Solve the Problem by Integration $t$ (In Min) Required to Form $x$

question 190

Multiple Choice

Solve the problem by integration.
-Under specified conditions, the time $t$ (in min) required to form $x$ grams of a substance during a chemical reaction is given by $t = \int \frac { d x } { ( 7 - x ) ( 2 - x ) }$ . Find the equation relating $t$ and $x$ if $x = 0 g$ when $t = 0$ min.

• A) \(t = \frac { 1 } { 5 } \ln \left| \frac { 2 - x } { 7 - x } \right| - \frac { 1 } { 5 } \ln \frac { 2 } { 7 }\)
• B) \(t = \frac { 1 } { 5 } \ln \left| \frac { 7 - x } { 2 - x } \right| + \frac { 1 } { 5 } \ln \frac { 7 } { 2 }\)
• C) \(t = \frac { 1 } { 5 } \ln \left| \frac { 7 - x } { 2 - x } \right| - \frac { 1 } { 5 } \ln \frac { 7 } { 2 }\)
• D) \(t = \frac { 1 } { 5 } \ln \left| \frac { 2 - x } { 7 - x } \right| + \frac { 1 } { 5 } \ln \frac { 2 } { 7 }\)

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Definitions:

Grand Mean

The overall mean calculated from multiple sets of observations or groups.

Total Sum

The aggregate or combined total of all the values in a set of numbers.

F Distribution

A probability distribution that is used in ANOVA tests, describing the ratio of variances between and within samples.

Test Statistic

A value computed from sample data during a hypothesis test used to decide whether to reject the null hypothesis.