answer number 4 only 1. (a) Plot the point with cylindrical coordinates (2, 27/3, 1) and find its rectangularcoordinates.(b) Find cylindrical coordinates of the point with rectangular coordinates (3, – 3, –7).2. The point (0, 2 /3, –2) is given in rectangular coordinates. Find spheri cal coordinates for this point.3. The point (2, T/4, 7/3) is given in spherical coordinates. Plot the point and find its rectangular coordinates.V4-x²4. Evaluate ", L(r² + y®) dz dy dx.-24-x2Hint:This iterated integral is a triple integral over the solid regionz=Vx²+y?E ={(x, y, z) | –2 < x< 2, -/4 – x² < y< /4 – x², Vx² + y² < z < 2}and the projection of E onto the xy-plane is the disk x² + y² < 4. The lower surface ofE is the cone z =2Vx² + y² and its upper surface is the plane z = 2. (See Figure 9.)This region has a much simpler description in cylindrical coordinates:FIGURE 9

Cylindrical Coordinates: Put x= r cosθ and y=r sinθ and z=zthen, r = x2+y2 and θ =…

Answered: 4-x² 4. Evaluate [*, [* (r² + y°) dz dy…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 53E

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4-x² 4. Evaluate [*, [* (r² + y°) dz dy dx. 4-. Hint: This iterated integral is a triple integral over the solid region E = {(x, y, z) | –2

4-x² 4. Evaluate [, [ (r² + y°) dz dy dx. 4-. Hint: This iterated integral is a triple integral over the solid region E = {(x, y, z) | –2