Please solve the circle.

SECTION 1.6 Mathematical Models: Building Functions 109 A rectangle has one corner in quadrant I on the graph of y = 16 - x, another at the origin, a third on the positive 11. Geometry A wire 10 meters long is to be cut into two pieces. One piece will be shaped as a square, and the other piece -axis, and the fourth on the positive x-axis. See the figure. will be shaped as a circle. See the figure. a) Express the area A of the rectangle as a function of x. (b) What is the domain of A? 4x (c) Graph A = A (x). For what value of x is A largest? 10 m 10 - 4x 16 y = 16 -x2 x, y) (a) Express the total area A enclosed by the pieces of wire as a function of the length x of a side of the square. (0,0) ( 70) 4 x (b) What is the domain of A? (c) Graph A = A(x). For what value of x is A smallest? 8. A rectangle is inscribed in a semicircle of radius 2. See the 12. Geometry A wire 10 meters long is to be cut into two pieces. figure. Let P = (x, y) be the point in quadrant I that is a One piece will be shaped as an equilateral triangle, and the vertex of the rectangle and is on the circle. other piece will be shaped as a circle. (a) Express the total area A enclosed by the pieces of wire as a function of the length x of a side of the equilateral y = 14 -x2 triangle. P = (X, y) (b) What is the domain of A? (c) Graph A = A(x). For what value of x is A smallest? -2 13. Geometry A wire of length x is bent into the shape of a circle. (a) Express the area A of the rectangle as a function a) Express the circumference C of the circle as a function of x. of x. (b) Express the perimeter p of the rectangle as a function (b) Express the area A of the circle as a function of x. of x. 14. Geometry A wire of length x is bent into the shape of a (c) Graph A = A (x) . For what value of x is A largest? square. (d) Graph p = p (x) . For what value of zis p largest? a) Express the perimeter p of the square as a function 9.) A rectangle is inscribed in a circle of radius 2. See the figure. of x. Let P = (x, y) be the point in quadrant I that is a vertex of (b) Express the area A of the square as a function of x. the rectangle and is on the circle. 15. Geometry A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure. 2 P = (X, y) - 2 (a) Express the area A of the rectangle as a function of the - 21 radius r of the semicircle. x2 + yz = 4 (b) Express the perimeter p of the rectangle as a function of r. (a) Express the area A of the rectangle as a function 16. Geometry An equilateral triangle is inscribed in a circle of x. (b) Express the perimeter p of the rectangle as a function of radius r. See the figure. Express the circumference C of the circle as a function of the length x of a side of the of x. (c) Graph A = A(x). For what value of x is A largest? triangle. (d) Graph p = p(x) . For what value of x is p largest? Hint: First show that r2 = * 2 10. A circle of radius r is inscribed in a square. See the figure. (a) Express the area A of the square as a function of the 17. Geometry An equilateral triangle is inscribed in a circle of radius r of the circle. radius r. See the figure in Problem 16. Express the area A (b) Express the perimeter p of the square as a function of r. within the circle, but outside the triangle, as a function of the length x of a side of the triangle