use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth.
a rocket is launched from atop a 76-foot cliff with an initial velocity of 135 ft/s.
a. substitute the values into the vertical motion formula h-16t^2+ vt+c. let h = 0.
b. use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. round to the nearest tenth of a second.

A) 0 = -16t^2+135t+76

B) The rocket will take 9 seconds to hit the ground after it is launched.

Step-by-step explanation:

We have given:

A rocket is launched from atop a 76-foot cliff with an initial velocity of 135 ft/s.

A) Substitute the values into the vertical motion formula h-16t^2+ vt+c.

Let h = 0

h= -16t^2+ vt+c

Lets substitute the values v= 135 and c = 76

h = -16t^2+135t+76

Now lets say h=0:

0 = -16t^2+135t+76

B) Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.

The equation is:

0 = -16t^2+vt+c

0 = -16t^2+35t+76

Apply quadratic formula:

x = -b+/-√b^2-4ac/2a

t=-(135)+/-√(135)^2-4(-16)(76)/2(-16)

t = -135+/-√18225+4864/ -32

t=-135+/-√23089/ -32

t = -135+/-151.951 / -32

t = -135+151.951/ -32   , t = -135-151.951/ -32

t =  16.951/ -32             , t= -286.951 / -32

t= -0.5297                   , t = 8.967

Therefore we will consider the value t=8.967 which is equivalent to 9 seconds when we rounded off. The other value is negative.

The rocket will take 9 seconds to hit the ground after it is launched

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116