Answer:
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:
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Step-by-step explanation:
Answer:
<h2>
0.7</h2>
Step-by-step explanation:
A' is everything what is not A
So:
A' = {9, 10, 11, 12, 13, 15, 16}
Number of ways it can happen: |A'| = 7
Total number of outcomes: |Ω| = 10
Probability of an event happening:
Hello!
The graphs of sine and cosine are waves. Therefore, choice A and B are wrong.
The graph of f(x) = cot(x) is an inverse of f(x) = tan(x), so therefore the graph of f(x) = cot(x) has the lines similar to the graph above, but it's flipped.
So therefore, the graph shown above is choice C, f(x) = tan x.
To find the equation of the line in slope-intercept form, y = mx + b, we can start by solving for the slope. The slope compares the vertical change (the rise) to the horizontal change (the run) when moving from one fixed point to another along the line.
The slope formula is:
m = (y2 - y1)/(x2 - x1)
We need to select 2 pairs of points from your given table.
Let (x1, y1) = (1, 8)
(x2, y2) = (2, 10)
Plug these values into the formula:
m = (y2 - y1)/(x2 - x1)
m = (10 — 8)/(2 — 1)
m = 2/1 or 2.
Therefore, the slope of the line is 2.
Next, we need to figure out what the y-intercept of the line is. The y-intercept is the point where the line crosses the y-axis. The y-intercept is also the value of y when x = 0.
Looking at your given table, you have an ordered pair, (0, 6) — this is the y-intercept. The y-coordinate (6) is the value of “b” in the slope-intercept form, y = mx + b.
Now that we have our slope (m) = 2, and y-intercept (b) = 6, we can write our equation as follows:
y = 2x + 6
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