The distance d(v, w) between two vertices v and w in an undirected graph is defined as the minimal length of any path connecting these two vertices. If v and w are not connected, then d(v, w) = ∞. Now, define the diameter of the graph G = (V, E) as diam(G) = max d(v,w). v,wɛV And define the radius of the graph as rad(G) = min max d(v, w) . veV weV Prove that rad(G) < diam(G) < 2rad(G).

Q: Find the midpoint of the sides of the quadrilateral LOVE with vertices L(-3, -2), O (0, 6), V(4, 4),…

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Q: company is also shown. % Working % 67

A: * Hi! Thank you for the question, As per the honour code, we are allowed to answer three sub-parts…

Q: Find the distance from the point (5,8) to the circle x2 + Y2 + 2x + 6y + 3 = 0

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Q: Use slopes to show that the quadrilateral with vertices at (1, 3), (-5/2, 2), (-7/2, 4), and (2, 1)…

A: Given that Vertices of quadrilateral are A1, 3, B-72, 4, C-52, 2 and D2, 1   It is known that the…

Q: A rectangle has its vertices at M(1,1),N(6,1),O(6,5),and P(1,5).The rectangle is translated to the…

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Q: (x1,y1)=(4, 2),(x2,y2)=(3, 0),  (x3,y3)= (1, 7) and(x4,y4)=(8,2). Trace these points on graph, also…

A: Let A(4,2) , B(3,0) , C(1,7) , D(8,2)

Q: A figure has vertices A(2, 5), B(8, 12), and C(-7, -2). Add 3 to each x-value and subtract 4 from…

A: Given a figure has vertices A2,5, B8,12 and C-7,-2. Now, we have to add 3 to each x-value and…

Q: Show that the distance between the two points z1 and z2 in anArgand diagram is | z1 - z2 | .

A: Argand diagram:  1 It is a plot of complex numbers as point.  2In the complex plane using…

Q: The shortest distance from (−7,6,−8) to the xy-plane is

A: Since the plane is a xy-plane so, the point will be (-7,6,0).

Q: Determine what is the minimum distance from the origin to the line  y=-2x+5

A: topic - distance of line from origin

Q: Q2) Find the distance between the line y= - (x+2 ) & the center of the circle y + x – 4(x+ y )= 9

A: The center of the circle x2+y2-2ax-2by+c=0 is a, b Therefore, the center of the given circle…

Q: Find the area of the quadrangle with vertices Area = (5,1). (-4, 5). (-3,-4), and (4, -3).

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Q: 16. The diagonals of a parallelogram intersect at (-1,3). One of the sides of the parallelogram is…

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Q: Find the length of a semi-circle with endpoints at (1,3) and (4.7)/

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Q: Find the distance d between the points (1, 3) and (5, 6).

A: Our Aim is to find the distance between the points (1,3) and (5,6).

Q: Find the area of the parallelogram with vertices at (5, -2), (11, 3), (14, –8), and (20, -3).

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Q: A quadrilateral has the vertices D (-4, -1), E (0, -4), F (6.0) and G (0.4). Verify for each pair of…

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Q: Graph the solution of the system of inequalities. x20 y2-1 y≤3 2x + y ≤ 7

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Q: Solve the initial value-problem: Y with Y(0) (1,0). dt -1 4

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Q: A square has an area of 36 and one side that lies along the line y = 3. What could be the location…

A: To find the possible co-ordinates of square.

Q: A circle in the xy-plane has a diameter with endpoints (-1, 3) and (7,3). If the point (0,b) lies on…

A: Topic = circle