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<currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor protection-level="none" view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="193" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="45" left="24" top="24.75" width="459.75" height="30" align-x="24" align-y="36" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">Билет №5, задача №5.</f> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">Построим поверхности двух<sp count="2"/>цилиндров, имеющих </f> <f family="Arial Cyr" charset="204" size="12">зависимости: </f> <f family="Arial Cyr" charset="204" size="12">x = 4 - y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2</sup> </f> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/>z</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2</sup> </f> <f family="Arial Cyr" charset="204" size="12"> -4y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2 </sup> </f> <f family="Arial Cyr" charset="204" size="12">= 1.</f> </p> </text> </region> <region region-id="19" left="24" top="84" width="485.25" height="41.25" align-x="24" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12"> <i>Приложение</i> </f> <f family="Arial Cyr" charset="204" size="12">. Построим пересечение двух взаимно перпендикулярных цилиндров, используя ранее приведенные зависимости. Введём константы a<sp count="2"/>и h. Первая</f> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">характеризует направляющую цилиндра, а вторая - его высоту.</f> </p> </text> </region> <region region-id="190" left="30" top="138.75" width="30" height="15.75" align-x="43.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="189" left="84" top="138.75" width="36" height="15.75" align-x="103.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a1</ml:id> <ml:real>3</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="188" left="156" top="138.75" width="30" height="15.75" align-x="169.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">h</ml:id> <ml:real>5</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="187" left="246" top="138.75" width="255.75" height="13.5" align-x="246" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">Здесь -h<r<h,<sp count="2"/>-a<u<a<sp count="4"/> </f> </p> </text> </region> <region region-id="5" left="24" top="165.75" width="486" height="30.75" align-x="24" align-y="180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false">1. Цилиндрическая поверхность с направляющей в виде параболы </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">x = 4 - y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2</sup> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false">, имеющая</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false"> <sp count="2"/>ось </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false"> <i>0z, </i> </inlineAttr> </f> <inlineAttr font-style="normal" underline="false"> <f family="Arial Cyr" charset="204" size="12">так как</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <i> <inlineAttr underline="false"> <sp/> </inlineAttr> </i> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false">координата z в направляющей отсутствует</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <i> <inlineAttr underline="false">.</inlineAttr> </i> </f> </p> </text> </region> <region region-id="60" left="24" top="207" width="450" height="69.75" align-x="24" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Times New Roman Cyr" charset="204"> <i>Примечание</i> </f> <f family="Times New Roman Cyr" charset="204">. В системах компьютерной математики пространственные </f> <f family="Times New Roman Cyr" charset="204">графики строятся в правой системе координат, предполагающей по умолчанию следу</f> <f family="Times New Roman Cyr" charset="204">ющую последовательность осей: абсцисса, ордината и аппликата. Именно эта последовательность есть в опции CreateMesh(X,Y,Z,-h1<r<h2,-a1<u<a2,mesh).</f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Times New Roman Cyr" charset="204">Какие имена присва</f> <f family="Times New Roman Cyr" charset="204">ивать этим осям - не имеет значения. </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Times New Roman Cyr" charset="204">Если поверхность задается матрицей {M</f> <f family="Times New Roman Cyr" charset="204"> <sub>n,m</sub> </f> <f family="Times New Roman Cyr" charset="204">}, то </f> <f family="Times New Roman Cyr" charset="204">первый индекс (номер строки матрицы) - это абсцисса, второй (номер столбца матрицы) </f> <f family="Times New Roman Cyr" charset="204">- ордината, само значение компонента матрицы - будет аппликатой.</f> </p> </text> </region> <region region-id="55" left="30" top="294.75" width="469.5" height="43.5" align-x="30" align-y="306" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">1.1. Абсцисса X (см. рис. 1) задает в<sp count="2"/>декартовой системе координат (ДСК) переменную "y=u" направляющей </f> <f family="Arial Cyr" charset="204" size="12">x = 4 - y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2 </sup> </f> <f family="Arial Cyr" charset="204" size="12">цилиндра</f> <f family="Arial Cyr" charset="204" size="12">, которую будем изменять в интервале -a<y<a:</f> </p> </text> </region> <region region-id="63" left="42" top="354.75" width="57" height="15.75" align-x="83.25" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">X</ml:id> <ml:boundVars> <ml:id xml:space="preserve">r</ml:id> <ml:id xml:space="preserve">u</ml:id> </ml:boundVars> </ml:function> <ml:id xml:space="preserve">u</ml:id> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="65" left="30" top="381.75" width="469.5" height="30" align-x="30" align-y="396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">1.2. Ордината Y задает в ДСК </f> <f family="Arial Cyr" charset="204" size="12">переменную</f> <f family="Arial Cyr" charset="204" size="12"> "z=r" направляющей<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">x = 4 - y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2</sup> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">цилиндра</f> <f family="Arial Cyr" charset="204" size="12">, которую будем изменять в интервале -h<r<h:</f> </p> </text> </region> <region region-id="69" left="42" top="420.75" width="55.5" height="15.75" align-x="83.25" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y</ml:id> <ml:boundVars> <ml:id xml:space="preserve">r</ml:id> <ml:id xml:space="preserve">u</ml:id> </ml:boundVars> </ml:function> <ml:id xml:space="preserve">r</ml:id> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="70" left="30" top="441.75" width="469.5" height="30" align-x="30" align-y="456" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">1.3. Аппликата Z задает в<sp count="2"/>ДСК функцию от "y=u" направляющей </f> <f family="Arial Cyr" charset="204" size="12">x = 4 - y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2 </sup> </f> <f family="Arial Cyr" charset="204" size="12">цилиндра</f> <f family="Arial Cyr" charset="204" size="12">, которая будет условно аналогом оси 0x. </f> </p> </text> </region> <region region-id="82" left="60" top="487.5" width="79.5" height="21" align-x="99.75" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">r</ml:id> <ml:id xml:space="preserve">u</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:real>4</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">u</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="178" left="180" top="492.75" width="62.25" height="15.75" align-x="225.75" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z0</ml:id> <ml:boundVars> <ml:id xml:space="preserve">r</ml:id> <ml:id xml:space="preserve">u</ml:id> </ml:boundVars> </ml:function> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="83" left="30" top="522.75" width="447.75" height="30" align-x="30" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">Запишем эту поверхность цилиндра под именем Nz (напомним, что </f> <f family="Arial Cyr" charset="204" size="12">координата z в описании цилиндра x=f(y)=</f> <f family="Arial Cyr" charset="204" size="12">4 - y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2</sup> </f> <f family="Arial Cyr" charset="204" size="12"> отсутствует</f> <f family="Arial Cyr" charset="204" size="12">).</f> </p> </text> </region> <region region-id="80" left="36" top="576.75" width="54" height="15.75" align-x="67.5" align-y="588" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="7f977fae-9aa1-474d-af68-f2243af64a67" version-id="6d41484a-0eb3-4003-8e8c-2592378e86e6" branch-id="00000000-0000-0000-0000-000000000000" revision-num="23" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Компьют технол\ЗадачиИзЕфимова\КрИнт\Задача 8_85_Графика.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="4793d602-572c-4c0b-b1c2-90af0495a7f2" version-id="60f5608b-97e6-47b4-ac20-6bce563be408" branch-id="00000000-0000-0000-0000-000000000000" revision-num="17" is-modified="true" region-id="0" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Кратные интегралы\Построение поверхности\ВырезкаЧастиПоверхности.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">64932d8165938103c4f5d49116b73dab</contentHash> <ml:define> <ml:id xml:space="preserve">mesh</ml:id> <ml:real>40</ml:real> </ml:define> </ml:provenance> </math> <rendering item-idref="9"> <element-image-map> <box left="1.5" top="0.75" width="52.5" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="81" left="120" top="576.75" width="221.25" height="15.75" align-x="141.75" align-y="588" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Nz</ml:id> <ml:apply> <ml:id xml:space="preserve">CreateMesh</ml:id> <ml:sequence> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">Z</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">mesh</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="193" left="30" top="606.75" width="336" height="13.5" align-x="30" align-y="618" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">Зададим также поверхность N0: плоскость Z0(r,u) (см. рис.1.) </f> </p> </text> </region> <region region-id="181" left="120" top="642.75" width="240.75" height="15.75" align-x="143.25" align-y="654" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N0</ml:id> <ml:apply> <ml:id xml:space="preserve">CreateMesh</ml:id> <ml:sequence> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">Y</ml:id> <ml:id xml:space="preserve">Z0</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">a1</ml:id> </ml:apply> <ml:id xml:space="preserve">a1</ml:id> <ml:id xml:space="preserve">mesh</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="77" left="36" top="738" width="324.75" height="290.25" align-x="197.25" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <component hide-arguments="false" clsid-buddy="62e334b8-fdda-4b2b-9bb4-48def95f2af1" item-idref="12" disable-calc="false"> <inputs> <ml:matrix rows="1" cols="2" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:sequence> <ml:id xml:space="preserve">Nz</ml:id> <ml:id xml:space="preserve">N0</ml:id> </ml:sequence> <ml:placeholder/> </ml:matrix> </inputs> <outputs/> </component> <rendering item-idref="13"/> </region> <region region-id="79" left="30" top="1047.75" width="226.5" height="16.5" align-x="30" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">Рис.1. Цилиндр с направляющей </f> <f family="Arial Cyr" charset="204" size="12">x = 4 - y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2.</sup> </f> </p> </text> </region> <region region-id="96" left="24" top="1082.25" width="496.5" height="36" align-x="24" align-y="1092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Times New Roman Cyr" charset="204" size="11"> <i>Примечание</i> </f> <f family="Times New Roman Cyr" charset="204" size="11">. Порядок следования компонент [X, Y, Z] в CreateMesh можно менять произвольно. </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Times New Roman Cyr" charset="204" size="11">При этом их семантика "абсцисса, ордината и аппликата" будет отождествляться </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Times New Roman Cyr" charset="204" size="11">в соответствии с позицией компоненты в векторе [_, _, _].</f> </p> </text> </region> <region region-id="132" left="12" top="1131.75" width="486" height="57.75" align-x="12" align-y="1146" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false">2. Цилиндрическая поверхность с направляющей в виде гиперболы </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">z</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2</sup> </f> <f family="Arial Cyr" charset="204" size="12"> -4y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2 </sup> </f> <f family="Arial Cyr" charset="204" size="12">= 1</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false">, имеющая</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr underline="false"> <sp count="2"/>ось </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <i> <inlineAttr underline="false">0x, </inlineAttr> </i> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false">так как</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <i> <inlineAttr underline="false"> <sp/> </inlineAttr> </i> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false">координата </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <i> <inlineAttr underline="false">x</inlineAttr> </i> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false"> в направляющей отсутствует</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <i> <inlineAttr underline="false">. </inlineAttr> </i> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false">Отметим, что </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">выбранные </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false"> произвольно здесь имена (Y1, Z1, X1) позиционно привязаны к </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">абсциссе, ординате и аппликате и иного значения не имеют.</f> </p> </text> </region> <region region-id="146" left="24" top="1200.75" width="469.5" height="30" align-x="24" align-y="1212" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">2.1. Пусть абсцисса Y1 (см. рис. 2) задает в<sp count="2"/>ДСК переменную "y=u" направляющей </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">z</f> <f family="Arial Cyr" charset="204" size="12"> = (1+4*y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2</sup> </f> <f family="Arial Cyr" charset="204" size="12">)^(1/2)</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12"> <sup> <sp/> </sup> </f> <f family="Arial Cyr" charset="204" size="12">цилиндра</f> <f family="Arial Cyr" charset="204" size="12">, которую будем изменять в интервале -a<y<a:</f> </p> </text> </region> <region region-id="147" left="48" top="1254.75" width="63" height="15.75" align-x="95.25" align-y="1266" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Y1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">r</ml:id> <ml:id xml:space="preserve">u</ml:id> </ml:boundVars> </ml:function> <ml:id xml:space="preserve">u</ml:id> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="135" left="30" top="1293.75" width="469.5" height="30" align-x="30" align-y="1308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">2.2. Ордината Z1 задает в ДСК функцию</f> <f family="Arial Cyr" charset="204" size="12"> "z=f(y)=</f> <f family="Arial Cyr" charset="204" size="12">(1+4*y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2</sup> </f> <f family="Arial Cyr" charset="204" size="12">)^(1/2)</f> <f family="Arial Cyr" charset="204" size="12">" направляющей<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">цилиндра, которую зададим, как имеющую две ветви гиперболы, так</f> </p> </text> </region> <region region-id="150" left="54" top="1343.25" width="105" height="23.25" align-x="99.75" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">r</ml:id> <ml:id xml:space="preserve">u</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">u</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="153" left="192" top="1343.25" width="111.75" height="23.25" align-x="237.75" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">Z2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">r</ml:id> <ml:id xml:space="preserve">u</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:neg/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">u</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="137" left="30" top="1389.75" width="469.5" height="30" align-x="30" align-y="1404" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">2.3. Аппликата X задает в<sp count="2"/>ДСК </f> <f family="Arial Cyr" charset="204" size="12">переменную</f> <f family="Arial Cyr" charset="204" size="12"> "x=r" направляющей<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">z</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2</sup> </f> <f family="Arial Cyr" charset="204" size="12"> -4y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2 </sup> </f> <f family="Arial Cyr" charset="204" size="12">= 1</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">цилиндра</f> <f family="Arial Cyr" charset="204" size="12">, которую будем изменять в интервале -h<r<h как</f> <f family="Arial Cyr" charset="204" size="12"> условный аналог оси цилиндра - 0x. </f> </p> </text> </region> <region region-id="155" left="132" top="1434.75" width="61.5" height="15.75" align-x="179.25" align-y="1446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">X1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">r</ml:id> <ml:id xml:space="preserve">u</ml:id> </ml:boundVars> </ml:function> <ml:id xml:space="preserve">r</ml:id> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="176" left="24" top="1464.75" width="261" height="13.5" align-x="24" align-y="1476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">Итак, построение этих цилиндров дано на рис.2.</f> </p> </text> </region> <region region-id="39" left="36" top="1494.75" width="240" height="15.75" align-x="58.5" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Nx</ml:id> <ml:apply> <ml:id xml:space="preserve">CreateMesh</ml:id> <ml:sequence> <ml:id xml:space="preserve">Y1</ml:id> <ml:id xml:space="preserve">Z1</ml:id> <ml:id xml:space="preserve">X1</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">mesh</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="41" left="36" top="1524.75" width="245.25" height="15.75" align-x="63.75" align-y="1536" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">nNx</ml:id> <ml:apply> <ml:id xml:space="preserve">CreateMesh</ml:id> <ml:sequence> <ml:id xml:space="preserve">Y1</ml:id> <ml:id xml:space="preserve">Z2</ml:id> <ml:id xml:space="preserve">X1</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">h</ml:id> </ml:apply> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">mesh</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="160" left="48" top="1566" width="181.5" height="210" align-x="138" align-y="1566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <component hide-arguments="false" clsid-buddy="62e334b8-fdda-4b2b-9bb4-48def95f2af1" item-idref="20" disable-calc="false"> <inputs> <ml:matrix rows="1" cols="2" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:sequence> <ml:id xml:space="preserve">Nx</ml:id> <ml:id xml:space="preserve">nNx</ml:id> </ml:sequence> <ml:placeholder/> </ml:matrix> </inputs> <outputs/> </component> <rendering item-idref="21"/> </region> <region region-id="157" left="84" top="1785.75" width="250.5" height="16.5" align-x="84" align-y="1800" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">Рис.2. Цилиндр с направляющей </f> <f family="Arial Cyr" charset="204" size="12">z</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2</sup> </f> <f family="Arial Cyr" charset="204" size="12"> -4y</f> <f family="Arial Cyr" charset="204" size="12"> <sup>2 </sup> </f> <f family="Arial Cyr" charset="204" size="12">= 1.</f> </p> </text> </region> <region region-id="174" left="42" top="1830.75" width="439.5" height="27" align-x="42" align-y="1842" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">Чтобы правильно совместить рис.1 и рис.2<sp count="2"/>необходимо выбрать рисунок</f> <f family="Arial Cyr" charset="204" size="12">, отвечающий содержанию задачи. Очевидно это рис.1 Nz.<sp count="2"/> </f> </p> </text> </region> <region region-id="165" left="60" top="1902" width="181.5" height="210" align-x="150" align-y="1902" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <component hide-arguments="false" clsid-buddy="62e334b8-fdda-4b2b-9bb4-48def95f2af1" item-idref="22" disable-calc="false"> <inputs> <ml:matrix rows="1" cols="4" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:sequence> <ml:id xml:space="preserve">Nx</ml:id> <ml:id xml:space="preserve">nNx</ml:id> <ml:id xml:space="preserve">Nz</ml:id> <ml:id xml:space="preserve">N0</ml:id> </ml:sequence> <ml:placeholder/> <ml:placeholder/> <ml:placeholder/> </ml:matrix> </inputs> <outputs/> </component> <rendering item-idref="23"/> </region> <region region-id="169" left="54" top="2136.75" width="213" height="27" align-x="54" align-y="2148" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">Рис.3. Вырезаемая гиперболическими </f> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">цилиндрами Nx, nNx в Nz поверхность.</f> </p> </text> </region> <region region-id="177" left="48" top="2184.75" width="465.75" height="27" align-x="48" align-y="2196" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12">Площадь вырезаемой поверхности как видно из рис.3 бесконечна, если её не ограничить снизу плоскостью X=0. </f> </p> </text> </region> </regions> <binaryContent> <item item-id="1" 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