document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147563>Question 147563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An astronaut on the moon tosses a ball upwards; when will the ball initially be 35 feet above the lunar surface if the ball's height (feet) follows: h(t) = -2.6t^2 + 32.1t + 5.5, and t is in seconds from release?<BR>\n" );
document.write( "a. 1 second<BR>\n" );
document.write( "b. 2 seconds<BR>\n" );
document.write( "c. .5 seconds<BR>\n" );
document.write( "d. 13.2 seconds </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107948 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=107948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-2.6t%5E2+%2B+32.1t+%2B+5.5 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-2.6t%5E2+%2B+32.1t+%2B+5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35+=+-2.6t%5E2+%2B+32.1t+%2B+5.5 ALIGN=MIDDLE  ALT=\"35+=+-2.6t%5E2+%2B+32.1t+%2B+5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29=35 ALIGN=MIDDLE  ALT=\"h%28t%29=35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2835%29=10%28-2.6t%5E2%2B32.1t%2B5.5%29 ALIGN=MIDDLE  ALT=\"10%2835%29=10%28-2.6t%5E2%2B32.1t%2B5.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 10 to clear out the decimals.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=350=-26t%5E2%2B321t%2B55 ALIGN=MIDDLE  ALT=\"350=-26t%5E2%2B321t%2B55\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-26t%5E2%2B321t%2B55-350 ALIGN=MIDDLE  ALT=\"0=-26t%5E2%2B321t%2B55-350\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 350 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-26t%5E2%2B321t-295 ALIGN=MIDDLE  ALT=\"0=-26t%5E2%2B321t-295\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for t\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%28321%29+%2B-+sqrt%28+%28321%29%5E2-4%28-26%29%28-295%29+%29%29%2F%282%28-26%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-%28321%29+%2B-+sqrt%28+%28321%29%5E2-4%28-26%29%28-295%29+%29%29%2F%282%28-26%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-26 ALIGN=MIDDLE  ALT=\"a=-26\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=321 ALIGN=MIDDLE  ALT=\"b=321\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-295 ALIGN=MIDDLE  ALT=\"c=-295\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-321+%2B-+sqrt%28+103041-4%28-26%29%28-295%29+%29%29%2F%282%28-26%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-321+%2B-+sqrt%28+103041-4%28-26%29%28-295%29+%29%29%2F%282%28-26%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=321 ALIGN=MIDDLE  ALT=\"321\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=103041 ALIGN=MIDDLE  ALT=\"103041\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-321+%2B-+sqrt%28+103041-30680+%29%29%2F%282%28-26%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-321+%2B-+sqrt%28+103041-30680+%29%29%2F%282%28-26%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-26%29%28-295%29 ALIGN=MIDDLE  ALT=\"4%28-26%29%28-295%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30680 ALIGN=MIDDLE  ALT=\"30680\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-321+%2B-+sqrt%28+72361+%29%29%2F%282%28-26%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-321+%2B-+sqrt%28+72361+%29%29%2F%282%28-26%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30680 ALIGN=MIDDLE  ALT=\"30680\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=103041 ALIGN=MIDDLE  ALT=\"103041\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72361 ALIGN=MIDDLE  ALT=\"72361\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-321+%2B-+sqrt%28+72361+%29%29%2F%28-52%29 ALIGN=MIDDLE  ALT=\"t+=+%28-321+%2B-+sqrt%28+72361+%29%29%2F%28-52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-26 ALIGN=MIDDLE  ALT=\"-26\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-52 ALIGN=MIDDLE  ALT=\"-52\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-321+%2B-+269%29%2F%28-52%29 ALIGN=MIDDLE  ALT=\"t+=+%28-321+%2B-+269%29%2F%28-52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72361 ALIGN=MIDDLE  ALT=\"72361\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=269 ALIGN=MIDDLE  ALT=\"269\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-321+%2B+269%29%2F%28-52%29 ALIGN=MIDDLE  ALT=\"t+=+%28-321+%2B+269%29%2F%28-52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-321+-+269%29%2F%28-52%29 ALIGN=MIDDLE  ALT=\"t+=+%28-321+-+269%29%2F%28-52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-52%29%2F%28-52%29 ALIGN=MIDDLE  ALT=\"t+=+%28-52%29%2F%28-52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=++%28-590%29%2F%28-52%29 ALIGN=MIDDLE  ALT=\"t+=++%28-590%29%2F%28-52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1 ALIGN=MIDDLE  ALT=\"t+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+295%2F26 ALIGN=MIDDLE  ALT=\"t+=+295%2F26\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So our answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1 ALIGN=MIDDLE  ALT=\"t+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+295%2F26 ALIGN=MIDDLE  ALT=\"t+=+295%2F26\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "where the second answer approximates <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+11.346 ALIGN=MIDDLE  ALT=\"t+=+11.346\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So when the ball is initially at 35 feet, the time is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1 ALIGN=MIDDLE  ALT=\"t+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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