Solve the Initial Value Problem for Y as a Function $$\sqrt { x ^ { 2 } - 81 } \frac { d y } { d x } = 1 , x > 9 , y ( 18 ) = \ln ( 2 + 9 \sqrt { 3 } )$$

question 80

Multiple Choice

Solve the initial value problem for y as a function of x.
- $$\sqrt { x ^ { 2 } - 81 } \frac { d y } { d x } = 1 , x > 9 , y ( 18 ) = \ln ( 2 + 9 \sqrt { 3 } )$$

• A) \(y = \ln \left( x + \sqrt { x ^ { 2 } - 81 } \right) + \ln ( 2 + 9 \sqrt { 3 } )\)
• B) \(y = \frac { 1 } { 18 } \ln \left( \frac { x + 9 } { x - 9 } \right) + \ln 9\)
• C) \(y = \ln \left( x + \sqrt { x ^ { 2 } - 81 } \right) + \ln ( 2 + 9 \sqrt { 3 } ) - \ln ( 18 + 9 \sqrt { 3 } )\)
• D) \(y = \ln | \sec x + \tan x | + \ln ( 2 + 9 \sqrt { 3 } )\)

Describe the legal remedies available to parties within an agency relationship when contractual obligations are not met.

Examine the principles of liability, including tort and contract liability, within the context of agency relationships.

Discuss the termination of agency relationships and the methods for providing constructive notice of termination.

Outline the differences between agents and independent contractors and the legal implications of each classification.

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Definitions:

Total Revenue

The total amount of income generated by the sale of goods or services by a company.

Average Cost

The total cost of production divided by the quantity of output produced, representing the cost per unit of output.

Marginal Cost

The rise in overall expenses incurred from manufacturing an extra unit of a good or service.

Economic Profit

The separation between total proceeds and cumulative costs, covering both explicit financial outlays and implied expenses.