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

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Evaluate SFdS\iint _ { S } \mathbf { F } \cdot d \mathbf { S } , where S is the boundary surface of the solid sphere E:x2+y2+z24E : x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 4 and F=3xi+4yj+5zk\mathbf { F } = 3 x \mathbf { i } + 4 y \mathbf { j } + 5 z \mathbf { k }

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Definitions:

Oxygen

A chemical element (O) essential for aerobic respiration in living organisms.

Lactate

A compound produced during the breakdown of glucose in the absence of oxygen, often associated with muscle fatigue.

ATP Concentration

The quantity of adenosine triphosphate present within a cell, a critical factor in cellular energy storage and supply for various metabolic functions.

Active Cells

Cells that are engaged in metabolic processes, often characterized by growth, repair, or replication.

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