Solve the Problem $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 64 } = 1$

question 79

Multiple Choice

Solve the problem.
-A homeowner wants to make an elliptical rug from a 30-foot by 10-foot rectangular piece of carpeting.
a. What lengths of the major and minor axes would maximize the area of the new rug?
b. Write an equation of the ellipse with maximum area. Use a coordinate system with the origin at the center
Of the rug and horizontal major axis.

• A) a. Major axis: 32 feet. Minor axis: 16 feet
• b. \(\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 64 } = 1\)
• B) a. Major axis: 15 feet. Minor axis: 5 feet
• b. \(\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 25 } = 1\)
• C) a. Major axis: 30 feet. Minor axis: 10 feet
• b. \(\frac { x ^ { 2 } } { 900 } + \frac { y ^ { 2 } } { 100 } = 1\)
• D) a. Major axis: 30 feet. Minor axis: 10 feet
• b. \(\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 25 } = 1\)

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Definitions:

Homo Habilis

An extinct species of early human that lived in Africa, known for using stone tools.

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Specialized cells within the nervous system that transmit information to other nerve cells, muscle cells, or gland cells, primarily through electrical and chemical signals.

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Newly explored or identified areas within a field of study or geographical locations.

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The organ located in the head of vertebrates that coordinates the body's actions and reactions by transmitting signals to and from different parts of the body.