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Chapter 13: Q 6 (page 1065)

For what values of $a \in [0, π]$ in the spherical coordinate
system is the graph $φ = a$ not a cone?

Short Answer

Expert verified

The required answer is $ϕ = α = \frac{π}{2}$ not a cone.

Step by step solution

01

Determine the values whether the given spherical coordinate system is a cone or not

$α = \frac{π}{2}$ It represents a spherical plane in the $x y$ -plane.

As a result, $α = \frac{π}{2}$ it does not depict a cone.

As a result, $ϕ = α = \frac{π}{2}$ it is not a cone.

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Most popular questions from this chapter

Evaluate the sums in Exercises 23–28.

$\sum_{j = 1}^{3} \sum_{k = 1}^{2} k^{j}$

Find the masses of the solids described in Exercises 53–56.

The solid bounded above by the hyperboloid with equation $z = x^{2} - y^{2}$ and bounded below by the square with vertices (2, 2, −4), (2, −2, −4), (−2, −2, −4), and (−2, 2, −4) if the density at each point is proportional to the distance of the point from the plane with equationz = −4.

Explain how to construct a Riemann sum for a function of three variables over a rectangular solid.

In Exercises 61–64, let R be the rectangular solid defined by

$R = \{(x, y, z) | 0 \leq a_{1} \leq x \leq a_{2}, 0 \leq b_{1} \leq y \leq b_{2}, 0 \leq c_{2} \leq z \leq c_{2}\} .$

Assume that the density of R is uniform throughout.

(a) Without using calculus, explain why the center of

mass is $(\frac{a_{1} + a_{2}}{2}, \frac{b_{1} + b_{2}}{2}, \frac{c_{1} + c_{2}}{2}) .$

(b) Verify that $(\frac{a_{1} + a_{2}}{2}, \frac{b_{1} + b_{2}}{2}, \frac{c_{1} + c_{2}}{2})$ is the center of mass by using the appropriate integral expressions.

Evaluate each of the double integral in the exercise 37-54 as iterated integrals

$\int \int_{R} (y^{2}) d A W h e r e R = {(x, y) | - 3 \leq x \leq 2, - 2 \leq y \leq 2}$

See all solutions

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