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A) Prove the following theorem by considering two distinct cases. For any integer n, n2 + n is even.
B) If x = r2 - s2 and y = 2rs for any integers r and s, then x2 + y2 = z2 for some nonnegative integer z. State the hypothesis of this sentence and the conclusion. Give a direct proof of the statement
A house wall may be approximated as two 1.2 cm layers of fiber insulating board, a 8 cm layer of loosely packed asbestos, and 10 cm layer of common brick. Assuming convective heat
if the sides of a triangle ABC vary in such a way that it''s circum-radius remains constant. prove that, da/cos A+db/cos B+dc/cos C =0
If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 decimal places, of the corresponding temperature function T1(u,v) at the point (u,v) =
i
in the diagram shown below, the fuel tank which is of uniform cross section and of length 8m is position so that the rear of the tank is 19 metres from the datum. the mass of the f
given sample A : HAS SIZE 6,MEAN 8,VARIANCE 16 AND SAMPLE B:has size 10,mean 20 and variance 36 .calculate pooled sample variance
#quExample - Electronics application of 3×3 System of Equations Find the electric currents shown by solving the matrix equation (obtained using Kirchhoff''s Law) arising from this
y''=2xy/x^2-y^2
The number ways of choosing 2 boys and 2 girls in a class for a game of mixed doubles is 1620. Then, what is the number of ways of choosing 2 students in the class?
The displacement x meters of a mass from a fixed point about which it is oscillating is given by x=2.3cos?10pt+4.2sin?10pt where t is the time in seconds Express the displaceme
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