$\text { Solve } \frac { d y } { d x } = x ^ { 2 } \sqrt { x - 32 }$

question 109

Multiple Choice

$\text { Solve } \frac { d y } { d x } = x ^ { 2 } \sqrt { x - 32 }$

• A) \(y = \frac { 2 ( x - 32 ) ^ { 5 / 2 } } { 105 } \left( 23 x ^ { 2 } + 384 x + 7168 \right) + C\)
• B) \(y = \frac { 2 ( x - 32 ) ^ { 5 / 2 } } { 15 } \left( 23 x ^ { 2 } + 352 x + 7168 \right) + C\)
• C) \(y = \frac { ( x - 32 ) ^ { 3 / 2 } } { 15 } \left( 23 x ^ { 2 } + 352 x + 7168 \right) + C\)
• D)\(y = \frac { 2 ( x - 32 ) ^ { 3 / 2 } } { 105 } \left( 15 x ^ { 2 } + 384 x + 8192 \right) + C\)
• E)\(y = \frac { ( x - 32 ) ^ { 3 / 2 } } { 105 } \left( 15 x ^ { 2 } + 384 x + 8192 \right) + C\)

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Definitions:

Consumption Expenditures

The total amount spent by consumers on goods and services.

Net Capital Outflow

The investment gap where residents of a country engage in foreign asset acquisition versus foreign entities buying up local assets.

Net Exports

The value of a country's total exports minus its total imports, representing the balance of trade between a country and its trading partners.

Saving

The portion of income not spent on consumption, often put aside for future use or investment.