document.write( "Question 1084628: the altitude of a triangle is increasing at a rate of 1 cm/min
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Algebra.Com's Answer #698709 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( ">>the altitude (height h) of a triangle is increasing \r\n" );
document.write( "at a rate of 1 cm/min<< \r\n" );
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document.write( "\"dh%2Fdt\"\"%22%22=%22%22\"\"matrix%281%2C2%2C1%2Ccm%2F%28min%29%29\"\r\n" );
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document.write( ">>while the area A of the triangle is increasing at a \r\n" );
document.write( "rate of 2cm^2 /min.<< \r\n" );
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document.write( "\"dA%2Fdt\"\"%22%22=%22%22\"\"matrix%281%2C2%2C2%2Ccm%5E2%2F%28min%29%29\"\r\n" );
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document.write( ">>at what rate is the base of the triangle changing...<<\r\n" );
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document.write( "\"A\"\"%22%22=%22%22\"\"expr%281%2F2%29%2Ab%2Ah\"\r\n" );
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document.write( "\"dA%2Fdt\"\"%22%22=%22%22\"\"expr%281%2F2%29%28b%2Aexpr%28dh%2Fdt%29%2Bh%2Aexpr%28db%2Fdt%29%29\" \r\n" );
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document.write( "Substitute \"dA%2Fdt\"\"%22%22=%22%22\"\"2\" and \"dh%2Fht\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "\"2\"\"%22%22=%22%22\"\"expr%281%2F2%29%28b%2A%281%29%2Bh%2Aexpr%28db%2Fdt%29%29\"\r\n" );
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document.write( "Multiply both side by 2\r\n" );
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document.write( "\"4\"\"%22%22=%22%22\"\"2%2Aexpr%281%2F2%29%28b%2Bh%2Aexpr%28db%2Fdt%29%29\"\r\n" );
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document.write( "\"4\"\"%22%22=%22%22\"\"b%2Bh%2Aexpr%28db%2Fdt%29\"\r\n" );
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document.write( "We will need b and h to solve for \"db%2Fdt\".\r\n" );
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document.write( ">>when the altitude (height h) is 10cm and the area is 100cm^2?<<\r\n" );
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document.write( "We go back to the area formula:\r\n" );
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document.write( "\"A\"\"%22%22=%22%22\"\"expr%281%2F2%29%2Ab%2Ah\"\r\n" );
document.write( "\"100\"\"%22%22=%22%22\"\"expr%281%2F2%29%2Ab%2A10\"\r\n" );
document.write( "\"100\"\"%22%22=%22%22\"\"5%2Ab\"\r\n" );
document.write( "\"20\"\"%22%22=%22%22\"\"b\"\r\n" );
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document.write( "Substitute \"h\"\"%22%22=%22%22\"\"10\" and \"b\"\"%22%22=%22%22\"\"20\" in\r\n" );
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document.write( "\"4\"\"%22%22=%22%22\"\"b%2Bh%2Aexpr%28db%2Fdt%29\"\r\n" );
document.write( "\"4\"\"%22%22=%22%22\"\"20%2B10%2Aexpr%28db%2Fdt%29\"\r\n" );
document.write( "\"-16\"\"%22%22=%22%22\"\"10%2Aexpr%28db%2Fdt%29\"\r\n" );
document.write( "\"%28-16%29%2F10\"\"%22%22=%22%22\"\"db%2Fdt\"\r\n" );
document.write( "\"-1.6\"\"%22%22=%22%22\"\"db%2Fdt\"\r\n" );
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document.write( "The negative sign means the base is DEcreasing\r\n" );
document.write( "at the rate of -1.6 cm/min at that instant.\r\n" );
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document.write( "Edwin
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