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a) Let V = f1, 2, :::, 7g and define R on V by xRy iff x - y is a multiple of 3. You should know by now that R is an equivalence relation on V . Suppose that this is so. Explain the partition of V induced by R.
b) Let A = {1, 2, 3, 4} and define R on P(A) -{Ø} by xRy iff x ∩y ≠Ø. Is R an equivalence relation? Describe
how does sin of x equal negative 1/3
Derivatives of Hyperbolic Functions : The last set of functions which we're going to be looking at is the hyperbolic functions. In several physical situations combinations of e
Rates of Change and Tangent Lines : In this section we will study two fairly important problems in the study of calculus. There are two cause for looking at these problems now.
From a sheet of cardboard in the shape of a square of side 14 cm, a piece in the shape of letter B is cut off. The curved side of the letter consists of two equal semicircles & the
The Timbuktu post office has only 3 cents and 7 cents stamps having run out of all other denominations. What are the six amounts of postage that cannot be created? How do you know
A 125-foot tower is located on the side of a mountain that is inclined at 32° to the horizontal. A guy wire is to be fitted to the top of the tower and anchored at a point 55 feet
Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means
Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections. Two vectors are parallel if they have
A large pipe dispenses 750 gallons of water in 50 seconds. At this rate, how long will it take to dispense 330 gallons? Find out the number of gallons per second by dividing 75
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