For constants a, b, c, and d, show that the equation x 2 y 2 z 2 2ax 2by 2cz d describes a sphere centered at (a, b, c) with radius r, where r 2 d a 2 b 2 c 2 , provided d a 2 b 2 c 2 0 ...

We complete the squares by adding a b c to both sides of the given e ...

For constants a, b, c, and d, show that the equation x 2 + y 2 +

Question:

For constants a, b, c, and d, show that the equation

x² + y² + z² - 2ax - 2by - 2cz = d

describes a sphere centered at (a, b, c) with radius r, where r² = d + a² + b² + c², provided d + a² + b² + c² > 0.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

See More Books

Question Posted: Apr 13, 2019 07:38 AM

See More Questions

Assume that u, v, and w are vectors in R 3 that form the sides of a triangle (see figure). Use the following steps to prove that the medians intersect at a point that divides each median in a 2:1...
Express the dot product of u and v in terms of the components of the vectors.
Consider the following vectors u and v. Sketch the vectors, find the angle between the vectors, and compute the dot product using the definition u v = |u| |v| cos . u = 4i and v = 6j
X H H H HCZO HONH HO HN. HOC H A variety of electrophiles (EY) will react with benzene, and derivatives of benzene, to yield substitution products. Halogenation of OH benzene rings is an reaction...
Describe the difficulties you might encounter in applying explosion welding in a factory environment in urban areas?
Body-Builders, Inc., produces two basic types of weight-lifting equipment, Model 9 and Model 14. Pertinent data are as follows: The weight-lifting craze is such that enough of either Model 9 or Model...
How to establish the terms of the attorney-client agreement?
1. Clearly, Farrah Gray is a master of integrated promotion. List the promotional methods he has used and why he may have selected each. 2. What is the most interesting part of his story for you?...
c. Put Price without Dividends: Assume that LEW pays no dividends. What is the BSM price of a put with an exercise price of $95 that matures in 73 days (assume that a year is 252 days)?
Ellipses Corp is a small business that operates in Herndon, VA. The company is located at10 Period Lane, Herndon, VA 20170. Its federal Employer Identification Number is 77-7777777, and its...
Prove that the midpoint of the line segment joining P(x 1 , y 1 , z 1 ) and Q(x 2 , y 2 , z 2 ) is X1 + x2 y1 + y2 Z1 + Z2 2
In contrast to the proof in Exercise 81, we now use coordinates and position vectors to prove the same result. Without loss of generality, let P(x 1 , y 1 , 0) and Q(x 2 , y 2 , 0) be two points in...
Victor Grimm is confused about how accounting information flows through the accounting system. He believes the flow of information is as follows. a. Debits and credits posted to the ledger. b....
An action by the landlord that denies the tenant the use of the pre mises. a. abandonment b. assignment c. condition d. covenant e. eviction f. lease g. lessee h. lessor i. periodic tenancy j. quiet...
Carelessness that results in injury to another person or his or her property. a. conversion b. contributory ne gligence c. defamation d. liability e. libel f. negligence g. nuisance h. slander i....
The right of a tenant to use the premises without unreasonable interference from the landlord or third parties. a. abandonment b. assignment c. condition d. covenant e. eviction f. lease g. lessee h....
Rensch left two diamond rings for cleaning at Riddles Mall in Rapid City, South Dakota. Riddles had advertised free ring cleaning to the public. When Rensch returned for the rings, he found that a...
A tenants voluntary surrender of possession of leased premises. a. abandonment b. assignment c. condition d. covenant e. eviction f. lease g. lessee h. lessor i. periodic tenancy j. quiet enjoyment...
"The more authority that is delegated to non-managers, the less authority managers have." Is this necessarily a true statement? Explain.
Do animals have rights? If so, what are they? What duties do human beings have toward animals? Does KFC protect animal welfare at an acceptable level?
Suppose that r is the position vector of a particle moving along a plane curve and dA / dt is the rate at which the vector sweeps out area. Without introducing coordinates, and assuming the necessary...
What are the vector and parametric equations for ideal projectile motion? How do you find a projectiles maximum height, flight time, and range? Give examples.
Write a in the form a = a T T + a N N at the given value of t without finding T and N. r(t) = (t + 1)i + 2tj + t 2 k, t = 1
Suppose Stocks A, B and C are the only three component stocks in a benchmark index. The number of shares outstanding of Stocks A, B and C are 369,000 shares, 327,000 shares, and 240,000 shares,...
Botanists have determined that some species of weed grow in a circular pattern. For one such species, the area A , in square meters, can be approximated by A ( t ) = 0.004 t 2 , where t is the time...
Book Print ciences Gallatin Carpet Cleaning is a small, family-owned business operating out of Bozeman, Montana. For its services, the company has always charged a flat fee per hundred square feet of...

For constants a, b, c, and d, show that the equation x 2 + y 2 +

Question:

Step by Step Answer:

We complete the squares by adding a b c to both sides of the given e...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions