Solve the Initial Value Problem $$\frac { \mathrm { ds } } { \mathrm { dt } } = 16 \mathrm { t } \left( 4 \mathrm { t } ^ { 2 } - 1 \right) ^ { 3 } , \quad \mathrm {~s} ( 1 ) = - 1$$

question 7

Multiple Choice

Solve the initial value problem.
- $$\frac { \mathrm { ds } } { \mathrm { dt } } = 16 \mathrm { t } \left( 4 \mathrm { t } ^ { 2 } - 1 \right) ^ { 3 } , \quad \mathrm {~s} ( 1 ) = - 1$$

• A) \(\mathrm { s } = \left( 4 \mathrm { t } ^ { 2 } - 1 \right) ^ { 4 } - 82\)
• B) \(\mathrm { s } = \frac { 1 } { 2 } \left( 4 \mathrm { t } ^ { 2 } - 1 \right) ^ { 4 } - \frac { 83 } { 2 }\)
• C) \(s = \frac { 1 } { 2 } \left( 4 t ^ { 2 } - 1 \right) ^ { 4 }\)
• D) \(s = \frac { 1 } { 2 } \left( 4 t ^ { 2 } - 1 \right) ^ { 4 } - 1\)

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Definitions:

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A now-discredited theory that suggested the bumps on the skull could predict mental traits and character traits.

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A collection of beliefs or practices mistakenly regarded as being based on scientific method, lacking empirical support and reproducibility.

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An individual who actively engages in analysis, synthesis, and evaluation of information gathered from observation, experience, or communication.

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Practical judgment concerning everyday matters, or a basic ability to perceive, understand, and judge in a manner that is shared by (common to) nearly all people.