document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199938>Question 1199938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cliff left point A at 8:00 A.M walking east at 3 kph. Renz left point A at 9:00 A.M walking north at 4 kph. The distance between the two boys since 8:00 A.M may be expressed as d(t)= √(〖at〗^2-2βt+β) where d and t denote the respective distance and time. Find a+β. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848203 by </B><A HREF=/tutors/aboutme.mpl?userid=textot><B>textot(100)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=textot><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=848203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Determine the Distances Traveled**\r<BR>\n" );
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document.write( "* **Cliff:** Since Cliff started 1 hour earlier and walks at 3 kph, he has traveled 3 km east by 9:00 AM.<BR>\n" );
document.write( "* **Renz:** Let 't' be the time in hours since 9:00 AM. Renz travels 4t kilometers north.\r<BR>\n" );
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document.write( "**2. Use Pythagorean Theorem**\r<BR>\n" );
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document.write( "* The distance between Cliff and Renz at time 't' can be found using the Pythagorean theorem:\r<BR>\n" );
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document.write( "   d(t) = √[(Cliff's distance)² + (Renz's distance)²] <BR>\n" );
document.write( "   d(t) = √[(3 + 3t)² + (4t)²] <BR>\n" );
document.write( "   d(t) = √(9 + 18t + 9t² + 16t²) <BR>\n" );
document.write( "   d(t) = √(25t² + 18t + 9)\r<BR>\n" );
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document.write( "**3. Compare with the Given Expression**\r<BR>\n" );
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document.write( "* Compare the derived expression with the given expression: <BR>\n" );
document.write( "    * d(t) = √(at² + 2βt + β) <BR>\n" );
document.write( "    * d(t) = √(25t² + 18t + 9)\r<BR>\n" );
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document.write( "* We can see that:<BR>\n" );
document.write( "    * a = 25<BR>\n" );
document.write( "    * 2β = 18 <BR>\n" );
document.write( "        * β = 9\r<BR>\n" );
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document.write( "**4. Calculate a - β**\r<BR>\n" );
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document.write( "* a - β = 25 - 9 = 16\r<BR>\n" );
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document.write( "**Therefore, a - β = 16.**<BR>\n" );
document.write( " </SPAN>\n" );
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