Penguins huddle together to stay warm in very cold weather. (See Figure 12.85 .) Suppose that a certain type of penguin has a circular cross-section approximately 14 inches in diameter (so that if you looked down on the penguin from above, the shape you would see would be a circle, 14 inches in diameter). Suppose that a group of this type of penguin is huddling in a large circular cluster, about 20 feet in diameter. (All the penguins are still standing upright on the ground; they are not piled on top of each other.)
Figure 12.85 Penguins in a huge cluster.
- Assuming that the penguins are packed together tightly, estimate how many penguins are in this cluster. (You might use areas to do this.) Is this an overestimate or an underestimate? Explain.
- The coldest penguins in the cluster are the ones around the circumference. Approximately how many of these cold penguins are there at any given time? Explain.
- So that no penguin gets too cold, the penguins take turns being at the circumference. How many minutes per hour does each penguin spend at the circumference if each penguin spends the same amount of time at the circumference? Explain.
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
Additional Math Textbook Solutions
Pathways To Math Literacy (looseleaf)
Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)
Finite Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
Differential Equations: An Introduction to Modern Methods and Applications
- Refer to the shaft shown in Figure 6-4. Determine the missing dimensions in the table using the dimensions given. All dimensions are in inches.arrow_forwardLaying Phone Cable City A lies on the north bank of a river that is 1 mile wide. You need to run a phone cable from City A to City B, which lies on the opposite bank 5 miles down the river. You will lay L miles of the cable along the north shore of the river, and from the end of that stretch of cable you will lay W miles of cable running under water directly toward City B. See Figure 2.108. Figure 2.108 You will need the following fact about right triangles: A right triangle has two legs, which meet at the right angle, and the hypotenuse, which is the longest side. An ancient and beautiful formula, the Pythagorean theorem, relates the lengths of the three sides: Lengthofhypotenuse=Lengthofoneleg2+Lengthofotherleg2 a. Find an appropriate right triangle that shows that W=1+(5L)2 b. Find a formula for the length of the total phone cable P from City A to City B as a function of L. c. Make a graph of the total phone cable length P as a function of L, and explain what the graph is showing. d. What value of L gives the least length for the total phone cable? Draw a picture showing the least-length total phone cable.arrow_forwardA parabolic reflector for a car headlight forms a bowl shape that is 6 in. wide at its opening and 3 in. deep, as shown in the figure at the left. How far from the vertex should the filament of the bulb be placed if it is to be located at the focus?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL