Question

A rectangle is bounded by the x-axis and the semicircle y = sqrt(36 - x²). The domain of the rectangle is determined by the values of:

A) x
B) y
C) x and y
D) Area of the rectangle

Answer 1

The domain of the rectangle under the semicircle y = sqrt(36 - x²) is determined by the values of x, specifically within the interval [-6, 6].

The correct option is A.

Step-by-step explanation:

The domain of a rectangle that is bounded by the x-axis and the semicircle y = sqrt(36 - x²) is determined by the values of x. The semicircle's equation is derived from the circle equation x² + y² = 36, where the circle has a radius of 6.

Because we are dealing with a semicircle that lies above the x-axis, the domain of this shape will be the range of x-values for which the function y = sqrt(36 - x²) is defined, which corresponds to the interval [-6, 6].

The y-values are determined by the function itself for a given x-value within this domain. Thus, only the x-values define the horizontal span of the rectangle under the semicircle, which is also the domain of the rectangle.

The correct option is A.