document.write( "Question 615575: the height of a model rocket can be measure by the function H(t)=720t-16t^2, where t is time measured in seconds, and H is measured in feet. how long does it take the rocket to reach its highest point, and how high does it get \n" ); document.write( "

Algebra.Com's Answer #387233 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"++H%28t%29=720t-16t%5E2+\"$
\n" ); document.write( "Find 2 points where the height of the rocket is zero
\n" ); document.write( "One point is at (0,0) because
\n" ); document.write( " $\"++H%28t%29=720%2A0-16%2A0%5E2+\"$
\n" ); document.write( " $\"+H%280%29+=+0+\"$
\n" ); document.write( "Now set $\"+H%28t%29+=+0+\"$
\n" ); document.write( " $\"+0+=+720t+-+16t%5E2+\"$
\n" ); document.write( " $\"+0+=+t%2A%28+720+-+16t%29+\"$
\n" ); document.write( "This is true if $\"+t+=+0+\"$ or if
\n" ); document.write( " $\"+720+-+16t+=+0+\"$
\n" ); document.write( " $\"+16t+=+720+\"$
\n" ); document.write( " $\"+t+=+45+\"$
\n" ); document.write( "So, the 2nd point is at (45,0)
\n" ); document.write( "The midpoint of this parabola is at $\"+%28+0+%2B+45+%29+%2F+2+=+22.5+\"$ sec
\n" ); document.write( "The find the height at this time,
\n" ); document.write( " $\"+H%2822.5%29+=+720%2A22.5+-+16%2A22.5%5E2+\"$
\n" ); document.write( " $\"+H%2822.5%29+=+16200+-+8100+\"$
\n" ); document.write( " $\"+H%28+22.5%29+=+8100+\"$
\n" ); document.write( "The maximum height is 8,100 ft
\n" ); document.write( "Here's the plot where height is in hundreds of feet
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-5%2C+50%2C+-15%2C+100%2C+7.2x+-+.16x%5E2+%29+\"$ \n" ); document.write( "

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