Solve the Problem $\frac { \mathrm { dw } } { \mathrm { dt } }$

question 115

Multiple Choice

Solve the problem.
-Evaluate $\frac { \mathrm { dw } } { \mathrm { dt } }$ at $\mathrm { t } = \frac { 5 } { 2 } \pi$ for the function $\mathrm { w } = \frac { \mathrm { xy } } { \mathrm { z } } ; \mathrm { x } = \sin \mathrm { t } , \mathrm { y } = \cos \mathrm { t } , \mathrm { z } = \mathrm { t } ^ { 2 }$ .

• A) \(- \frac { 4 } { 25 } \left( \frac { 1 } { \pi ^ { 2 } } \right)\)
• B) \(\frac { 1 } { 2 } \left( \frac { 1 } { \pi ^ { 2 } } \right)\)
• C) \(- \frac { 1 } { 2 } \left( \frac { 1 } { \pi ^ { 2 } } \right)\)
• D) \(- \frac { 1 } { 2 } \left( \frac { 1 } { \pi } \right)\)

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Definitions:

Expected Value

The weighted average of all possible values that a random variable can take on, with weights being the probabilities of each outcome.

Expected Value

The forecasted value of a variable, determined by adding together all potential values, each weighted by its likelihood of happening.

Risk Neutral

A situation or attitude where an individual or entity is indifferent to risk when making a decision.

Risk Lovers

Individuals or entities who prefer or are attracted to investments or situations with a higher level of uncertainty and potential for greater returns.