document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192718>Question 1192718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The car is moving south at a constant speed of 40km/h. The second car was initially located 60 km west of the first car, moving southeast at 50 km/h. What is the minimum distance between these two cars? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848819 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=848819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'm not sure what amarjeeth123 is doing but their solution is completely incorrect. <BR>\n" );
document.write( "Perhaps they are blindly using AI. Or they might have mixed up two different problems.\r<BR>\n" );
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document.write( "ikleyn has the correct steps and correct answer. <BR>\n" );
document.write( "The approximate answer will vary depending how your teacher wants you to round it.\r<BR>\n" );
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document.write( "You can use a graphing tool such as <a  rel=nofollow HREF=\"https://www.geogebra.org/calculator\">GeoGebra</a> or <a  rel=nofollow HREF=\"https://www.desmos.com/calculator\">Desmos</a> to verify.<BR>\n" );
document.write( "I'll use the 1st option.\r<BR>\n" );
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document.write( "Before plotting the function, let's set up the window parameters.<BR>\n" );
document.write( "There are many options to go with, but this is what I picked<BR>\n" );
document.write( "xMin = -1<BR>\n" );
document.write( "xMax = 3<BR>\n" );
document.write( "yMin = -10<BR>\n" );
document.write( "yMax = 30<BR>\n" );
document.write( "These parameters will help us see the overall shape of the curve.<BR>\n" );
document.write( "The curve will appear to be parabolic, but it's not an actual parabola.<BR>\n" );
document.write( "The key point we're after is the lowest point to determine minimum distance.\r<BR>\n" );
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document.write( "The function to plot would be<BR>\n" );
document.write( "d(x) = sqrt((4100-2000*sqrt(2))*x^2-3000x*sqrt(2)+3600)<BR>\n" );
document.write( "which is the same as writing<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28x%29+=+sqrt%28%284100-2000%2Asqrt%282%29%29%2Ax%5E2-3000x%2Asqrt%282%29%2B3600%29 ALIGN=MIDDLE  ALT=\"d%28x%29+=+sqrt%28%284100-2000%2Asqrt%282%29%29%2Ax%5E2-3000x%2Asqrt%282%29%2B3600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the distance function ikleyn mentioned in her steps. <BR>\n" );
document.write( "I'm using x in place of t so the function can be plotted, and also took the square root of both sides.\r<BR>\n" );
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document.write( "You can type that function into the GeoGebra input bar.<BR>\n" );
document.write( "To save time and avoid potential typos, here is what to copy/paste into the input bar.<BR>\n" );
document.write( "<font color=blue>sqrt((4100-2000*sqrt(2))*x^2-3000x*sqrt(2)+3600)</font>\r<BR>\n" );
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document.write( "If you prefer to use Desmos, then you should not copy/paste what is shown in blue above.<BR>\n" );
document.write( "Instead you should copy/paste this<BR>\n" );
document.write( "<font color=blue>\sqrt{(4100-2000\sqrt{2})x^2-3000x\sqrt{2}+3600}</font><BR>\n" );
document.write( "This is the <a  rel=nofollow HREF=\"https://en.wikipedia.org/wiki/LaTeX\">LaTex</a> format of the distance expression which Desmos knows how to process.<BR>\n" );
document.write( "Desmos cannot handle stuff like sqrt(2) when it is pasted in. Instead of displaying the square root it displays the literal text string \"sqrt\" without quotes. \r<BR>\n" );
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document.write( "Whichever graphing tool you end up using, click on the lowest point of the curve to have the coordinates (1.66826,<font color=red>7.8151</font>) show up.<BR>\n" );
document.write( "Those decimal values are approximate.<BR>\n" );
document.write( "At around t = 1.66826 hours, the two cars would be at a minimum distance of roughly <font color=red>7.8151 km</font>.<BR>\n" );
document.write( "The approximate answer will vary depending how you round it.\r<BR>\n" );
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document.write( "There isn't a way to change the rounding precision in Desmos. Use GeoGebra if you need more accuracy. Click the gear icon, go to \"settings\", then click the next gear icon to bring up the \"global\" submenu.\r<BR>\n" );
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document.write( "Answer: <font color=red>7.8151 km (approximate)</font><BR>\n" );
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