题目
EMAT012 Week 9 Practice Quiz
匹配题
A solid 𝐸 is bounded by the parabolic cylinder 𝑧 = 4 − 𝑥 2 and the planes 𝑦 = 2 𝑥 , 𝑧 = 0 , and 𝑦 = 0 . We want to set up the six possible descriptions of the solid 𝐸 . The picture below shows six diagrams and the six descriptions of 𝐸 . Match each diagram on the right with a correct corresponding description on the left. 1: Diagram 1 2: Diagram 2 3: Diagram 3 4: Diagram 4 5: Diagram 5 6: Diagram 6
选项
A.Description 5
B.Description 4
C.Description 1
D.Description 2
E.Description 6
F.Description 3
查看解析
标准答案
Please login to view
思路分析
The task asks us to match each diagram of the solid E with its corresponding description among six possibilities. We are given the six descriptions and the six diagrams, and the provided answer sequence is: Diagram 1 → Description 5, Diagram 2 → Description 4, Diagram 3 → Description 1, Diagram 4 → Description 2, Diagram 5 → Description 6, Diagram 6 → Description 3. I will evaluate each option to show why it fits or does not fit based on the defining equations and bounds for E.
Option analysis for each answer choice:
Option 1 (Description 5): This description defines E by certain inequalities that bound x, y, z with the parabolic surface z = 4 − x^2, and by planes such as y = 2x, z = 0, and y = 0. Diagram 1 must depict a region bounded by the same surfaces: the parabolic cylinder z = 4 − x^2, and the planes y = 2x, z = 0, y = 0, along with an appropriate x-range. If Diagram 1 visually shows a region in space enclosed by these surfaces (parabolic cap in z, a wedge in y determined by y between 0 and 2x, and z between 0 and 4−x^2) th......Login to view full explanation登录即可查看完整答案
我们收录了全球超50000道考试原题与详细解析,现在登录,立即获得答案。
类似问题
Part 1Evaluate the following integral in cylindrical coordinates.ModifyingAbove ModifyingBelow Integral from nothing to nothing With 5 width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With StartRoot 25 minus x squared EndRoot width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With StartRoot x squared plus y squared EndRoot width 0 left parenthesis x squared plus y squared right parenthesis Superscript negative 1 divided by 2 Baseline dz font size decreased by 4 dy font size decreased by 4 dx5∫ 025−x2∫0 x2+y2∫0x2+y2−1/2 dz dy dx Part 1ModifyingAbove ModifyingBelow Integral from nothing to nothing With 5 width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With StartRoot 25 minus x squared EndRoot width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With StartRoot x squared plus y squared EndRoot width 0 left parenthesis x squared plus y squared right parenthesis Superscript negative 1 divided by 2 Baseline dz font size decreased by 4 dy font size decreased by 4 dx5∫ 025−x2∫0 x2+y2∫0x2+y2−1/2 dz dy dxequals=[input]enter your response here (Type an exact answer, using piπ as needed.)
Part 1Evaluate the following integral in cylindrical coordinates.ModifyingAbove ModifyingBelow Integral from nothing to nothing With 2 width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With 3 StartRoot 2 EndRoot divided by 2 width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With StartRoot 9 minus x squared EndRoot width x e Superscript negative x squared minus y squared Baseline dy font size decreased by 4 dx font size decreased by 4 dz2∫ 032/2∫0 9−x2∫xe−x2−y2dy dx dz Part 1ModifyingAbove ModifyingBelow Integral from nothing to nothing With 2 width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With 3 StartRoot 2 EndRoot divided by 2 width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With StartRoot 9 minus x squared EndRoot width x e Superscript negative x squared minus y squared Baseline dy font size decreased by 4 dx font size decreased by 4 dz2∫ 032/2∫0 9−x2∫xe−x2−y2dy dx dzequals=[input]negative \frac StartSet 3−\frac{3 (Type an exact answer, using piπ as needed.)
Part 1Evaluate the following integral in cylindrical coordinates.ModifyingAbove ModifyingBelow Integral from nothing to nothing With 2 width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With 3 StartRoot 2 EndRoot divided by 2 width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With StartRoot 9 minus x squared EndRoot width x e Superscript negative x squared minus y squared Baseline dy font size decreased by 4 dx font size decreased by 4 dz2∫ 032/2∫0 9−x2∫xe−x2−y2dy dx dz Part 1ModifyingAbove ModifyingBelow Integral from nothing to nothing With 2 width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With 3 StartRoot 2 EndRoot divided by 2 width 0 ModifyingAbove ModifyingBelow Integral from nothing to nothing With StartRoot 9 minus x squared EndRoot width x e Superscript negative x squared minus y squared Baseline dy font size decreased by 4 dx font size decreased by 4 dz2∫ 032/2∫0 9−x2∫xe−x2−y2dy dx dzequals=[input]enter your response here (Type an exact answer, using piπ as needed.)
Part 1[table] Use a triple integral to find the volume of the solid bounded by the surfaces zequals=2e Superscript yey and zequals=22 over the rectangle StartSet left parenthesis x,y right parenthesis : 0 less than or equals x less than or equals 1, 0 less than or equals y less than or equals ln 4 EndSet{(x,y): 0≤x≤1, 0≤y≤ln4}. | ln 4ln411xxyyzz [/table] Part 1The volume of the solid is [input]enter your response here [input] ▼ units. cubic units. square units. empty selection (Type an exact answer.)
更多留学生实用工具
希望你的学习变得更简单
加入我们，立即解锁 海量真题 与 独家解析，让复习快人一步！