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51. MODELING REAL LIFE The Moeraki Boulders are stone spheres along the coast of New Zealand. A 1 S formula for the radius of a sphere is r = where 2 V TT S is the surface area of the sphere. Find the surface area of a Moeraki Boulder with a radius of 3 feet.

51. MODELING REAL LIFE The Moeraki Boulders are stone spheres along the coast of New Zealand. A 1 S formula for the radius of a sphere is r = where 2 V TT S is the surface area of the sphere. Find the surface area of a Moeraki Boulder with a radius of 3 feet.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 37E
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## Algebra 2 with Calculus and Geometry ### 51. Modeling Real Life The **Moeraki Boulders** are stone spheres along the coast of New Zealand. A formula for the radius of a sphere is \( r = \frac{1}{2} \sqrt{\frac{S}{\pi}} \), where \( S \) is the surface area of the sphere. Find the surface area of a Moeraki Boulder with a radius of 3 feet. ### 52. Drawing Conclusions **"Hang time"** is the time you are suspended in the air during a jump. Your hang time \( t \) (in seconds) is given by the function \( t = 0.5h \), where \( h \) is the height (in feet) of the jump. Suppose a wallaby and a skier jump with the hang times shown. ### Image Details #### Graph At the top of the image, there is a graph displaying the function \( y = 2 \sqrt{x} - 4 \). The graph is plotted on a standard Cartesian plane with the x-axis representing the independent variable \( x \) and the y-axis representing the dependent variable \( y \). The plot of the function shows an upward curve starting from the point (4,0), reflecting the square root function transformed by a vertical stretch and a vertical downward shift. ### Visuals The image includes a photo of a wallaby in the lower left and a skier in the lower right, indicating their different jump heights and hang times mentioned in problem 52.
Transcribed Image Text:## Algebra 2 with Calculus and Geometry ### 51. Modeling Real Life The **Moeraki Boulders** are stone spheres along the coast of New Zealand. A formula for the radius of a sphere is \( r = \frac{1}{2} \sqrt{\frac{S}{\pi}} \), where \( S \) is the surface area of the sphere. Find the surface area of a Moeraki Boulder with a radius of 3 feet. ### 52. Drawing Conclusions **"Hang time"** is the time you are suspended in the air during a jump. Your hang time \( t \) (in seconds) is given by the function \( t = 0.5h \), where \( h \) is the height (in feet) of the jump. Suppose a wallaby and a skier jump with the hang times shown. ### Image Details #### Graph At the top of the image, there is a graph displaying the function \( y = 2 \sqrt{x} - 4 \). The graph is plotted on a standard Cartesian plane with the x-axis representing the independent variable \( x \) and the y-axis representing the dependent variable \( y \). The plot of the function shows an upward curve starting from the point (4,0), reflecting the square root function transformed by a vertical stretch and a vertical downward shift. ### Visuals The image includes a photo of a wallaby in the lower left and a skier in the lower right, indicating their different jump heights and hang times mentioned in problem 52.
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