Solve the Problem $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = 16 - \mathrm { x } ^ { 2 } - \mathrm { y } ^ { 2 }$

question 171

Multiple Choice

Solve the problem.
-Find an equation for the level curve of the function $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = 16 - \mathrm { x } ^ { 2 } - \mathrm { y } ^ { 2 }$ that passes through the point $( \sqrt { 2 } , \sqrt { 5 } )$ .

• A) \(x ^ { 2 } + y ^ { 2 } = - 7\)
• B) \(x ^ { 2 } - y ^ { 2 } = 7\)
• C) \(x ^ { 2 } + y ^ { 2 } = 23\)
• D) \(x ^ { 2 } + y ^ { 2 } = 7\)

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Definitions:

Trading Possibilities Curves

A graphical representation depicting the range of goods and services that a country can produce and trade given its resources and technology.

Substitutability

The degree to which one product or service can be replaced by another to satisfy the same need or want.

Comparative Advantage

Comparative advantage refers to the ability of an entity to produce a good or service at a lower opportunity cost compared to others.

Production

The process of creating goods or services by combining various resources like labor, materials, and technology.