document.write( "Question 968480: Please help,\r
\n" ); document.write( "\n" ); document.write( "The volume of water in a tank at a particular time (measured in seconds) is given by V (t) = 5t(2 − t) m3. Find the rate of change of the volume of water in the tank from first principles (using the definition of the rate of change). \n" ); document.write( "

Algebra.Com's Answer #591833 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
During the time, $\"dt\"$ ,
\n" ); document.write( " $\"dV%2Fdt=%28V%28t%2Bdt%29-V%28t%29%29%2Fdt\"$
\n" ); document.write( " $\"V%28t%2Bdt%29=5%28t%2Bdt%29%282-%28t%2Bdt%29%29\"$
\n" ); document.write( " $\"V%28t%2Bdt%29=%285t%2B5dt%29%282-t-dt%29\"$
\n" ); document.write( " $\"V%28t%2Bdt%29=%2810t-5t%5E2-5tdt%29%2B%2810dt-5tdt-5%28dt%29%5E2%29\"$
\n" ); document.write( " $\"V%28t%2Bdt%29=10t-5t%5E2-10tdt%2B10dt-5%28dt%29%5E2\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"V%28t%2Bdt%29-V%28t%29=10t-5t%5E2-10tdt%2B10dt-5%28dt%29%5E2-10t-5t%5E2\"$
\n" ); document.write( " $\"V%28t%2Bdt%29-V%28t%29=-10tdt%2B10dt-5%28dt%29%5E2\"$
\n" ); document.write( "and,
\n" ); document.write( " $\"%28V%28t%2Bdt%29-V%28t%29%29%2Fdt=-10t%2B10-5dt\"$
\n" ); document.write( "But $\"dt\"$ becomes infinitesimally small so,
\n" ); document.write( " $\"%28V%28t%2Bdt%29-V%28t%29%29%2Fdt=-10t%2B10\"$
\n" ); document.write( " $\"dV%2Fdt=-10t%2B10\"$ \n" ); document.write( "

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