The Pentagon Is Planning to Build a New Satellite That $V = \frac { 4 } { 3 } \pi r ^ { 3 }$

question 65

Multiple Choice

The Pentagon is planning to build a new satellite that will be spherical. As is typical in these cases, the specifications keep changing, so that the size of the satellite keeps growing. In fact, the radius of the planned satellite is growing 0.9 foot/week. Its cost will be $1,400 per cubic foot. At the point when the plans call for a satellite 8 feet in radius, how fast is the cost growing (The volume of a solid sphere of radius r is $V = \frac { 4 } { 3 } \pi r ^ { 3 }$ .)

• A) \(\frac { \mathrm { d } P } { \mathrm {~d} t } = \frac { \$ 3,584,000 \pi } { \text { week } }\)
• B) \(\frac { \mathrm { d } P } { \mathrm {~d} t } = \frac { \$ 40,320 \pi } { \text { week } }\)
• C) \(\frac { \mathrm { d } P } { \mathrm {~d} t } = \frac { \$ 230 \pi } { \text { week } }\)
• D) \(\frac { \mathrm { d } P } { \mathrm {~d} t } = \frac { \$ 161,280 \pi } { \text { week } }\)
• E) \(\frac { \mathrm { d } P } { \mathrm {~d} t } = \frac { \$ 322,560 \pi } { \text { week } }\)

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Definitions:

Operant Conditioning

A learning process in behavioral psychology where the strength of a behavior is modified by reinforcement or punishment.

Deterministic View

The belief that all events, including human actions, are ultimately determined by causes external to the will, implying that there is no free will.

Conscious Free Will

The ability of individuals to make choices and decisions based on their own conscious reasoning and volition.

Physiological Measurement

The quantitative assessment of biological parameters in humans or animals, which can include heart rate, blood pressure, and hormone levels.