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1. For a function f : Z → Z, let R be the relation on Z given by xRy iff f(x) = f(y). (a) Prove that R is an equivalence relation on Z. (b) If for every x ? Z, the equivalenc
a man can row a bangka at a rate of 5 km/h in still water. It takes 10 minutes longer to row upstream a distance of 2km than he takes to row downstream. What is the rate of the cur
find the domain of the function f(x) = (| sin inverse sin x | - cos inverse cos x) ^ 1/2
In a periscope, a pair of mirrors is mounted parallel to each other as given. The path of light becomes a transversal. If ∠2 evaluate 50°, what is the evaluation of ∠3? a. 50°
Jennifer ?ipped a coin three times and got heads each time. What is the probability in which she gets heads on the further ?ip? The probability of heads does not modify based o
The Fourier series expansion for the periodic function, f ( t ) = |sin t | is defined in its fundamental interval. Taking π = 3.142, calculate the Fourier cosine series app
If A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0. Ans : AP = PB ⇒ AP 2 = PB 2 (∝ + 4) 2
Q. Graphing Sets of Numbers? Ans. To graph a set of numbers on a number line means to plot, or locate, those positions on the line. The number that corresponds to a poin
Logarithmic functions have the following general properties If y = log a x, a > 0 and a ≠1, then The domain of the function
If p,q,r are roots of x^3-3x^2+4x-7=0 (p+2)(q+2)(r+2)=
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