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Write the equation in spherical coordinates. (a) x2 + y2 + Z2 = 64 (b) x2...
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2...
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph.
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph.
Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2 + y2 +z" 1 and x2 + y2 + z2-4 given that the density at each point P(x, y, z) is inversely proport...
Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2 + y2 +z" 1 and x2 + y2 + z2-4 given that the density at each point P(x, y, z) is inversely proportional to the distance from P to the origin and 8(o, 3,02 15 pts] (0, 1,0)-2/m3 from P to the origin and
Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2...
Let D be the solid spherical "cap" given by x2 + y2 + z2 < 16...
Let D be the solid spherical "cap" given by x2 + y2 + z2 < 16 and 2 > 1. Set up, but do not evaluate, a triple integral representing the volume of D in cylindrical coordinates.
Use spherical coordinates. Evaluate (4 − x2 − y2) dV, where H is the solid hemisphere...
Use spherical coordinates.
Evaluate
(4 − x2 − y2) dV, where H is
the solid hemisphere x2 + y2 + z2
≤ 16, z ≥ 0.
H
PLE 2 The point (0, 5 3 , −5) is given in rectangular coordinates. Find spherical...
PLE 2 The point (0, 5 3 , −5) is given in rectangular coordinates. Find spherical coordinates for this point. SOLUTION From the distance formula we have ρ = x2 + y2 + z2 = 0 + 75 + 25 = 10 Correct: Your answer is correct. and so these equations give the following. cos(φ) = z ρ = -1/2 Correct: Your answer is correct. φ = $$ Incorrect: Your answer is incorrect. cos(θ) = x ρ sin(φ) = θ...
Consider the solid enclosed by x2 + y2 + z2 = 2z and z2 = 3(x2 + y2) in the 1st octant.
Consider the solid enclosed by x2 + y2 + z2 = 2z and z2 = 3(x2 + y2) in the 1st octant. a) Set up a triple integral using spherical coordinates that can be used to find the volume of the solid. Clearly indicate how you get the limits on each integral used. b) Using technology, or otherwise, evaluate the triple integral to find the volume of the solid.
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 +...
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 + z2 = 32. Consider (a) Write an iterated integral for the triple integral in rectangular coordinates. (b) Write an iterated integral for the triple integral in cylindrical coordinates. (c) Write an iterated integral for the triple integral in spherical coordinates. (d) Evaluate one of the above iterated integrals.
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 +...
question 12 , please sketch it by your hand , do not use computer graph θ varies from 0 to 2 π. φ varies from 0 to π/4 while 0 is constant. find 9-10 Write the equation in spherical coordinates. 9. (...
question 12 , please sketch it by your hand , do not use
computer graph
θ varies from 0 to 2 π. φ varies from 0 to π/4 while 0 is constant. find 9-10 Write the equation in spherical coordinates. 9. (a) :2-x2 + y2 10. (a) a-2r+y- (b) x2 +z2 = 9 (b) x + 2y+ 3:-1 11-14 Sketch the solid described by the given inequalities. 15. A solid lies above the cone:- + y and below the sphere...
Write the equation with rectangular coordinates. r2 = 5 cos20 a. (x2 + y2)2 = 5(x2...
Write the equation with rectangular coordinates. r2 = 5 cos20 a. (x2 + y2)2 = 5(x2 + y2) ob. (x2 + y2)2 = 6(x2 –y?) Oc. (x² + y2)2 = 6(x2+y?) O d. (x+y?)? = 6(x2-y?) O e. (x2+x2)? = 5(x2-y2)
1. (13 pts.) Use spherical coordinates to set up the triple integral for the solid that is constructed from a portion of a sphere, x2 +y2 +Z2-1 that lies above the cone φ = π/4 . Do NOT evaluate....
1. (13 pts.) Use spherical coordinates to set up the triple integral for the solid that is constructed from a portion of a sphere, x2 +y2 +Z2-1 that lies above the cone φ = π/4 . Do NOT evaluate.
1. (13 pts.) Use spherical coordinates to set up the triple integral for the solid that is constructed from a portion of a sphere, x2 +y2 +Z2-1 that lies above the cone φ = π/4 . Do NOT evaluate.
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph.
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph.
Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2 + y2 +z" 1 and x2 + y2 + z2-4 given that the density at each point P(x, y, z) is inversely proportional to the distance from P to the origin and 8(o, 3,02 15 pts] (0, 1,0)-2/m3 from P to the origin and
Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2...
Let D be the solid spherical "cap" given by x2 + y2 + z2 < 16 and 2 > 1. Set up, but do not evaluate, a triple integral representing the volume of D in cylindrical coordinates.
Use spherical coordinates.
Evaluate
(4 − x2 − y2) dV, where H is
the solid hemisphere x2 + y2 + z2
≤ 16, z ≥ 0.
H
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 + z2 = 32. Consider (a) Write an iterated integral for the triple integral in rectangular coordinates. (b) Write an iterated integral for the triple integral in cylindrical coordinates. (c) Write an iterated integral for the triple integral in spherical coordinates. (d) Evaluate one of the above iterated integrals.
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 +...
question 12 , please sketch it by your hand , do not use
computer graph
θ varies from 0 to 2 π. φ varies from 0 to π/4 while 0 is constant. find 9-10 Write the equation in spherical coordinates. 9. (a) :2-x2 + y2 10. (a) a-2r+y- (b) x2 +z2 = 9 (b) x + 2y+ 3:-1 11-14 Sketch the solid described by the given inequalities. 15. A solid lies above the cone:- + y and below the sphere...
Write the equation with rectangular coordinates. r2 = 5 cos20 a. (x2 + y2)2 = 5(x2 + y2) ob. (x2 + y2)2 = 6(x2 –y?) Oc. (x² + y2)2 = 6(x2+y?) O d. (x+y?)? = 6(x2-y?) O e. (x2+x2)? = 5(x2-y2)
1. (13 pts.) Use spherical coordinates to set up the triple integral for the solid that is constructed from a portion of a sphere, x2 +y2 +Z2-1 that lies above the cone φ = π/4 . Do NOT evaluate.
1. (13 pts.) Use spherical coordinates to set up the triple integral for the solid that is constructed from a portion of a sphere, x2 +y2 +Z2-1 that lies above the cone φ = π/4 . Do NOT evaluate.
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