2. Let S₁ be the hemisphere with Cartesian equation z = 6 - 36x² - y² and S₂ be theupper nappe of the cone x² + y² - 3z² = 0.a. The curve of intersection of S₁ and S₂ is a circle. Find the radius and the coordinates ofthe center of this circle.b. Find an equation in spherical coordinates for S₁.c. Let G₂ the solid enclosed by S₁ and S₂.a. Set up an iterated triple integral in cylindrical coordinates that yields the volume ofG₂. Do not evaluate the integral.b. Find the volume of G₂ using a triple integral in spherical coordinates.

Answered: Image /qna-images/answer/59876a29-bf5c-452e-a799-61ab56be4ee3.jpg

Answered: 2. Let S₁ be the hemisphere with…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter11: Addition And Subtraction Of Decimal Fractions

Section: Chapter Questions

Problem 18A: Refer to the plate shown in Figure 117 and determine the following distances. All dimensions are in...

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Similar questions

Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
Refer to the plate shown in Figure 117 and determine the following distances. All dimensions are in inches. a. The horizontal center distance between the 0.265" diameter hole and the 0.150" diameter hole. b. The horizontal center distance between the 0.385" diameter hole and the 0.150" diameter hole. c. The distance between edge A and the center of the 0.725" diameter hole. d. The distance between edge B and the center of the 0.385" diameter hole. e. The distance between edge B and the center of the 0.562" diameter hole.
Refer to the prisms of Exercises 1 and 2. Which of these have symmetry with respect to one or more planes?
Find the center C and the radius a for the spheres (x + 2)2 + y2 + (z - 2)2 = 8
Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-Klein model, solve: to When X2+Y2<=1, find the point F(x,y) that is the intersection lxy with the sphere E
If the infinite curve y = e−5x, x ≥ 0, is rotated about the x-axis, find the area of the resulting surface.
Consider two spheres, defined by x^2 + y^2 + z^2 = 1 and (x − 2)^2 + (y − 6)^2 + (z − 3)^2 = 16, respectively. How close are the spheres from touching?
A mirror for a reflecting telescope has the shape of a (finite) paraboloid of diameter 8 inches and depth 1 inch. How far from the center of the mirror will the incoming light collect?
find an equation of the form ρ = f (θ , φ) in spherical coordinates for the following surfaces x2 − y2 = 4
The accompanying figure shows a spherical cap of height h cut from a sphere of radius r. Show that the surface area S of the cap is S = 2πrh.[Hint: Revolve an appropriate portion of the circle x² + y² = r² about the y-axis.]
The surface defined by the equation z= 4x2 + y2 is called an elliptical paraboloid. a. Write the equation with x = 0. What type of curve is represented by this equation? b. Write the equation with y = 0. What type of curve is represented by this equation? c. Write the equation with z = 0. What type of curve is represented by this equation?

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