I didn't get all the part with the tiles, but here's the general answer:
given a polynomial
we have that is a factor of
if and only if k is a root of
, i.e. if
So, given the polynomial
We can check if is a factor by evaluating
:
So, is not a factor.
Similarly, we can evaluate to check if
are factors:
So, only is a factor of
Answer:
# after 5 seconds, the ball strikes the ground
# The ball reaches maximum height at t = 1.5 seconds
# The max height is 196 feet
Step-by-step explanation:
The equation is:
t is the time
d(t) is the distance traveled
Initial height is 160 feet and initial velocity is 48 ft/sec
If we want to find the time it takes the ball to hit the ground, we let d(t) equal to 0 and find t. Shown below:
We disregard t = -2 since time can't be negative. We take t = 5
Thus, after 5 seconds, the ball strikes the ground.
The equation is a quadratic of the form:
Matching equations, we can say:
a = -16
b = 48
c = 160
The time when ball reaches max height is given as:
Substituting, we find:
The ball reaches maximum height at t = 1.5 seconds
The max height can be found by putting t = 1.5 into the original equation. Shown below:
The max height is 196 feet