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What is the perpendicular bisector equation of the line y equals 5x plus 10 spanning the parabola y equals x squared plus 4?
If: y = 5x +10 and y = x^2 +4
Then: x^2 +4 = 5x +10
Transposing terms: x^2 -5x -6 = 0
Factorizing the above: (x-6)(X+1) = 0 meaning x = 6 or x = -1
Therefore by substitution endpoints of the line are at: (6, 40) and (-1, 5)
Midpoint of line: (2.5, 22.5)
Slope of line: 5
Perpendicular slope: -1/5
Perpendicular bisector equation: y-22.5 = -1/5(x-2.25) => 5y = -x+114.75
Perpendicular bisector equation in its general form: x+5y-114.75 = 0
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What is the perpendicular bisector equation of the line y equals x plus 5 spanning the circle x2 plus 4x plus y2 -18y plus 59 equals 0?
Equation of line: y = x+5 Equation of circle: x^2 +4x +y^2 -18y +59 = 0 The line intersects the circle at: (-1, 4) and (3, 8) Midpoint of line (1, 6) Slope of line: 1 Perpendicular slope: -1 Perpendicular bisector equation: y-6 = -1(x-1) => y = -x+7 Perpendicular bisector equation in its general form: x+y-7 = 0
Prove that a graph G is connected and only if it has a spanning tree?
Proving this is simple. First, you prove that G has a spanning tree, it is connected, which is pretty obvious - a spanning tree itself is already a connected graph on the vertex set V(G), thus G which contains it as a spanning sub graph is obviously also connected. Second, you prove that if G is connected, it has a spanning tree. If G is a tree itself, then it must "contain" a spanning tree. If G is connected and not a tree, then it must have at least one cycle. I don't know if you know this or not, but there is a theorem stating that an edge is a cut-edge if and only if it is on no cycle (a cut-edge is an edge such that if you take it out, the graph becomes disconnected). Thus, you can just keep taking out edges from cycles in G until all that is left are cut-gees. Since you did not take out any cut-edges, the graph is still connected; since all that is left are cut-edges, there are no cycles. A connected graph with no cycles is a tree. Thus, G contains a spanning tree. Therefore, a graph G is connected if and only if it has a spanning tree!
How do you count spanning trees in a graph?
Cayleys formula states that for a complete graph on nvertices, the number of spanning trees is n^(n-2). For a complete bipartite graph we can use the formula p^q-1 q^p-1. for the number of spanning trees. A generalization of this for any graph is Kirchhoff's theorem or Kirchhoff's matrix tree theorem. This theorem looks at the Laplacian matrix of a graph. ( you may need to look up what that is with some examples). For graphs with a small number of edges and vertices, you can find all the spanning trees and this is often quicker. There are also algorithms such as depth-first and breadth-first for finding spanning trees.
What does wanga means?
Wanga is from the bantu languages spanning from central to southern African. And means "MINE"
What two elements will exist in a converged network with one spanning tree?
root bridge and Priority
