document.write( "Question 1173002: The volume of a square box is 200 cm3 ≤ 𝑉 ≤ 810 cm3
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Algebra.Com's Answer #798162 by mccravyedwin(407)\"\" \"About 
You can put this solution on YOUR website!
I'll answer in reverse order:

\n" ); document.write( "2. Express the volume of the square box in terms of x.
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document.write( "\"V=l%2Aw%2Ah\"\r\n" );
document.write( "\"V=%282x-5%29%2A%282x-5%29%2A%28x%2B3%29\"\r\n" );
document.write( "\"200+%3C=+V+%3C=+810\"\r\n" );
document.write( "\"200+%3C=+l%2Aw%2Ah+%3C=+810\"\r\n" );
document.write( "\"200+%3C=+b%2Ab%2Ah+%3C=+810\"\r\n" );
document.write( "\"200+%3C=+%282x-5%29%2A%282x-5%29%2A%28x%2B3%29+%3C=+810\"\r\n" );
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document.write( "Multiplying that out,\r\n" );
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document.write( "\"200+%3C=+4x%5E3+-+8x%5E2+-35+x+%2B+75+%3C=+810\"\r\n" );
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document.write( "We find the values of x at the endpoints 200 and 810:\r\n" );
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document.write( "\"4x%5E3+-+8x%5E2+-35+x+%2B+75+=+200\" and \"4x%5E3+-+8x%5E2+-35+x+%2B+75+=+810\"\r\n" );
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document.write( "\"4x%5E3+-+8x%5E2+-35+x+-+125+=+0\" and \"4x%5E3+-+8x%5E2+-35+x+%2B+75+=+810\"\r\n" );
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document.write( "Using synthetic division to factor them both, we get:\r\n" );
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document.write( "\"%28x+-+5%29%284x%5E2+%2B+12x+%2B+25%29=0\" and \"%28x+-+7%29%284x%5E2+%2B+20x+%2B+105%29=0\"\r\n" );
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document.write( "Those have 5 and 7 respectively as their only real solutions\r\n" );
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document.write( "The volume (2x-5)*(2x-5)*(x+3) is steadily increasing as the volume increases\r\n" );
document.write( "from 200 cm3 to 810 cm3.\r\n" );
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document.write( "So the interval for x corresponding to \"200%3C=V%3C=810\" is \"5%3C=x%3C=7\".\r\n" );
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1. Give the area of the base in terms of x.
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document.write( "Area of the square base = base2 = (2x-5)2.\r\n" );
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document.write( "We build that up from this inequality:\r\n" );
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document.write( "\"5%3C=x%3C=7\"\r\n" );
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document.write( "We multiply all three sides by 2:\r\n" );
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document.write( "\"2%2A4%3C=2%2Ax%3C=2%2A7\"\r\n" );
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document.write( "\"8%3C=2x%3C=14\"\r\n" );
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document.write( "We subtract 5 from all three sides:\r\n" );
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document.write( "\"8-5%3C=2x-5%3C=14-5\"\r\n" );
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document.write( "\"3%3C=2x-5%3C=9\"\r\n" );
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document.write( "We square all three sides (which keeps the same inequality since they are > 1).\r\n" );
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document.write( "\"3%5E2%3C=%282x-5%29%5E2%3C=9%5E2\"\r\n" );
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document.write( "\"9%3C=matrix%281%2C4%2CArea%2Cof%2Csquare%2Cbase%29%3C=81\"\r\n" );
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document.write( "Edwin
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