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# quadratic

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The equation y = -6t^2 + 83t describes the height (in feet) of a projectile seconds after it is launched from the surface of Mars at 83 feet per second. In how many seconds will the projectile first reach 77 feet in height? Express your answer as a decimal rounded to the nearest tenth.

Jan 26, 2021

### 3+0 Answers

#1
+1

y = 77

77 = -6t^2 + 83t

-6t^2 + 83t - 77 = 0    now use Quadratic Formula to solve for 't'

you will get two answers for t...one is for the projectile going up (the smaller 't' obviously) and the other is on the way down

a = -6   b = 83     c = 87

$$t = {-(83) \pm \sqrt{(83)^2-4(-6)(87)} \over 2(-6)}$$

Jan 26, 2021
#2
+116126
+1

Don't really need the  Q formula

-6t^2  +  83t    -77   = 0             factor

(-6t  + 77)  ( t - 1)  =   0

Set each factor to 0  and solve for  t

-6t  + 77  = 0                             t  - 1     =  0

-6t  = -77                                    t   = 1  (second)  =  time  to  first reach 77 ft

t =  -77/-6  = 77/6 sec

Jan 26, 2021
#3
0

"Don't really need the  Q formula"

IF you can factor the equation !          Thanx , Chris !

Guest Jan 26, 2021