Explain why it is likely that the distributions of the following variables will be

8/22/16 MA 26100 Multivariable Calculus Introduction: Professor: Dr. Joseph Chen, Purdue University Office Hours: MWF 9:00 – 11:00 AM in MATH 848 Textbook: Calculus: Early Transcendentals – 7 Edition, Stewart Exam Dates: Exam 1 – 9/29/16, Exam 2 – 11/8/16 (100 Points Each), Final – TBD (200 Points) Class is worth 550 Points Review: 12.1, 3 Dimensional Coordinate System  Points are given in Cartesian, (x,y,z), format  Distance between 2 points [(x ,y ,z ) and (x ,y ,z )] given by: 1 1 1 2 2 2 √(x −x ) +(y −y ) +(z −z ) =d 2 o 2 1 2 1 2 1 o This is known as the distance formula  The equation for a sphere with center at (h, k, l) and a radius r is given as follows: 2 2 2 2 o (x−h) +(y−k) +(z−l) =r o This is the standard form of the equation EX. 1 Identify the center and radius of a sphere with the equation: 2 2 2 x +y +z =4x−2y+4 SOLUTION We need to first convert this equation to standard form by completing the square, which will result in the following equation x −4x+y +2 y+z =4 2  Get all the variables to one side 2 2 2  Complete the square x −4x+4+y +2y+1+z =4+4+1  Simplify 2