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Question: Show that every planar graph G can be colored using five or fewer colors.
The famous Art Gallery Problem asks how many guards are needed to see all parts of an art gallery, where the gallery is the interior and boundary of a polygon with n sides. To state this problem more precisely, we need some terminology.A point x inside or on the boundary of a simple polygon P covers or sees a point y inside or on P if all points on the line segment xy are in the interior or on the boundary of P. We say that a set of points is a guarding set of a simple polygon P if for every point y inside P or on the boundary of P there is a point x in this guarding set that sees y. Denote by G(P) the minimum number of points needed to guard the simple polygon P. The art gallery problem asks for the function g(n), which is the maximum value of G(P) over all simple polygons with n vertices. That is, g(n) is the minimum positive integer for which it is guaranteed that a simple polygon with n vertices can be guarded with g(n) or fewer guards.
Determine the per annum interest rate required for an investment with continuous compound interest to triple in 6 years. Express your answer as a percent. Enter an exact answer or round to three decimal places, for example 10.227%. Don't include t..
A building is 372 feet tall. For a class project, Kari is to make a scale model of the building to place in the front hall display case. The display case is 29 inches tall. Which scale will allow her to make the tallest model that will fit in the ..
A carton can hold 1000 unit cubes that measure
1. Find an equation of the line that passes through (-3, 5) and is parallel to the line with equation 5x - 2y = 10. Write the new equation in point-slope form.
The cross section of a large circular conduit has seven smaller equal circular conduits within it. The conduits are tangent to each other as shown in Fig.
Write initial value problems to determine the velocity of the rocket, with t being a function of time for (a) 0 ≤ t ≤ 35 (b) 35 ≤ t ≤ T.
Savannah has a water bottle that is a rectangular prism the bottle measures 7 centimeters by 5 centimeters by 18 centimeters and she filled it completely with water then she drank 1/4 of the volume of water in her water bottle how many cubic cent..
Rectangular trench is to be dug which is to be 240 ft long, 90 ft wide and 9 ft deep. A large dumb truck can carry 20 cubic yards in a load. How many truck loads will be required to remove
Find the equation of the least-squares line for the given data. Draw a scatter diagram for the given data.
What is the fee if the project is completed 4 days after the deadline
Examples of Probability and Statistics in Real Life, Can you think of situations in the business world or other real life situations where you would need to calculate or estimate probabilities?
Find the directional derivative of the function at the given point in the direction of the vector v.
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