SOLUTION: The height h(t), in feet, of an airborn tee-shirt t seconds after being launched can be approximated by h(t)=-15t^2+105t+10, 0<= t <=10. Find the time when the shirt will reach a f

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Question 733322: The height h(t), in feet, of an airborn tee-shirt t seconds after being launched can be approximated by h(t)=-15t^2+105t+10, 0<= t <=10. Find the time when the shirt will reach a fan 190ft above ground level?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=-15t%5E2%2B105t%2B10+
+h%28t%29+=+190+ ft
+190+=-15t%5E2%2B105t%2B10+
+-15t%5E2+%2B+105t+-+180+=+0+
+-t%5E2+%2B+7t+-+12+=+0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-1+
+b+=+7+
+c+=+-12+
+t+=+%28+-7+%2B-+sqrt%28+7%5E2+-+4%2A%28-1%29%2A%28-12%29+%29%29+%2F+%282%2A%28-1%29%29+
+t+=+%28+-7+%2B-+sqrt%28+49+-+48+%29%29+%2F+%28-2%29+
+t+=+%28+-7+%2B-+sqrt%28+1+%29%29+%2F+%28-2%29+
+t+=+%28+-7+%2B+1+%29+%2F+%28-2%29+
+t+=+3+
also
+t+=+%28+-7+-+1+%29+%2F+%28-2%29+
+t+=+4+
There are 2 times when it is 190 ft above ground, 3 sec and 4 sec
check:
+graph%28+400%2C+400%2C+-2%2C+10%2C+-200%2C+20%2C+-15%2Ax%5E2+%2B+105x+-+180+%29+