Area and Volume

5 ? x ? 0. 5. Find the area of the region enclosed by the graphs of f and g. (Total 6 marks) 2. Let f(x) = Aekx + 3. Part of the graph of f is shown below. The y-intercept is at (0, 13). (a)Show that A =10. (2) (b)Given that f(15) = 3. 49 (correct to 3 significant figures), find the value of k. (3) (c)(i)Using your value of k, find f? (x). (ii)Hence, explain why f is a decreasing function. iii)Write down the equation of the horizontal asymptote of the graph f. (5) Let g(x) = –x2 + 12x – 24. (d)Find the area enclosed by the graphs of f and g. (6) (Total 16 marks) 3. The following diagram shows the graphs of f (x) = ln (3x – 2) + 1 and g (x) = – 4 cos (0. 5x) + 2, for 1 ? x ? 10. (a)Let A be the area of the region enclosed by the curves of f and g. (i)Find an expression for A. (ii)Calculate the value of A. (6) (b)(i)Find f ? (x). (ii)Find g? (x). (4) c)There are two values of x for which the gradient of f is equal to the gradient of g. Find both these values of x. (4) (Total 14 marks) 4. The graph of f(x) = , for –2 ? x ? 2, is shown below. The region enclosed by the curve of f and the x-axis is rotated 360Â ° about the x-axis. Find the volume of the solid formed. (Total 6 marks) 5. The graph of y = between x = 0 and x = a is rotated 360Â ° about the x-axis. The volume of the solid formed is 32?. Find the value of a. (Total 7 marks) Area and Volume 5 ? x ? 0. 5. Find the area of the region enclosed by the graphs of f and g. (Total 6 marks) 2. Let f(x) = Aekx + 3. Part of the graph of f is shown below. The y-intercept is at (0, 13). (a)Show that A =10. (2) (b)Given that f(15) = 3. 49 (correct to 3 significant figures), find the value of k. (3) (c)(i)Using your value of k, find f? (x). (ii)Hence, explain why f is a decreasing function. iii)Write down the equation of the horizontal asymptote of the graph f. (5) Let g(x) = –x2 + 12x – 24. (d)Find the area enclosed by the graphs of f and g. (6) (Total 16 marks) 3. The following diagram shows the graphs of f (x) = ln (3x – 2) + 1 and g (x) = – 4 cos (0. 5x) + 2, for 1 ? x ? 10. (a)Let A be the area of the region enclosed by the curves of f and g. (i)Find an expression for A. (ii)Calculate the value of A. (6) (b)(i)Find f ? (x). (ii)Find g? (x). (4) c)There are two values of x for which the gradient of f is equal to the gradient of g. Find both these values of x. (4) (Total 14 marks) 4. The graph of f(x) = , for –2 ? x ? 2, is shown below. The region enclosed by the curve of f and the x-axis is rotated 360Â ° about the x-axis. Find the volume of the solid formed. (Total 6 marks) 5. The graph of y = between x = 0 and x = a is rotated 360Â ° about the x-axis. The volume of the solid formed is 32?. Find the value of a. (Total 7 marks)

Dr. Browns Medical Office Case Study Example | Topics and Well Written Essays - 1750 words

Dr. Browns Medical Office - Case Study Example The physician's office is an independently run office that also functions as a business organization in itself, and it must compete with other local physician's offices. The organization is named after the physician, Dr. Brown, and is referred to as "Dr. Brown's Medical Office." The medical office, which focuses in dermatology, has provided a good organizational structure to assist adult learners and those working to gain knowledge of the field. Trainees, for instance, are always working under somebody, and they usually participate in several aspects of examinations and do other jobs around the office. The training is a very hands on experience. The office also continues to offer training courses and opportunities to learn one on one with the doctor as necessary, thus encouraging the learners. The business is attempting to improve its prospects by moving its skin care products online and thus reaching a larger target audience, since it had always been recognized as a local business. Therefore, an analysis of this organization and its interactions with its adult learners is necessary to understanding how the business could better focus on use of technology and the Internet to achieve goals. Dr. Brown's office has been in business for twenty-one years. They are a local business venture and provide many services. Since the dermatology services offered at this office are not always covered by health insurance, the company must do what they can to keep prices low and attract customers. A variety of local advertising is used in local newspapers and pamphlets. The advertising focuses on the services offered, and the fact that the services here are usually better priced than services at other local offices. The company has been successful, even regardless of the recent recession. It has been able to retain its customers by offering price slashes and returning customer discounts. Furthermore, it has also ventured into offering its own skin care line, which can be sold nationwide on a website, and thus increase the target audience of the company. Therefore, while the company has been hurt a bit by the recession, it has managed to keep itself progressing. It has always welcomed students and adult learners into its environment to assist them with learning about various skin procedures. Sometimes these adult learners work under internship status, and others are assistants that are hired by the company. Both of these adult learners are usually still attending college and learning about both skin care and the business aspects of this type of industry. The environment of the office is very friendly and very clean. It emulates the feeling of a very well-taken care of office. The office itself is located in an old house, and when renovating the office it was decided to keep some of the more "homey" aspects of the house. The waiting room is setup with couches for comfortability, as it is very inviting to the customers. However, the actual rooms set up for patients to visit the doctors are all setup to meet medical standards. Each has a sink, the necessary medical supplies for the various procedures and check-ups involved, and a place for the patients to lie down. The environment itself has the employees function on a variety of levels. Depending on the procedures that occur that day, the adult learners may or may not be

The film Jimi - All Is By My Side Essay Example | Topics and Well Written Essays - 1250 words

The film Jimi - All Is By My Side - Essay Example The biggest disappointment in the film was that when the audience expected some depiction of creativity and humor on Jimi, they were shown depression and a gloomy tale that indicated Jimi as a speechless mystic who had no spirit. Instead of the director showing Jimi in tour within Europe and performing music, the director only showed violence, overdoses, and mental breakdowns. This is quite an unprofessional film making and would probably make the audience wish the film was over. One would feel like they are watching an interpretation of the events. The article by Ian Inglis, â€Å"Popular Music History on Screen: The Pop/Rock Biopic† According to Ian’s article, the film followed the expectation of the biopic. In the film, one can see how Hendrix grew to stardom as he passed through the hardships. However, biopic films are always very predictable and turn out to be boring. The film producers decided to choose the year before Hendrix was a superstar. A fascinating thing about the film is that it does not only indicate to the viewers the particular period in Hendrix’s life but also teases it out in a popular figure. Hendrix has been a hero of his own and Benjamin manages to convey a character that was quite difficult. It is the conflicting and philosophical elements of Hendrix’s characters that prove to be quite compelling. One can get the notion that if he had not been found playing guitar in New York, Hendrix would have been satisfied playing the guitar anywhere and buying some second-hand clothes.