Calculus

A rectangle is inscribed in a semicircle with radius 8. The variable x is half the length of the rectangle. Write an expressions for the perimeter and area of the rectangle in terms of x.

  1. 👍
  2. 👎
  3. 👁
  1. Draw the diagram. It should be clear that the height of the rectangle is
    √(8^2 - x^2)

    Now you have the height and the length (2x), so the rest is a cinch.

    1. 👍
    2. 👎
    👤
    oobleck

Respond to this Question

First Name

Your Response

Similar Questions

  1. AP Calculus

    A rectangle is inscribed between the parabolas y=4x^2 and y=30-x^2. what is the maximum area of such a rectangle? a)20root2 b)40 c)30root2 d)50 e)40root2

  2. pre-calc

    a semicircle of radius r=3x is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle 1. express the area A if the rectangke as a function 2 express the perimeter P of the rectamgle as a

  3. geometry

    An isosceles triangle has two 10.0-inch sides and a 2w-inch side. Find the radius of the inscribed circle of this triangle, in the cases w = 5.00, w = 6.00, and w = 8.00. Then Write an expression for the inscribed radius r in

  4. geometry circle

    A 16 cm by 12 cm rectangle is inscribed in a circle.. find the radius of the circle. ~answer

  1. Calculus

    A rectangle is bounded by the x-axis and the semicircle y = sqrt(36-x^2). What length and width should the rectangle have so that its area is a maximum? I understand that 2xy = A and that 4x + 2y = P, but I'm not sure how to solve

  2. Geometry

    Which step is the same when constructing an inscribed square and an inscribed equilateral triangle? A.Connect every arc along the circle. B.Construct a circle of any arbitrary radius. C.Set the compass width to greater than half

  3. Calculus

    "A rectangle is inscribed in a semicircle of radius 2 cm. Find the largest area of such a rectangle". There is a diagram, but I think the question makes it clear enough what is going on. I'm having problems finding a relationship

  4. Calculus

    A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus, the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 20 ft, find the dimensions of the window so

  1. Math

    A rectangle ABCD is inscribed in a circle of radius 'a'. Find the 'area of the rectangle' function and state the domain.

  2. Calculus

    Find the area of the largest rectangle that fits inside a semicircle of radius 10 (one side of the rectangle is along the diameter of the semicircle).

  3. Calc

    A rectangle is to be inscribed in a semicircle of radius 8, with one side lying on the diameter of the circle. What is the maximum possible area of the rectangle?

  4. Math

    A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window with maximum area if the total perimeter is 16 feet. X = the width of the rectangle. Y =

You can view more similar questions or ask a new question.