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The sum of the angles in a triangle varies according to the geometry in which the triangle lies.
1. Prove that the statement "There exists a triangle with a sum of angles greater than 180 degrees" is true in spherical geometry.
2. Prove that the statement "The sum of the angles in any triangle is 180 degrees" is true in Euclidean geometry.
Note: The attached "Parallel Postulate to Triangles Diagram" may prove useful in relating the parallel postulate to triangles.
3. Prove that the statement, "Rectangles do not exist," is true in hyperbolic geometry.
A manufacturing company has 10 machines in continous operation during a workday. The probability that an individual machine will break down during the day is .10
Find the slope-intercept form of a line that is the perpendicular bisector of a line segment connecting (-7,3) and (1,17)
What are some similarities and differences between permutations and combinations? Give a real-life example of either a permutation or combination.
Poisson Distribution: Birth-Death Process. The McDougal Sandwich Shop has two windows available for serving customers, who arrive at a Poisson rate of 40/hr. Service time is exponentially distributed with a mean of 2 min.
How many solution sets do systems of linear inequalities have? Must solutions to systems of linear inequalities satisfy both inequalities?
Determine if the following chemical equation is a kinetically paced reaction: 4NO + 4NH3 + O2 = N2 + 6H2O In other words, is there a kinetic rate equation that can be presented simply that defines the pace of the above reaction
Check that N(t) = t/(1 +ct) is a solution of the differential equation dN/dt = N^2/t^2. Treat c as an unspecified constant.
Explain A developer can buy a piece of property that will produce a profit of $16,000 with probability
Find the fundamental matrix for differential equation.
Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). Also, suppose that f(a) = f(b) and that c is a real number in the interval such that f'(c) = 0.
Find is the median of the data
Compare the advantages and disadvantages of substitution and elimination methods with the matrix method to solve systems of linear equations and the relationship these have with matrix method solving.
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