The magnitude of the range R of exhaust temperatures (in degrees Fahrenheit) in an

Chapter 8, Problem 104

(choose chapter or problem)

Thermodynamics   The magnitude of the range R of exhaust temperatures (in degrees Fahrenheit) in an experimental diesel engine is approximated by the model

\(R=\frac{2000(4-3 x)}{(11-7 x)(7-4 x)}\),     \(0 \leq x \leq 1\)

where x is the relative load (in foot-pounds).

(a) Write the partial fraction decomposition of the rational function.

(b) The decomposition in part (a) is the difference of two fractions. The absolute values of the terms give the expected maximum and minimum temperatures of the exhaust gases. Use a graphing utility to graph each term.

Text Transcription:

R=frac{2000(4-3x)}{(11-7x)(7-4x)}

0 <= x <= 1