Solve for the Specified Variable $$\mathrm { L } = 2 \pi \mathrm { rh } + 2 \pi \mathrm { r } ^ { 2 } \text {; for } \mathrm { r }$$

question 120

Multiple Choice

Solve for the specified variable. Assume that all other variables are nonzero
- $$\mathrm { L } = 2 \pi \mathrm { rh } + 2 \pi \mathrm { r } ^ { 2 } \text {; for } \mathrm { r }$$

• A) \(\mathrm { r } = \frac { \pi \mathrm { h } \pm \sqrt { \pi ^ { 2 } \mathrm {~h} ^ { 2 } + 2 \pi \mathrm { L } } } { 2 \pi }\)
• B) \(r = \frac { - \pi h \pm \sqrt { \pi ^ { 2 } h ^ { 2 } - 2 \pi L } } { 2 \pi }\)
• C) \(r = \frac { - \pi h \pm \sqrt { \pi ^ { 2 } h ^ { 2 } + 2 \pi L } } { \pi }\)
• D) \(r = \frac { - \pi h \pm \sqrt { \pi ^ { 2 } h ^ { 2 } + 2 \pi L } } { 2 \pi }\)

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Definitions:

Risk-free Return

The theoretical return on an investment with no risk of financial loss, typically less than the return on riskier investments.

Defined Contribution Plan

A retirement plan where an employee, employer, or both make contributions on a regular basis, with future benefits fluctuating based on investment earnings.

Risk-free Return

The return on an investment with no risk of financial loss, typically associated with government bonds or other highly trustworthy securities.