Find the Area of the Surface Given By $z = f ( x , y ) \text { over the region } R \text {. }$

question 89

Multiple Choice

Find the area of the surface given by $z = f ( x , y ) \text { over the region } R \text {. }$ $\begin{array} { l } f ( x , y ) = x y \\R = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \leq 100 \right\}\end{array}$

• A) \(\frac { 2 } { 3 } ( 101 \sqrt { 101 } - 1 ) \pi\)
• B) \(\frac { 2 } { 3 } ( 1 - 101 \sqrt { 101 } ) \pi\)
• C) \(\frac { 2 } { 3 } ( 101 \sqrt { 101 } - 1 )\)
• D) \(\frac { 3 } { 4 } ( 101 \sqrt { 101 } - 1 ) \pi\)
• E) \(\frac { 2 } { 3 } ( 100 \sqrt { 101 } - 1 ) \pi\)

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Definitions:

Mass Extinction

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Climate Change

Substantial changes in global or regional climate patterns, notably since the late 20th century, largely attributed to increased levels of atmospheric carbon dioxide produced by fossil fuels.

End-Permian Extinction

The largest mass extinction event in Earth's history, occurring around 252 million years ago and resulting in the extinction of a significant proportion of marine and terrestrial species.

UV-B Radiation

A portion of the ultraviolet spectrum with wavelengths from 280 to 315 nanometers, known for its biological effects, including DNA damage and vitamin D synthesis in skin.