A football kicker boots the ball from the 15 yard line to the 35 yard line. The equation can be modeled by the the following: y = - .054(x - h)(x - k)where h and k are where the football lands (x-intercepts). What was the maximum height that the football reached?

The maximum height that the football reached = 5.4 yards (16.2 feet)

Step-by-step explanation:

The initial location of the ball = 15 yard line

The final location of the ball = 35 yard line

The equation of the ball's motion can be modeled as follows;

y = -0.054·(x - h)·(x - k)

Where;

h and k are the x-intercepts which are the points where the ball lands or where the ball is in contact with the ground

Given that the kicker kicks the ball from the ground on the 15 yard line and the ball lands on the ground at the 35 yard line, we can write

h = 15 yard line

k = 35 yard line

Therefore;

y = -0.054·(x - 15)·(x - 35) = -0.054·x² + 2.7·x-28.35

The maximum height is found by differentiating the function with respect to x and equating the result to 0 as follows;

d(-0.054·x² + 2.7·x-28.35)/dx = 2.7 - 0.108·x = 0

x = 2.7/0.108 = 25

Therefor, at the maximum point, we have;

x = 25

∴ y = -0.054·(25 - 15)·(25 - 35) = -0.054×10×(-10) = 5.4

The maximum height that the football reached = 5.4 yards = 16.2 feet.

answer: (1,3) and (-2,0) i think.

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)