The function f(x) = –10(x)(x – 4) represents the approximate height of a projectile launched from the ground into the air as a function of time in seconds, x. how long, from launch to landing, does the projectile stay in the air?

For 4 seconds the projectile will be in the air.

Step-by-step explanation:

The function f(x) = –10(x)(x – 4) represents the approximate height of a projectile launched from the ground into the air as a function of time in seconds, x.

Now, if the projectile stays for x seconds in the air then after x seconds its height will be zero.

Hence, 0 = - 10x(x - 4)

⇒ x = 0 or x = 4

Now, x cannot be 0 as at time = 0 the projectile starts its motion.

So, for 4 seconds the projectile will be in the air. (Answer)

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).