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1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
Q) In a lottery ,a person chooses six different natural numbers at random 1to 20,and if there six numbers match with the six numbers already fixed by the lottery committee ,he win
As we saw in the previous section computing Laplace transforms directly can be quite complex. Generally we just utilize a table of transforms when actually calculating Laplace tran
We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a
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1) Compute the center of mass of the solid of unit density 1 bounded (in spherical coordinates) by p=1 and by φ is greater than or equal 0 and less than or equal pi/4
A rescue and ?re squad places a 15 ft ladder against a burning building. If the ladder is 9 ft from the base of the building, how far up the building will the ladder reach? a. 8
Slope of Tangent Line : It is the next major interpretation of the derivative. The slope of the tangent line to f ( x ) at x = a is f ′ ( a ) . Then the tangent line is given by,
Evaluate the convergence of the algorithms: From the convergence proof of power method, LR and QR algorithm for the computation of eigenvalues we see that the easiest case to
Problem 1. Find the maximum and the minimum distance from the origin to the ellipse x 2 + xy + y 2 = 3. Hints: (i) Use x 2 + y 2 as your objective function; (ii) You c
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