Open Library - открытая библиотека учебной информации

Открытая библиотека для школьников и студентов. Лекции, конспекты и учебные материалы по всем научным направлениям.

Категории

Образование Solution
просмотров - 176

Example 1

The upward velocity of a rocket is given at three different times in the following table

Time, t Velocity, v
s m/s
106.8
177.2
279.2

The velocity data is approximated by a polynomial as

The coefficients for the above expression were found in Chapter 5 to be given by

Find the values of a1, a2, a3 using Naïve Guass Elimination. Find the velocity at seconds.

Forward Elimination of Unknowns: Since there are three equations, there will be two steps of forward elimination of unknowns.

First step: Divide Row 1 by 25 and then multiply it by 64

[Row 1] 2.56 gives Row 1 as

Subtract the result from Row 2

Divide Row 1 by 25 and then multiply it by 144

[Row 1] 5.76 gives Row 1 as

Subtract the result from Row 3

Second step: We now divide Row 2 by –4.8 and then multiply by –16.8

[Row 2] 3.5 gives Row 2 as

Subtract the result from Row 3

Back substitution: From the third equation

Substituting the value of a3 in the second equation,

Substituting the value of in the first equation,

Hence the solution vectoris

The polynomial that passes through the three data points is then

Since we want to find the velocity at seconds, we could simply substitute each value of in and find the corresponding velocity. For example, at

However we could also find all the needed values of velocity at t = 6, 7.5, 9 and 11 seconds using matrixmultiplication.

So if we want to find it is given by

Example 2

Use Naïve GaussEliminationto solve

Use six significant digits with chopping in your calculations.


Читайте также


  • - The environmental problems and their solutions

    A) Read the text and fill in the table below. Controlling pollution depends on the efforts of the government, scientists, environmental organizations, and individuals. The government’s strategy is to control pollution. For this purpose the government should enforce lawswhich state that all plants and factories must make use of the up-to-date purificatoryequipment, filters, etc. Factories and plants violating environmental protection laws should be imposed heavy fines on. Such fines might... [читать подробенее]


  • - Solutions

    Written_by(X,Y). Clauses Long_novel (title) Written_by(author, title) Book(title, pages) Predicates Domains title, author = symbol pages= unsignedwritten_by(fleming, "DR NO"). written_by(melville, "MOBY DICK"). book("MOBY DICK", 250). book("DR NO", 310). long_novel (Title) :- written_by(_, Title), book(Title, Length),Length > 300. Намагаючись виконати цільове... [читать подробенее]


  • - OBSTACLES AND SOLUTIONS

    RADIATION, LONELINESS HAUNT CHORNOBYL'S NEIGHBOURS The sunlight reflects dully off a sign along the road «ATTENTION: Forbidden Area». It is a wasteland disguised as rustic paradise. This is a place where an invisible poison of radiation released during the 1986 ChomobyP meltdown has seeped into the land and people's psyche. Yet some know no other home. «We were born here and we will die here,» says an elderly peasant woman. «There can be not other way. It is our fate». It is a... [читать подробенее]


  • - Solution - раствор

    Crater - кратер Influenza - грипп To relocate -переселиться To credit - приписывать Vocabulary of the text Dmitriy Ivanovich Mendeleev Exercise 18. Define what parts of speech the italicized words belong to. Translate the sentences into Russian. Use the dictionary if necessary. 1) Priestley's work was published in 1774. 2) The students of our group work hard at their English.3) He experiments on this substance to make... [читать подробенее]


  • - Протокол RARP (Reverse Adress Resolution Protocol)

    Протокол ARP (Adress Resolution Protocol) В локальных сетях, построенных, например, по топологии Ethernet и имеющих подключение к Internet-шлюзу любой сетевой интерфейс имеет физический Ethernet-адрес, действующий в рамках локальной сети, а компьютер – IP-адрес, действующий в... [читать подробенее]


  • - Dissolution of the Monasteries

    In 1534, Cromwell initiated a Visitation of the Monasteries ostensibly to examine their character, in fact, to value their assets with a view to expropriation. The Crown was undergoing financial difficulties, and the wealth of the church, in contrast to its political weakness, made appropriation of church property both tempting and feasible. Suppression of monasteries in order to raise funds was not unknown previously. Cromwell had done the same thing on the instructions of Cardinal Wolsey to... [читать подробенее]


  • - Preparing the composition for full-resolution output

    Exporting to SWF You can also use After Effects to export compositions as SWF files for playback within a web browser. However, certain types of artwork are more suitable than others for export to SWF. Rasterized images and some effects can’t be represented by vectors, and therefore are not efficiently saved to SWF format. You can export them, but the files will be larger in size. Also, it’s helpful when exporting items to SWF to place all your layers within a single composition... [читать подробенее]


  • - Creating a render-settings template for full resolution

    Creating templates for the rendering process In previous lessons, you selected individual render and output-module settings on those occasions when you output your compositions. In this lesson, you’ll create templates for both render settings and output-module settings. These templates are presets that you can use to streamline the setup process when you render items for the same type of delivery format. After you define these templates, they appear in the Render Queue panel on the... [читать подробенее]


  • - Creating a low-resolution output-module template

    Next, you’ll create a second output-module template with settings appropriate for producing a low-resolution test version of the movie. In this case, the settings that you’ll select are also appropriate for a web version of the movie. 1Choose Edit > Templates > Output Module to open the Output Module Templates dialog box. 2In the Settings area, click New to create a new template. 3In the Output Module Settings dialog box, for Format, choose QuickTime. 4For Post-Render Action,... [читать подробенее]


  • - ARP (address resolution protocol) протокол

    ARP, RARP протоколы Зарезервированные IP адреса Маска 255.255.255.0 IP 192.168.234.100 IP and Маска = номер сети IP and (not Маска) = номер узла в сети IP адрес Описание IP-адрес с нулевым номером хоста используется для адресации ко всей сети. 127.0.0.1 IP адрес своего же... [читать подробенее]