calculus

posted by .

consider a point on a circle x2+y2=1.At what rate Y is changing with respect to X when the point is at X=1/2....

  • calculus -

    There are two points on the circle with x = 1/2:
    (1/2, sqrt3/2) and (1/2,-sqrt3/2)

    Which one are you talking about?

    Anyway, what you want is dy/dx.
    Use a ^ sign before exponents.
    x^2 + y^2 = 1
    Use implicit differentiation.
    2x + 2y*dy/dx = 0
    dy/dx = -x/y = -1/sqrt3 or 1/sqrt3
    depending upon which of the two points you are talking about.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calc

    If a point moves on the hyperbola x^2-4y^2=36 in such a way that x-coordinate increases at constant rate of 20 units per second. How fast is the y coordinated changing at point (10,4)?
  2. Calculus

    A particle is moving along the curve whose equation is (xy^3)/(1+y^2)= 8/5. Assume the x-coordinate is increasing at the rate of 6 units/second when the particle is at the point (1,2). At what rate is the y-coordinate of the point …
  3. physics

    A block of mass m = 4.30 kg is released from rest from point circle a and slides on the frictionless track shown in the figure below. (Assume ha = 5.20 m.) B=3.20 c=2.00 (a) Determine the block's speed at points circle b and circle …
  4. Math

    Answer check please: Consider the circle (x-3)^2 + (y+1)^2 = 169. The point (15,4) is on the circle. Find an equation for the line that is tangent to the circle at this point. I got y= 5/12x-9/4.
  5. physics

    A roller-coaster car of mass 1.80 103 kg is initially at the top of a rise at point circle a. It then moves 40.8 m at an angle of 50.0° below the horizontal to a lower point circle b. (a) Find both the potential energy of the system …
  6. Calculus

    1. The radius of a sphere is expanding at a rate of 14 in/min. a) Determine the rate at which the volume is changing when the radius is 8 in. b) Determine the rate at which the surface area is changing when the radius is 8 in. 2. A …
  7. Calculus

    1. The radius of a sphere is expanding at a rate of 14 in/min. a) Determine the rate at which the volume is changing when the radius is 8 in. b) Determine the rate at which the surface area is changing when the radius is 8 in. 2. A …
  8. Calculus

    A point is moving along the curve xy=12. When the point is at (4,3), the x-coordinate decreases at the rate of 2cm/sec. How fast is the y-coordinate changing at that point?
  9. Calculus Reposted

    A point is moving along the curve xy=12. When the point is at (4,3), the x-coordinate decreases at the rate of 2cm/sec. How fast is the y-coordinate changing at that point?
  10. Calculus

    The shoreline of a lake is a circle with diameter 3 km. Peter stands at point E and wants to reach the diametrically opposite point W. He intends to jog along the north shore to a point P and then swim the straight line distance to …

More Similar Questions