The plane 4x - 3y + 8z = 5 intersects the cone z 2 = x 2

Question:

The plane 4x - 3y + 8z = 5 intersects the cone z² = x² + y² in an ellipse.

(a) Graph the cone and the plane, and observe the elliptical intersection.
(b) Use Lagrange multipliers to find the highest and lowest points on the ellipse.

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: 978-1285741550

8th edition

Authors: James Stewart

See More Books

Question Posted: Apr 10, 2019 09:38 AM

See More Questions

Find a basis for (a) The plane given by the equation z -2 y = 0 in R3; (b) The plane given by the equation 4x+3y-z = 0 in R3; (c) The hyperplane x + 2y + z - u> = 0 in R4.
The plane P1 has the equation 4x - y + 5z = 2. For each of the planes P1 in Exercise 18, determine whether P1 and P are parallel, perpendicular, or neither. In exercise 18 (a) 2x + 3y - z = 1 (b) 4x...
Find an equation for the plane through (- 2, 1, 5) that is perpendicular to the planes 4x - 2y + 2z = - 1 and 3x + 3y - 6z = 5.
An excise tax of $1.00 per gallon of gasoline placed on the suppliers of gasoline would shift the supply curve Multiple Choice O down by $1.00. down by more than $1.00. up by $1.00. up by less than...
On May 15, Wild Quest Clothiers borrowed some money on a 4-month note to provide cash during the slow season of the year. The interest rate on the note was 8%. At the time the note was due, the...
Water is flowing from Location 1 to 2 in this pipe expansion. D 1 and V 1 are known at the inlet. D 2 and p 2 are known at the outlet. What equation(s) do you need to solve for the inlet pressure p 1...
Understand how work is structured. (pp. 294296)
Hurricane Inc. purchased a portfolio of available-for-sale securities in 2014, its first year of operations. The cost and fair value of this portfolio on December 31, 2014, was as follows: On June...
Sunland Inc. produces and sells the products. Unit data concerning each product is shown below. Product D E $ 202.80 $302.40 $ 265.20 Selling price Direct labor costs Other variable costs 33.80 98.80...
Draft a quarterly cash budget for the Zoo Extravaganza (ZE) for the first two quarters of the coming year. Use just the information in this problem. 1. Interest is paid on the last day of the year...
The plane x + y + 2z = 2 intersects the paraboloid z = x 2 + y 2 in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin.
Find the maximum and minimum values of f subject to the given constraints. Use a computer algebra system to solve the system of equations that arises in using Lagrange multipliers. (If your CAS finds...
Columbia Trust wants its annually, semiannually, and monthly compounded five-year GICs all to have an effective interest rate of 5.75%. What nominal annual rates should it quote for the three...
City Feb. Cases March Cases April Cases New York 19 56 189 Los Angeles 6 12 201 Chicago 0 3 14 Houston 19 19 272 Philadelphia 0 1 5 Phoenix 23 78 289 San Antonio 6 9 95 San Diego 3 38 258 Dallas 4 13...
Maximize z = 2x+2y x+6y <30 4x + 2y 32 Subject to I 0 W O 0 Maximum is I = y= at
2. Determine the unknown force. a) Fret 3 N Right b) Fret 10. N Down F-22 N F?5N c) Feet 12 N Up F-28 N d) Fret 10. N Right F? F-12N e) Fret = 0 F-16N E-? F-12N F-15 N F-? F-30 N F-25 N F-32 N F=24N...
If y = ( x ^ 3 + 7 ) ^ x , compute y ' ( 1 ) .
To calculate activity expected duration time, the following parameter is essential? Question 7 options: Distribution time of the unit. Time associated with the failure of the unit. Optimistic or...
Listed below are birth weights (in kilograms) of male babies born to mothers on a special vitamin supplement (based on data from the New York State Department of Health). Test the claim that this...
Quality Chicken grows and processes chickens. Each chicken is disassembled into five main parts. Information pertaining to production in July 2012 is: Joint cost of production in July 2012 was $50. A...
Sketch graphs of the following exponential function. For each, find the value of x where it is equal to 7.0. For the increasing functions, find the doubling time, and for the decreasing functions,...
Sketch graphs of the following exponential function. For each, find the value of x where it is equal to 7.0. For the increasing functions, find the doubling time, and for the decreasing functions,...
Sketch graphs of the following exponential function. For each, find the value of x where it is equal to 7.0. For the increasing functions, find the doubling time, and for the decreasing functions,...
Diplomatic Security Service provides Airport Transportation and Surveillance Service to Foreign Diplomats in Guyana. The company has two support departments - Information Systems and Equipment...
Q1: A disparity of bargaining power between the parties to a contract may result in unfair terms but a court is not likely to consider the contract unconscionable. Group of answer choices a. True b....
Life Tool Manufacturing has a system in place to recall products that prove to be dangerous at some time after manufacture and distribution. This represents which element of the due care theory?...

The plane 4x - 3y + 8z = 5 intersects the cone z 2 = x 2

Question:

Step by Step Answer:

a After plotting z x y the top half of the cone and the plane z54x3y8 we see the ellipse formed by t...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions