Concept explainers
APPLICATIONS
Beehives In a beehive each cell is a regular hexagonal prism, as shown in the figure. The amount of wax
Bees instinctively choose
(a) Use a graphing device to graph
(b) For what value of
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Algebra and Trigonometry (MindTap Course List)
- View from a Satellite The figures on the next page indicate that the higher the orbit of satellite, the more of the earth the satellite can see. Let ,s, and h be as in the figure, and assume that the earth is a sphere of radius 3960 mi. a Express the angle as a function of h. b Express the distance s as a function of . c Express the distance s as a function of h. Hint: Find the composition of the functions in parts a and b. d If the satellite is 100 mi above the earth, what is the distance s that it can see? e How high does the satellite have to be to see both Los Angeles and New York, 2450 mi apart?arrow_forwardForce The force F (in pounds) on a person’s back when he or she bends over at an angle from an upright position is modeled by F=0.6Wsin+90sin12 where W represents the person’s weight (in pounds). (a) Simplify the model. (b) Use a graphing utility to graph the model, where W=185and090. (c) At what angle is the force maximized? At what angle is the force minimized?arrow_forwardThe designers of a water park have sketched a preliminary drawing of a new slide (see figure). (a) Find the height h of the slide. (b) Find the angle of depression from the top of the slide to the end of the slide at the ground in terms of the horizontal distance d a rider travels. (c) Safety restrictions require the angle of depression to be no less than 25 and no more than 30. Find an interval for how far a rider travels horizontally.arrow_forward
- Geometry A trough for feeding cattle is 4 meters long and its cross sections are isosceles triangles with the two equal sides being 12 meter (see figure). The angle between the two sides is . (a) Write the volume of the trough as a function of /2. (b) Write the volume of the trough as a function of and determine the value of such that the volume is maximized.arrow_forwardHeight of a Mountain To calculate the height h of a mountain, angles and and distance d are measured, as shown in the figure below. a Show that h=dcotcot b Show that h=dsinsinsin() c Use the formulas from parts a and b to find the height of a mountain if =25, =29 and d=800 ft. Do you get the same answer from each formula?arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage