document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=378590>Question 378590</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is -16^2 + 96 feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tossed is -16^2 +80t feet.<BR>\n" );
document.write( "a)	Find the polynomial D (t) that represents the difference in the heights of the two balls.<BR>\n" );
document.write( "b)	How much higher is the red ball 2 seconds after the balls are tossed?<BR>\n" );
document.write( "c)	In reality, when does the difference in the heights stop increasing?\r<BR>\n" );
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document.write( "I need them worked out so I can write them down. I need to see it so I can understand it also. I hope someone can help me.<BR>\n" );
document.write( "Thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #268928 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=268928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is -16^2 + 96 feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tossed is -16^2 +80t feet.<BR>\n" );
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document.write( "a)Find a polynomial D(t) that represents the difference in the heights of the two balls.<BR>\n" );
document.write( "D(t) = (-16t^2 + 96t) - (-16t^2 +80t)<BR>\n" );
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document.write( "Remove brackets<BR>\n" );
document.write( "D(t) = -16t^2 + 96t + 16t^2 - 80t<BR>\n" );
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document.write( "combine like terms:<BR>\n" );
document.write( "D(t) = 16t<BR>\n" );
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document.write( "b)How much higher is the red ball 2 seconds after the balls are tossed?<BR>\n" );
document.write( "D(t) = 16(2)<BR>\n" );
document.write( "D(t) = 32 ft difference after 2 seconds<BR>\n" );
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document.write( "c) In reality, when does the difference in the heights stop increasing?<BR>\n" );
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document.write( "Obviously, when one of the balls hits the ground<BR>\n" );
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document.write( "Find when the lowest ball hits the ground (h=0)<BR>\n" );
document.write( "-16t^2 + 80t = 0<BR>\n" );
document.write( "Factor out -16t<BR>\n" );
document.write( "-16t(t - 5) = 0<BR>\n" );
document.write( "t = 5 seconds when the difference stops increasing;<BR>\n" );
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document.write( "A graph illustrates this well<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+8%2C+-20%2C+150%2C+-16x%5E2%2B96x%2C+-16x%5E2%2B80x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+8%2C+-20%2C+150%2C+-16x%5E2%2B96x%2C+-16x%5E2%2B80x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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