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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
Demonstrates that f ( x ) = 4 x 5 + x 3 + 7 x - 2 has accurately one real root. Solution From basic Algebra principles we know that since f (x) is a 5 th degree polynomi
find the domain of the function f(x) = (| sin inverse sin x | - cos inverse cos x) ^ 1/2
Using the formulas and properties from above find out the value of the subsequent summation. c The first thing that we require to do here is square out the stuff being summe
The revenue and cost functions for producing and selling quantity x for a certain production facility are given below. R(x) = 16x - x 2 C(x) = 20 + 4x a) Determine the p
Multiply following. (a) (4x 2 -x)(6-3x) (b) (2x+6) 2 Solution (a) (4x 2 - x )(6 - 3x ) Again we will only FOIL this one out. (4x 2 - x )(6 - 3x) = 24x 2 -
If the vertices of a triangle are (1, k), (4, -3), (-9, 7) and its area is 15 sq units, find the value(s) of k..
In figure, the incircle of triangle ABC touches the sides BC, CA, and AB at D, E, and F respectively. Show that AF+BD+CE=AE+BF+CD= 1/2 (perimeter of triangle ABC), Ans:
Differentials : In this section we will introduce a notation. We will also look at an application of this new notation. Given a function y = f ( x ) we call dy & dx differen
Everything stored on a computer can be represented as a string of bits. However, different types of data (for example, characters and numbers) may be represented by the same strin
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