The horsepower of an engine is a function of it's bore: , with the bore measured in mm. The bore of the engine depends on the temperature: , with the temperature measure in degrees Fahrenheit.
Horsepower as a function of temperature is given by
The rate of change of horsepower with respect to bore is
=
The rate of change of bore with respect to temperature is
=
The rate of change of horsepower with respect to temperature is
=
Your answers to the last three questions should be of the form
=formula with units
The abbreviations for units are "hp" for horsepower, "F" for temperature in Fahrenheit, and "mm" for millimeters.
You can earn partial credit on this problem.