2f-+Variation

 **__Variation: Direct, Inverse, and Joint (Sections 2.5, 8.1) __**

 __Notes __ :
 * d=r t ** → d and t vary directly
 * r = d /t **→ r and <span style="color: rgb(17, 23, 167);">t vary inversely
 * <span style="color: rgb(23, 17, 176);">t = <span style="color: rgb(181, 13, 13);">d /<span style="color: rgb(82, 13, 201);">r ** →<span style="color: rgb(101, 21, 213);"> r and <span style="color: rgb(216, 14, 14);">d vary inversely

//Direct Variation// y= k//x//

k= y///x//

//Inverse Variation// y= k///x//

//x//y=k

* "k" is the constant of variation" <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; color: rgb(210, 25, 25);"> <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; color: rgb(210, 25, 25);"><span style="color: rgb(17, 14, 14);"> __Examples:__ 1.) //p// varies directly with //t// and inversely with //s²//. When //t//=12, //s//=3, and //p//=2.

p= kt/s² 2= k(12)/3² 18=12k
 * 3/2= k**

//General Equation that Relates to the Variables// p= 3/2t/s² p= 3t/2s²

2.) //z// varies inversely with //c²//. When //z//= 24, //c//= 0.5. What is //z// when //c//=2?

zc²=k (24)(0.5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; color: rgb(210, 25, 25);"><span style="color: rgb(17, 14, 14);">²= k (24)(.25)=k
 * k=6**

z(2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; color: rgb(210, 25, 25);"><span style="color: rgb(17, 14, 14);">²= 6 4z=6 z= 6/4
 * z= 3/2**

__Other:__ //For additional notes:// http://www.regentsprep.org/Regents/math/algtrig/ATE7/Direct%20Variation.htm http://www.regentsprep.org/Regents/math/algtrig/ATE7/Inverse%20Variation.htm

//For additional practice problems:// http://www.regentsprep.org/Regents/math/algtrig/ATE7/variation%20practice%201.htm http://www.regentsprep.org/Regents/math/algtrig/ATE7/variation%20practice%202.htm

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; color: rgb(210, 25, 25);"><span style="color: rgb(17, 14, 14);">//**<span style="color: rgb(59, 130, 232);">--danceteamgirl-- **//