document.write( "Question 1099839: I am in College Algebra but the question seemed to fit in this category...The base and sides of a container are made of wood panels. The container does not have a top. The base and sides are rectangular. The width is x cm. The length is 4 times the width. The volume is 600 cm^3. Determine the minimum surface area to two decimal places. \n" ); document.write( "

Algebra.Com's Answer #714336 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Since the tutor @ankor@dixie-net.com made several mistakes in his solution, I re-write and edit it in correct way.\r
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document.write( "The container does not have a top.\r\n" );
document.write( "The base and sides are rectangular. \r\n" );
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document.write( "The width is x cm. The length is 4 times the width.\r\n" );
document.write( "The volume is 600 cm^3.\r\n" );
document.write( "Determine the minimum surface area to two decimal places. \r\n" );
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document.write( "let h = the height of the box\r\n" );
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document.write( "Given\r\n" );
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document.write( "x = the width\r\n" );
document.write( "4x = the length\r\n" );
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document.write( "Volume\r\n" );
document.write( "4x * x * h = 600\r\n" );
document.write( "4x^2 * h = 600\r\n" );
document.write( "h = \r\n" );
document.write( "cancel the 4\r\n" );
document.write( "h =                    <<<---=== I replaced 120 by 150\r\n" );
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document.write( "Surface area\r\n" );
document.write( "S.A. =(4x*x) + 2(4x*h) + 2(x*h)\r\n" );
document.write( "S.A. = 4x^2 + 8xh + 2xh\r\n" );
document.write( "S.A. = 4x^2 + 10xh\r\n" );
document.write( "replace h with \r\n" );
document.write( "S.A. = 4x^2 + 10x*\r\n" );
document.write( "Cancel x\r\n" );
document.write( "S.A. = 4x^2 + \r\n" );
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document.write( "plot the equation y = 4x^2 + (1500/x), where y = the surface area\r\n" );
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document.write( "Taking the derivative y' = 8x - 1500/x^2 = ,    <<<---=== I re-wrote this part\r\n" );
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document.write( "you will find the minimum surface area occurs when x = = 5.72  \r\n" );
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document.write( "Find the minimum surface area\r\n" );
document.write( "S.A. = \r\n" );
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document.write( "Answer  S.A. = 393.1 cm^2. \r\n" );
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