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In Problems 27 to 30, rotate the given quadric surface to principal axes. What is the name of the surface? What is the shortest distance from the origin to the surface?
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Mathematical Methods in the Physical Sciences
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- Sketch a graph of each surface. Then, match each surface to its brief description in words.arrow_forward1. (a.) Name the given quadric surface and give its axis. (b.) Sketch the surface. (c.) Name its trace on y = 4. -10022 + 36y? + 22522 = 900arrow_forwardA surface is defined by the following equation: 9x2 + 16y2 + 9z2 = 25. Sketch the intersection between this surface and the xy, xz, and yz planes.arrow_forward
- 1. (a.) Name the given quadric surface and give its axis. (b.) Sketch the surface. (c.) Name its trace on y = -3. - 100x? – 36y + 22522 = 900arrow_forwardConsider the following equation of a quadric surface. y² = z² X 100 25 + a. Find the intercepts with the three coordinate axes, if they exist. b. Find the equations of the xy-, xz-, and yz-traces, if they exist. c. Identify and sketch a graph of the surface. A. The surface intersects the x-axis at x = 0. (Use a comma to separate answers as needed.) B. There are no x-intercepts. Find the y-intercepts, if they exist. Select the correct choice and fill in any answer boxes within your choice. A. The surface intersects the y-axis at y = 0. (Use a comma to separate answers as needed.) B. There are no y-intercepts. Find the z-intercepts, if they exist. Select the correct choice and fill in any answer boxes within your choice. A. The surface intersects the z-axis at z = 0 . (Use a comma to separate answers as needed.) B. There are no z-intercepts. b. Find the equation of the xy-trace, if it exists. Select the correct choice and fill in any answer boxes within your choice. The trace is not a…arrow_forwardConsider the following equation of a quadric surface. 2 2 y² z² 441 441 2 X 441 + = 1 a. Find the intercepts with the three coordinate axes, if they exist. b. Find the equations of the xy-, xz-, and yz-traces, if they exist. c. Sketch a graph of the surface. a. Find the x-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The x-intercept(s) is/are located at x = -21,21. (Use a comma to separate answers as needed.) B. There are no x-intercepts. Find the y-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept(s) is/are located at y = 21, -21. (Use a comma to separate answers as needed.) B. There are no y-intercepts. Find the z-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The z-intercept(s) is/are located at z = (Use a comma to separate…arrow_forward
- What type of quadratic surface with equation x2 + 6y² - 4z² = 2. a. hyperbolic paraboloid b. ellipsoid C. elliptic hyperboloid with one sheet d. elliptic hyperboloid with two sheetsarrow_forwardHelp with the following question. Please answer all parts of the question.arrow_forwardConsider the following equation of a quadric surface. y² 25 100 + = z² a. Find the intercepts with the three coordinate axes, if they exist. b. Find the equations of the xy-, xz-, and yz-traces, if they exist. c. Identify and sketch a graph of the surface. a. Find the x-intercepts, if they exist. Select the correct choice and fill in any answer boxes within your choice. A. The surface intersects the x-axis at x = (Use a comma to separate answers as needed.) B. There are no x-intercepts.arrow_forward
- 4. For each equation given below, write down the name of the surface it represents. The options are: plane, cylinder, sphere, ellipsoid, one-sheeted hyperboloid, two-sheeted hyperboloid, elliptic paraboloid, hyperbolic paraboloid, or elliptic cone. y² 5 7 (a) + z2 34 (b) )x² + 4y² = = 5 = 0 (c) (i) x² + y² − z² = 1 Answer: Answer: Answer:arrow_forwardConsider the following equation of a quadric surface. 2 У 2 X 4 =Z a. Find the intercepts with the three coordinate axes, if they exist. b. Find the equations of the xy-, xz-, and yz-traces, if they exist. c. Sketch a graph of the surface.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
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