4. The period of a pendulum is the time the pendulum takes to swing back and forth. The period, t (in seconds), of a pendulum of length d (in inches) is given by d = 9.78t2. The longest pendulum in the world is part of a clock on a building in Tokyo, Japan. This pendulum is about 74 feet (888 inches) long. What is the period of the pendulum? 88 8 - 9. 78+? 9 0. 79 75 = 19.5) 9. 78 9. 78 85. From 1970 to 2000, the prize money, P (in dollars), at the Professional Golf Association Championship can be approximated by the model P = 2875t2 + 220,000, where t is the year, with t = 0 corresponding to 1970. During which year was the prize money first over $1,350,000? 93 , 6 4347 19 . 9 3 7 2 1 1 3 0 0 0 0 = 2 875 +2 1, 3 50, 000 - 2875+2+ 220, 000 2875 2 475 - 220 , 000 - 2201 00 0 6. From 1980 to 2000, the profit, P (in dollars), of a company could be modeled by P = 9400t2 + 525,000, where t = 0 corresponds to 1980. According to this model, when would the company have a profit of approximately $2,600,000? 21 6 00 / 60 0 = 946 0 + 2 + 525 000 2, 600, 000 = 940010) + 5250607. Find the distance between the edges of two consecutive stair steps as shown. Approximate the length of the handrail shown above the stairs. You are driving from Deerfield to Campbellsport in Ohio. Highway 14 is under construction, so you drive 5.5 miles north on Route 255, then 5.8 miles west on Interstate 76. How many miles longer is this route than taking Highway 14? 9. According to legend, in 1589 the Italian scientist Galileo Galilei dropped campbellsport two rocks of different weights from the top of the Learning Tower of Pisa. 225 He wanted to show that the rocks would hit the ground at the same time. Given that the tower's height is about 177 feet, how long would it have taken for the rocks to hit the ground? 14 10. On any planet the height h (in feet) of a falling object t seconds after it is tdropped can be modeled by h = , t2 + ho where he is the objects initial height and g is the acceleration (in feet per second squared) due to the planet's gravity. Find the time it would take a rock dropped from a height of 200 feet to hit the ground on the following planets. a. Mars: g = 12 ft/ sec b. Jupiter: g = 81 ft/ sec2 c. Pluto: g = 2.1 ft/ sec 11. The equation h = 0.019s2 gives the height h (in feet) of the largest ocean waves when the wind speed is s knots. How fast is the wind blowing if the largest waves are 15 feet high? 16x 12. The aspect ratio of a TV screen is the ratio of the screen's width to its height. For most TVs, the aspect ratio is 16:9. What are the width and height of the screen for a 42 inch TV? (Note: TV sizes refer to the length of the screen's diagonal. 9x 42 13. Building codes often require that buildings be able to withstand a certain amount of wind pressure. The pressure P (in pounds per square foot) from wind blowing at s miles per hour is given by P = 0.00256s2. A two story building is required to withstand a wind pressure of 20 lbs/ ft2. How fast can the wind be blowing before it produces excessive stress on the building