Question

The height in meters of a rocket launched from the ground after t seconds is modeled by h(t)=-9.8r^2+49t. Graph a graph representing the interval of time when the rocket will be higher than 40 meters

Answer 1

first, find where it is equal to 40 meters and find where it is above it

40=-9.8t²+49t
9.8t²-49t+40=0

using quadratic formula
t=1.02746 and x=3.97254
test a point in the middle
h(2)=58.8
that is higher

so the interval would be from x=1.02746 to 3.9754
1.02746<x<3.9754 is the interval

to graph it, graph h(t)=-9.8t²+49t-40 and the part where it is above the x axis is where it is higher than 40 meters

Answer 2

9.8t^2-49t+40=0

t=(49±√833)/19.6

t≈1.027, 3.97

1.027<t<3.97