Precalculus: Functions and Graphs is designed to make this transition seamless, by focusing now on all the skills that you will need in the future. Preparation is the foundation of success, and Precalculus: Functions and Graphs will help you succeed in this course and beyond. Examples and exercises that relate back to the opener are included in the chapter. These graphical galleries are designed to help the students link the visual aspects of various families of functions to the properties of the functions. Art Annotations have been added in order to make the mathematical art a better learning tool and easier for students to use.
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Check 14 in the original equation as shown in Fig. A tank can be filled by a small pipe in 12 hours or a large pipe in 8 hours. How long will it take to fill the tank if the small pipe is used alone for 2 hours and then both pipes are used until the tank is full? True or False? The perimeter of any rectangle is the product of its length and width. Two numbers that have a sum of -3 can be represented by x and -3 - x.
Solve each formula for the specified variable. The use of the formula is indicated in parentheses. The 2. To compete in the 2. Solve the formula for D. Finding the Freeboard Solve the formula in the previous exercise for F.
Write a formula that expresses rate R as a function of distance D and time T in uniform motion. Write a formula that expresses time T as a function of distance D and rate R in uniform motion. Write a formula that expresses the width W of a rectangle as a function of its area A and length L. Write a formula that expresses the width W of a rectangle as a function of its perimeter P and length L.
Write a formula that expresses the radius r of a circle as a function of its diameter d. Write a formula that expresses the diameter d of a circle as a function of its radius r. Use the appropriate formula to solve each problem. Circumference of a Circle If the circumference of a circular sign is 72p in. Fahrenheit Temperature If the temperature at 11 P.
Target Heart Rate For a cardiovascular workout, fitness experts recommend that you reach your target heart rate and stay at that rate for at least 20 minutes www. To find your target heart rate find the sum of your age and your resting heart rate, then subtract that sum from Art Auction A buyer paid 2. Investment Income Tara paid one-half of her game-show winnings to the government for taxes. Solve each problem. See the strategy for problem solving on pages 14— Trimming a Garage Door A carpenter used 30 ft of molding in three pieces to trim a garage door.
If the long piece was 2 ft longer than twice the length of each shorter piece, then how long was each piece? Celsius Temperature If the temperature at 1 P. See the figure. If the saddle height is 37 in. To increase her production, she plans to increase both the length and width by 2 m.
If the new field is 46 m2 larger than the old field, then what are the dimensions of the old field? Fencing a Feed Lot Peter plans to fence off a square feed lot and then cross-fence to divide the feed lot into four smaller square feed lots. If he uses ft of fencing, then how much area will be fenced in? Start-Up Capital Norma invested the start-up capital for her Internet business in two hedge funds.
Both loans were for one year. If Brent made a total of 24 cents in interest, then how much did he lend to each one? Figure for Exercise 43 Fencing Dog Pens Clint is constructing two adjacent rectangular dog pens. Each pen will be three times as long as it is wide, and the pens will share a common long side. If Clint has 65 ft of fencing, what are the dimensions of each pen? Racing Speed Bobby and Rick are in a lap race on a onemile oval track. Bobby, averaging 90 mph, has completed two laps just as Rick is getting his car onto the track.
What speed does Rick have to average to be even with Bobby at the end of the tenth lap? Rowing a Boat Boudreaux rowed his pirogue from his camp on the bayou to his crab traps. Going down the bayou, he caught a falling tide that increased his normal speed by 2 mph, but coming back it decreased his normal speed by 2 mph. Going with the tide, the trip took only 10 min; going against the tide, the trip took 30 min.
At the halfway point he noticed that he had been averaging 80 mph, while his company requires his average speed to be 60 mph.
What must be his speed for the last half of the trip so that he will average 60 mph for the entire trip? Use d or simply make up a distance. When Northside and Southside were closed, all workers transferred to the new Eastside plant to make up its entire work force.
How many hours would it take to harvest the crop with both combines operating?
032150111x - Precalculus: Functions and Graphs by Dugopolski, Mark