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:

Taxable Income

The portion of income that is subject to taxation after allowances, deductions, and exemptions.

Progressive Taxes

A tax system in which the tax rate increases as the taxable amount increases, meaning higher income individuals pay a higher percentage of their income in taxes.

State and Local Taxes

Taxes imposed by state and local government entities that can include income, sales, and property taxes.

Form 1040EZ

Form 1040EZ was a simplified tax form for individuals without dependents and with an income under a certain threshold; it is no longer in use as of 2018, replaced by the Form 1040.