document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153645>Question 1153645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A light shines toward the ground from the top of a building wall that is 40 ft<BR>\n" );
document.write( "high. A kid in a tree house that is 25ft to the right of the building drops an apple from the same height (40 ft). How fast is the shadow of the apple moving along the ground ½ sec later? Assume the apple falls at a distance 𝑠 = 16𝑡^2 in t seconds. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #776041 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=776041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first draw it:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28+600%2C+600%2C+-10%2C+15%2C+-10%2C+10%2C%0D%0A%0D%0Acircle%280%2C8%2C.14%29%2Ccircle%285%2C8%2C.12%29%2C%0D%0Agreen%28line%285%2C8%2C5%2C0%29%29%2Ccircle%285%2C5.2%2C.12%29%2Ccircle%2814%2C0%2C.12%29%2Cgreen%28line%280%2C8%2C14%2C0%29%29%2C%0D%0Alocate%280.5%2C4%2C40ft%29%2Clocate%282.5%2C0.5%2C25ft%29%2Clocate%287.5%2C0.5%2Cx-25ft%29%2Clocate%285%2C5.6%2C%281%2F2%29s-later%29%2Clocate%285.3%2C3%2C40ft-s%29%2Cline%280%2C-1%2C14%2C-1%29%2Clocate%285%2C-0.5%2Cx%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+15%2C+-10%2C+10%2C+0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "given: \r<BR>\n" );
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document.write( "a building wall that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40ft ALIGN=MIDDLE  ALT=\"40ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > high<BR>\n" );
document.write( "a tree house that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25ft ALIGN=MIDDLE  ALT=\"25ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the right of the building<BR>\n" );
document.write( "the shadow of the apple moving along the ground <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec later\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=16%F0%9D%91%A1%5E2 ALIGN=MIDDLE  ALT=\"s=16%F0%9D%91%A1%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds \r<BR>\n" );
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document.write( "two right triangles are similar, means corresponding sides are proportional\r<BR>\n" );
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document.write( "so,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x-24%29=40%2F%2840-s%29 ALIGN=MIDDLE  ALT=\"x%2F%28x-24%29=40%2F%2840-s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2840-s%29=40%28x-24%29 ALIGN=MIDDLE  ALT=\"x%2840-s%29=40%28x-24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2840x%29-xs=cross%2840x%29-960 ALIGN=MIDDLE  ALT=\"cross%2840x%29-xs=cross%2840x%29-960\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-xs=-960 ALIGN=MIDDLE  ALT=\"-xs=-960\"   DISABLED_style= \"max-width:90%; height:auto;\" >....multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xs=960 ALIGN=MIDDLE  ALT=\"xs=960\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=960%2Fs ALIGN=MIDDLE  ALT=\"x=960%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Differentiating with respect to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dx%2Fdt=-%28960%2Fs%5E2%29%28ds%2Fdt%29 ALIGN=MIDDLE  ALT=\"dx%2Fdt=-%28960%2Fs%5E2%29%28ds%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We are given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=16t%5E2 ALIGN=MIDDLE  ALT=\"s=16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >⇒ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ds%2Fdt+=+32t ALIGN=MIDDLE  ALT=\"ds%2Fdt+=+32t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " At <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1%2F2 ALIGN=MIDDLE  ALT=\"t+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+16%281%2F2%29%5E2=16%2F4+=+4 ALIGN=MIDDLE  ALT=\"s+=+16%281%2F2%29%5E2=16%2F4+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ds%2Fdt+=+32%2F2+=+16 ALIGN=MIDDLE  ALT=\"ds%2Fdt+=+32%2F2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Plugging these in we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dx%2Fdt=-%28960%2F4%5E2%29%2816%29%28ft%2Fs%29=-960%28ft%2Fs%29 ALIGN=MIDDLE  ALT=\"dx%2Fdt=-%28960%2F4%5E2%29%2816%29%28ft%2Fs%29=-960%28ft%2Fs%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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