document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102209>Question 102209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Building on question 95079, I have the part that goes like this:The only part of the height equation that we have not discussed is the constant. You have<BR>\n" );
document.write( "probably noticed that the constant is always equal to the initial height of the ball (80 m in<BR>\n" );
document.write( "our previous exercises). Now, let’s have you develop a height equation.<BR>\n" );
document.write( "A ball is thrown upward from the roof of a building 100 m tall with an initial velocity<BR>\n" );
document.write( "of 20 m/s. Use this information for exercises 35 to 38.<BR>\n" );
document.write( "35. Science and medicine. Write the equation for the height of the ball.<BR>\n" );
document.write( "36. Science and medicine. When will the ball reach a height of 80 m?\r<BR>\n" );
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document.write( "I am trying to solve #36. So far I have:\r<BR>\n" );
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document.write( "h=-5t^2+20t+100<BR>\n" );
document.write( "0=t^2-4-20<BR>\n" );
document.write( "0= 4+or-sqrt-5^2-4*1*-20/2*1<BR>\n" );
document.write( "=4+or-sqrt16+80/2<BR>\n" );
document.write( "4=+or-sqrt96/2<BR>\n" );
document.write( "4+9.8/2=13.8/2=6.9<BR>\n" );
document.write( "4-9.8/2=5.8/2=2.9\r<BR>\n" );
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document.write( "am I anywhere near where I need to be? \r<BR>\n" );
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document.write( "Thank you so much.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74280 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=74280\">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=-5t%5E2%2B20t%2B100 ALIGN=MIDDLE  ALT=\"h=-5t%5E2%2B20t%2B100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation (assuming you did everything right for problem 35)\r<BR>\n" );
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document.write( "When the height is 80, this means h=80\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80=-5t%5E2%2B20t%2B100 ALIGN=MIDDLE  ALT=\"80=-5t%5E2%2B20t%2B100\"   DISABLED_style= \"max-width:90%; height:auto;\" > So plug in h=80\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-5t%5E2%2B20t%2B20 ALIGN=MIDDLE  ALT=\"0=-5t%5E2%2B20t%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 80 from both sides\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( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2%2Bbt%2Bc=0 ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\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%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2At%5E2%2B20%2At%2B20=0 ALIGN=MIDDLE  ALT=\"-5%2At%5E2%2B20%2At%2B20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-5 ALIGN=MIDDLE  ALT=\"a=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=20 ALIGN=MIDDLE  ALT=\"b=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=20 ALIGN=MIDDLE  ALT=\"c=20\"   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+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A-5%2A20+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A-5%2A20+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-5, b=20, and c=20\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+sqrt%28+400-4%2A-5%2A20+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+400-4%2A-5%2A20+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 20 to get 400  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+sqrt%28+400%2B400+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+400%2B400+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A20%2A-5 ALIGN=MIDDLE  ALT=\"-4%2A20%2A-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400 ALIGN=MIDDLE  ALT=\"400\"   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+=+%28-20+%2B-+sqrt%28+800+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+800+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+20%2Asqrt%282%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+20%2Asqrt%282%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+20%2Asqrt%282%29%29%2F-10 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+20%2Asqrt%282%29%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -5 to get -10\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B+20%2Asqrt%282%29%29%2F-10 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B+20%2Asqrt%282%29%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+-+20%2Asqrt%282%29%29%2F-10 ALIGN=MIDDLE  ALT=\"t+=+%28-20+-+20%2Asqrt%282%29%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-20%2F-10%2B20%2Asqrt%282%29%2F-10 ALIGN=MIDDLE  ALT=\"t=-20%2F-10%2B20%2Asqrt%282%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-20%2F-10-20%2Asqrt%282%29%2F-10 ALIGN=MIDDLE  ALT=\"t=-20%2F-10-20%2Asqrt%282%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2-2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"t=2-2%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2%2B2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"t=2%2B2%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "However, since a negative time doesn't make sense, our only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4.82842712474619 ALIGN=MIDDLE  ALT=\"t=4.82842712474619\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So at about 4.8 seconds the ball will be 80 m high<BR>\n" );
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