document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218172>Question 218172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help finding the equation of the upper half of the circle and the domain.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2By%5E2=10+ ALIGN=MIDDLE  ALT=\"+x%5E2%2By%5E2=10+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I am particularly having trouble finding the domain.\r<BR>\n" );
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document.write( "Thank you in advance.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164335 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=164335\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equation of the circle is x^2 + y^2 = 10<BR>\n" );
document.write( "solve for y:<BR>\n" );
document.write( "y^2 = 10-x^2<BR>\n" );
document.write( "y = +/- sqrt(10-x^2))<BR>\n" );
document.write( "You want the upper half of the circle only, so you want:<BR>\n" );
document.write( "y = sqrt(10-x^2))<BR>\n" );
document.write( "You will reject y = -sqrt(10-x^2) because that would give you the bottom half of the circle which you don't want.<BR>\n" );
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document.write( "Your domain is determined by sqrt(10-x^2))<BR>\n" );
document.write( "Your domain has to result in real values of y in your range.<BR>\n" );
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document.write( "If sqrt(10-x^2) is positive or 0, then your equation is valid because that would result in real values of y in your range.<BR>\n" );
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document.write( "If sqrt(10-x^2) is negative, then your equation is invalid because you would have the square root of a negative number which would not result in real values of y in your range.<BR>\n" );
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document.write( "You need to find out when 10-x^2 is >= 0<BR>\n" );
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document.write( "add x^2 to both sides of this equation to get:<BR>\n" );
document.write( "10 >= x^2<BR>\n" );
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document.write( "multiply both sides of this equation by -1 to get:<BR>\n" );
document.write( "-10 <= -x^2<BR>\n" );
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document.write( "add x^2 to both sides of this equation and add 10 to both sides of this equation to get:<BR>\n" );
document.write( "x^2 <= 10<BR>\n" );
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document.write( "Your domain will result in real values of y in your range when x^2 <= 10.<BR>\n" );
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document.write( "x^2 is <= 10 when x < sqrt(10) and when -x > - sqrt(10)<BR>\n" );
document.write( "Let x = sqrt(10), then x^2 = 10<BR>\n" );
document.write( "Let x = -sqrt(10), then x^2 = 10<BR>\n" );
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document.write( "Your domain is when -sqrt(10) <= x <= sqrt(10)<BR>\n" );
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document.write( "A graph of your equation is shown below:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Csqrt%2810-x%5E2%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Csqrt%2810-x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "since sqrt(10) = +/- 3.16227766, the graph looks accurate as far as the naked eye can see.<BR>\n" );
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