particle moves along the curve y= sqrt 1+x cubed. As it reaches the point (2,3) the y-corrdinate is increasing at a rate of 4cm/s. How fast is the x-coordinate of the point changing at that instant?
  6. Calculus

    A particle moves along the curve y = sqr(1+x^3). As it reaches the point (2,3), the y-coordinate is increasing at a rate of 4 cm/s. How fast is the x-coordinate of the point changing at that instant.
  7. Calculus

    A particle moves along the curve y = sqr(1+x^3). As it reaches the point (2,3), the y-coordinate is increasing at a rate of 4cm/s. How fast is the x-coordinate of the point changing at that instant?
  8. Calculus HELP

    A particle is moving along the curve y=5 sqrt (2x+6). As the particle passes through the point (5,20 , its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin …
  9. calc

    A particle moves along the curve below. y = sqrt(8 + x^3) As it reaches the point (2, 4), the y-coordinate is increasing at a rate of 5 cm/s. How fast is the x-coordinate of the point changing at that instant?
  10. Calculus

    A particle moves along the curve y=lnx so that its abscissa is increasing at a rate of 2 units per second. At what rate is the particle moving away from the origin as it passes through the point (1,e)?

More Similar Questions