document.write( "Question 815469: If A varies directly to x and A varies inversely to y.If x varies directly to t and y varies directly to t.Find how A varies to t \n" ); document.write( "

Algebra.Com's Answer #490993 by jsmallt9(3758) $\"\"$ $\"About$

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From \"A varies directly to x\" we get:
\n" ); document.write( " $\"A+=+k%5B1%5D%2Ax\"$
\n" ); document.write( "(I'm using subscripts on the constants of variation because there are more than one and I want to name them as k's.)
\n" ); document.write( "From \"x varies directly to t\" we get:
\n" ); document.write( " $\"x+=+k%5B2%5D%2At\"$

\n" ); document.write( "We are looking for how A varies to t. So we do not want x in the equation. The second equation is already solved for x. Using this we can substitute into the first equation for x:
\n" ); document.write( " $\"A+=+k%5B1%5D%2A%28k%5B2%5D%2At%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"A+=+k%5B1%5D%2Ak%5B2%5D%2At\"$
\n" ); document.write( "Since $\"k%5B1%5D\"$ and $\"k%5B2%5D\"$ are constants, so it their product. So if we let $\"k%5B3%5D+=+k%5B1%5D%2Ak%5B2%5D\"$ our equation becomes:
\n" ); document.write( " $\"A+=+k%5B3%5D%2At\"$
\n" ); document.write( "which is an equation of direct variation. So A varies directly with t.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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