Answer:
The walk will cost $8164.
Step-by-step explanation:
Given:
Diameter of the circular pond (D) = 24 yd
Width of the gravel path (x) = 2 yd
Cost per yard of the path = $50
Now, radius of the circular pond is half of the diameter and is given as:
Now, area of the pond is given as:
Area of the complete path including the pond area is given as:
Now, area of the gravel path can be obtained by subtracting the pond area from the total outer area. This gives,
Now, using unitary method,
Cost of 1 square yard of path = $50
∴ Cost of 163.28 square yard of path = 50 × 163.28 = $8164
Hence, the walk will cost $8164.
Let w = cos(x)
The given equation turns into -5w^2 + 4w + 1 = 0. Use the quadratic formula to find that the two solutions, in terms of w, are:
The solution w = 1 leads to cos(x) = 1 which then becomes x = 0, x = 2pi, x = 4pi, etc. The general way to write this is x = 2pi*n where n is any integer. These angles are in radian mode.
The solution w = -0.2 leads to cos(x) = -0.2 which becomes x = arccos(-0.2) = 1.77215 approximately assuming your teacher wants the angle in radian mode. Unfortunately, I don't know the exact value of x here. There may not be an exact value, or finding this exact value may be well beyond the scope of this course.
Traveling along the x-axis, we have
On the other hand, along the y-axis we get
Therefore the limit doesn't exist.
Sure this question comes with a set of answer choices.
Anyhow, I can help you by determining one equation that can be solved to determine the value of a in the equation.
Since, the two zeros are - 4 and 2, you know that the equation can be factored as the product of (x + 4) and ( x - 2) times a constant. This is, the equation has the form:
y = a(x + 4)(x - 2)
Now, since the point (6,10) belongs to the parabola, you can replace those coordintates to get:
10 = a (6 + 4) (6 - 2)
Therefore, any of these equivalent equations can be solved to determine the value of a:
10 = a 6 + 40) (6 -2)
10 = a (10)(4)
10 = 40a
