Solution: In 9–20, determine whether the equation is exact.

An Introduction to Thermal Physics 1
Problem 35P According to the Sackur-Tetrode equation, the entropy of a monatomic ideal gas can become negative when its temperature (and hence its energy) is sufficiently low. Of course this is absurd, so the Sackur-Tetrode equation must be invalid at very low temperatures. Suppose you start with a s

Classical Mechanics 0
In many problems in the calculus of variations, you need to know the length ds of a short segment of a curve on a surface, as in the expression (6.1). Make a table giving the appropriate expressions for ds in the following eight situations: (a) A curve given by y = y(x) in a plane, (b) same but x = x

OpenIntro Statistics 3
The figure on the right shows three unimodal and symmetric curves: the standard normal (z) distribution, the \(t\)-distribution with 5 degrees of freedom, and the \(t\)-distribution with 1 degree of freedom. Determine which is which, and explain your reasoning.

Anatomy & Physiology 1
Langerhans cells are commonly found in the ________. a. stratum spinosum b. stratum corneum c. stratum granulosum d. stratum basale

Stats Modeling the World 4
Margin of error A medical researcher estimates the percentage of children exposed to lead-based paint, adding that he believes his estimate has a margin of error of about 3%. Explain what the margin of error means.

Biology 2e by Openstax
Figure 34.11 Which of the following statements about the digestive system is false? a. Chyme is a mixture of food and digestive juices that is produced in the stomach. b. Food enters the large intestine before the small intestine. c. In the small intestine, chyme mixes with bile, which emulsifies fat

Urban Economics 8
Consider a manufacturing firm that occupies two hectares of land. The firm produces 10 tons of output per day and sells its output at a price of $80 per ton. The firm does not engage in factor substitution as the price of land changes. Intraurban transportation is on trucks, with a unit cost of $12 p

Biochemistry 9
How do d-amino acids differ from l-amino acids? What biological roles are played by peptides that contain d-amino acids?