problems 84,85,86,87
Applications rises 83-87 refer to the following: The magnitude of an earthquake is measured on the Richter Scale, us the formula R(D) = 108 ( 7 ) Where I represents the actual intensity of the earthquake, and I, is a baseline intensity used for comparison 03. Richter Scale If the intensity of an earthquake is 10000 times the baseline intensity I, what is it magnitude on the Richter scale? 84. Richter Scale If the intensity of an earthquake is a million times the baseline intensity I, what is it magnitude on the Richter scale? 85. Great Earthquakes The great San Francisco earthquake of 1906, the most powerful earthquake in Northern California's recorded history, is estimated to have registered 7.8 on the Richter scale Express its intensity in terms of I. (Source: U.S. Geological Survey) 86. Great Earthquakes In 1984, another significant earthquake in San Francisco registered 6.1 on the Richter scale. Express its intensity in terms of I . 87. Earthquake Intensity What is the ratio of the intensity of a quake that measures 7.1 on the Richter scale to the intensity of one that measures 4.2? Exercises 88 and 89 refer to the following: The PH of a chemical solution is given by PH = -log[H+ ] where [H ] is the concentration of hydrogen ions in the solution, in units of moles per liter. (One mole is 6.02 X 1023 molecules.) 88. Chemistry Find the pH of a solution for which [H*] = 0.001 moles per liter. 89. Chemistry Find the PH of a solution for which [H*] = 10-4 moles per liter. 90. Astronomy The brightness of a star is designated on a numerical scale called magnitude, which is defined by the formula M (1) = - 1082.5 I where I is the energy intensity of the star and I, is the baseline intensity used for comparison. A decrease of one unit in magnitude represents an increase in energy intensity by a factor of 2.5. (Source: National Aeronautics and Space Agency) a. If the star Spica has magnitude 1, find its intensity in terms of I. b. The star Sirius, the brightest star other than the sun, has magnitude - 1.46. Find its intensity in terms of I . What is the ratio of the intensity of Sirius to that of Spica? 91. Computer Science Computer programs perform many kinds of sorting. It is preferable to use the least amount of computer time to do the sorting, where the measure of computer time is the number of operations that the computer needs to perform. We discuss two methods of sorting: the bubble sort and the heap sort. It is known that the bubble sort algorithm requires approximately 12 operations to sort a list of n items, while the heap sort algorithm requires approximately nlog, n operations to sort n items. a. To sort 100 objects, how many operations are required by the bubble sort? by the heap sort? sthingorqua b. Make a table of the number of operations required for the bubble sort to sort a list of n items, with n ranging from 5 to 20 in steps of 5. If the number of items sorted is doubled from 10 to 20, what is the corresponding increase in the number of operations? c. Rework part (b) for the heap sort. d. Which algorithm, the bubble sort or the heap sort, is more efficient? Why? e. In the same window, graph the functions that give the number of operations for the bubble sort and the heap sort. Let n range from 1 to 20. Which function is growing faster and why? Note that you will have to choose the vertical scale carefully so that the n log n function does not get "squashed."
