Find Two Functions Defined Implicitly by the Given Relation $$x ^ { 2 } - y ^ { 2 } = 100$$

question 174

Multiple Choice

Find two functions defined implicitly by the given relation.
- $$x ^ { 2 } - y ^ { 2 } = 100$$

• A) \(y = \sqrt { x ^ { 2 } - 100 }\) or \(y = \sqrt { x ^ { 2 } + 100 }\)
• B) \(y = + ( x - \sqrt { 100 } )\) or \(y = - ( x - \sqrt { 100 } )\)
• C) \(y = + \sqrt { x ^ { 2 } - 100 }\) or \(y = - \sqrt { x ^ { 2 } - 100 }\)
• D) \(y = x - \sqrt { 100 }\) or \(y = x + \sqrt { 100 }\)

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Definitions:

Contribution Margin

The amount by which the sale of a product exceeds its variable costs, indicating how much contributes to covering fixed costs and generating profit.

Initial Cash Outlay

The initial sum of money required to start an investment or project, often including costs such as purchase price, setup fees, and licensing.

Scenario Analysis

A method of examining potential future scenarios by evaluating different possible results.

Sales Quantity

The total number of units of a product sold in a particular period of time.