Find the Rectangular Equation for the Surface by Eliminating the Parameters

question 44

Multiple Choice

Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function $\mathbf { r } ( u , v ) = 9 \cos v \cos u \mathbf { i } + 9 \cos v \sin u \mathbf { j } + 6 \sin v \mathbf { k }$ .

• A) \(\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 6 } + \frac { z ^ { 2 } } { 6 } = 1\)
• B) \(\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 36 } + \frac { z ^ { 2 } } { 36 } = 1\)
• C) \(\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 81 } + \frac { z ^ { 2 } } { 81 } = 1\)
• D) \(\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 9 } + \frac { z ^ { 2 } } { 6 } = 1\)
• E)\(\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 81 } + \frac { z ^ { 2 } } { 36 } = 1\)

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Definitions:

Central Limit Theorem

A statistical theory that states that, given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.

Sample Mean

The average value of a set of observations or measurements taken from a sample.

Standard Error

A statistic that measures the variability or spread of sampling distribution means.

Sample Size

The quantity of measurements or repetitions contained within a statistical sample.