Find the Indicated System of Inequalities $x ^ { 2 } + y ^ { 2 } < 49$

question 91

Multiple Choice

Find the indicated system of inequalities.
-Write a system of inequalities that represents the points in the first quadrant less than 7 units from the origin.

• A) \(x ^ { 2 } + y ^ { 2 } < 49\)
• \(\begin{array}{l}
• x>0 \\
• y<0
• \end{array}\)
• B) \(x ^ { 2 } + y ^ { 2 } < 49\)
• \(\begin{array}{l}
• x>0 \\
• y>0
• \end{array}\)
• C) \(x + y < 3\)
• \(\begin{array}{l}
• x>0 \\
• y>0
• \end{array}\)
• D) \(x < 7\)
• \(\begin{array}{l}
• y<7 \\
• x>0 \\
• y>0
• \end{array}\)

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Definitions:

Competitive Pure Exchange Economy

An economic model where agents trade existing goods without the production of new goods, guided purely by their own self-interest to find an equilibrium.

Contract Curve

In economics, a curve that shows the efficient allocations of goods or services that benefit two parties in an exchange, assuming no externalities.

Utility Function

A mathematical representation of how different combinations of goods or services produce levels of happiness or satisfaction for an individual or entity.

Pareto Optimal

A state of allocation of resources in which it is impossible to make any individual better off without making at least one individual worse off, indicating an efficient distribution of goods and resources.