I. Set up a triple integral in Cartesian coordinates whose value gives the average temperature of the cylindrical region W bounded by the planes z = 0, z = 2, and the cylinder x² + y² = 1. The temperature distribution is T = f(x, y, z) = 50c²+². Evaluate using the Wolfram Alpha. (Ans: 85.9)

Q: Convert the polar equation θ =π/2 to a rectangular equation. Then use a rectangular coordinate…

A: Given polar equation is θ=π2 To convert given equation into rectangular equation. Solution: In…

Q: C) Replace the following polar equation by equivalent Cartesian equation. rsine Inr + In cose %3D

A: We can replace the given polar equation by equivalent Cartesian equation as below.

Q: (-vz, .주) Convert from polar to cartesian coordinates

A:

Q: Convert the rectangular equation y = 3 to a polar equation that expresses r in terms of θ .

A: Given:y=3

Q: 3. Convert the polar equation to a rectangular equation. r = 64

A: Given,             r = 64 We have to convert the polar equation to a rectangular equation.