Question

HELP ASAP PLEASE!!

the heights of two different projectiles after they launched are modeled by f(x) and g(x).

Answer 1

Explanation:

According to the table, function g(x) reaches the max height of 33, approx.

The equation of motion is f(x) = -16x^2 + 42x + 12. We need to determine the maximum of this function. To do this, find the x-coordinate of the vertex, which is x = -b/(2a), or x = -42/(2*-16), or 1.31 sec.

Evaluating f(x) = -16x^2 + 42x + 12 at x = 1.31 sec, we get f(1.31) = 39.6.

So it appears that f(x) has a higher max than does g(x); the difference is approx. 39.6 - 33, or 6.6

Answer 2

The approximate difference in the maximum height achieved by the two projectiles is 5.4 ft. (Option C).

How to calculate the difference between two maximum heights?

The approximate difference in the maximum height achieved by the two projectiles is calculated as follows;

The given function of one of the projectile;

f(x) = -16x² + 42x + 12

The function of the second projectile shown in the table, shows that the maximum of the function, g is 33

g(1) = 33 ft (maximum height)

The maximum height attained by the projectile with f(x) function occurs at x = 1

f(1) = -16(1)² + 42(1) + 12

f(1) = 38 ft

The difference between two maximum heights;

Δh = f(1) - g(1)

Δh = 38 ft - 33 ft

Δh = 5 ft

The option that is approximately 5 ft is option C (5.4 ft).