How to Sketch Any Graph by Eye

1. Plot x = 0 Equations in math are useful but they’re also kind of inefficient – for each x value, you have to do a separate calculation to figure out what y is. Graphs take that equation and turn it into a visual, something you can look at and immediately see what happens at different values of x, how the function changes, and more! However, when you first learn graphs it’s all about memorizing basic equations and what their graphs will look like, starting with the slope-intercept form of linear equations. However, as you move on to trickier equations like quadratics and trigonometry, you’re often asked to memorize forms of equations like these – - where you have to memorize the exact equation setup and what each term means on the graph, whether it’s the vertex, slope, intercepts, scaling, horizontal or vertical shifts, or more! But why memorize all those a’s, c’s, k’s, and h’s if it’s only going to be useful in a few specific cases?! Instead, the next time you need to know what a graph of a function should look like, try these steps to quickly sketch out any graph! To demonstrate, we’re going to use the equation: It looks similar to polynomial equations you may have seen in class, but it’s cubic, so we don’t have any obvious equation forms to use to set up the graph. So, how do we graph that function? 1. Plot x = 0 The first thing we want to do is get some points up on our graph, so we want to pick the ones that will be easy to calculate. For almost any equation, plugging in x = 0 and solving for y is fast and easy to do by eye, and almost always doable without a calculator. For our example equation: So, the first point we’ll put on our graph is (0, -4). a. If you can easily find it, plot y = 0 Next, in some cases, y = 0 is pretty easy to solve for too. If you can solve for y = 0 quickly, it’s another good point to solve for right away. In this case: So, now we have point (-2, 0) to add to our graph! b. Bonus – plot a few easy to calculate points like x = 1 x = -1 Depending on the graph, it might be easy to plug in small integers like 1 or -1. The more points you can add to your graph, the more you can see what shape it will eventually take. However, stick to points that are easy to calculate. The purpose of this method is to find just a few points quickly – if you’re going to calculate every point on the graph, you aren’t saving yourself any time! For this equation, we’ll get: and So we now have four points: (0,-4), (-2,0), (1, -18), and (-1, -2). Let’s plot these points and see how they look! We can start to see the graph take shape, but we’ll need more info before we’re done. 2. Figure out what happens when x is really big (in the positive and negative direction) Whatever line we draw is going to have to end with arrows at both ends, to let us know what happens as we go further along the x-axis both in the positive and negative direction. This is what’s called â€Å"end behavior†. To figure out what it is, we’re going to plug two numbers in to our original equation – a big positive number and a big negative number. Now, we’re not actually going to pick a number and use our calculator to find what happens, we’re just going to see how the parts of the equation will affect the end result. For example, plugging a big positive number in our cubic function will get: Adding 1 to a big positive number will barely change it - then, when we cube it, it will become a really big positive number. However, a really big positive number will become negative when multiplied by -2, and subtracting 2 won’t make much of a difference so the end result will be a really big negative number. If we try the same thing for the other side of the graph, plugging in a big negative number for x, we will get: A big negative number cubed is a really big negative number – but this time when it’s multiplied by -2 it will become a really big positive number. o, for our graph, we found that at large positive x, y is large and negative, and at large negative x, y is large and positive. Let’s add that to our graph with arrows. 3. Optional - look for any â€Å"significant† x-values Some equations have unusual features or special points that you can spot by looking at the equation – pay attention in particular for any points where a big part of the equation could become zero. This could help you find roots, asymptotes, or other places where the shape of the graph changes in an unusual way. For example, with the equation we’ve been looking at, That term is interesting because if x = -1 the whole portion of the equation will become zero. Of course, we already found that point earlier, but this tells us that x = -1 is a â€Å"special† point in the equation – it’s possible that the shape of the graph will shift somehow here. 4. Connect the dots and finish! At this point we’ve done all we can – we have a few points on the graph, we know what it’ll look like at the ends, and we’ve identified any unusual points or features. We might not know exactly what they are, but we’re ready to draw something. Now, we still might not know exactly what the shape of the graph is, but here you can use the basics for each main equation. We know that our line is going to be smooth and as simple as possible while still hitting all our points. If we know generally what kind of equation it is (polynomial, radical, exponential) we have at least some guess what the general shape would be. For our example, we have enough points to sketch out one side of our equation, but the negative side is a bit unclear, so let’s think about what we can say about another type of polynomial, the quadratic equation. For our cubic function, we know that quadratic functions are always symmetric around their vertex, but that doesn’t quite work because we know that in one direction we’ll end up positive, and the other we need to go negative. So, let’s guess something similar – maybe our â€Å"special† point at x = -1 is like a vertex, but at that point the shape of the graph is the same, but moving in the opposite direction. (I’ve put a dashed line down at x = - 1 for reference, but of course that wouldn’t be part of the real final graph.) Here we go! It’s not a perfect graph, but in a few quick steps we at least know in general what this graph is going to look like. In case you’re wondering, here’s what this equation looks like when it’s graphed by a computer. This method works for a massive range of functions – polynomials, radicals, exponentials, logarithms, trig functions, and more! Just be careful once you get to functions with multiple y or terms: in those cases, the graphs will be unusual, complex shapes, so graph lots of (x, y) points before trying to connect all the dots! Are you interested in connecting with a mathematics tutor in New York, Boston, or online? ; Want to read more mathematics blog posts? Read on below! Four Mathematicians You Should Know What is Spectral Geometry? What is a Limit, Anyways? Mathematical Concepts Explained

Marketing Analysis Marketing Strategy - 1546 Words

For instance, deciding on a product line/range requires that the marketing strategist have a definite understanding of all relevant contender items (as well as the corresponding pricing structures) with a specific end goal to establish appropriate juxtaposition and comparison and decide on suitable business choices for diversifying. Competitor analysis is a crucial part of marketing strategy. It is sometimes said that some firms don t lead this sort of investigation deliberately enough. Rather, some ventures work on what is called casual impressions, guesses, and instinct accordingly, which can lead to what marketers refer to as blindspots that can derail an organisation. Stephen Philips from market research agency Tonic says: â€Å"Last†¦show more content†¦However, that information barely touches the surface, and it doesn t provide the necessary insight on competitors that can appropriately inform business strategy. If US B2B firms want to successfully counter the competition, a more in-depth analysis of the marketplace is required†. Whilst this may be true of a minority of incompetent marketing analysts and small time entrepreneurs who cannot afford a decent marketing professional the fact of the matter is that the majority of marketing professionals take competitor analysis extremely seriously and are very diligent in doing so. Philips neglected to give examples of the businesses he supposedly surveyed nor did he indicate how many businesses he surveyed. Considering he is a market research professional (probably looking to obtain more work) one must take his findings with a grain of salt. However he is correct in saying that businesses must do a competitor analysis if they are serious about succeeding. During the past two weeks I have surveyed 20 UK B2B companies (including Shopkit Ltd, Elesa, Industrial Cranes and Parts) and they all confirmed that they do detailed competitor analysis. Some of them have a dedicated marketing department and most of them have hired a marketing agency to do various marketing acti vities including a competitor analysis in the past two years. Shopkit’s managing director said that it is crucial to know the competitor’s strengths. He goes on to say that in terms of strategy he has

Exxon Valdez Oil Spill Essay - 1835 Words

Exxon Valdez Oil Spill ABSTRACT nbsp;nbsp;nbsp;nbsp;nbsp;In March of 1989, the Exxon Valdez oil tanker ran aground on Bligh Reef in Prince William Sound, Alaska. An eighteen foot wide hole was ripped into the hull, and 10.9 million gallons of crude oil spilled into the ocean. In the following weeks, many things transpired. This paper will discuss the cleanup, the damage, and the results of the biggest oil spill in United States history. nbsp;nbsp;nbsp;nbsp;nbsp;On March 24, 1989, in Prince William Sound Alaska, the Exxon Valdez was moving South West after leaving Port Valdez. The ship was carrying over fifty million gallons of crude oil. When the Valdez was only twenty-eight miles from the port, it ran aground on Bligh reef.†¦show more content†¦Fishermen would leave in the morning and return when their boat was filled with oil. The oil that they scooped out was then deposited at special collection sites. The fishermen also used their boats to help with the deployment of containment booms. The booms would be fastened behind the boats and then dragged into place. However, the booms were not always helpful do to choppy seas. Many fishermen also became temporary employees of Exxon, receiving excellent pay on an hourly basis. nbsp;nbsp;nbsp;nbsp;nbsp;The cleanup was a long and tiring process which was plagued by many difficulties. Inexperience was a major problem. Coast Guard Vice Admiral Clyde Robbins explained in disgust that, quot;It was almost as if that spill was the first one that they had ever had.quot; The equipment was not ready and not in perfect shape and the response teams were not equipped to deal with a spill of the magnitude that occurred. Other difficulties arose due to the format that was used by the executive committee in charge of the cleanup spill. They had set themselves up in such a way that every member of the committee had veto power. This was a result of the original conflicts that took place between corporations the state government and the National government. It was nearly impossible to get all of the members of the committee to agree on one particular plan of action. nbsp;nbsp;nbsp;nbsp;nbsp;The natural factors also made the cleanup a difficultShow MoreRelatedThe Exxon Valdez Oil Spill1718 Words   |  7 PagesThe Exxon Valdez A corporation has a moral duty to ensure that their products and operations do not cause harm to society and the environment. There are significant factors that must be taken into consideration to ensure the proper response is put forth if disaster rears its ugly head. Many times, when disaster strikes, companies do not always make the appropriate response, or they do not remediate the problem efficiently enough to maximize their efforts. 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Cloud Based Storage for Future Generation Computer -myassignmenthelp

Question: Discuss about theCloud Based Storage for Future Generation Computer. Answer: Introduction Cloud computing is the systematic paradigm of IT or information technology, which solely enables the extraordinary access to the collection of all types of systematic resources that are configurable in nature (Hashizume et al. 2013). The services that are of higher level are consequently provisioned with extremely less managerial effort on the connectivity of Internet. This particular paradigm, cloud computing always relied on specific resource sharing and thus achieving or obtaining the coherence or scale economy. This can be termed as the similar to the public utility (Rittinghouse and Ransome 2016). The third party clouds are eventually enabled by the organizations for focusing on their business processes and also for reducing the IT infrastructure costs. Cloud based storage can be simply defined as the typical data storage model where bulk amount of digital data is being stored by the users (Garg, Versteeg and Buyya 2013). Various and innumerable servers are spanned by the physic al storage and the hosting company owns as well as manages the physical environment of the cloud. The following report provides a detailed discussion on the cloud based storage. It is an important step in technology and advancement in the cloud computing. This report will depict the various advantages as well as the disadvantages of any particular cloud based storage. The popular and significant examples of the cloud based storages will also be provided here. Discussion Definition of Cloud Based Storage A cloud storage or cloud based storage is the location or warehouse where any type of data is kept irrespective of its size (Dinh et al. 2013). It can also be termed as a specific service where all types of data is properly maintained, controlled, manipulated or even backed up. This type of service is always available to the user or the client so that they have the easy access from anywhere in the world by means of the Internet. The company of the cloud provider makes the data always available for its users by simply keeping all the files on any external server (Yang and Jia 2014). The most significant fact or advantage in this type of scenario is that the users after utilizing the cloud storages access their data with utmost ease as well as convenience. However, many a times this type of service becomes extremely costly and unaffordable (Rittinghouse and Ransome 2016). Moreover, the users or the clients of the cloud storage should be aware of the fact that the backing up of their co nfidential data or information is highly required and recommended as data recovery from the cloud storage is comparatively slower in comparison to the other local backups or local storage. The accessing of the cloud storage is usually done by a co located service of cloud computer or by various applications, which use the APIs like cloud storage gateway, systems of web based content management or eventually by any web service application programming interface or API (Garg, Versteeg and Buyya 2013). Architecture of Cloud Storage The architecture of any particular cloud based storage is very simple yet complicated. The cloud storage is significantly based on the extremely high virtualized infrastructure (Arora, Parashar and Transforming 2013). This cloud storage is more like a broad cloud computing when the accessible interfaces are taken into consideration. Moreover, the other features like scalability, flexibility, instant elasticity, multi tenancy and the metered resources are also considered here (Fernando, Loke and Rahayu 2013). The services of any cloud storage is properly used from the off premises service like Amazon S3 or is deployed on premises services like ViON Capacity Services (Ren et al. 2015). Any typical cloud storage normally refers to the service of hosted object storage; however the other kinds of storages of data are always available as the service such as block storage. The services of the object storage such as Microsoft Azure, Amazon S3, several software of object storage like the Open stack Swift, research projects on distributed storage such as Vision Cloud or OceanStore, systems for object storage like Hitachi Content Platform or EMC Atmos are the most suitable examples of data storage, which could be properly hosted as well as deployed in a cloud storage (Yang and Jia 2014). This cloud storage is eventually made up of various distributed resources, however acts as single resource, either in the architecture of cooperative cloud storage or federated cloud storage. It also comprises of higher fault tolerance with the help of redundancy as well as data distribution (Li et al. 2013). The cloud storage architecture can also be defined as the highly durable with the versioned copies creation and is always consistent in regards to the data replica. Popular Examples of Cloud Based Storages There are various popular examples of cloud based storages available in the market. They are as follows: i) Dropbox: The most important example of the cloud storage in todays world is the Dropbox. It provides its clients with the core ability to share their complete folders and files with all the other users of Dropbox (Stefanov and Shi 2013). The main advantage of this particular activity of Dropbox is that it enables various updates that are properly viewed by each and every collaborator. Collaboration process is increased with this activity (Rittinghouse and Ransome 2016). The users who do not use Dropbox have to install the software and thus they can view the file without any type of complexity. Moreover, they can eve edit the file within the software. The storage capacity of this particular cloud storage is 2 gigabytes and it is completely free of cost (Wang et al. 2013). The strengths of this cloud storage mainly include the easy usability and extremely intuitive interface. The weakness of Dropbox is that the lowest capacity of free storage can be reviewed. ii) Google Drive: This is another most important and significant example of cloud based storage. The collaboration of the Google Drive is extremely simple. The clients of this cloud storage should have their own distinct accounts. All the updates and the edits are to be properly synced to the Google Drive (Li et al. 2013). The documents that the users have the permission for accessing, will solely receive specific notifications whenever the changes are being made. The storage capacity is much higher than Dropbox. Google Drive offers up to 5 Gigabytes of free data storage. The most significant strength of this cloud storage is that it has an in built editor for documents so that no other software is required for editing purposes (Dinh et al. 2013). The main weakness of Google Drive is that the process of sharing is not that easy and supportive as the Dropbox and thus the Google Drive application set up is required. Microsoft Sky Drive: The third most important and significant example of popular cloud based storage is the Microsoft Sky Drive. This particular storage is as popular as the previous two are (Terry et al. 2013). The collaboration of the Microsoft Sky Drive is done in a systematic way. The colleagues can simply access the files of Sky Drive without signing up in any particular account of Sky Drive. Each and every document is solely and simultaneously updated online with all the colleagues (Yang and Jia 2014). This particular cloud based storage of Microsoft Sky Drive is supported on both the Windows as well as iPhone operating systems. It is extremely efficient and the clients can view, share, update or edit their files with the help of a phone or a tablet (Hashizume et al. 2013). It provides the maximum storage capacity of 7 gigabytes, which is much more than Google Drive and Dropbox. The main strength of this cloud storage is that it offers free storage for the options that are bein g reviewed in the documents. The weakness of Microsoft Sky Drive is that it is not as user friendly as Google Drive and Dropbox. Advantages Cloud based storages comprise of various important advantages. Following are the few most significant advantages of any cloud storage. i) Usability: This is the first most significant advantage of cloud storage. The usability of any typical cloud storage is very high and thus this can be used by the clients or the users easily (Yang and Jia 2014). Each and every service of cloud storage has various folders with confidential data or information. The usability enables them to drag as well as drop the files within the local storage and the cloud storage. ii) Bandwidth Allowance: Each and every service of cloud storage has a specific restriction for data storage in their bandwidth (Stanek et al. 2014). This is known as the bandwidth of the cloud storage. It helps the users to maintain budget and does not incur more cost. Cheap: The third most important advantage of the cloud storage is that it is exclusively cheaper when compared to the other local storages (Goyal 2014). As this does not incur much cost, it is easily utilized and afforded by all organizations or companies. Moreover, the cloud storages help to reduce the annual business operating costs to at least three percentage. iv) Disaster Recovery Plan: The fourth important advantage of any particular cloud storage is the presence of disaster recovery plan. It is always recommended to every business that an emergency backup plan should be present in case of any disaster (Hashizume et al. 2013). Cloud storages can act as backup plans and thus can be accessed any time. v) Easy Accessibility: The last advantage of the cloud based storage is that is easily accessible from any part of the world through the connection of Internet. These above mentioned advantages help the users to understand why cloud storage is utilized by various multinational organizations for reducing their managerial effort (Fernando, Loke and Rahayu 2013). Disadvantages In spite of having these several advantages, there are few significant disadvantages in the cloud storages. These disadvantages are given below: i) Dependent on Internet: This is the major disadvantage of any cloud based storages. No operation is possible without the help of Internet connection (Yang and Jia 2013). This particular type of storage is completely dependent on the Internet connection and thus is often termed as the most dependent storage in comparison to others. ii) Data Security: The second most important demerit of the cloud storage is the lack of data security (Dinh et al. 2013). There are always concerns of data security and privacy and has chances of data losses remotely. Restricted Bandwidth Allowance: Although bandwidth allowance is an advantage for few organizations, it can be dangerous for the rest of the companies (Fernando, Loke and Rahayu 2013). The moment any particular client or user reaches the point of bandwidth allowance, automatically huge amount of cost is incurred and this often becomes a major issue for the company. This restricted bandwidth allowance do not have any alarm that the user might know how much data or allowance, he is using (Hashizume et al. 2013). Thus, few organizations avoid cloud storages. These above mentioned disadvantages clearly depict the position of cloud storage in market and to all the users. Conclusion Therefore, from the above report, conclusion can be drawn that cloud computing can be defined as the methodical hypothesis of information technology, which solely allows all the unexpected admittance to the compilation of all types of methodical resources that are configurable in nature. Cloud based storage can be defined as the distinctive data storage model where huge amount of digital data is being kept by the clients. Various servers are spanned by the physical storage and the respective hosting company owns as well as manages the physical environment of the cloud. The above report has provided a brief discussion on the topic of cloud based storage. It is a vital movement in the technology and an advancement in cloud computing. This report has even depicted the various advantages as well as the disadvantages of any particular cloud based storage with proper details. The popular and significant examples of the cloud based storages are also given in the report. References Arora, R., Parashar, A. and Transforming, C.C.I., 2013. Secure user data in cloud computing using encryption algorithms.International journal of engineering research and applications,3(4), pp.1922-1926. Dinh, H.T., Lee, C., Niyato, D. and Wang, P., 2013. A survey of mobile cloud computing: architecture, applications, and approaches.Wireless communications and mobile computing,13(18), pp.1587-1611. Fernando, N., Loke, S.W. and Rahayu, W., 2013. Mobile cloud computing: A survey.Future generation computer systems,29(1), pp.84-106. Garg, S.K., Versteeg, S. and Buyya, R., 2013. A framework for ranking of cloud computing services.Future Generation Computer Systems,29(4), pp.1012-1023. Goyal, S., 2014. Public vs private vs hybrid vs community-cloud computing: A critical review.International Journal of Computer Network and Information Security,6(3), p.20. Hashizume, K., Rosado, D.G., Fernndez-Medina, E. and Fernandez, E.B., 2013. An analysis of security issues for cloud computing.Journal of internet services and applications,4(1), p.5. Li, Z., Wilson, C., Jiang, Z., Liu, Y., Zhao, B.Y., Jin, C., Zhang, Z.L. and Dai, Y., 2013, December. Efficient batched synchronization in dropbox-like cloud storage services. InACM/IFIP/USENIX International Conference on Distributed Systems Platforms and Open Distributed Processing(pp. 307-327). Springer, Berlin, Heidelberg. Ren, Y.J., Shen, J., Wang, J., Han, J. and Lee, S.Y., 2015. Mutual verifiable provable data auditing in public cloud storage.,16(2), pp.317-323. Rittinghouse, J.W. and Ransome, J.F., 2016.Cloud computing: implementation, management, and security. CRC press. Stanek, J., Sorniotti, A., Androulaki, E. and Kencl, L., 2014, March. A secure data deduplication scheme for cloud storage. InInternational Conference on Financial Cryptography and Data Security(pp. 99-118). Springer, Berlin, Heidelberg. Stefanov, E. and Shi, E., 2013, May. Oblivistore: High performance oblivious cloud storage. InSecurity and Privacy (SP), 2013 IEEE Symposium on(pp. 253-267). IEEE. Terry, D.B., Prabhakaran, V., Kotla, R., Balakrishnan, M., Aguilera, M.K. and Abu-Libdeh, H., 2013, November. Consistency-based service level agreements for cloud storage. InProceedings of the Twenty-Fourth ACM Symposium on Operating Systems Principles(pp. 309-324). ACM. Wang, C., Chow, S.S., Wang, Q., Ren, K. and Lou, W., 2013. Privacy-preserving public auditing for secure cloud storage.IEEE transactions on computers,62(2), pp.362-375. Yang, K. and Jia, X., 2013. An efficient and secure dynamic auditing protocol for data storage in cloud computing.IEEE transactions on parallel and distributed systems,24(9), pp.1717-1726. Yang, K. and Jia, X., 2014. DAC-MACS: Effective data access control for multi-authority cloud storage systems. InSecurity for Cloud Storage Systems(pp. 59-83). Springer, New York, NY.