Section 2.5 Formulas and Applications from Geometry 137 315 - 160 = 9C + 160 - 160 Subtract 160 from each side. 155 = 9C Simplify. 155 9 = 9C 9 Divide each side by 9. 17.2 = C Simplify. So, 63°F is equivalent to 17.2°C. 1c. The formula d = rt calculates the distance, d, traveled by an object going at an average rate r for time t. A cruise ship travels from Fort Lauderdale, Florida, to San Juan, Puerto Rico, in 45.5 hr at an average speed of 24 knots (about 27.6 mph). What is the distance the ship traveled? Solution 1c. d = rt d = (27.6)(45.5) d = 1255.8 Replace r with 27.6 and t with 45.5. Multiply. The cruise ship traveled 1255.8 mi. S l i Student Check 1 Use the formula and the given values to solve for the missing variable. a. The formula I = Prt is used to calculate simple interest for an investment of P dollars at an annual interest rate, r, for t years. Find the value of I if P = $1000, r = 5%, and t = 3. b. The formula C = 5 9 (F - 32) is used to convert degrees Fahrenheit (F ) to degrees Celsius (C ). Find the value of F if C = 50°. c. The world’s fastest passenger train, the Harmony Express in China, opened in December 2009. It travels at an average speed of 217 mph from Wuhan, China, to Guangzhou, China. It takes 3 hr to complete the trip. Use the formula d = rt to calculate the distance between the cities of Wuhan and Guangzhou. (Source: http://www.telegraph.co.uk/news/worldnews/asia/china/7230137/China-steams-ahead-withworlds fastest-train.html) Perimeter, Area, and Circumference As presented in Chapter 1, the perimeter of a polygon is the distance around the outside of the figure. In other words, it is the sum of the lengths of the sides of the polygon. The distance around a circle is called the circumference of the circle. The area of a figure is the number of square units it takes to cover the inside of the figure. (A square unit is a square whose length and width are both 1 unit long.) The formulas for some common shapes are provided. Triangle B c h a A b C P = a + b + c A = 1 2 bh Rectangle w l P = 2l + 2w A = lw Square s P = 4s A = s2 Circle r C = 2πr A = πr2 Objective 2 ▶ Use perimeter, area, and circumference formulas.
hendricks_beginning_algebra_1e_ch1_3
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