document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206903>Question 1206903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small radio transmitter broadcasts in a 21 mile radius. If you drive along a straight line from a city 25 miles north of the transmitter to a second city 29 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844649 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=844649\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Circle equation<BR>\n" );
document.write( "(x-h)^2 + (y-k)^2 = r^2<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "(h,k) = center<BR>\n" );
document.write( "r = radius\r<BR>\n" );
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document.write( "Let's place the radio transmitter at the origin. Meaning h = 0 and k = 0.<BR>\n" );
document.write( "The radius is r = 21 in this case.<BR>\n" );
document.write( "The circle equation will then update to x^2+y^2 = 441<BR>\n" );
document.write( "Points inside the circle, or on the boundary, will get the radio signal. \r<BR>\n" );
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document.write( "A = (0,25) is where you start from since it is 25 miles north of the transmitter.<BR>\n" );
document.write( "B = (29,0) is where you are driving to, which is 29 miles east of the transmitter.<BR>\n" );
document.write( "I'll skip a few steps, but you should find the equation of line AB is y = (-25/29)x + 25\r<BR>\n" );
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document.write( "We have this system of equations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2%2By%5E2+=+441%2C+y+=+expr%28-25%2F29%29x+%2B+25%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2%2By%5E2+=+441%2C+y+=+expr%28-25%2F29%29x+%2B+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use substitution to plug the second equation into the first one to end up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28expr%28-25%2F29%29x+%2B+25%29%5E2+=+441 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28expr%28-25%2F29%29x+%2B+25%29%5E2+=+441\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Skipping a few more steps, the solutions to that equation are approximately: x = 5.48588 and x = 19.24127<BR>\n" );
document.write( "These are the x coordinates of the intersection points of the line and circle.<BR>\n" );
document.write( "Since we're looking at approximate solutions, it seems reasonable to assume your teacher will allow you to use a graphing calculator to make quick work of this equation. <BR>\n" );
document.write( "Note: The exact solutions involve very large messy numbers.\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.48588+%3C=+x+%3C=+19.24127 ALIGN=MIDDLE  ALT=\"5.48588+%3C=+x+%3C=+19.24127\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then points on line AB are inside the circle or on the circle's boundary. <BR>\n" );
document.write( "Otherwise, you'll be outside of the circle and won't pick up the signal.\r<BR>\n" );
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document.write( "Use those x values to determine the corresponding paired y values.<BR>\n" );
document.write( "x = 5.48588 leads to y = 20.2708<BR>\n" );
document.write( "Let point C be located at (5.48588, 20.2708)<BR>\n" );
document.write( "x = 19.24127 leads to y = 8.4127<BR>\n" );
document.write( "Let point D be located at (19.24127, 8.4127)\r<BR>\n" );
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document.write( "Diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=math_tutor2020&illustration_name=UploadedScreenshot_50.png\"><BR>\n" );
document.write( "The diagram was made with <a  rel=nofollow HREF=\"https://www.geogebra.org/calculator\">GeoGebra</a> which is a useful tool to verify many types of math problems.\r<BR>\n" );
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document.write( "Use the distance formula to determine these approximate segment lengths<BR>\n" );
document.write( "AB = 38.28838<BR>\n" );
document.write( "CD = 18.1611<BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "CD/AB = 18.1611/38.28838 = 0.47432\r<BR>\n" );
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document.write( "For roughly 47.432% of the trip, you'll be able to pick up this particular radio signal.<BR>\n" );
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