document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102923>Question 1102923</A>: <I><SPAN STYLE=\"word-break: break-all;\"> P varies jointly as T and the square of&#8203; Q, and P=16 when T=17 and Q=4. Find P when T=2 and Q=8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717683 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13209)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=717683\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The described joint variation means<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+k%28T%29%28Q%5E2%29 ALIGN=MIDDLE  ALT=\"P+=+k%28T%29%28Q%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where k is a constant of variation.<br><BR>\n" );
document.write( "One way to find the answer to your problem is to use the given values of P, T, and Q to determine the value of k and then use that value of k with the new values of Q and T to find the new value of P:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+k%2817%29%284%5E2%29 ALIGN=MIDDLE  ALT=\"16+=+k%2817%29%284%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+17k%2816%29 ALIGN=MIDDLE  ALT=\"16+=+17k%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+17k ALIGN=MIDDLE  ALT=\"1+=+17k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+1%2F17 ALIGN=MIDDLE  ALT=\"k+=+1%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+%281%2F17%29%282%29%288%5E2%29+=+128%2F17 ALIGN=MIDDLE  ALT=\"P+=+%281%2F17%29%282%29%288%5E2%29+=+128%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Another way to work a problem like this, which I like to at least try to use, is to just consider how each changed \"input\" value changes the \"output\" value.<br><BR>\n" );
document.write( "In this problem, the value of T changes from 17 to 2; since the value of P varies directly with T, the value of P gets multiplied by 2/17.<BR>\n" );
document.write( "And in this problem the value of Q changes from 4 to 8, so it is doubled.  Since P varies directly as the square of Q, the value of P gets multiplied by 4.<br><BR>\n" );
document.write( "All together, the original P value of 16 gets multiplied by (2/17) and by 4, giving the new P value as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2A%282%2F17%29%2A4+=+128%2F17 ALIGN=MIDDLE  ALT=\"16%2A%282%2F17%29%2A4+=+128%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "You should try to learn both methods; for different problems, depending on the given numbers, one or the other of the two methods might be the easier one to use. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );