Find the area of the surface x² -6y-2z = 0 that lies above the triangle bounded by the lines x= 1, y=0, and y = 3x.The surface area is(Type an exact answer, using radicals as needed.)

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Answered: Find the area of the surface x²-6y-2z=0…

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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Identify the quadric surface for the equation y² - x² = 16. a parabolic cylinder a hyperbolic paraboloid an elliptic cylinder a hyperboloid of two sheets a hyperbolic cylinder Determine the intercepts of the quadric surface. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in the form of a comma-separated list of point coordinates in the form (*, *, *). Enter DNE if the surface and the axes does not intersect.) intercept(s): (0,0,0) Incorrect Determine the traces of the quadric surface. (Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the surface and the plane are not traced. If a trace of the surface in the plane is a point, give your answer as point coordinates in the form (*, *, *).) the trace in the xy-plane: Incorrect the trace in the xz-plane: Incorrect the trace in the yz-plane: Incorrect
4a
High school students used Pick's theorem to determine the area of leaves, which biologists need to do. The formula is A = + I – 1, where b is the number of boundary points and I is the number of 2 interior points in a figure that has been traced on Geoboard Dot Paper.t (a) Use your knowledge of triangles and other shapes to find the area (in square units) of the figure on the left pictured above. square units (b) Calculate the area (in square units) of the figure on the left pictured above using Pick's theorem. square units (c) Determine the area (in square units) of the leaf on the right pictured above using Pick's theorem. (Round your answer to one decimal place.) square units
Q2.A: Find the surface area of a quarter of the sphere x2 + y2 + z2 = 4.

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Find the area of the surface x²-6y-2z=0 that lies above the triangle bounded by the lines x= 1, y = 0, and y = 3x. The surface area is (Type an exact answer, using radicals as needed.)