Question 19 1 pts Compute the volume SSSx 1dV where X is the solid defined by...
Compute the volume SSSx 1 dV where X is the solid defined by x2 + y2 < 4,0 Sz<10., A) 20 B) 407 C) 201 D) 801 ОА ОС OD OB Question 20 What is the absolute value of the Jacobian of : x = uv, y = u2 + v2 at the input point (u, v) = (2, 3)?
Let F(x, y, z) = 4i – 3j + 5k and S be the surface defined by z = x2 + y2 and x2 + y2 < 4. Evaluate SJ, F.nds, where n is the upward unit normal vector.
Question 4. (20 pts) Use polar
coordinates to find the volume of the solid between z= x^2+y^2 and
z=3-x^2-y^2
Question 4. (20 pts) Use polar coordinates to find the volume of the solid between z = x2 + y2 and 2 = 3 – 22 – yº.
Question 4. (20 pts) Use polar coordinates to find the volume of the solid between z = x2 + y2 and z= = 3 – x2 - y2
Let F(x,y,z) = 4i – 3j + 5k and S be the surface defined by z= x2 + y2 and 22 + y2 < 4. Evaluate SJ, F. nds, where n is the upward unit normal vector.
Question 3 1 pts Calculate Sw y DV using cylindrical coordinates, where W is the solid: z? + y2 < 4, 2 > 0 y 0, 0 <z<6.
Question 4. (20 pts) Use polar coordinates to find the volume of the solid between z = x2 + y2 and 2 = 3 - 22 - y2.
Let W be the solid: 0 < x,0 <y, 0 <z < 20 – 2y - X., What is S? S 20-2y 20-2y-2 SJSW 1DV = ſ s 1 dz dar dy S 0 0 Question 18 W is the same solid as in Question 17. What is T?: 20 T 20-2y-2 SSSw 1dV = SS S 1 dz dy dx. 0 0 0 A) 10 B) 20 C) 10 – C 2 D) 10 - y
i will rate. thanks.
[20 pts) Let Q be the solid region Q={ (1,Y,Z): 2Vx2 + y2 < < <2} The density at each point (1,y,z) of Q is given as o(x, y, z) = x2 + y2 + z2. Calculate the moment of inertia about the z-axis, 1,, by hand, showing all work.
MAT MATH213 Lectur... X © 10/12 142% 10 Problem 4- Compute the volume of the solid inside the sphere x2 + y2 + x2 = Rº between the two planes z = a and 2 = b where 0 <a<b<R. 2 R² = a + (² R²= 6² + ď 61 R y С