Find the value of a function defined by a right pyramid that has a square base in the xy-plane. −1≤ x ≤ 1, −1≤ y ≤ 1, the vertex at (0, 0, 9) and f(x, y, z) = x². The graph shows a pyramid with the vertex at (0,0,3). Your problem will have a different value for the vertex. Round your answer to four decimal places. N 2- T -1 -0.5 0 X Pyramid 0.5 -0.50 05
Find the value of a function defined by a right pyramid that has a square base in the xy-plane. −1≤ x ≤ 1, −1≤ y ≤ 1, the vertex at (0, 0, 9) and f(x, y, z) = x². The graph shows a pyramid with the vertex at (0,0,3). Your problem will have a different value for the vertex. Round your answer to four decimal places. N 2- T -1 -0.5 0 X Pyramid 0.5 -0.50 05
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Text Transcription:**
Find the value of a function defined by a right pyramid that has a square base in the xy-plane.
\[
-1 \leq x \leq 1, \quad -1 \leq y \leq 1, \quad \text{the vertex at } (0, 0, 9) \quad \text{and} \quad f(x, y, z) = x^2.
\]
The graph shows a pyramid with the vertex at \( (0, 0, 3) \). Your problem will have a different value for the vertex. Round your answer to four decimal places.
---
**Diagram Explanation:**
The diagram illustrates a three-dimensional right pyramid with a square base. The base is located in the xy-plane, ranging from \( -1 \) to \( 1 \) on both the x and y axes. The pyramid is colored in shades of green and yellow to represent its three-dimensional structure. The apex of the pyramid is at the point \((0, 0, 3)\), which is indicated by its position on the z-axis. The graph effectively displays the spatial dimensions and orientation of the pyramid and is designed to give a visual representation of the mathematical problem described.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd20dfe5a-a4c1-4793-9f05-a80ad59a67d4%2F2e6216ec-f96a-4414-a7a1-e50d031865f5%2Fh7ckd6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Text Transcription:**
Find the value of a function defined by a right pyramid that has a square base in the xy-plane.
\[
-1 \leq x \leq 1, \quad -1 \leq y \leq 1, \quad \text{the vertex at } (0, 0, 9) \quad \text{and} \quad f(x, y, z) = x^2.
\]
The graph shows a pyramid with the vertex at \( (0, 0, 3) \). Your problem will have a different value for the vertex. Round your answer to four decimal places.
---
**Diagram Explanation:**
The diagram illustrates a three-dimensional right pyramid with a square base. The base is located in the xy-plane, ranging from \( -1 \) to \( 1 \) on both the x and y axes. The pyramid is colored in shades of green and yellow to represent its three-dimensional structure. The apex of the pyramid is at the point \((0, 0, 3)\), which is indicated by its position on the z-axis. The graph effectively displays the spatial dimensions and orientation of the pyramid and is designed to give a visual representation of the mathematical problem described.
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