document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124469>Question 124469</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0073268623/algebrahomeworkh>Elementary and Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Suppose Charle O'Brian hits a baseball straight upward at 150 ft/sec from a height of 5 ft.<BR>\n" );
document.write( "Use the formula to determine how long it takes the ball to return to the earth.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91231 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=91231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation you are looking for is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+V%5Bo%5Dt+%2B+h%5Bo%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+V%5Bo%5Dt+%2B+h%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D ALIGN=MIDDLE  ALT=\"V%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the initial velocity of + 150 ft/s and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bo%5D ALIGN=MIDDLE  ALT=\"h%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the initial height of 5 ft.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substituting these values into the equation results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+150t+%2B+5 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+150t+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "in which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29 ALIGN=MIDDLE  ALT=\"h%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the height of the ball above the ground at time t. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "You are interested in finding the time it takes for the ball to rise up as high as it will go, and <BR>\n" );
document.write( "then finally fall back to the ground where its height will be zero feet. So substitute<BR>\n" );
document.write( "zero for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29 ALIGN=MIDDLE  ALT=\"h%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-16t%5E2+%2B+150t+%2B+5 ALIGN=MIDDLE  ALT=\"0+=+-16t%5E2+%2B+150t+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "which (by switching sides) in the more standard form of a quadratic equation is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2+%2B+150t+%2B+5+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2+%2B+150t+%2B+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This in standard form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2+%2B+bt+%2B+c ALIGN=MIDDLE  ALT=\"at%5E2+%2B+bt+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > in which a = -16, b = +150, and c = 5. The quadratic<BR>\n" );
document.write( "formula tells you that for such standard form quadratic equations the answers for t will be<BR>\n" );
document.write( "in the form:<BR>\n" );
document.write( ".<BR>\n" );
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;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute the above values for a, b, and c and the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-150+%2B-+sqrt%28+150%5E2-4%2A%28-16%29%2A5+%29%29%2F%282%2A%28-16%29%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-150+%2B-+sqrt%28+150%5E2-4%2A%28-16%29%2A5+%29%29%2F%282%2A%28-16%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Determine the term under the radical.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%5E2+=+22500 ALIGN=MIDDLE  ALT=\"150%5E2+=+22500\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%2A%28-16%29%285%29=320 ALIGN=MIDDLE  ALT=\"%28-4%29%2A%28-16%29%285%29=320\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "So the term under the radical becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22500+%2B+320+=+22820 ALIGN=MIDDLE  ALT=\"22500+%2B+320+=+22820\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute this and the equation is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-150+%2B-+sqrt%28+22820%29%29%2F%282%2A%28-16%29%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-150+%2B-+sqrt%28+22820%29%29%2F%282%2A%28-16%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "And <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2822820%29+=+151.0629008 ALIGN=MIDDLE  ALT=\"sqrt%2822820%29+=+151.0629008\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute this square root into the equation and you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-150+%2B-+151.0629008%29%2F%282%2A%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-150+%2B-+151.0629008%29%2F%282%2A%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The denominator multiplies out to -32 which makes the equation for t become:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-150+%2B-+151.0629008%29%2F%28-32%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-150+%2B-+151.0629008%29%2F%28-32%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "t must be a positive value (negative t doesn't make sense). Since the denominator is<BR>\n" );
document.write( "negative, the numerator must also be negative to give a positive answer for t. The only way<BR>\n" );
document.write( "to make the numerator negative is if both terms in the numerator are negative. Therefore, you<BR>\n" );
document.write( "can forget about the + sign in the numerator and you only need to solve the equation:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-150+-+151.0629008%29%2F%28-32%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-150+-+151.0629008%29%2F%28-32%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Combining the two terms in the numerator results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-301.0629008%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-301.0629008%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and dividing the numerator by the denominator results in an answer of:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+9.40821565 ALIGN=MIDDLE  ALT=\"t+=+9.40821565\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "This rounds of to an answer of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+9.41 ALIGN=MIDDLE  ALT=\"t+=+9.41\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem. <BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );