Find a Parametric Representation for the Surface Consisting of the Upper

question 59

Multiple Choice

Find a parametric representation for the surface consisting of the upper half of the ellipsoid $x ^ { 2 } + 5 y ^ { 2 } + z ^ { 2 } = 1$ .

• A) \(x = x , y = y , z = \sqrt { 1 + x ^ { 2 } + 5 y ^ { 2 } }\)
• B) \(x = x , y = y , z = \sqrt { 1 + x ^ { 2 } - 5 y ^ { 2 } }\)
• C) \(x = x , y = y , z = \sqrt { 1 - x ^ { 2 } + 5 y ^ { 2 } }\)
• D) \(x = x , y = y , z = \sqrt { 1 - x ^ { 2 } - 5 y ^ { 2 } }\)
• E) \(x = x , y = y , z = \sqrt { x ^ { 2 } + 5 y ^ { 2 } - 1 }\)
• F) \(x = x , y = y , z = \sqrt { x ^ { 2 } - 5 y ^ { 2 } - 1 }\)
• G) \(x = x , y = y , z = \sqrt { - x ^ { 2 } + 5 y ^ { 2 } - 1 }\)

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Definitions:

Cross Elasticity

A measure of the responsiveness of demand for one product in relation to a price change in another, highlighting substitute or complementary relationships between products.

Demand

The desire to own anything, coupled with the power to obtain it.

Price Increase

A rise in the cost of goods and services, which can be caused by factors such as inflation, increased production costs, or higher demand.

Demand Curves

Graphs displaying the relationship between the price of a good and the quantity demanded by consumers, typically downward sloping.