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How to find total no. of unordered pairs of disjoint subsets of a finite set? Solution) Suppose A and B are two such disjoint subsets of the set S. Then every element can go into A or B or the set S (3 choices). We only require to exclude the possibility of all elements choosing to be in S itself. Therefore the number of ways is 3n-1
if the sum of lengths of hypotenuse and a side of right triangle are given, prove the area of the triangle is maximum when angle between them is pi/3
Determine the general solution to 2t 2 y'' + ty' - 3y = 0 It given that y (t) = t -1 is a solution. Solution Reduction of order needs that a solution already be iden
in one point of the circle only one tangent can be drawn. prove
A 25 foot ladder just reaches the top of a house and forms an angle of 41.5 degrees with the wall of the house. How tall is the house?
Download the data on Gas Mileage. This is a sample of 81 passenger cars with information about gas consumption and other technical details. a. Estimate the following
Decision-Making Under Conditions of Uncertainty With decision making under uncertainty, the decision maker is aware of different possible states of nature, but has insufficient
Solve 4 cos(t )= 3 on[-8,10]. Solution : Here the first step is identical to the problems in the previous section. First we need to isolate the cosine on one side by itself & t
Cylinder The below equation is the common equation of a cylinder. x 2 /a 2 + y 2 /b 2 = 1 This is known as a cylinder whose cross section is an ellipse. If a = b we
The width of a rectangle is 30.5% of its length l. Write a formula for the area and perimeter of the rectangle in terms of l only
A sample of students had a mean age of 35 years along with a standard deviation of 5 years. A student was randomly picked from a group of 200 students. Determine the probability
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