Find the spherical equation for the hyperboloid of two sheets x² – y² – 2² = 1.
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Q: The part of the hyperboloid 4x 2 - 4y2 - z2 =4 that lies in front of the yz-plane
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Q: Which of them are tr 1) Ellipsoid de + 16: Hyperbakid II) =D4- Sy-9 Perbled IV) Sphere
A: The equation of ellipsoid is of the form x2a2+y2b2+z2c2=1 So, (I) is true.
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Q: Question 9 Which surface has the following equation? a2-2y = 32 O Cylinder O Plane O Paraboloid O…
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Q: Identify the type of surface represented by the given equation. 를 - 2.2 2 8. O Parabolic cylinder…
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Q: 2.a. Write the equation of the surface r? + y? = 4y in cylindrical coordinates. b. Classify the…
A: To convert to the cylindrical coordinates, we need to make the following substitutions: x=rcos(θ);…
Q: The surface z² = 1 is a hyperboloid of 36 25 one sheet. Select one: True False
A: The hyperboloid of one sheet given by the equation x2A2 + y2B2 - z2C2 = 1
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A: If a hyperboloid is defined as f(x,y,z)=0, then the tangent plane at the point (a, b, c) is:…
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Q: Find the center C and the radius a for the spheres x2 + y2 + z2 + 4x - 4z = 0
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Q: In three dimensions, the cylinder x? + z2 – 10x – 6z – 2 = 0 has radius k i +tj+ and the axis line…
A: Radius =6 r(t)= (5+6cos(thetha))i+tj+(3+6sin(thetha)k
Q: find an equation of the form r = f (θ , z) in cylindrical coordinates for the following surfaces.…
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Q: (b) Find a parameterization, in spherical coordiantes, for the ellipsoid 4x2 + 9y2 + 2²/4 = 1 that…
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Q: find an equation of the form ρ = f (θ , φ) in spherical coordinates for the following surfaces z =…
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Q: Given hyperbola x2 − y2 = 1 9 16 how do you determine the focal length?
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Q: Find the center C and the radius a for the spheres x2 + y2 + z2 - 4x + 6y - 10z = 11
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Q: - Find the area of the ellipse which is parametrically expressed as =a cos o and y=b sin ø, and…
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Q: (b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at the point (1,…
A: We have to find the equation of the tangent plane to the hyperboloid x² + 3y² − 3z² = 1 at the point…
Q: The equation z? = 10 – x² – y? defines a/an %3D a) ellipsoid c) paraboloid b) cone d) hyperboloid
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Q: Find the equation of spheres passing through the circle x+y+z'-6x-2z+5 =0, y = 0 and touching the…
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Q: Find the point on the ellipsoid x2 + y2/4 + z2/9 = 1 for which x + y + z is largest.
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Q: What is the highest point on the ellipse that is the intersection of the plane z+y+ 2z = 2 and the…
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Q: find an equation of the form r = f (θ , z) in cylindrical coordinates for the following surfaces.…
A: Given: The surface, x2+y2+z2=4.
Q: Find the center C and the radius a for the spheres (x + 2)2 + y2 + (z - 2)2 = 8
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Q: .2 The surface z? = 1 is a 25 - - 36 hyperboloid of one sheet. Select one: OTrue OFalse
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Q: Find the center C and the radius a for the spheres 3x2 + 3y2 + 3z2 + 2y - 2z = 9
A: Given: The equation of sphere as 3x2+3y2+3z2+2y-2z=9, To find: The center C and radius a for the…
Q: Find the center C and the radius a for the spheres x2 + y2 + z2 - 6y + 8z = 0
A: To Determine: Find the center C and the radius a for the spheres Given: we have an equation…
Q: Find the equation of the surface of revolution generated by rotating the parabola y = z^2 around the…
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Q: Find the center C and the radius a for the spheres (x - 1)2 + (y - 2)2 + (z + 1)2 = 103 + 2x + 4y -…
A: Standard equation of sphere is given as x-x12+y-y12+z-z12=r2, where x1,y1,z1 is center of sphere and…
Q: Which of them are true? I) 1 Ellipsoid 4 II) y? = 4x² + 16z² Hyperboloid III) x = 4 – 5y? – 9z?…
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Q: Prove that the surface of the given equation is an ellipsoid. Hence, determine its center. 9x +4y…
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Q: Try to sketch by hand the curve of intersection of the parabolic cylinder y = x2 and the top half of…
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Q: Eliminate the parameter 0 and obtain the standard form of the rectangular equation. hyperbola: x = h…
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Q: Find the cylindrical equation for the ellipsoid 4x2 + 4y² + 2² = 1.
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Q: I am having trouble solving this.
A: To find the area of the overlap between the interior of the ellipses given below.
Q: . Find the cylindrical equation for the ellipsoid 4r² + 4y² + z² = 1.
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Q: The ellipse y? q? + = 1 x2 %3D a2 62 is rotated about the x-axis to form an ellipsoid. Find the…
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Q: The solid that is common to the interior below the hemisphere z = /80 – x² – y2 and above - the…
A: Set up a triple integral.
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- Find an equation in rectangular coordinates for the surface represented by the cylindrical equation r = 2 cos , and sketch its graph.find an equation of the form r = f (θ , z) in cylindrical coordinates for the following surfaces. x2 + y2 = 4Find an equation in rectangular coordinates for the surface represented by the cylindrical equation r2 cos 2 + z2 + 1 = 0
- Find an equation for the paraboloid z=x^2+y^2 in spherical coordinates.find an equation of the form ρ = f (θ , φ) in spherical coordinates for the following surfaces z = x 2+ y2Find an equation in rectangular coordinates for the surface represented by the cylindrical equation r = 3, and sketch its graph.
- What is the surface area of the three dimensional solid formed by rotating the following parametric equations around the x-axis and then the y-axis? x(t) = 3t2 y(t) = cos(πt) + 2Find the center C and the radius a for the spheres (x - 1)2 + (y - 2)2 + (z + 1)2 = 103 + 2x + 4y - 2zFind an equation in cylindrical coordinates for the surface represented by the rectangular equation z = x2 + y2 − 11
- Suppose that a cylindrical container of radius r and height L is filled with a liquid with volume V , and rotated along the y-axis with constant angular speed ω. This makes the liquid rotate, and eventually at the same angular speed as the container. The surface of the liquid becomes convex as the centrifugal force on the liquid increases with the distance from the axis of the container. The surface of the liquid is a paraboloid of revolution generated by rotating the parabola y = h + ω2x2/2g around the y-axis, where g is gravitational acceleration and h is shown below. (You can take g=32ft/s2 or 9.8m/s2). Express h as a function of ω. (2) At what angular speed ω will the surface of the liquid touch the bottom? At what speed will it spill over the top? (3) Suppose the radius of the container is 2 ft, the height is 7 ft, and the container and liquid are rotating at the same constant angular speed ω. The surface of the liquid is 5 ft below the top of the tank at the central…What is the size of the largest segment parallel to the y axis inside the ellipsoid determined by the equation below? 4x2+5y2+3z2+6x+8y+5z−4=0Find the center C and the radius a for the spheres x2 + y2 + z2 + 4x - 4z = 0