document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206150>Question 1206150</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown vertically upward with an initial velocity of 48  feet per second. The distance s​ (in feet) of the ball from the ground after t seconds is  s=48t−16t2<BR>\n" );
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document.write( "(a) At what time t will the ball strike the​ ground?<BR>\n" );
document.write( "​(b) For what time t is the ball more than 20 feet above the​ ground? </SPAN>\n" );
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document.write( "(a) The ball hits the ground when s, the height of the ball above the ground, is zero:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48t-16t%5E2=0 ALIGN=MIDDLE  ALT=\"48t-16t%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28t%29%283-t%29=0 ALIGN=MIDDLE  ALT=\"16%28t%29%283-t%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: at 3 seconds<br><BR>\n" );
document.write( "(b) We want the height of the ball to be greater than 20 feet:<br><BR>\n" );
document.write( "It's awkward to solve the quadratic inequality.  Instead, solve an equation to find the times when the height of the ball is exactly 20 feet.  Then use common sense to get the answer.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48t-16t%5E2=20 ALIGN=MIDDLE  ALT=\"48t-16t%5E2=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16t%5E2-48t%2B20=0 ALIGN=MIDDLE  ALT=\"16t%5E2-48t%2B20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4t%5E2-12t%2B5=0 ALIGN=MIDDLE  ALT=\"4t%5E2-12t%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282t-5%29%282t-1%29=0 ALIGN=MIDDLE  ALT=\"%282t-5%29%282t-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2.5 ALIGN=MIDDLE  ALT=\"t=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0.5 ALIGN=MIDDLE  ALT=\"t=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The ball is 20 feet off the ground at t=0.5 seconds and t=2.5 seconds, so it is more than 20 feet above the ground between those two times.<br><BR>\n" );
document.write( "ANSWER: between t=0.5 second and t=2.5 seconds<br><BR>\n" );
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