Complete the proof of Theorem 34.1 (that is, prove that R[x] is a commutative ring)

Fundamentals of Physics 10
In Fig. 26-33, a battery of potential difference V ! 12 V is connected to a resistive strip of resistance R ! 6.0 0. When an electron moves through the strip from one end to the other, (a) in which direction in the figure does the electron move, (b) how much work is done on the electron by the electr

Campbell Biology 9
A black guinea pig crossed with an albino guinea pig produces 12 black offspring. When the albino is crossed with a second black one, 7 blacks and 5 albinos are obtained. What is the best explanation for this genetic outcome? Write genotypes for the parents, gametes, and offspring.

Physics: Principles with Applications 7
(II) Determine the net torque on the 2.0-m-long uniform beam shown in Fig. 8-45. All forces are shown. Calculate about (a) point C, the \(\mathrm{CM}\), and (b) point P at one end. Equation Transcription:

Anatomy & Physiology 1
Visit this website (http://openstaxcollege.org/l/ electenergy) to learn about electrical energy and the attraction/repulsion of charges. What happens to the charged electroscope when a conductor is moved between its plastic sheets, and why?

Anatomy & Physiology 1
Voltage-gated Na+ channels open upon reaching what state? a. resting potential b. threshold c. repolarization d. overshoot

Principles of Economics 6
The New York Times reported (Feb. 17, 1996) that subway ridership declined after a fare increase: There were nearly four million fewer riders in December 1995, the first full month after the price of a token increased 25 cents to $1.50, than in the previous December, a 4.3 percent decline. a. Use the

Statics and Mechanics of Materials 1
Compute the moment of the 100-lb force about A, (a) by using the definition of the moment of a force, (b) by resolving the force into horizontal and vertical components, (c) by resolving the force into components along AB and in the direction perpendicular to AB.

Biology: The Dynamic Science 5
Which of the following represents an example of qualitative phenotypic variation? a. the lengths of peoples toes b. the body sizes of pigeons c. human ABO blood types d. the birth weights of humans e. the number of leaves on oak trees