Find a Parametric Representation for the Part of the Elliptic $x + y ^ { 2 } + 8 z ^ { 2 } = 9$

question 144

Multiple Choice

Find a parametric representation for the part of the elliptic paraboloid $x + y ^ { 2 } + 8 z ^ { 2 } = 9$ that lies in front of the plane $x = 0$ . Select the correct answer.

• A) \(x = x , y = \sqrt { 9 - x - 8 z ^ { 2 } } , z = z\)
• B) \(x = x , y = \pm \sqrt { 9 - x - 8 z ^ { 2 } } , z = z\)
• C) \(x = 9 - y ^ { 2 } - 8 z ^ { 2 } , \mathrm { y } = y , z = y , 0 \leq y ^ { 2 } + 8 z ^ { 2 } \leq 3\)
• D) \(x = 9 - y ^ { 2 } - 8 z ^ { 2 } , y = y , z = y , y ^ { 2 } + 8 z ^ { 2 } \geq 9\)
• E) \(x = 9 - y ^ { 2 } - 8 z ^ { 2 } , \mathrm { y } = y , z = y , y ^ { 2 } + 8 z ^ { 2 } \leq 9\)

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Definitions:

Marginal Tax Rate

The rate at which an additional dollar of income is taxed, serving as a useful measure of the impact of taxes on incentives to earn more.

Average Tax Rate

The ratio of the total amount of taxes paid to the taxpayer's total taxable income.

Federal Income Tax

A tax levied by the federal government on individuals' and businesses' annual earnings, used to fund public services and government obligations.

Marginal Tax Rate

The rate at which the last dollar of income is taxed, indicating the taxation rate for each additional dollar earned.