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

question 40

Multiple Choice

Find the area of the surface given by $z = f ( x , y ) \text { over the region } R \text {. }$ $f ( x , y ) = 3 - 2 x + 5 y$ $R$ : square with vertices $( 0,0 ) , ( 4,0 ) , ( 4,4 ) , ( 0,4 )$

• A) \(30 \sqrt { \frac { 4 } { 30 } }\)
• B) \(16 \sqrt { 31 }\)
• C) \(16 \sqrt { 61 }\)
• D) \(4 \sqrt { 30 }\)
• E) \(16 \sqrt { 30 }\)

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Definitions:

Purple Loosestrife

An invasive plant species with tall spikes of purple flowers, often found in wetlands, affecting native habitats and biodiversity.

Native Vegetation

Plant species that are indigenous to a specific area, having developed naturally without human intervention.

Wetland Species

Plants and animals specially adapted to live in wetland ecosystems, such as swamps, marshes, and bogs.

Non-targeted Species

Organisms that are unintentionally affected by human activities or control measures aimed at other species.