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# Quadratic formula

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A rocket is launched from the top of a 70 foot cliff with an ititial velocity of 100 feet per second.  The height, h, of the rocket after t seconds is givin by the equation h=-16t^2 +100t + 70/  How laong after the rocket is launched will it be 30 feet from the ground. round to the nearest tenth

Aug 16, 2017

### Best Answer

#1
+1

Given the formula:  h  =  -16t2 + 100t + 70  and given the value:  h = 30,  what is the value of t?

30  =  -16t2 + 100t + 70

0  =  -16t2 + 100t + 40                                                       subtract 30 from both sides

0  =  -4t2 + 25t + 10                                                           divide both sides by 4

a = -4     b = 25     c = 10                                                     use the quadratic formula

t  =  [ -b +/- sqrt( b2 - 4·a·c ) ] / (2·a)

t  =  [ -25 +/- sqrt( (25)2 - 4·(-4)·(10 ) ] / (2·-4)

t  =  [ -25 +/- sqrt( 625 + 160) ] / (-8)

t  =  [ -25 +/- sqrt( 785) ] / (-8)

t = -0,377     or     t = 6.627

Since t must be positive, t = 6.6

Aug 16, 2017

### 2+0 Answers

#1
+1
Best Answer

Given the formula:  h  =  -16t2 + 100t + 70  and given the value:  h = 30,  what is the value of t?

30  =  -16t2 + 100t + 70

0  =  -16t2 + 100t + 40                                                       subtract 30 from both sides

0  =  -4t2 + 25t + 10                                                           divide both sides by 4

a = -4     b = 25     c = 10                                                     use the quadratic formula

t  =  [ -b +/- sqrt( b2 - 4·a·c ) ] / (2·a)

t  =  [ -25 +/- sqrt( (25)2 - 4·(-4)·(10 ) ] / (2·-4)

t  =  [ -25 +/- sqrt( 625 + 160) ] / (-8)

t  =  [ -25 +/- sqrt( 785) ] / (-8)

t = -0,377     or     t = 6.627

Since t must be positive, t = 6.6

geno3141 Aug 16, 2017
#2
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