Find the Average Value of F(x, Y, Z) Over the Given

question 207

Multiple Choice

Find the average value of F(x, y, z) over the given region.
-F(x, y, z) = xyz over the rectangular solid in the first octant bounded by the coordinate planes and the planes x = 5, y = 6, z =10

• A) 25
• B) \(\frac { 50 } { 3 }\)
• C) \(\frac { 75 } { 4 }\)
• D) \(\frac { 75 } { 2 }\)

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Definitions:

Regressive

Relating to a taxation mechanism where the tax rate decreases as the taxable amount increases, disproportionately affecting lower-income earners.

Largest Source

The most significant origin or provider of something, often used in the context of energy production, emissions, or resources.

Average Tax Rate

The ratio of the total amount of taxes paid to the total tax base (taxable income or spending), showing the fraction of income that is paid in taxes.