document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129723>Question 129723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have some problems I got wrong on my test. Please explain step by step what I should have done. I am allowed four, so here they are.\r<BR>\n" );
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document.write( "1.) Pizza Unlimited has the following prices for pizzas. Price is related to diameter by a quadratic equation. Fit a quadratic equation into the data points (8, 3.39), (12, 5.12), and (16, 7.29). <BR>\n" );
document.write( "Diameter                         Price<BR>\n" );
document.write( "8 inch                             $3.39<BR>\n" );
document.write( "12 inch                           $5.12              <BR>\n" );
document.write( "16 inch                           $7.29<BR>\n" );
document.write( "A.)	Price =what quadratic equation?<BR>\n" );
document.write( "B.)	Using the equation find the price of a 14 inch pizza.<BR>\n" );
document.write( "I know the answers, but I did the problem wrong, will you please show me the steps? How did they get the equation?<BR>\n" );
document.write( "Answer A:   0.01375x^2 +0.1575x+1.25<BR>\n" );
document.write( "Answer B:   14 inch pizza costs $ 6.15\r<BR>\n" );
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document.write( "2.) Solve for x. (x-6)^2 + (x+1)^2 = 0<BR>\n" );
document.write( "The solutions are 5 + 7 i /2,    5-7 i/2<BR>\n" );
document.write( "How do I know when to place the “ I “ one there?<BR>\n" );
document.write( "Please show the step by step way to get this solution.\r<BR>\n" );
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document.write( "3.) What is the maximum product of two numbers whose sum is -6? What numbers yield this product? The max product is?<BR>\n" );
document.write( "I put the max product at 9 (incorrect) and the numbers yielding this product at -3, -3 (correct)<BR>\n" );
document.write( "However when I did the same problem with -16 instead of -6, I got 49 for the max product and it was correct. I thought the max product was the number in question squared. How do I get the max product?\r<BR>\n" );
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document.write( "4.) Solve the formula for the given number. Assume all variables represent positive numbers.<BR>\n" );
document.write( "(N=n^2 – 19 n)/6; for n<BR>\n" );
document.write( "I got n = (19 + sqrt sign 361 + 36 N)/2 (incorrect)<BR>\n" );
document.write( "The answer is n = (19 + sqrt sign 361 + 24 N)/2<BR>\n" );
document.write( "What did I do wrong, please show me the steps. \r<BR>\n" );
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document.write( "Thanks for all your help!!!!!!!!!!  :o)\r<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 #94740 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=94740\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) By data it is given that price is related to diameter by a quadratic equation.\r<BR>\n" );
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document.write( "A general quadratic equation is given by f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "We shall write it as y = f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "==> y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So now lets plug in all the given set of values, in the form of co-ordinates. This implies that it forms 3 equations.\r<BR>\n" );
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document.write( "3.39 = 64a + 8b + c  ------------(1)\r<BR>\n" );
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document.write( "5.12 = 144a + 12b + c  -----------(2)\r<BR>\n" );
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document.write( "7.29 = 256a + 16b + c -----------(3) \r<BR>\n" );
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document.write( "Let solve them simlutaneously.\r<BR>\n" );
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document.write( "Subtracting (1) & (2), we get:\r<BR>\n" );
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document.write( "1.73 = 80a + 4b --------------(4) \r<BR>\n" );
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document.write( "subtracting (2) & (3), we get:\r<BR>\n" );
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document.write( "2.17 = 112a + 4b ------------(5) \r<BR>\n" );
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document.write( "subtracting (4) & (5) \r<BR>\n" );
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document.write( "0.44 = 32a \r<BR>\n" );
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document.write( "==> a = 0.01375 \r<BR>\n" );
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document.write( "Now by back substituion we find b\r<BR>\n" );
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document.write( "1.73 - 1.1 = 4b \r<BR>\n" );
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document.write( "0.63 = 4b\r<BR>\n" );
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document.write( "==> b = 0.1575 \r<BR>\n" );
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document.write( "substitute the a and b value in one of the equations. So we get:\r<BR>\n" );
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document.write( "3.39 = 0.88 + 1.26 + c\r<BR>\n" );
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document.write( "3.39 - 2.14 = c\r<BR>\n" );
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document.write( "c = 1.25\r<BR>\n" );
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document.write( "Thus the quadratic equation would be \r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01375x%5E2+%2B+0.1575x+%2B+1.25 ALIGN=MIDDLE  ALT=\"0.01375x%5E2+%2B+0.1575x+%2B+1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Price of a 14 inch pizza would be just plug in x = 14 in the above equation we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0.01375%2814%29%5E2+%2B+0.1575%2814%29+%2B+1.25 ALIGN=MIDDLE  ALT=\"y+=+0.01375%2814%29%5E2+%2B+0.1575%2814%29+%2B+1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y = $6.15 \r<BR>\n" );
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document.write( "==============================================================================\r<BR>\n" );
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document.write( "2) Solve for x. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%5E2+%2B+%28x%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-6%29%5E2+%2B+%28x%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0\r<BR>\n" );
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document.write( "The given equation can be written as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+36+-+12x+%2B+x%5E2+%2B+1+%2B+2x ALIGN=MIDDLE  ALT=\"x%5E2+%2B+36+-+12x+%2B+x%5E2+%2B+1+%2B+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-+10x+%2B+37+ ALIGN=MIDDLE  ALT=\"2x%5E2+-+10x+%2B+37+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0 \r<BR>\n" );
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document.write( "Using the quadratic formula we find the roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Substituting for the values we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28+100-4%2A2%2A37+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28+100-4%2A2%2A37+%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+14i%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+14i%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Taking 2 as a common factor we get:\r<BR>\n" );
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document.write( "So the roots are: 5 + 7i/2 and 5 - 7i/2 \r<BR>\n" );
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document.write( "The solutions are 5 + 7 i /2, 5-7 i/2\r<BR>\n" );
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document.write( "3) What is the maximum product of two numbers whose sum is -6? What numbers yield this product? The max product is?\r<BR>\n" );
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document.write( "Let x and y be the two numbers.\r<BR>\n" );
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document.write( "It is given that the product is maximum and the sum is negative six.\r<BR>\n" );
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document.write( "so lets find the multiples of 6. They are + -1, +- 2, +-3, +-6 \r<BR>\n" );
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document.write( "Taking them 2 at a time we find that -3 and -3 when added gives us -6 \r<BR>\n" );
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document.write( "And their product gives us 9 which is the maximum number.\r<BR>\n" );
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document.write( "Hence the solution.\r<BR>\n" );
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document.write( "4) solve for \"n\" \r<BR>\n" );
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document.write( "N = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+%96+19n ALIGN=MIDDLE  ALT=\"n%5E2+%96+19n\"   DISABLED_style= \"max-width:90%; height:auto;\" >/6\r<BR>\n" );
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document.write( "This can be written as:\r<BR>\n" );
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document.write( "6N = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+-+19n ALIGN=MIDDLE  ALT=\"n%5E2+-+19n\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+-+19n+-+6N+=+0+ ALIGN=MIDDLE  ALT=\"n%5E2+-+19n+-+6N+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the quadratic formula we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%28-b+%2B-sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"n+=+%28-b+%2B-sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Substituing for the values, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%2819+%2B-+sqrt%28361+%2B+4%2A1%2A6N%29%29%2F2 ALIGN=MIDDLE  ALT=\"n+=+%2819+%2B-+sqrt%28361+%2B+4%2A1%2A6N%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%2819+%2B-+sqrt%28361+%2B+24N%29%29%2F2 ALIGN=MIDDLE  ALT=\"n+=+%2819+%2B-+sqrt%28361+%2B+24N%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Thus the solution.\r<BR>\n" );
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document.write( "Regards\r<BR>\n" );
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document.write( "If you stil have any doubts you can get back to me.. I'm a online teacher.. I'll help you..\r<BR>\n" );
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