Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
The region consisting of all points between (but not on) the spheres of radius $ r $ and $ R $ centered at the origin, where $ r < R $.
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Connor Painter
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 3
Chapter 12
Vectors and the Geometry of Space
Section 1
Three-Dimensional Coordinate Systems
Vectors
Missouri State University
Campbell University
Oregon State University
Boston College
Lectures
02:56
In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.
11:08
In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.
01:28
The region consisting of a…
01:42
01:55
Write inequalities to desc…
02:46
$\mathbf{F}=\langle z-x, x…
01:38
Intersecting spheres One s…
05:30
A sphere has center in the…
in this problem. We're trying to find an inequality to describe the region of space between two different spheres centered at the origin. One with radius. Little are shown in blue and one with radius big are shown in red. You can imagine this region of space as a thick spirit Kal Shell, where the center is hollow. But the region between Radius little, R and big are is solid. So let's answer this question using ideas from the chapter. First, we know that the equation for a sphere centred at the origin is X squared, plus y squared plus C squared. Equals are square. Now I'm using a curse of our because the printers are already in use. Once you specify a value for cursive R, you get all of the points X y Z that lie on the surface of this sphere. What if we want to know all the points strictly inside this fear? Not on the surface, but actually inside? Well, it's almost exactly the same thing. It's X squared plus y squared plus C squared. But the equality changes to one inequality, a less fan in this case, since for inside. So that says X squared plus y squared plus C squared less than cursive r squared. And you kind of look at that that inequality and say, Well, that actually looks like all the points on every sphere that has radius less fan course of our and you would be exactly right. That's exactly the same thing as the whole volume inside anyway, Now we can use this knowledge. Thio, Thio, Compute the answer this question. It really just falls right out. We have two conditions are first condition is that our points have to be outside. Little are their second condition is that they have to be inside capital. Mathematically, this means we have X squared plus y squared plus C squared is greater than little r squared, and we also have X squared plus y squared. Plus C squared is less than a Capital R squared, and we're actually done. But we can combine these inequalities in a nice, happy way like so throw that little R squared over to the left. We have little R squared is less than X squared, plus y squared plus C squared. It's less than Capital R squared, and now it's clear that we have the set of all X y Z that is in between the two radio I little R and Capital R, and that is the answer.
View More Answers From This Book
Find Another Textbook
01:43
A fruit seller had some apples. he sells 20% apples and still has 80 apples.…
02:49
A wooden solid is made up of a cylinder with hemispherical ends. If the whol…
03:30
A student has applied for admission to two management Institutes A and B. He…
02:01
(Use Hypergeometric Distribution) A lot of 12 compressor tanks is checked to…
03:50
Delta Airlines quotes a flight time of 4 hours, 3 minutes for a particular f…
01:52
(Use Hypergeometric Distribution) A recent study found that 2 out of every 1…
02:25
Alice and Bob are playing a game where in each round, each of them rolls…
02:51
The time to failure of a component in an electronic device has an exponentia…
04:44
A dating service has as clients six recently divorced couples. Each client w…
01:49
The average number of homes sold by the Acme Realty Company is 2 homes p…