calculus

posted by .

at a certain instant the base of a triangle is 5 inches and is increasing at the rate of 1 inch per minute. At the same instant, the height is 10 inches and is decreasing at the rate of 2.5 inches per minute. Is the area of the triangle increasing or decreasing? justify you answer.

  • calculus -

    a = bh/2
    da/dt = h/2 db/dt + b/2 dh/dt
    = 10/2 (1) + 5/2 (-2.5)
    = -1.25 in^2/min

  • calculus -

    Ok. Just do it the brute-force way.

    Initially, the area is 1/2 x 5 x 10 = 25
    After one minute, the area is 1/2 x 6 x 7.5 = 22.5
    After two minutes, the area is 1/2 x 7 x 5 = 17.5

    You can see that the area is decreasing.

    In terms of derivatives, the rate of change is exactly what a derivative is.

    You can say +1 d/dx for the base and -2.5 d/dx for the height.

    Overall that's a decrease in 1 - 2.5 = -1.5 inches every minute.

    If you look at the equation for a triangle 1/2 x b x h, the overall value will be less because you're losing -1.5 inches overall.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    When air expands adiabatically (without gaining or losing heat), its pressure and volume are related by the equation PV^1,4=C where C is a constant. Suppose that a a certain instant the volume is 520 cubic centimeters and the pressure …
  2. Calculus

    The edge of a cube is increasing at a rate of 2 inches per minute. At the instant when the volume is 27 cubic inches, how fast is the volume changing?
  3. calculus

    When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV^{1.4}=C where C is a constant. Suppose that at a certain instant the volume is 580 cubic centimeters, and the …
  4. Calculus

    When air expands adiabatically (without gaining or losing heat), its pressure and volume are related by the equation where is a constant. Suppose that at a certain instant the volume is cubic centimeters and the pressure is kPa and …
  5. AP calculus AB

    At the instant when the radius of a cone is 3 inches, the volume of the cone is increasing at the rate of 9 pi cubic inches per minute. If the height is always 3 times the radius, find the rate of change of the radius at that instant.
  6. calculus

    At the instant when the radius of a cone is 3 inches, the volume of the cone is increasing at the rate of 28.27433388 cubic inches per minute. If the height is always 3 times the radius, find the rate of change of the radius at that …
  7. calculus help please

    At the instant when the radius of a cone is 3 inches, the volume of the cone is increasing at the rate of 9 pi or 28.27433388 cubic inches per minute. If the height is always 3 times the radius, find the rate of change of the radius …
  8. Calculus

    Let V be the volume of a right circular cone having height h and radius r and assume that h and r vary with time. a. Express the time rate of change of the cylinder in terms of h, r and their rates of change. b. At a certain instant, …
  9. Calculus

    At a certain instant, each edge of a cube is 5 inches long and the volume is increasing at the rate of 2 cubic inches per minute. How fast is the surface area of the cube increasing?
  10. Calculus

    Assume the dimensions of a rectangle are continuously changing in a way so that the area, A, of the rectangle remains constant. If the base of the rectangle is increasing at a rate of 3 inches per second, at what rate is the height …

More Similar Questions