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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
A spherical holding tank whose radius to the outer surface is 10 feet is constructed of steel 1 inch thick. How many cubic feet of steel is require to construct the holding tank? R
Solve sin (α /7) =0 . Solution By Using a unit circle it isn't too difficult to see that the solutions to this equation are, α /7 = 0 + 2 ? n ⇒ α = 14 ? n
Basic indefinite integrals The first integral which we'll look at is the integral of a power of x. ∫x n dx = (x n +1 / n + 1)+ c, n
The Stefan-Boltzmann law can be employed to estimate the rate of radiation of energy H from a surface of copper sphere with radius = 0.15 ±0.01 m, as in H=AesT^4 where H is in watt
The last topic that we have to discuss in this section is that of parallel & perpendicular lines. Following is a sketch of parallel and perpendicular lines. Suppose that th
find the modulus Z=(2-i)(5+i12)/(1+i2)^3
what is the greatest projection range down an inclined plane? how we will calculate that?
what is the least number of faces and bases the paperweight could have?
Example Determinant: Determine the determinant of each of the following matrices. Solution : For the 2 x 2 there isn't much to perform other than to plug this in
Solve following 4e 1+3 x - 9e 5-2 x = 0 . Solution Here the first step is to get one exponential on every side & then we'll divide both sides by one of them (that doesn'
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