Select the Graph That Represents the Given Conic Section $r = \frac { 13 } { 5 - 5 \sin \theta }$

question 5

Multiple Choice

Select the graph that represents the given conic section. If the conic is a parabola, specify (using rectangular coordinates) the vertex and directrix. If the conic is an ellipse, specify the center, the eccentricity, and the lengths of the major and minor axes. If the conic is a hyperbola, specify the center, the eccentricity, and the lengths of the transverse and conjugate axes. $r = \frac { 13 } { 5 - 5 \sin \theta }$

• A) Vertex: \(\left( 0 , \frac { 13 } { 10 } \right)\) Directrix: \(y = \frac { 13 } { 5 }\)
• B) Vertex: \(\left( - \frac { 13 } { 10 } , 0 \right)\) Directrix: \(x = - \frac { 13 } { 5 }\)
• C) Center: \(( 0,0 )\) Eccentricity: \(\frac { 5 } { 13 }\) Major axis length: \(\frac { 26 } { 5 }\) Minor axis length: \(\frac { 10 } { 13 }\)
• D) Vertex: \(\left( \frac { 13 } { 10 } , 0 \right)\) Directrix: \(x = \frac { 13 } { 5 }\)
• E) Vertex: \(\left( 0 , - \frac { 13 } { 10 } \right)\) Directrix: \(y = - \frac { 13 } { 5 }\)

Describe features and implications of plans proposed at the Constitutional Convention (Virginia Plan, New Jersey Plan).

Understand the policies and significance of the Northwest Ordinance of 1787.

Recognize the challenges and responses related to American navigation rights and economic policies under the Articles of Confederation.

Comprehend the role and responsibilities conferred by the Constitution on different branches of government and specific positions.

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Definitions:

Marginal Productivity Theory

An economic theory that explains how the value of a factor of production depends on its marginal contribution to the output.

Purely Competitive

A market structure characterized by a large number of buyers and sellers, homogeneous products, and free entry and exit from the market.

Marginal Revenue Product

This is the additional revenue generated by employing one more unit of a factor, such as labor or capital.

Marginal Productivity Theory

An economic theory proposing that input costs, such as wages, are determined by the additional output produced by the last unit of input used.