Let Let S₁ Be the Sphere of Radius $5$ Centered at the Origin, Oriented Outward and Let S₂ Be

question 83

Short Answer

Let $\vec { F } = \frac { x } { \left( x ^ { 2 } + 5 y ^ { 2 } + 2 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { i } + \frac { y } { \left( x ^ { 2 } + 5 y ^ { 2 } + 2 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { j } + \frac { z } { \left( x ^ { 2 } + 5 y ^ { 2 } + 2 z ^ { 2 } \right) ^ { 3 / 2 } } \vec { k }$ Let S₁ be the sphere of radius $5$ centered at the origin, oriented outward and let S₂ be the sphere of radius $2$ centered at the origin, also oriented outward.
Do you expect the value of $\int _ { S _ { 2 } } \vec { F } \cdot \vec { d A }$ to be larger, smaller or the same as $\int _ { S _ { 1 } } \vec { F } \cdot \vec{ d A }$ ?

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Definitions:

Actual Materials

The real quantity and cost of materials used in the production process, as opposed to estimated or standard materials.

Material Price Variance

The difference between the actual cost of direct materials used in production and the standard cost of those materials.

Standard Purchase Price

The predetermined cost of acquiring goods, set for budgeting and costing purposes.

Actual Purchase Price

Actual Purchase Price refers to the actual amount paid for goods or materials, including additional costs such as delivery charges and taxes.