document.write( "Question 184347: 114. Surface area of a cube. The formula A =6V^2/3 gives
\n" ); document.write( "the surface area of a cube in terms of its volume V. What is the volume of a cube with surface area 12 square feet? \r
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\n" ); document.write( "\n" ); document.write( "110. Winston works faster. Winston can mow his dad’s lawn in 1 hour less than it takes his brother Willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone?
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\n" ); document.write( "\n" ); document.write( "114. Maximizing profit. The total profit (in dollars) for sales of x rowing machines is given by P(x)=-0+2x^2+300x-200 . What is the profit if 500 are sold? For what value of x will the profit be at a maximum?
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Algebra.Com's Answer #138461 by edjones(8007)\"\" \"About 
You can put this solution on YOUR website!
A =6V^(2/3)
\n" ); document.write( "6V^(2/3)=12
\n" ); document.write( "v^(2/3)=2 divide each side by 6
\n" ); document.write( "v^2=2^3 cube each side
\n" ); document.write( "v=2^(3/2)ft^3 Take sqrt of each side.
\n" ); document.write( "=sqrt(8)
\n" ); document.write( "=sqrt(4*2)
\n" ); document.write( "=2sqrt(2)
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\n" ); document.write( "Let n=winston's time
\n" ); document.write( "willie's time=n+1
\n" ); document.write( "In 1 hr winston can do 1/n of the job.
\n" ); document.write( "In 1 hr willie can do 1/(n+1) of the job
\n" ); document.write( "Together they can do 1/2 the job in 1 hr
\n" ); document.write( "1/n + 1/(n+1) = 1/2
\n" ); document.write( "2(n+1)+2n=n(n+1) Multiply each side by the LCM 2n(n+1)
\n" ); document.write( "2n+2+2n=n^2+n
\n" ); document.write( "4n+2=n^2+n
\n" ); document.write( "n^2-3n-2=0 subtract the left side from the right.
\n" ); document.write( "n=3.56...hrs winston's time. (see below)
\n" ); document.write( "4.56...hrs willie's time.
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\n" ); document.write( "I don't think you copied the 3rd question corectly because as written it gives a minimum not a maximum.
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\n" ); document.write( "Ed
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-3x%2B-2+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-3%29%5E2-4%2A1%2A-2=17\".
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\n" ); document.write( " Discriminant d=17 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--3%2B-sqrt%28+17+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+17+%29%29%2F2%5C1+=+3.56155281280883\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-3%29-sqrt%28+17+%29%29%2F2%5C1+=+-0.56155281280883\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-3x%2B-2\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-3x%2B-2+=+%28x-3.56155281280883%29%2A%28x--0.56155281280883%29\"
\n" ); document.write( " Again, the answer is: 3.56155281280883, -0.56155281280883.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-2+%29\"

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