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The Bakhshali Manuscript is an ancient work ofIndian/Hindu mathematics dating from around the fourth century A.D., although some of its materials undoubtedly come from many centuries before. It consists of about 70 leaves or sheets of birch bark containing mathematical problems and their solutions. Many of its problems are so-called equal-ization problems that lead to systems oflinear equations. One such problem on the frag-ment shown is the following:
One merchant has seven asava horses, a second has nine haya horses, and a third has ten camels. They are equally well offin the value of their animals if each gives two animals, one to each ofthe others. Find the price of each animal andthe total value ofthe animals possessed by each merchant.
Let x be the price of an asava horse, let y be the price of a haya horse, let z be the price of a camel, and the let K be the total value of the animals possessed by each merchant. Then the conditions of the problem lead to the following system of equations:
5x + y + z = K
x + 7y + z = K
x + y + 8z = K
- Express Equations (5) as a homogeneous linear system of three equations in four unknowns (x, y, z, and K), and show that the solution set has one arbitrary parameter.
- Find the smallest solution for which all four variables are positive integers.
- Show that the solution given in the example is included among your solutions
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- In a classic study in the are of problem solving, Katona (1940) compared the effectiveness of two methods of instruction. One group of participants was shown the exact, step-by-step procedure for solving a problem and was required to memorize the solution. Participants in a second group were encouraged to study the problem and find the solution of their own. They were given helpful hints and clues, but the exact solution was never explained. The study included the problem in the following figure showing a pattern of five squares made of matchsticks. The problem is to change the pattern into exactly four squares by moving only thee matches. (All matches must be used, non can be removed, and all the squares must be the same size.) After 3 weeks, both groups returned to be tested again. The two groups did equally well on the matchstick problem they had learned earlier. But when they were given new problems (similar to the matchstick problem), the memorization group had much lower scores…arrow_forwardA professor determines a final grade based on attendance, two papers, three major tests, and a final exam. Each of these activities has a total of 100 possible points. However, the activities carry different weights. Attendance is worth 6%, each paper is worth 8%, each test is worth 19%, and the final is worth 21%. (a) What is the average for a student with 84 on attendance, 78 on the first paper, 89 on the second paper, 68 on test 1, 80 on test 2, 95 on test 3, and 81 on the final exam? (Enter your answer to one decimal place.) (b) Compute the average for a student with the above scores on the papers, tests, and final exam, but with a score of only 30 on attendance. (Enter your answer to one decimal place.) (c)A performance evaluation for new sales representatives at Office Automation Incorporated involves several ratings done on a scale of 1 to 10, with 10 the highest rating. The activities rated include new contacts, successful contacts, total contacts, dollar volume of sales, and…arrow_forwarda.) Make a list of the amounts of money one can have that cannot be reduced to a smaller number of coins. (Hint: there are seven possible amounts.) One of the amounts is (d+e). b.) Make an addition table for Glosian money. It should be a seven by seven table, with a row and column for each of the amounts you found in the previous problem. For example, your table shouldshow that (d+e)+d=f c.) One of the seven amounts you found in the previous problem can be considered to be the zero of Glosian money, since adding it to a collection of coins does not change the collection’s value (after trading to get the smallest possible number of coins, of course.) Which amount is the zero forGlosian money? d.) The opposite of an amount is the amount you add to it to get the zero. Find the opposite of each of the seven amounts.arrow_forward
- PROBLEM 03: The Jokia Cell Phone Company manufactures two models of cell phones - the Wombat and the Sloth. Each Wombat phone uses 2.5 ounces of gold leaf and 3 ounces of plastic, whereas each Sloth phone uses 2 ounces of gold leaf and 2 ounces of plastic. Each day, the company has only 370 ounces of gold leaf and 420 ounces of plastic to be used for making cell phones. If the company makes the correct number of each type of phone on a given day to use up all of the available gold leaf and plastic, how many Wombat phones will be made? A) 60 B) 100 C) 50 D) 90 E) 110 N) none of the abovearrow_forwardScientists have found a way to distinguish chronic-fatigue syndrome (CFS) from post-treatment Lyme disease by different proteins in a patient's spinal fluid. In a study of 4334 patients, the results to the right were found. (a) How many had the protein for Lyme only? (b) How many had the normal protein only? (c) How many had none of the proteins? 1654 had the protein for normal patients, CFS, and post-treatment Lyme disease; 1754 had the protein for CFS and Lyme; 820 had the protein for CFS only; 2660 had the protein for CFS; 1759 had the normal protein as well as the one for Lyme; 2625 had the protein for Lyme; 2648 had the normal protein. (a) There were 766 patients who only had the protein for Lyme. (Type a whole number.) (b) There were patients who only had the normal protein. (Type a whole number.)arrow_forward
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
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