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Evaluate SFdS\iint _ { S } \mathbf { F } \cdot d \mathbf { S }

question 118

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Evaluate SFdS\iint _ { S } \mathbf { F } \cdot d \mathbf { S } , that is, find the flux of F across S. F(x,y,z)=4xi+2yj+4k\mathbf { F } ( x , y , z ) = 4 x \mathbf { i } + 2 y \mathbf { j } + 4 \mathbf { k } ; S is the part of the paraboloid z=x2+y2z = x ^ { 2 } + y ^ { 2 } between the planes z = 0 and z = 5; n points upward.

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Definitions:

Independent Watchdog

An organization or body that operates independently to oversee and report on the effectiveness, legality, or morality of specific activities or organizations.

Phenylthiourea (PTC)

A chemical compound that tastes bitter to some people and tasteless to others, used in genetic and sensory studies.

Tasters

Individuals who sample food or drink for quality, taste, and texture, often employed in the food industry to ensure products meet established standards.

Non-tasters

Individuals who have a reduced ability or inability to taste certain compounds, often genetic in origin.

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