Complete the Square to Determine Whether the Equation $x ^ { 2 } + 4 x - 8 y + 36 = 0$

question 15

Essay

Complete the square to determine whether the equation $x ^ { 2 } + 4 x - 8 y + 36 = 0$ represents an ellipse, a parabola, a hyperbola, or a degenerate conic. Then sketch the graph of the equation. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the vertex, focus and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. If the equation has no graph, explain why.

Understand the role of marginal output and marginal physical product in economic analysis.

Understand the concept of Marginal Revenue Product (MRP) and its significance in resource hiring decisions.

Identify the relationship between the demand for resources and the demand for the final product.

Analyze factors influencing the demand for labor and land in various scenarios.

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Definitions:

Oligopolies

Market structures in which a few companies dominate the industry, limiting competition and potentially leading to higher prices for consumers.

Collusion

A secret or illegal cooperation between parties, typically to cheat or deceive others, often seen in contexts like business practices or trade.

Market Share

The percentage of total sales volume in a market captured by a brand, product, or company.

Herfindahl-Hirschman Index

A measure of market concentration used to determine the level of competition within an industry, calculated by squaring the market share of each firm within the industry.