document.write( "Question 946580: When the shot whose path is released at an angle of 65°, its height, g(x), in feet, can be modeled by: g(x) = —0.04x2 + 2.1x + 6.1 where x is the shot’s horizontal distance, in feet, from its point of release. Use this model to solve the following: (a) What is the maximum height, to the nearest tenth of a foot, of the shot and how far from its point of release does this occur? (b) What is the shot’s maximum horizontal distance, to the nearest tenth of a foot, or the distance of the throw? (c) from what height was the shot released? \n" ); document.write( "

Algebra.Com's Answer #577484 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+g%28x%29+=+-.04x%5E2+%2B+2.1x+%2B+6.1+\"$
\n" ); document.write( "This is in the form:
\n" ); document.write( " $\"+g%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"$ where
\n" ); document.write( " $\"+a+=+-.04+\"$
\n" ); document.write( " $\"+b+=+2.1+\"$
\n" ); document.write( " $\"+c+=+6.1+\"$
\n" ); document.write( "-------------
\n" ); document.write( "(a)
\n" ); document.write( "The $\"+x+\"$ component of the maximum
\n" ); document.write( "height is :
\n" ); document.write( " $\"+x%5Bmax%5D+=+-b%2F%282a%29+\"$
\n" ); document.write( " $\"+x%5Bmax%5D+=+-%282.1%29%2F%282%2A%28-.04%29%29+\"$
\n" ); document.write( " $\"+x%5Bmax%5D+=+2.1+%2F+.08+\"$
\n" ); document.write( " $\"+x%5Bmax%5D+=+26.25+\"$
\n" ); document.write( "--------------------
\n" ); document.write( " $\"+g%5Bmax%5D+=+-.04%2A%28+26.25+%29%5E2+%2B+2.1%2A26.25+%2B+6.1+\"$
\n" ); document.write( " $\"+g%5Bmax%5D+=+-27.5625+%2B+55.125+%2B+6.1+\"$
\n" ); document.write( " $\"+g%5Bmax%5D+=+33.6625+\"$
\n" ); document.write( "To the nearest 10th, the maximum height
\n" ); document.write( "is 33.7 ft
\n" ); document.write( "The maximum height is reached 26.25 ft
\n" ); document.write( "from the point of release
\n" ); document.write( "-----------------------
\n" ); document.write( "(b)
\n" ); document.write( " $\"+g%28x%29+=+-.04x%5E2+%2B+2.1x+%2B+6.1+\"$
\n" ); document.write( " $\"+-.04x%5E2+%2B+2.1x+%2B+6.1+=+0+\"$
\n" ); document.write( "Use the quadratic formula
\n" ); document.write( " $\"+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+-.04+\"$
\n" ); document.write( " $\"+b+=+2.1+\"$
\n" ); document.write( " $\"+c+=+6.1+\"$
\n" ); document.write( " $\"+x+=+%28+-2.1+%2B-+sqrt%28+2.1%5E2+-+4%2A%28-.04%29%2A6.1+%29%29+%2F+%282%2A%28-.04%29%29+\"$
\n" ); document.write( " $\"+x+=+%28+-2.1+%2B-+sqrt%28+4.41+%2B+.976%29%29+%2F+%28-.08%29+\"$
\n" ); document.write( " $\"+x+=+%28+-2.1+-+sqrt%28+5.386+%29%29+%2F+%28+-.08+%29+\"$
\n" ); document.write( " $\"+x+=+%28+-2.1+-+2.32078+%29+%2F+%28+-.08+%29+\"$
\n" ); document.write( " $\"+x+=+%28+-4.42078+%29+%2F+%28+-.08+%29+\"$
\n" ); document.write( " $\"+x+=+55.2596+\"$
\n" ); document.write( "The maximum horizontal distance is:
\n" ); document.write( "55.3 ft to the nearest tenth
\n" ); document.write( "-------------------------
\n" ); document.write( "(c)
\n" ); document.write( "To find height from which shot is released, se the
\n" ); document.write( "horizontal distance, $\"+x+\"$ to $\"+0+\"$
\n" ); document.write( " $\"+g%280%29+=+-.04%2A0%5E2+%2B+2.1%2A0+%2B+6.1+\"$
\n" ); document.write( " $\"+g%280%29+=+6.1+\"$
\n" ); document.write( "The shot was released from a height of 6.1 ft
\n" ); document.write( "---------------------------
\n" ); document.write( "Here's a plot:
\n" ); document.write( " $\"+g%28x%29+=+-.04x%5E2+%2B+2.1x+%2B+6.1+\"$
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-6%2C+60%2C+-4%2C+40%2C+-.04x%5E2+%2B+2.1x+%2B+6.1++%29+\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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