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Further Mathematics

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solve 3sinh^2(2x) + 11sinh(2x) = 4 for x, giving your answer(s) in terms of the natural log.

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...

Answered by William Michael O. • Further Mathematics tutor

2069 Views

Write (1+2i) /(2-i) in form x+iy

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

Answered by Rahil M. • Further Mathematics tutor

2247 Views

Find the eigenvalues for the matrix (4/2/3,2/7/0,-2/1/8)

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...

Answered by Tutor136255 D. • Further Mathematics tutor

1914 Views

Find the shortest distance between the lines r = (1, 5, 6) + y(-2, -1, 0) and r = (1, 7, -3) + z(2, 0, 4)

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, -...

Answered by Abhinav H. • Further Mathematics tutor

1966 Views

How would you use the Integration Factor method to solve an ordinary first-order linear differential equation?

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...

Answered by Kelvin C. • Further Mathematics tutor

2252 Views