Pre-Calculus

A rectangle is bounded by the x-axis and the semicircle y = √36 – x2, as shown in the figure below. Write the area A of the rectangle as a function of x, and determine the domain of the area function.
A =
all real numbers except x = 36
all real numbers except x = 6
0 < x < 6
0 < x < 36
all real numbers

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. I don't see any "figure below" , but I can surmise your figure shows a quarter circle in the first quadrant with a rectangle, whose base is along the x-axis, its height along the y-axis and it touches the quarter circle at (x,y)

    Area = xy
    = x√(36-x^2) or x(36-x^2)^(1/2)

    for the domain, we have to make sure that the number under the √ does not become negative, so
    0 < x < 6

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    A base of a solid is the region bounded by y=e^-x, the x axis, the y axis, and the line x=2. Each cross section perpendicular to the x-axis is a square Find the volume of the solid

  2. calculus

    A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30ft, find the dimensions of the window so that the greatest possible amount of light is admitted. I keep screwing up in

  3. math

    Question 13 of 21 The drawing is composed of a rectangle and a semicircle. Find the area of the figure to the nearest unit. A figure is composed of a rectangle and a semi-circle. The top edge of the rectangle measures 10

  4. Calculus

    1. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6. y = x, y = 0, y = 5, x = 6 2. Use the method of cylindrical shells to find the volume V generated by

  1. 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

  2. calculus

    1. Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = sin(x), y = 0, π/2 ≤ x ≤ π; about the x−axis 2. Find the volume V obtained by rotating the region bounded by the curves

  3. Calculus

    A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 31 feet? A =

  4. Math

    This figure consists of a rectangle and semicircle. What is the area of this figure? Use 3.14 for π. A shape made up of a rectangle of the left and a semicircle on the right. The rectangle has a width of 15 meters and a height of

  1. Parabola Ques

    Find the point P on the parabola y^2 = 4ax such that area bounded by parabola, the X-axis and the tangent at P is equal to that of bounded by the parabola, the X-axis and the normal at P.

  2. calculus

    Consider the functions f(x) = (x^3 / (x^4+1)) and g(x) = (x / (x^4+1)). Let R denote the region in the first quadrant bounded by the curves y = f(x) and y = g(x). Find the exact volume of the solid that has R as its base if every

  3. Math

    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 30 ft, find the dimensions of the window so

  4. Calculus

    A rectangle is bounded by the x-axis and the semicircle y=ã(25-x^2). Question is, what length and width should the rectangle have so that its area is a maximum, and what is the maxuimum area? Area= length*width = 2x*y=

View more similar questions or ask a new question.