Some of the steps for completing the square to solve
x2 + 5x = 2 are shown.
x2 + 5x = 2
x2 + 5x + (startfraction 5 over 2 endfraction) squared = 2 + (startfraction 5 over 2 endfraction) squared
(x + startfraction 5 over 2 endfraction) squared = startfraction 33 over 4 endfraction
which are solutions of x2 + 5x = 2? check all that

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.

Because air contracts as it cools, the air pressure inside a freezer is typically lower than on the outside. why do ice cubes inside a freezer tend to shrink over time? a. the ice dissolves oxygen from the air, forming a denser crystalline matrix. b. the ice reacts chemically with carbon dioxide in the air, forming gaseous carbon compounds. c. the ice melts, and then the liquid freezes as ice crystals on the bottom of the freezer. d. the ice sublimes, and then the water vapor deposits as ice crystals on the sides of the freezer.

The magnitude of the amount of energy released by burning a fuel source, measured in energy per unit mass, is called its fuel value. note that the fuel value is the negative of the isobaric specific heat of combustion for the fuel. if all the energy obtained from burning 1.23 pounds of butane with a fuel value of 10.85 kcal/g is used to heat 128.0 kg of water at an initial temperature of 18.3 °c, what is the final temperature? note that 1 lb = 453.6 g.