document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=823745>Question 823745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle has one vertex in quadrant I on the graph of y=10-x^2, another at the origin, one on the positive x-axis, and one on the positive y-axis.  <BR>\n" );
document.write( "a.) Express the area A of the rectangle as a function of x.<BR>\n" );
document.write( "b.) Find the largest area A that can be enclosed by the rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #495855 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=495855\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "y = 10 - x^2<BR>\n" );
document.write( "y = -x^2 + 10<BR>\n" );
document.write( "---<BR>\n" );
document.write( "it is well known that the area of a rectangle is maximized when its sides are of equal length, in other words, when the rectangle is a square<BR>\n" );
document.write( "as such:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = x = -x^2 + 10<BR>\n" );
document.write( "-x^2 - x + 10 = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the above quadratic equation is in standard form, with a=-1, b=-1, and c=10<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to solve the quadratic equation, by using the quadratic formula, copy and paste this:<BR>\n" );
document.write( "-1 -1 10<BR>\n" );
document.write( "into this solver: https://sooeet.com/math/quadratic-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "this quadratic has two real roots (the x-intercepts), which are:<BR>\n" );
document.write( "x = -3.70156212<BR>\n" );
document.write( "x = 2.70156212<BR>\n" );
document.write( "---<BR>\n" );
document.write( "negative length doesn't make sense for this problem, so use the positive root:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = length = 2.70156212 units<BR>\n" );
document.write( "y = width = 2.70156212 units<BR>\n" );
document.write( "NOTE: the problem statement does not specify units, but these could be any linear unit, such as m, cm, ft, etc.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answerA:<BR>\n" );
document.write( "express the area A of the rectangle as a function of x:<BR>\n" );
document.write( "A(x) = x * (-x^2 + 10)<BR>\n" );
document.write( "A(x) = -x^3 + 10x<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answerB:<BR>\n" );
document.write( "find the largest area A that can be enclosed by the rectangle:<BR>\n" );
document.write( "A = maximum area = (2.70156212)*(2.70156212)<BR>\n" );
document.write( "A = maximum area = 7.298437888218896 sq.units<BR>\n" );
document.write( "NOTE: the problem statement does not specify units, but these could be any square unit, such as m^2, cm^2, ft^2, etc.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );