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:

Corporate Bond

A debt security issued by a corporation to raise funding, which promises to pay back with interest.

Annuities

Financial products that provide a stream of payments over time to the holder, often used for retirement purposes.

Retirement Years

The period of life after one ceases working full time based on achieving a certain age or financial status.

Annual Return

The percentage change in an investment's value over a one-year period, including any dividends or interest, reflecting the compound annual growth rate.