document.write( "Question 1187065: A manufacturer wants to build a rectangular stainless tank with a holding capacity of 120 cubic feet. The manufacturer wants the dimensions of the tank to be x feet wide by x + 1 feet long by x² + 1 feet high. What should be the dimensions of the tank? \n" ); document.write( "

Algebra.Com's Answer #818011 by ikleyn(52847) $\"\"$ $\"About$

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document.write( "The \"volume\" equation is\r\n" );
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document.write( "    x*(x+1)*(x^2+1) = 120   cubic feet.\r\n" );
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document.write( "One solution can be easily guessed:  x = 3.\r\n" );
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document.write( "Indeed,  3*(3+1)*(3^2+1) = 3*4*10 = 12*10 = 120.\r\n" );
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document.write( "Next, notice that the function x*(x+1)*(x^2+1)  is monotonically increased.\r\n" );
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document.write( "It means that x = 3  is the UNIQUE solution to the \"volume\" equation, and THERE IS NO other real solution.\r\n" );
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document.write( "ANSWER.  Under given conditions, the unique set of the dimensions of the tank is 3 ft, 4 ft, and 10 ft.\r\n" );
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