Consider the Paraboloid $z = x ^ { 2 } + y ^ { 2 }$

question 48

Multiple Choice

Consider the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ . Which of the following space curves have as their range points lying on this paraboloid?

• A)r (t) = \(\langle t \sin t , t \cos t , t \rangle , t \in \mathbb { R }\)
• B)r (t) = \(\left\langle t ^ { 2 } , t \sin t , t \cos t \right\rangle , t \in \mathbb { R }\)
• C)r (t) = \(\left\langle t \cos t , t \sin t , t ^ { 2 } \right\rangle , t \in \mathbb { R }\)
• D)r (t) = \(( \sqrt { t } \sin t , t , \sqrt { t } \cos t ) , t > 0\)
• E)r (t) = \(( \sqrt { t } \sin t , \sqrt { t } \cos t , t \} , t > 0\)

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Definitions:

Government Tax

Monetary charges imposed by a government on individuals, corporations, and transactions to finance government spending and services.

Labor-Market Policies

Measures and regulations implemented to influence the operation and outcomes of the labor market, including job creation, unemployment insurance, and minimum wage laws.

Coordinates

Numerical values that determine the position of a point or object in a space, typically defined by x and y axes in a two-dimensional space, or x, y, and z in three-dimensional space.

Scientific Method

A method of research with defined steps that include experiments and careful observation to validate or disprove a hypothesis.