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:

Ecological Efficiency

A measure of the energy transfer between different trophic levels in an ecosystem, typically representing how much energy from a lower level is available for use at the next level.

Trophic Level

The position that an organism occupies in a food chain, which is a measure of its feeding level.

Decomposers

Organisms, such as bacteria and fungi, that break down dead organisms and waste materials into simpler substances.

Ecological Efficiency

The efficiency with which energy is transferred from one trophic level to the next in an ecosystem, notably low due to the second law of thermodynamics.