Questions
EMAT012 Week 9 Practice Quiz
Matching
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
Options
A.Description 5
B.Description 4
C.Description 1
D.Description 2
E.Description 6
F.Description 3
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Step-by-Step Analysis
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 explanationLog in for full answers
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