calc

posted by .

can you just show me how to set this up? or a formula that could help? im confused.
The length of a rectangle is increasing at 3 ft/min and the width is decreasing at 2 ft/min. When the length is 50 ft and the width is 20 ft, at what rate is the rectangle decreasing?

  • calc -

    Let the width of the rectangle be x ft
    let the length of the rectangle be y ft

    Area = xy
    d(Area)/dt = x dy/dt + y dx/dt

    given: dx/dt = -2 and dy/dt = 3
    so when x = 20 and y = 50

    d(Area)/dt = 20(3) + 50(-2)
    = -40

    At that moment, the area is decreasing at a rate of 40 ft^2/min

  • calc -

    thank you so much!!!!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. algebra , help

    Can someone help me set up the equations thanks. Directions: Solve each of the following applications. Give all answers to the nearest thousandth. Problem: Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal …
  2. Math. fast please!

    The length of a rectangle is 3 cm and the width is 2 cm. find the length of the diagonal. Is there a formula to do this?
  3. mat117/algebra

    The area of a rectangle of length x is given by 3x^2 + 5x. Find the width of the rectangle. Show me the formula and how to use it please. area= length times width 3x^2 + 5x = x * width divide both sides by x, then you have width.
  4. College Algebra

    Suppose that the length of a rectangle is 3 inches longer than the width and that the perimeter of the rectangle is 78. Set up an equation involving only L, the length of the rectangle. Solve this equation algebraically to find the …
  5. math

    Suppose that the width of a rectangle is 5 inches shorter than the length and that the perimeter of the rectangle is 50 inches. The formula for the perimeter of a rectangle is P=2L+2W. a) Set up an equation for the perimeter involving …
  6. math

    the length of a rectangle is 7 times as long as its width. if the perimeter is 72 meters what is the length and width of the rectangle?
  7. calculas

    if the length is decreasing at a rate of 2 in./min. while width is increasing at a rate of 2 in./min., what must be true about area of the rectangle
  8. Algebra/geometry

    a rectangle has a width of 4 cm less than it's length. if a new rectangle is formed by increasing the width 5 cm and decreasing the length 3 cm, the area of this resulting rectangle is 177 cm squared. what are the dimensions of the …
  9. Calculus

    The length of rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of 3cm/s. When the length is 20cm and the width is 10cm, how fast is the area of the rectangle increasing?
  10. AP CALC. AB

    Two sides of a triangle have lengths 13 m and 17 m. The angle between them is increasing at a rate of 5 degrees/ min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60 degrees/min?

More Similar Questions