document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208736>Question 1208736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The window of a house is 6m above ground. A rocket is set off from the ground at an initial velocity of 20m/s.<BR>\n" );
document.write( "For how many seconds will the rocket be at or above the window?<BR>\n" );
document.write( "Use the equation<BR>\n" );
document.write( "S(T)= -4.9T^2 + VoT + So to model the position S for a given time T, where Vo is the initial Velocity. </SPAN>\n" );
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document.write( "V<sub>0</sub> = initial velocity = 20 meters per second<BR>\n" );
document.write( "s<sub>0</sub> = initial height = 0 meters because it was launched on the ground\r<BR>\n" );
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document.write( "S(t) = -4.9t^2 + V<sub>0</sub>t + s<sub>0</sub><BR>\n" );
document.write( "S(t) = -4.9t^2 + 20t + 0<BR>\n" );
document.write( "S(t) = -4.9t^2 + 20t<BR>\n" );
document.write( "y = -4.9x^2 + 20x\r<BR>\n" );
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document.write( "Using a graphing tool like <a  rel=nofollow HREF=\"https://www.geogebra.org/calculator\">GeoGebra</a> or <a  rel=nofollow HREF=\"https://www.desmos.com/calculator\">Desmos</a> (among many other options), you should get the following graph<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28500%2C500%2C-2%2C5%2C-5%2C25%2C%0D%0Agraph%28500%2C500%2C-2%2C5%2C-5%2C25%2C-100%2C-4.9x%5E2+%2B+20x%29%2C%0D%0Aline%28-10%2C6%2C10%2C6%29%2C%0D%0A%0D%0Acircle%280.326%2C6%2C0.02%29%2Ccircle%280.326%2C6%2C0.03%29%2Ccircle%280.326%2C6%2C0.04%29%2Ccircle%280.326%2C6%2C0.05%29%2Ccircle%283.756%2C6%2C0.02%29%2Ccircle%283.756%2C6%2C0.03%29%2Ccircle%283.756%2C6%2C0.04%29%2Ccircle%283.756%2C6%2C0.05%29%2C%0D%0A%0D%0Alocate%280.326%2B0.1%2C6-0.5%2C%22A%22%29%2Clocate%283.756-0.15%2C6-0.5%2C%22B%22%29%2C%0D%0Alocate%281.5%2C3.8%2C%22A+=+%280.326%2C6%29%22%29%2C%0D%0Alocate%281.5%2C2.8-0.5%2C%22B+=+%283.756%2C6%29%22%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = -4.9x^2+20x is the parabola<BR>\n" );
document.write( "y = 6 is the horizontal line\r<BR>\n" );
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document.write( "The parabola and horizontal line intersect at points A and B.<BR>\n" );
document.write( "A = (0.326,6)<BR>\n" );
document.write( "B = (3.756,6)<BR>\n" );
document.write( "The decimal values are approximate. Round them however your teacher instructs.<BR>\n" );
document.write( "Another way to find these decimal solutions is to use the quadratic formula to solve -4.9x^2 + 20x - 6 = 0.\r<BR>\n" );
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document.write( "Therefore, the rocket's height is at or above 6 meters on the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.326+%3C=+t+%3C=+3.756 ALIGN=MIDDLE  ALT=\"0.326+%3C=+t+%3C=+3.756\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the portion of the curve between A and B.<BR>\n" );
document.write( "This duration is <font color=red>roughly 3.43 seconds</font> because 3.756-0.326 = <font color=red>3.43</font>\r<BR>\n" );
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document.write( "More practice is found <a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1208731.html\">here</a><BR>\n" );
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