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3sinh^2(2x) + 11sinh(2x) - 4 = 0 --> (3sinh(2x) - 1)(sinh(2x) + 4) = 0 --> sinh(2x) = 1/3, sinh(2x) = -4(e^(2x) - e^(-2x))/2 = 1/3 --> e^(4x) -(2/3)e^(2x) - 1 = 0 --> e^(2x) = 1/3 + 2sqrt(5)/3...

(1+2i) (2+i)/(2+i)(2-i) = (2-2+4i+i)/5 = 5i/5 = i

8,5,6Add '-x-' to each of the three terms on the leading diagonalCalculate the determinant of the 3x3 matrix and set equal to zero (property of eigenvalues)Factorise to find values of x, for which the det...

Vector joining the two lines = (1, 5, 6) - (1, 7, -3) = (0, -2, 9)Normal vector to the two lines = (-2, -1, 0) x (2, 0, 4) = (-4, 8, 2) = 2(-2, 4, 1)Hence, using the dot product, shortest distance = (0, -...

The word "ordinary" means that there are only two variables, "first-order" means that the highest derivative is the first derivative and "linear" means that the highest power...