This is a written question, worth 12 points. DO NOT place the problem code on the answer sheet. A...
A solid is bounded above by a portion of the hemisphere z= 2 – – 72 . And below by the cone z = 2 + y2 , with a < 0 and y < 0. Part a: Express the volume of the solid as a triple integral involving 2, y and z. Part b: Express the volume of the solid as a triple integral in cylindrical coordinates. Parte: Express the volume of the solid as a triple integral in...
(a) Let R be the solid in the first octant which is bounded above by the sphere 22 + y2+2 2 and bounded below by the cone z- r2+ y2. Sketch a diagram of intersection of the solid with the rz plane (that is, the plane y 0). / 10. (b) Set up three triple integrals for the volume of the solid in part (a): one each using rectangular, cylindrical and spherical coordinates. (c) Use one of the three integrals...
Question 10 Your answer is CORRECT. This is a written question, worth 14 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1023 Given: P(E) = 0.38, P(F) = 0.68, and P(E U F) = 0.82 Part a: Find P(En F). Part b: Find P( EF). Part : Find P(FE). Part d: Are the events E...
7/10 324-x and the cone 5) (27 points) Let D be the solid region bounded by the paraboloid a) (8 points) Sketch D and set up triple integrals in rectangular coordinates representing the dzdyda volume of D according to the order of integration dedyd Open with (9 points) Set up triple integrals in rectangular coordinates representing the volume of D b) according to the order of integration drdedy 8/10 (4 points) Set up triple integrals in cylindrical coordinates representing the...
11. Evaluate S. 'S*(1 + 3x2 + 2y?) dx dy. 12. Find the volume in the first octant of the solid bounded by the cylinder y2 + z2 = 4 and the plane x = 2y. Graph for Problem 12 13. Find the volume under the paraboloid z = 4 - x2 - y2 and above the xy-plane. N Consider the solid region bounded above by the sphere x + y + z = 8 and bounded below by the...
This is a written question, worth 15 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1123 Assume the length X in minutes for a phone conversation is a random variable with probability density function: f(x) = { ce-116 x > 0 elsewhere a/ Determine the value of c b/ Determine the probability that the phone...
2) (27 points) Let D be the region bounded from below by the plane : 0, from above by the plane z-2J3 and laterally by the hyperboloid of one sheet x2 + y2-1-24. a) (3 points) Draw the region D. b) (12 points) Set up triple integrals representing the volume of D in spherical coordinates according to the order of integration dp do de c) (12 points) Set up triple integrals representing the volume of D in cylindrical coordinates according...
5a. The solid E lies above the cone z =V3V2 + y and below the sphere cº + y2 + 2 = 9. Completely set up, but DO NOT EVALUATE, the triple integral Ssse (y+z)dV in spherical coordinates. Show appropriate work for obtaining the limits of integration and include a sketch. Your answer should be completely ready to evaluate. (9 points) 5b. Completely set up, but DO NOT EVALUATE, the same triple integral ple (y + x)2V from part (a),...
Cale3 Final Take Home (19S) NAME ID Dac Monday (May 6> (Show sact valuc and Show all your work by using both Cyl coordinates for hoth part I and part 2) Cylindrical & Spherical 1. Find the volume of the solid E between +y') fa cone and-xta semi-sphere) by evaluanting the triple insegral V-ldrby any coondinates 2. will he the denominuo i 2 Fins the centroithEbre, Illis an the -axi) he er f formula for the centroid)y
Cale3 Final Take...
Please show all steps. Thank you, need to verify what I'm doing
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1. (20 points) Suppose B is the solid region inside the sphere 2+ y2 +2 4, above the plane = 1, and in the first octant (z, y, z 0)、z, y and z are measured in meters and the density over B is given by the function p(z, y, z)-(12 + y2 + ?)-1 kg/m3 (a) Set up and write the triple integral that gives the mass...