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

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)\(y = \frac { ( x - 32 ) ^ { 3 / 2 } } { 105 } \left( 15 x ^ { 2 } + 384 x + 8192 \right) + C\)

---

Definitions:

Openness

The willingness to consider new ideas, experiences, and the vulnerability to be open to emotions and thoughts.

Conscientiousness

A personality trait characterized by being diligent, careful, thorough, organized, and vigilant in one’s endeavors and responsibilities.

Agreeableness

A personality trait characterized by kindness, cooperation, and a tendency towards harmonious social interactions.

Motivational Factor

Elements or conditions within the environment or within individuals that incite enthusiasm and persistence towards achieving a goal.