Find the distance between the points (4, 3) and (0, 6).
2 answers:
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Step-by-step explanation:
66. Δy = -3.4 Δx
Δy/Δx = -3.4
The slope of the line is -3.4. Slope-intercept equation of the line is:
y = -3.4x + b
Plug in the given point to find b:
2 = -3.4(4) + b
b = 15.6
Therefore, the equation is y = -3.4x + 15.6.
Use the equation to find the y coordinates.
68. Repeat the same steps as 66.
Δy = -1.7 Δx
Δy/Δx = -1.7
The slope of the line is -1.7. Slope-intercept equation of the line is:
y = -1.7x + b
Plug in the given point to find b:
3 = -1.7(-7) + b
b = -8.9
Therefore, the equation is y = -1.7x − 8.9.
Use the equation to find the x or y coordinates.
We will investigate how to determine Hamilton paths and circuits
Hamilton path: A path that connect each vertex/point once without repetition of a point/vertex. However, the starting and ending point/vertex can be different.
Hamilton circuit: A path that connect each vertex/point once without repetition of a point/vertex. However, the starting and ending point/vertex must be the same!
As the starting point we can choose any of the points. We will choose point ( F ) and trace a path as follows:
The above path covers all the vertices/points with the starting and ending point/vertex to be ( F ). Such a path is called a Hamilton circuit per definition.
We will choose a different point now. Lets choose ( E ) as our starting point and trace the path as follows:
The above path covers all the vertices/points with the starting and ending point/vertex are different with be ( E ) and ( C ), respectively. Such a path is called a Hamilton path per definition.
One more thing to note is that all Hamilton circuits can be converted into a Hamilton path like follows:
The above path is a hamilton path that can be formed from the Hamilton circuit example.
But its not necessary for all Hamilton paths to form a Hamilton circuit! Unfortunately, this is not the case in the network given. Every point is in a closed loop i.e there is no loose end/vertex that is not connected by any other vertex.