Solve the Equation $- 6 + \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } \approx 9.950$

question 159

Multiple Choice

Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places.
-ln x + ln (x + 6) = 4

• A) \(- 6 + \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } \approx 9.950\)
• B) \(\frac { - 6 - \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } } { 2 } \approx - 10.975\)
• C) \(\frac { - 6 + \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } } { 2 } \approx 4.975\)
• D) \(\frac { - 6 + 2 \sqrt { 36 + \mathrm { e } ^ { 4 } } } { 2 } \approx 6.518\)

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Definitions:

Independent Variables

Variables in an experiment or statistical model that are manipulated or categorized to determine their effect on dependent variables without being affected by any other variable in the model.

Homoscedasticity

A term in statistics describing a situation where all random variables across a dataset have the same finite variance.

Normality Of Errors

An assumption in many statistical models that the errors in the predictions are normally distributed.

Independence Of Errors

Pertains to a condition in statistical analyses where the errors of a model’s predictions are not correlated with each other.