document.write( "Question 475836: An arrow is fired straight up from the ground with an initial velocity of176 feet per second. Its height ,s(t), in feet at any time is given by the function s(t)=-16t^2+176t. Find the interval of time for which the height of the arrow is greater than 160 feet. \n" ); document.write( "
Algebra.Com's Answer #326308 by lwsshak3(11628)\"\" \"About 
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An arrow is fired straight up from the ground with an initial velocity of176 feet per second. Its height ,s(t), in feet at any time is given by the function s(t)=-16t^2+176t. Find the interval of time for which the height of the arrow is greater than 160 feet.
\n" ); document.write( "**
\n" ); document.write( "calculating time at which arrow reaches 160 ft
\n" ); document.write( "s(t)=-16t^2+176t
\n" ); document.write( "160=-16t^2+176t
\n" ); document.write( "0=-16t^2+176t-160
\n" ); document.write( "0=16t^2-176t+160
\n" ); document.write( "0=16t^2-176t+160
\n" ); document.write( "Divide by 16
\n" ); document.write( "0=t^2-11t+10
\n" ); document.write( "0=(t-1)(t-10)
\n" ); document.write( "t=1 sec (time at which arrow reaches 160 ft)
\n" ); document.write( "t=10 sec (reject, exceeds time arrow reaches maximum height)
\n" ); document.write( "..
\n" ); document.write( "Calculating time at which arrow reaches maximum height
\n" ); document.write( "y=-16t^2+176t
\n" ); document.write( "completing the square
\n" ); document.write( "y=-16(t^2-11+121/4)+484
\n" ); document.write( "y=-16(t-11/2)^2+484
\n" ); document.write( "arrow reaches maximum height at 11/2 or 5.5 sec
\n" ); document.write( "..
\n" ); document.write( "Arrow takes 1 sec to reach 160 ft on the way up, plus 4.5 more sec to reach maximum and 4.5 more sec to descend to 160 ft on the way down.
\n" ); document.write( "So, interval of time arrow is above 160 ft is: 1 < t < 10, that is, between 1 and 10 seconds \n" ); document.write( "
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