document.write( "Question 1208173: At sea level, the weight of the atmosphere exerts a pressure of 14.7 pounds per square inch, commonly referred to as 1 atmosphere of pressure. As an object descends in water, pressure P and depth d are linearly related. In salt water, the pressure at a depth of 33 ft is 2 atms, or 29.4 pounds per square inch.
\n" ); document.write( "(A) Find a linear model that relates pressure P (in pounds per square inch) to depth d (in feet).
\n" ); document.write( "(B) Interpret the slope of the model.
\n" ); document.write( "(C) Find the pressure at a depth of 80 ft.
\n" ); document.write( "(D) Find the depth at which the pressure is 6 atms. \n" ); document.write( "

Algebra.Com's Answer #846403 by ikleyn(52807) $\"\"$ $\"About$

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\n" ); document.write( "At sea level, the weight of the atmosphere exerts a pressure of 14.7 pounds per square inch,
\n" ); document.write( "commonly referred to as 1 atmosphere of pressure. As an object descends in water, pressure P
\n" ); document.write( "and depth d are linearly related. In salt water, the pressure at a depth of 33 ft is 2 atms,
\n" ); document.write( "or 29.4 pounds per square inch.
\n" ); document.write( "(A) Find a linear model that relates pressure P (in pounds per square inch) to depth d (in feet).
\n" ); document.write( "(B) Interpret the slope of the model.
\n" ); document.write( "(C) Find the pressure at a depth of 80 ft.
\n" ); document.write( "(D) Find the depth at which the pressure is 6 atms.
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document.write( "From the problem, when an object descents in water from the surface to the depth of 33 ft,\r\n" );
document.write( "the pressure changes from 1 atm to 2 atm.\r\n" );
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document.write( "So, the rate of the pressure change is   =  atm/ft (atmosphere per foot of the depth).\r\n" );
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document.write( "Therefore, we can write the general formula for the pressure\r\n" );
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document.write( "    P = 1 +   in atmospheres    (1)\r\n" );
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document.write( "or\r\n" );
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document.write( "    P = 14.7 +  in pounds per square inch,    (2)\r\n" );
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document.write( "where d is the depth below the surface, in feet.  \r\n" );
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document.write( "The last formula (2) is the answer to question (A), which is complete at this point.\r\n" );
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document.write( "In formula (2), the slope is the rate   = 0.4455  of a pound per foot of the depth \r\n" );
document.write( "and per square inch of the surface area.  It is the answer to question (B).\r\n" );
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document.write( "To answer (C), you should substitute d= 80 ft into formula (1) or (2) and make simple arithmetic.\r\n" );
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document.write( "From (1), you will get the pressure in atmospheres.\r\n" );
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document.write( "From (2), you will get the pressure in pounds per square inch.\r\n" );
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document.write( "To answer (D), you should solve this equation for d\r\n" );
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document.write( "    14.7 +  = 6*14.7.\r\n" );
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document.write( "You will get the answer in feet of the depth.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Happy calculations and happy solving !\r
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\n" ); document.write( "\n" ); document.write( "In this problem, working units for pressure are atmosphere and pounds per square inch.\r
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\n" ); document.write( "\n" ); document.write( "The problem and my solution teach you to work freely with different units of measurements.\r
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