document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=570989>Question 570989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.) Suppose that x and y are real numbers with x + 3y =20.<BR>\n" );
document.write( "a.)Find the smallest value of x^2 + y^2.<BR>\n" );
document.write( "b)Find the greatest value of xy.<BR>\n" );
document.write( "c.) Find the smallest value of (x-y)^2.<BR>\n" );
document.write( "d.)The greatest value of y^2 - x^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2,) Sally worked 50 hrs last week and made $495 for the week. For every hour worked over 40 hours, her job pays time and a half. What is sally's hourly pay rate. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367897 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=367897\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.) Suppose that x and y are real numbers with x + 3y =20.<BR>\n" );
document.write( "a.)Find the smallest value of x^2 + y^2.<BR>\n" );
document.write( "b)Find the greatest value of xy.<BR>\n" );
document.write( "c.) Find the smallest value of (x-y)^2.<BR>\n" );
document.write( "d.)The greatest value of y^2 - x^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2,) Sally worked 50 hrs last week and made $495 for the week. For every hour worked over 40 hours, her job pays time and a half. What is sally's hourly pay rate.<BR>\n" );
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document.write( "a) Express y in terms of x:<BR>\n" );
document.write( "y = (1/3)(20-x)<BR>\n" );
document.write( "So x^2 + y^2 = x^2 + [(1/3)(20-x)]^2 = x^2 + (1/9)(400-40x+x^2)<BR>\n" );
document.write( "Collecting terms gives (10/9)x^2 -(40/9)x + 400/9<BR>\n" );
document.write( "This expression is minimized when the derivative equals 0:<BR>\n" );
document.write( "(20/9)x - 40/9 = 0<BR>\n" );
document.write( "This gives x = 2<BR>\n" );
document.write( "So y = (1/3)(20-2) = 6<BR>\n" );
document.write( "So the smallest value is 2^2 + 6^2 = 40<BR>\n" );
document.write( "b) xy = (x/3)*(20-x) = (20/3)x - (1/3)x^2<BR>\n" );
document.write( "The expression will be a maximum when the derivative=0:<BR>\n" );
document.write( "0 = 20/3 - (2/3)x<BR>\n" );
document.write( "This gives x = 10<BR>\n" );
document.write( "Therefore y = 10/3<BR>\n" );
document.write( "The maximum value is 10*10/3 = 100/3<BR>\n" );
document.write( "...I'll leave the other two for you to do...<BR>\n" );
document.write( "2) Let x = Sally's hourly pay<BR>\n" );
document.write( "Her total pay will be the hourly pay times 40 hrs plus 10 hrs working at time and a half:<BR>\n" );
document.write( "495 = 40x + 10*3x/2 = 40x + 15x = 55x<BR>\n" );
document.write( "This gives x = 9<BR>\n" );
document.write( "Her hourly salary is $9 </SPAN>\n" );
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