## Algebra 2 with Calculus and Geometry### 51. Modeling Real LifeThe **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#### GraphAt 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.### VisualsThe 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.

Since the student has posted multiple questions and does not mention any specific question, so we…

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 and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

## 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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