Example 2
a sprinkler rotates in a circular pattern and sprays water over a distance of 12 feet. what is the area of the circular
region covered by the sprinkler? express your answer to the nearest square foot.
draw a diagram to assist you in solving the problem. what does the distance of 12 feet represent in this problem?

The volume of gas a balloon can hold varies directly as the cube of its radius. imagine a balloon with a radius of 3 inches can hold 81 cubic inches of gas. how many cubic inches of gas must be released to reduce the radius down to 2 inches?

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.