Find the Domain and Range and Describe the Level Curves $$f ( x , y ) = \sqrt { 25 - x ^ { 2 } - y ^ { 2 } }$$

question 166

Multiple Choice

Find the domain and range and describe the level curves for the function f(x,y) .
- $$f ( x , y ) = \sqrt { 25 - x ^ { 2 } - y ^ { 2 } }$$

• A) Domain: all points in the \(x y\)-plane satisfying \(x ^ { 2 } + y ^ { 2 } = 25\); range: real numbers \(0 \leq z \leq 5\); level curves: circles with centers at \(( 0,0 )\) and radii \(r , 0 < r \leq 5\)
• B) Domain: all points in the \(x y\)-plane; range: real numbers \(0 \leq z \leq 5\); level curves: circles with centers at ( 0 , 0 ) and radii \(r , 0 < r \leq 5\)
• C) Domain: all points in the \(x y\)-plane; range: all real numbers; level curves: circles with centers at \(( 0,0 )\)
• D) Domain: all points in the \(x y\)-plane satisfying \(x ^ { 2 } + y ^ { 2 } \leq 25\); range: real numbers \(0 \leq z \leq 5\); level curves: circles with centers at \(( 0,0 )\) and radii \(r , 0 < r \leq 5\)

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Definitions:

Statistical Discrimination

A decision-making process that uses statistical or probability information on groups rather than individuals, leading to potential biases.

Long Run

The Long Run is a time period in economics during which all factors of production and costs are variable, allowing for full industry adjustment.

Discriminating Firms

Companies that differentiate in their treatment or pricing of customers or employees, based on specific attributes or behaviors.

Statistical Discrimination

Decision-making based on statistical generalizations rather than individual merit, often resulting in unfair treatment of certain groups.