Find an Equation of the Sphere with Center $( 7 , - 5,7 )$

question 1

Multiple Choice

Find an equation of the sphere with center $( 7 , - 5,7 )$ that touches the $x y$ -plane.

• A) \(( x + 7 ) ^ { 2 } + ( y - 5 ) ^ { 2 } + ( z + 7 ) ^ { 2 } = 49\)
• B) \(( x + 7 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 49\)
• C) \(( x - 7 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 40\)
• D) \(( x - 7 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 49\)
• E) \(( x - 7 ) ^ { 2 } + ( y + 5 ) ^ { 2 } + ( z - 7 ) ^ { 2 } = 7\)

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Definitions:

Completeness

In decision theory, the idea that every set of choices can be ranked in an order of preference, allowing for a consistent choice under different scenarios.

Indifference Curve

A graph representing combinations of goods among which a consumer is indifferent, reflecting their preferences and utility.

Utility

In economics, the satisfaction or benefit derived by consuming a product or service; a measure of preferences over some set of goods and services.

Budget Line

A graphical representation of all possible combinations of two goods that an individual can afford with a given income and prices.