Stitz-Zeager_College_Algebra_e-book

What resultant force is applied to the keg 10

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: − y sin 3 = 2 − 2 and y = x sin 3 + y cos 3 = 2 + y 2 11.6 Hooked on Conics Again 829 and simplify. While this is by no means a trivial task, it is nothing more than a hefty dose of Beginning Algebra. We will not go through the entire computation, but rather, the reader should take the time to do it. Start by verifying that √ (x )2 x y 3 3(y )2 x= − + , 4 2 4 √ √ √ (x )2 3 x y (y )2 3 3(x )2 x y 3 (y )2 2 xy = − − , y= + + 4 2 4 4 2 4 √ To our surprise and delight, the equation 21x2 + 10xy 3 + 31y 2 = 144 in xy -coordinates 2 2 reduces to 36(x )2 + 16(y )2 = 144, or (x4) + (y9) = 1 in x y -coordinates. The latter is an ellipse centered at (0, 0) with vertices along the y -axis with (x y -coordinates) (0, ±3) and whose minor axis has endpoints with (x y -coordinates) (±2, 0). We graph it below. 2 y π 3 x y π 3 x √ 21x2 + 10xy 3 + 31y 2 = 144 √ The elimination of the troublesome ‘xy ’ term from the equation 21x2 + 10xy 3 + 31y 2 = 144 in Example 11.6.1 number 2 allowed us to graph the equation by hand using what we learned in Ch...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online