document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193387>Question 193387</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please check my work, thank you.\r<BR>\n" );
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document.write( "Practical Application of Quadratic Equations \r<BR>\n" );
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document.write( "1.	A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet? <BR>\n" );
document.write( "Ag = area of garden = 15 * 11 = 165 sq feet\r<BR>\n" );
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document.write( "Ap = area of gravel path = (15 + 2x)(11 + 2x) - 165\r<BR>\n" );
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document.write( "Ap = 165 + 52x + 4x^2 - 165\r<BR>\n" );
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document.write( "Ap = 4x^2 + 5x\r<BR>\n" );
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document.write( "where\r<BR>\n" );
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document.write( "x = width of the gravel path around the garden\r<BR>\n" );
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document.write( "and since the available gravel is 192 sq ft, then the above equation becomes\r<BR>\n" );
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document.write( "4x2 + 5x = 192\r<BR>\n" );
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document.write( "and rewriting,\r<BR>\n" );
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document.write( "4x2 + 5x - 192 = 0\r<BR>\n" );
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document.write( "Using the quadratic formula,\r<BR>\n" );
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document.write( "x = 6.33 feet\r<BR>\n" );
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document.write( "ANSWER: The width of the gravel path should be about 6' 4\".<BR>\n" );
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document.write( "2.	A business invests $8,000 in a savings account for two years.  At the beginning of the second year, an additional $2,500 is invested.  At the end of the second year, the account balance is $11,445.  What was the annual interest rate? \r<BR>\n" );
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document.write( "the annual interest rate = r <BR>\n" );
document.write( "$8,000 in a savings account for two years.--> 8000*(1+r)^2<BR>\n" );
document.write( "beginning of the second year, an additional $2,500 is invested-->2500*(100+r)<BR>\n" );
document.write( "8000*(1+r)^2 + 2500*(1+r) = 11,445<BR>\n" );
document.write( "suppose 100+r = A<BR>\n" );
document.write( "8000*A^2 + 2500*A = 11,445<BR>\n" );
document.write( "8000*A^2 + 2500*A - 11,445 = 0<BR>\n" );
document.write( "A = 1.05<BR>\n" );
document.write( "r = 0.05 or 5 % Ans.\r<BR>\n" );
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document.write( "3.	Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle. \r<BR>\n" );
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document.write( "Let R = rate of Steve<BR>\n" );
document.write( "150/R – 150/(R + 20) = 2<BR>\n" );
document.write( "150(R+ 20) – 150(R) = 2(R)(R + 20)<BR>\n" );
document.write( "150R + 3000 – 150R = 2Rē + 40R<BR>\n" );
document.write( "0 = 2Rē + 40R – 3000 <BR>\n" );
document.write( "Rē + 20R – 1500 = 0<BR>\n" );
document.write( "(R + 50)(R – 30) = 0<BR>\n" );
document.write( "(R + 50) = 0<BR>\n" );
document.write( "R = –50 Discard, negative rate<BR>\n" );
document.write( "(R – 30) = 0<BR>\n" );
document.write( "R = 30 mph (speed of vehicle)\r<BR>\n" );
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document.write( "4.	The Hudson River flows at a rate of 5 miles per hour.  A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours.  What is the speed of the boat in still water?<BR>\n" );
document.write( "Let R = rate of patrol boat<BR>\n" );
document.write( "40/(R – 5) + 40(R + 5) = 6<BR>\n" );
document.write( "40(R + 5) + 40(R + 5) = 6(R + 5)(R – 5)<BR>\n" );
document.write( "40R – 200 + 40R + 200 = 6Rē – 150<BR>\n" );
document.write( "0 = 6Rē – 80R – 150<BR>\n" );
document.write( "3Rē – 40R – 75 = 0<BR>\n" );
document.write( "(3R + 5)(R – 15) = 0<BR>\n" );
document.write( "(3R + 5) = 0<BR>\n" );
document.write( "3R = –5<BR>\n" );
document.write( "R = –5/3 Discard, negative rate<BR>\n" );
document.write( "(R – 15) = 0<BR>\n" );
document.write( "R = 15 mph (speed of boat in still water) </SPAN>\n" );
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