document.write( "Question 1116932: Given that the energy(e) varies directly as the resistance(r) and inversely as the square of the distance(d) if e=32/25, r=8 and d=5
\n" ); document.write( "a) calculate the constant k
\n" ); document.write( "b) calculate r when e=16 and d=3
\n" ); document.write( "c) calculate d when r=5 and e=5/6
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Algebra.Com's Answer #731839 by KMST(5328) $\"\"$ $\"About$

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If $\"e\"$ varies directly as $\"r\"$ and inversely as $\"d%5E2\"$ (the square of d),
\n" ); document.write( "the relation is
\n" ); document.write( " $\"e=k%2Ar%2A%281%2Fd%5E2%29\"$ or $\"e=kd%2Fr%5E2\"$ , where $\"k\"$ is a constant.
\n" ); document.write( "You know that when $\"r=8\"$ and $\"d=5\"$ , $\"e=32%2F25\"$ .
\n" ); document.write( "Substituting those values into
\n" ); document.write( " $\"e=kd%2Fr%5E2\"$ ,
\n" ); document.write( "you get
\n" ); document.write( " $\"32%2F25=k%2A8%2F5%5E2\"$ ,
\n" ); document.write( "which you can solve for $\"k\"$ .
\n" ); document.write( " $\"32%2F25=k%2A8%2F5%5E2\"$
\n" ); document.write( " $\"32%2F25=k%2A8%2F25\"$
\n" ); document.write( " $\"32=k%2A8\"$
\n" ); document.write( " $\"32%2F8=k\"$
\n" ); document.write( " $\"highlight%28k=4%29\"$
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\n" ); document.write( "Now you know that the relation between $\"e\"$ , $\"r\"$ and $\"d%5E2\"$ ,
\n" ); document.write( "or between $\"e\"$ , $\"r\"$ and $\"d\"$ is
\n" ); document.write( " $\"e=4d%2Fr%5E2\"$ .
\n" ); document.write( "
\n" ); document.write( "To calculate $\"r\"$ when $\"e=16\"$ and $\"d=3\"$ ,
\n" ); document.write( "you substitute the known values into $\"e=4d%2Fr%5E2\"$ ,
\n" ); document.write( "and solve for $\"r\"$ .
\n" ); document.write( " $\"16=4%2A3%2Fr%5E2\"$
\n" ); document.write( " $\"r%5E2=4%2A3%2F16\"$
\n" ); document.write( " $\"r%5E2=3%2F4\"$ , and as you know $\"r\"$ is not a negative number,
\n" ); document.write( " $\"r=sqrt%283%2F4%29\"$
\n" ); document.write( " $\"highlight%28r=sqrt%283%29%2F2%29\"$ .
\n" ); document.write( "
\n" ); document.write( "When $\"r=5\"$ and $\"e=5%2F6\"$ , substituting into $\"e=4d%2Fr%5E2\"$ gives you
\n" ); document.write( " $\"5%2F6=4d%2F5%5E2\"$
\n" ); document.write( " $\"5%2F6=4d%2F25\"$
\n" ); document.write( " $\"25%2A5%2F%286%2A4%29=d\"$
\n" ); document.write( " $\"highlight%28d=125%2F24=5%265%2F24=approximately+5.21%29\"$ \n" ); document.write( "

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