# Math Pre Calc

 Direct variation when one quantity is a constant multiple of another quantity, we say that the quantities are directly proportional to one another Direct variation variables y=kx, where k is a nonzero constanty varies directly with xy is directly proportional to x constant k is called the constant of variation or constant of proportionality. Finding the Constant of Variation 1) write direct variation modely=kx2) label the variables and constant(usually will be solving for k) example:x= number of kWhy= cost (increases with x)k= cost per kWh 3) Substitute variables, and SOLVE FOR K Direct Variation with Powers Let x and y represent 2 quantitiesy=kxn where k is a nonzero constanty varies directly with the nth power of xy is directly proportional to the nth power of x (however many times x occurs, y varies) What is an example of Direct Variation with Powers? W=kH3 (equivalent to y=kx3) Statistics shows that weight in lbs is directly proportional to the cube of height (feet). Inverse Variation When one variable increased, the other decreased. ex: supply & demand (when price increased, demand decreases & vice versa.) Formula and quantities y= k x where k is a nonzero constant y varies inversely with x y is inversely proportional to x the constant k is called the constant of variation or constant of proportionality. Solving inverse variation y=k x x= price of houses in thousands of dollarsy=number of buyers select any point on the curve plug in points solve for k (x multiplied times y) plug back into original formula y= 100,000 = 50 2000 <---original question Joint variation one quantity is proportional to the product of two or more other quantities Example of joint variation I=Prt I = interest in dollarsP= initial amount in dollars r= nterest rate (expressed in decimal form) t= time in years total interest is proportional to these quantities Combined variation when direct variation and inverse variation occur at the same time Example of combined variation combined gas law in chemistry P=k T V P= pressureT= tempV= volumek= gas constant volume is inverse- volume decreases, pressure increasestemp is direct- temp increases, pressure increases AuthorJense133 ID71932 Card SetMath Pre Calc DescriptionModeling Variation Updated2011-03-10T01:10:13Z Show Answers