Solve the Problem $s$ And the Height $h$ By the Formula $\mathrm { V } = \frac { 1 } { 3 } \mathrm {~s} ^ { 2 } \mathrm {~h} .$

question 190

Multiple Choice

Solve the problem.
-The volume of a square pyramid is related to the length of a side of the base $s$ and the height $h$ by the formula $\mathrm { V } = \frac { 1 } { 3 } \mathrm {~s} ^ { 2 } \mathrm {~h} .$ How is $\mathrm { dV } / \mathrm { dt }$ related to $\mathrm { ds } / \mathrm { dt }$ if $\mathrm { h }$ is constant?

• A) \(\frac { \mathrm { dV } } { \mathrm { dt } } = \frac { 2 \mathrm {~s} } { 3 } \frac { \mathrm { ds } } { \mathrm { dt } }\)
• B) \(\frac { d V } { d t } = \frac { 2 h s } { 3 } \frac { d s } { d t }\)
• C) \(\frac { d V } { d t } = \frac { s ^ { 2 } } { 3 } \frac { d s } { d t }\)
• D) \(\frac { \mathrm { dV } } { \mathrm { dt } } = \frac { \mathrm { h } } { 3 } \frac { \mathrm { ds } } { \mathrm { dt } }\)

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Detailed tables or charts provided by tax authorities that dictate the tax rate applied to different levels of taxable income or expenditure.

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An area of the production, distribution, and trade of goods and services by different agents in a particular geographic region.

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A principle of taxation based on the belief that taxes should be levied according to an individual’s or entity’s capacity to pay, reflecting their income or wealth.

Progressive Tax Structure

A tax system in which the tax rate increases as the taxable amount increases, typically designed to distribute the tax burden more heavily on those with higher incomes.