An Electric Charge Is Spread Over a Rectangular Region $R = \{ ( x , y ) \mid 0 \leq x \leq 3,0 \leq y \leq 2 \}$

question 46

Multiple Choice

An electric charge is spread over a rectangular region $R = \{ ( x , y ) \mid 0 \leq x \leq 3,0 \leq y \leq 2 \}$ . Find the total charge on $R$ if the charge density at a point $( x , y )$ in $R$ (measured in coulombs per square meter) is $\sigma ( x , y ) = 4 x ^ { 2 } + y ^ { 3 }$ .

• A) 84 coulombs
• B) 222 coulombs
• C) 22 coulombs
• D) 56 coulombs

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Definitions:

Normal Distribution

A probability distribution which is even around the mean, indicating that data points closer to the mean occur more frequently than those further away from the mean.

Maintenance

The process of preserving equipment, machines, buildings, or systems through routine checkups, repairs, and replacements to ensure they remain in a safe and functional condition.

Redundant Part

A backup component or section in machinery, systems, or products, designed to take over in case the primary part fails.

Reliability

Reliability describes the ability of a system or component to perform its required functions under stated conditions for a specified period.