Let $f ( x , y ) = x ^ { 2 }$

question 8

Multiple Choice

Let $f ( x , y ) = x ^ { 2 }$ , and let $R = \{ ( x , y ) \mid 0 \leq x \leq 1,0 \leq y \leq 1 \}$ . Let R be partitioned into two subrectangles by the line $x = \frac { 1 } { 2 }$ , and let $\left( x _ { i } ^ { * } , y _ { j } ^ { * } \right)$ be the center of Rij. Calculate the double Riemann sum of f.

• A) \(\frac { 3 } { 16 }\)
• B) \(\frac { 1 } { 4 }\)
• C) \(\frac { 5 } { 16 }\)
• D) \(\frac { 3 } { 8 }\)
• E) \(\frac { 7 } { 16 }\)
• F) \(\frac { 1 } { 2 }\)
• G) \(\frac { 9 } { 16 }\)

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Definitions:

Environmental Racism

The practice of disproportionately situating hazardous waste sites, pollution-emitting industries, or landfills near communities of color or economically disadvantaged groups.

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Racial or ethnic groups that have historically faced social, economic, and political disadvantages and discrimination.

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A colloquial name for an area along the Mississippi River between Baton Rouge and New Orleans, known for a high concentration of industrial plants and associated with elevated cancer rates among its population.