The system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:
- y = (2/7)(x - 2)^2 - 6
- (x - 1)^2 + (y - 2)^2 = 5^2
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What are equations?</h3>
- The equation is described as the state of being equal and is commonly represented as a math expression with equal values on either side, or it refers to an issue in which many factors must be considered.
- 2+2 = 3+1 is an example of an equation.
To find the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse:
The vertex form of a quadratic function is given by: f(x) = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola, a is constant.
For the sailboat we have vertex: (h, k) = (2, -6) and one point: (-7, 8) that is f(-7) = 8.
We will find a using f(-7) = 8:
- f(-7) = a(-7-2)^2 - 6
- f(-7) = 49a - 6
- 49a - 6 = 8
- 49a = 14
- a = 14/49
- a = 2/7
The quadratic function for the sailboat is given by:
- f(x) = (2/7)(x - 2)^2 - 6 or y = (2/7)(x - 2)^2 - 6
The equation for a circle with a radius of 5 and center (1, 2) is:
- (x - 1)^2 + (y - 2)^2 = 5^2
Therefore, the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:
- y = (2/7)(x - 2)^2 - 6
- (x - 1)^2 + (y - 2)^2 = 5^2
Know more about equations here:
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The correct form of the question is given below:
A lighthouse is located at (1, 2) in a coordinate system measured in miles. a sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?
