document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=754534>Question 754534</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two projectiles are simultaneously launched. The height in meters , h(base 1) t and h(base 2)t of the first and second projectiles as a function of time t in seconds since the launch are given by the rules h(base 1)t = -2t^2+ 20t + 50 and h(base 2) = 2t +66 .<BR>\n" );
document.write( "a) How long after their launch will the two projectiles be at the same height?<BR>\n" );
document.write( "b) Over what interval of time since the launch is the first projectile higher than the second?\r<BR>\n" );
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document.write( "Can you please help me out? Thanks so much in advance:)<BR>\n" );
document.write( "Can you also please show the steps it would really help me understand:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #459148 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=459148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> h(base 1)t = -2t^2+ 20t + 50 and h(base 2) = 2t +66 .<BR>\n" );
document.write( "a) How long after their launch will the two projectiles be at the same height?<BR>\n" );
document.write( "Solve:<BR>\n" );
document.write( "-2t^2 + 20t + 50 = 2t+66<BR>\n" );
document.write( "-2t^2 + 18t - 16 = 0<BR>\n" );
document.write( "t^2 - 9t + 8 = 0<BR>\n" );
document.write( "(t-8)(t-1) = 0<BR>\n" );
document.write( "t = 1 second (1st time they are at the same height)<BR>\n" );
document.write( "t = 8 seconds (2nd time they are at the same height)<BR>\n" );
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document.write( "b) Over what interval of time since the launch is the first projectile higher than the second?<BR>\n" );
document.write( "1sec < t < 8 sec<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C100%2C-2x%5E2%2B20x%2B50%2C2x%2B66%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C100%2C-2x%5E2%2B20x%2B50%2C2x%2B66%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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