If is even, prove that –1 is even. If a is odd, prove that

An Introduction to Thermal Physics 1
Problem 36P In the course of pumping up a bicycle tire, a liter of air at atmospheric pressure is compressed adiabatically to a pressure of 7 atm. (Air is mostly diatomic nitrogen and oxygen.) (a) What is the final volume of this air after compression? ________________ (b) How much work is done in

Principles of General Chemistry 2
Problem 6P Draw a Lewis structure for (a) PH4+; (b) C2F4; (c) SbH3.

Anatomy & Physiology 1
Blood filtrate is captured in the lumen of the ________. a. glomerulus b. Bowman's capsule c. calyces d. renal papillae

Campbell Biology: Concepts & Connections 7
Of the following functional groups, which is/are polar, tending to make organic compounds hydrophilic? a. carbonyl b. amino c. hydroxyl d. carboxyl e. all of the above 1

Principles of Economics 6
Consider the following cost information for a pizzeria: Quantity Total Cost Variable Cost 0 dozen pizzas $300 $ 0 1 350 50 2 390 90 3 420 120 4 450 150 5 490 190 6 540 240 a. What is the pizzerias fixed cost? b. Construct a table in which you calculate the marginal cost per dozen pizzas using the inf

Urban Economics 8
The 19th century brought many changes in commuting, from walking to omni- buses, electric trolleys (streetcars), and subways. a. For each commuting method, draw a housing-price curve for a monocentric city, labeling each curve with the date on which the method was introduced. b. Over time, the feasib

Brief Applied Calculus
First make a substitution and then use integration by parts to evaluate the integral. \(\int t^{3} e^{-t^{2}} d t\)

Biochemistry 9
RECALL What are the similarities and differences between the reactions catalyzed by pyruvate dehydrogenase and \(\alpha\)-ketoglutarate dehydrogenase?