Answer:
6.12
Step-by-step explanation:
tan 27≈0.51
Know that tan=
0.51=
Multiply 12 on both sides
6.12=x
The Beechcraft 1900D is a commuter airplane with a fuel capacity of 665 gallons. The function that represents how the amount of
1 answer:
Given:
The function that represents how the amount of fuel changes as a function of distance flown is
where x represents miles flown, and f(x) represents the amount of fuel remaining.
To find:
The rate of change for this scenario.
Solution:
The slope intercept form of a linear function is
...(i)
Where, m is the slope or rate of change and b is the y-intercept.
We have,
...(ii)
On comparing (i) and (ii), we get
Therefore, the rate of change for this scenario is -0.9. It means, the amount of fuel in the airplane is decreasing by 0.9 gallons per mile.
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Lets make the graph of our systems of equations:
The blue line correspond to the equation x-y=3 and the red one correspond to 7x-y=-3. The lines intersect at point (-1,-4), then, the solution of the system is (-1,-4).
Answers:
(1 Question in written form): 7.2 inches.
(2 Question in the picture): Option (D) and
and
Explanations:
1. (Question in written form):
First you need to know the standard form of a parabola (considering it opens in +x direction and the vertex of the parabola is at origin), which is as follows:
Since the vertex of the parabola is at origin, h = 0 and k = 0. The above equation will now become:
---- (A)
Where p is the distance between the vertex and the focus of a parabola, which we need to find (or where the microphone should be placed).
As the vertex is assumed to be placed at the origin, the parabolic dish, which is 24 inches wide, will be split evenly on both sides of the y axis (as the opening of the parabola is in x-axis—stated above), giving the distance of 12 inches from each sides of y axis (12 inches + 12 inches = 24 inches). Since it (parabolic microphone) is 5 inches deep, the coordinates will become: (5, +12) and (5, -12).
Plug any of the points—(5,+12) or (5,-12)—in equation (A), you will get the following:
Hence, the correct answer is 7.2 inches.
2. (Question in the picture):
First we need to write the following equation in the standard form:
----- (B)
The standard form of parabola is:
----- (C)
Rearrange equation (B) and solve as follows:
You can write the above equation as follows:
----- (D)
Now compare equation (D) with (C), we will get:
Focus = (h+p, k) = (-3+(1/2), -1)
Now, to find x, use the following formula:
x = h - p
Hence, the correct option is (D) -> and