Answer:
Option A is correct.
The system of equation is inconsistent is;
2x+8y=6
5x+20y=2
Explanation:
* A system of equations is called an inconsistent system, if there is no solution because the lines are parallel.
* If a system has at least one solution, it is said to be consistent .
*A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions.
(A)
2x+8y=6
5x+20y=2
This is inconsistent, because as shown below in the graph of figure 1 that the lines do not intersect, so the graphs are parallel and there is no solution.
(B)
5x+4y=-14
3x+6y=6
this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 2 and also it is independent.
(C)
x+2y=3
4x+6y=5
this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 3.
(D)
3x-2y=2
6x-4y=4
this is a consistent system and has an infinite number of solutions, it is dependent because both equations represent the same line. as shown below in the graph of Figure-4.
Therefore, the only Option A system of equation is inconsistent.
The actual area of the tennis court is 264 m²
First use the scale to find the actual dimensions of the court:
1 cm : 0.8m
30 cm in the drawing would be:
= 0.8 x 30
= 24 m outside
13.75cm in the drawing would be:
= 0.8 x 13.75
= 11 m outside
Area of a rectangle (which is what the dimensions resemble):
= Length x width
= 24 x 11
= 264 m²
In conclusion, the area of the tennis court is 264 m²
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Answer:
$300,000
Step-by-step explanation:
Labor cost = $11,000
Parking cost= $7,000
Parking Labor cost = $ 18,000
Parking Revenue = ?
From the question, parking labor cost is 6% of Parking revenue.
6% = Parking Labor cost/ Parking Revenue------------------------------------ (1)
Further substituting in (1) gives:
6/100 = 18,000/ Parking Revenue
Making Parking Revenue the subject of the formula, we have:
Parking Revenue = (100 x 18,000)/6
= $300,000
We are given the parametric equations:
x = 6 cos θ
y = 6 sin θ
We know that the derivative of cos a = - sin a and the
derivative of sin a = cos a, therefore taking the 1st and 2nd
derivates of x and y:
d x = 6 (-sin θ) = - 6 sin θ
d^2 x = -6 (cos θ) = - 6 cos θ
d y = 6 (cos θ) = 6 cos θ
d^2 y = 6 (-sin θ) = - 6 sin θ
Therefore the values we are asked to find are:
dy / dx = 6 cos θ / - 6 sin θ = - cos θ / sin θ = - cot θ
d^2 y / d^2 x = - 6 sin θ / - 6 cos θ = sin θ / tan θ =
tan θ
We can find the value of the slope at θ = π/4 by using
the dy/dx:
dy/dx = slope = - cot θ
dy/dx = - cot (π/4) = - 1 / tan (π/4)
dy/dx = -1 = slope
We can find the concavity at θ = π/4 by using the d^2 y/d^2
x:
d^2 y / d^2 x = tan θ
d^2 y / d^2 x = tan (π/4)
d^2 y / d^2 x = 1
Since the value of the 2nd derivative is
positive, hence the concavity is going up or the function is concaved upward.
Summary of Answers:
dy/dx = - cot θ
d^2 y/d^2 x = tan θ
slope = -1
concaved upward
