# 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. 👁
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. 👎

## 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. ### 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

4. ### 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).

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

5. Find the volume of the solid generated by revolving the region bounded by y = x2, y = 0 and x = 1 about (a) the x-axis (b) the y-axis

3. ### maths

Find the area of the largest rectangle that can be inscribed in a semicircle of radius "r"?

4. ### fundamental theorem of calculus

Let f be the function shown below, with domain the closed interval [0, 6]. Let h(x) = integral from 0 to 2x-1 (f(t))dt. The graph is a semicircle above the x-axis with r=2 and center (2,0) connected to a semicircle below the

1. ### 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 30ft, find the dimensions of the window so

2. ### 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.

3. ### 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

4. ### 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?