Math Exercises Problem Example | Topics and Well Written Essays - 1000 words

Activities - Math Problem Example 1 A firm makes and sells q units of an item at cost =  £(575 † ½ q) which has unit expenses of  £(q2 †25q) and fixed expenses of  £45,000. (a) Write down articulations for: income, benefit and normal expense as far as output(q) of the firm. [1 mark] Income = (575 † ½ q ) q = 575q † ½ q2 Benefit = Revenue †Total Cost = 575q † ½ q2 - [(q2 †25q )q +45,000] = 575q † ½ q2 †q3 + 25q2 - 45,000 = †q3 + 24.5q2 + 575q - 45,000 Normal Cost = Total Cost/q = q2 †25q + 45,000/q (b) Find articulations for: negligible income, peripheral cost, minor benefit and minimal normal expenses regarding yield (q). [2 marks] Peripheral Revenue, Marginal Cost, Marginal Profit and Marginal Average Costs is the subordinate of Revenue, Cost, Profit, Average Costs . Since the subordinate of f(x) = xn is nxn-1, we have: Minor Revenue = 575 †q Minor Cost = 3q2 - 50q Minor Profit = - 3q2 + 49q +575 Minor Average Cost = 2q †25 - 45,000/q2 (since 1/q = q-1) (c) Find the yield levels of the firm that and affirm that the yield levels found do to be sure expand or limit these functions [ 1 mark] (i) Maximise income †¢ This is the diagram of Revenue = 575q † ½ q2 , we can see that it is expanded at q = 575. (ii) Minimise costs To limit costs, set minor expenses to 0 q = 50/3 or approx 17 units This is the chart of Costs = q3 - 25q2 + 45,000. We can see that the limit esteem is around at q =17. (iii) Maximize benefits To boost benefits, set minor benefits to 0 - 3q2 + 49q +575 = 0 Utilizing the quadratic recipe, we have: q = 23.23 , - 7.89 Ignoring the negative worth, we have: q = 23 units. This is the chart of Profit = - q3 + 24.5q2 + 575q - 45,000. We can see that the greatest worth is around at q=23. (iv) Minimize normal expenses To limit normal costs, set peripheral normal expenses to 0: 2q - 25 - 45,000/q2 = 0 (multiply the two sides by q2) 2q3 - 25q2 - 45,000 = 0 With the utilization of experimentation, we get the main conceivable incentive as: q = 33 units. This is the diagram of Average Cost = q2 - 25q + 45,000/q. We can see that the most extreme worth is roughly at q=33. 2. The interest work for an item is given by the accompanying articulation: q = 25 + 200 (p - 2) (a) Calculate the interest at costs 3 and 7 [1/2 imprint ] For p = 3: q = 25 + 200 (3 - 2) q = 25 + 200 q = 225 For p = 7: q = 25 + 200 (7 - 2) q = 25 + 40 q = 65 Answer in (Q,P) structure: (225,3), (65,7) (b) Calculate the ARC versatility of interest regarding cost between the costs given to some extent (an) and remark on whether request is versatile or inelastic between these prices. [1/2 mark] Earc = (Q2-Q1)/[(Q2+Q1)/2] (P2-P1)/[(P2+P1)/2] Earc = (65-225)/[(65+225)/2] (7-3)/[(7+3)/2] Earc = - 160/145 4/5 Earc = - 40 = - 1.38 29 Since a versatile great is the place value flexibility of interest is more prominent than one, we can consider that the interest is versatile between these costs. (c) Find an articulation for POINT versatility of interest with deference to cost regarding price. [ 1 mark] Ept = (q/p) * p/q The subordinate of q = 25 +200/(p-2) is q/p = 0 + - 1 (200) (p-2)- 2 Also, q = 25 +200/(p-2) Henceforth: Ept = [-200p/(p-2)2]/[25 +200/(p-2)] (d) Calculate POINT versatility of interest at costs 3 and 7 and remark on their qualities and on the connection between Circular segment and POINT elasticity [1/2 mark] Ept = [-200p/(p-2)2]/[25 +200/(p-2)] Ept (3) = (- 600/1)/225 = - 2.67 Ept (7) = - 56/65 = - 0.862 The estimation of circular segment flexibility is in the middle of the estimation of point versatility which is normal

History of the Lewis and Clark Expedition

History of the Lewis and Clark Expedition On May 14, 1804, Meriwether Lewis and William Clark left from St. Louis, Missouri with the Corps of Discovery and traveled west with an end goal to investigate and report the new terrains purchased by the Louisiana Purchase. With just a single demise, the gathering arrived at the Pacific Ocean at Portland and afterward returned back to St. Louis on September 23, 1806. The Louisiana Purchase In April 1803, the United States, under President Thomas Jefferson, bought 828,000 square miles (2,144,510 square km) of land from France. This land procurement is regularly known as the Louisiana Purchase. The grounds remembered for the Louisiana Purchase were those west of the Mississippi River yet they were to a great extent unexplored and in this manner totally obscure to both the U.S. what's more, France at that point. Along these lines, not long after the acquisition of the land President Jefferson mentioned that Congress support $2,500 for an exploratory endeavor west. Objectives of the Expedition When Congress endorsed the assets for the campaign, President Jefferson picked Captain Meriwether Lewis as its pioneer. Lewis was picked chiefly in light of the fact that he previously had some information on the west and was an accomplished Army official. Subsequent to making further courses of action for the undertaking, Lewis chose he needed a co-commander and chose another Army official, William Clark. The objectives of this campaign, as sketched out by President Jefferson, were to consider the Native American clans living in the zone just as the plants, creatures, topography, and landscape of the district. The undertaking was likewise to be a conciliatory one and help in moving control over the terrains and the individuals living on them from the French and Spanish to the United States. Moreover, President Jefferson needed the endeavor to locate an immediate conduit toward the West Coast and the Pacific Ocean so westbound extension and business would be simpler to accomplish in the coming years. The Expedition Begins Lewis and Clarks campaign authoritatively started on May 14, 1804, when they and the 33 other men making up the Corps of Discovery left from their camp close St. Louis, Missouri. The main bit of the undertaking followed the course of the Missouri River during which, they went through spots, for example, present-day Kansas City, Missouri, and Omaha, Nebraska. On August 20, 1804, the Corps encountered its solitary loss when Sergeant Charles Floyd passed on of an infected appendix. He was the first U.S. trooper to kick the bucket west of the Mississippi River. Not long after Floyds passing, the Corps arrived at the edge of the Great Plains and saw the territories a wide range of animal categories, the greater part of which were different to them. They likewise met their first Sioux clan, the Yankton Sioux, in a quiet experience. The Corps next gathering with the Sioux, be that as it may, was not as serene. In September 1804, the Corps met the Teton Sioux further west and during that experience, one of the boss requested that the Corps give them a vessel before being permitted to pass. At the point when the Corps cannot, the Tetons undermined savagery and the Corps arranged to battle. Before genuine threats started however, the two sides withdrew. The First Report The Corps endeavor at that point effectively proceeded upriver until winter when they halted in the towns of the Mandan clan in December 1804. While holding up out the winter, Lewis and Clark had the Corps assembled Fort Mandan close to introduce day Washburn, North Dakota, where they remained until April 1805. During this time, Lewis and Clark composed their first report to President Jefferson. In it, they chronicled 108 plant species and 68 mineral sorts. After leaving Fort Mandan, Lewis and Clark sent this report, alongside certain individuals from the campaign and a guide of the U.S. moved by Clark back to St. Louis. Isolating A short time later, the Corps proceeded with the course of the Missouri River until they arrived at a fork in late May 1805 and had to separate the endeavor to locate the genuine Missouri River. In the long run, they discovered it and in June the undertaking met up and crossed the streams headwaters. Presently the Corps showed up at the Continental Divide and had to proceed with their excursion riding a horse at Lemhi Pass on the Montana-Idaho verge on August 26, 1805. Arriving at Portland Once over the partition, the Corps again proceeded with their excursion in kayaks down the Rocky Mountains on the Clearwater River (in northern Idaho), the Snake River, lastly the Columbia River into what is available day Portland, Oregon. The Corps at that point, finally, arrived at the Pacific Ocean in December 1805 and assembled Fort Clatsop on the south side of the Columbia River to hold up out the winter. During their time at the stronghold, the men investigated the region, chased elk and other natural life, met Native American clans, and arranged for their excursion home. Coming back to St. Louis On March 23, 1806, Lewis and Clark and the remainder of the Corps left Fort Clatsop and started their excursion back to St. Louis. When arriving at the Continental Divide in July, the Corps isolated for a short time so Lewis could investigate the Marias River, a tributary of the Missouri River. They at that point rejoined at the intersection of the Yellowstone and Missouri Rivers on August 11 and came back to St. Louis on September 23, 1806. Accomplishments of the Lewis and Clark Expedition In spite of the fact that Lewis and Clark didn't locate an immediate conduit from the Mississippi River to the Pacific Ocean, their endeavor brought an abundance of information about the recently bought arrives in the west. For instance, the endeavor gave broad realities on the Northwests regular assets. Lewis and Clark had the option to record more than 100 creature species and more than 170 plants. They additionally brought back data on the size, minerals, and the geography of the zone. Moreover, the undertaking built up relations with the Native Americans in the district, one of President Jeffersons fundamental objectives. Beside the showdown with the Teton Sioux, these relations were to a great extent quiet and the Corps got broad assistance from the different clans they met in regards to things like food and route. For geological information, the Lewis and Clark undertaking gave far reaching information about the geology of the Pacific Northwest and delivered in excess of 140 maps of the district. To peruse increasingly about Lewis and Clark, visit the National Geographic site committed to their excursion or read their report of the campaign, initially distributed in 1814.

Reviewing SAT Practice Test 4 Essays

Reviewing SAT Practice Test 4 EssaysIn this brief article, I will share a couple of helpful resources that I found useful for reviewing SAT practice test 4 essays. While there are a number of sites that claim to provide study materials to help you ace your practice test, there is very little that will be of assistance in this situation.In my experience, the best practice tests to use in preparation for the SAT test include the 2020 practice test and the College Board SAT practice test. The two that I suggest is to not only review SAT practice test 4 essays, but also utilize the additional components that can be found on these two tests.The College Board SAT practice test has an essay writing section, which many students find valuable. When used, the essay samples tend to help students be able to answer the questions more confidently, making their answers more relevant.The College Board SAT practice test also provides a multiple-choice section. This will help you make your best guess at your highest scoring answer and will provide a good idea of the amount of time you will have to research and come up with that answer.In addition to using these two resources, it may be a good idea to utilize the SAT essay samples provided in the SAT test. The essays are important because it gives you a chance to evaluate your skills as well as how you respond to questions when preparing for the exam.I think that it is very important that you check your worksheet before taking the SAT practice test and review the essay sample and its answers when you have finished. This will give you the best opportunity to understand exactly what the answers are based on the information that you need.Another tip for reviewing SAT practice test is to spend more time analyzing the essay samples before you take the actual exam. Since there are many types of essay samples, as well as different levels of difficulty, it will be good to spend some time reviewing the sample and then examine the essay an d its answers carefully.Again, these are just a couple of tips that you may find useful for reviewing SAT practice test 4 essays. There are a number of resources available that will help you get the most out of your SAT prep, but make sure to check them out.