Answer fully : ) 30 pts
an object is launched from ground level with an initial velocity of 120 meters per second. for how long is the object at or above 500 meters (rounded to the nearest second)?

the equation that models the path of the object is y = -4.9t^2 + 120t.
a) 11 seconds
b) 12 seconds
c) 13 seconds
d) 14 seconds

D)14 seconds

Step-by-step explanation:

y = -4.9t^2 + 120t

We want to find out when y = 500

500 = -4.9t^2 + 120t

Subtract 500 from each side

500-500 = -4.9t^2 + 120t-500

0 =  -4.9t^2 + 120t-500

a=-4.9  b= 120 and c = -500

Using the quadratic formula

-b ±sqrt(b^2 -4ac)

2a

-120±sqrt(120^2 -4(-4.9)(-500))

2*(-4.9)

Solving this for the two solutions

t≈5.32415

t≈19.1656

The object will be above 500 meters between these two times

19.1656 - 5.32415 = 13.84145

This is approximately 14 seconds

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^