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In triangle XYZ: XZ = 10 cm; YZ = 8 cm; cos Z = 1/8. Calculate the length of XY.

We can use the cosine rule to determine the lenght of XY.
XY²= 10²+8²-2108cos ZXY² = 100+64-180(1/8) = 144XY = 12

Answered by Vencel H. • Maths tutor

5787 Views

Factorise this equation and then solve for x) 2x^2 - 3x-2

Do 2x -2 = -4List these factors Choose two of those factors which equal to -3x, in this case 1 and -4 (or the other way around)Rewrite the equation as 2x²+ x - 4x -2, then factorise this in tw...

Answered by Ellen C. • Maths tutor

4528 Views

Integrate x*(5e^x)

Using integration by parts let U=x therefore du=dx.Let dv=5e^x therefore v=5e^x.answer = x*5e^x - integral(5e^x) = (x-1)(5e^x)

Answered by Maximillian S. • Maths tutor

3111 Views

Differentiate y=(5x^4)cos(2x)

Using chain and product rule.dy/dx=(20x^3)cos(2x) - (10x^4)sin(2x)

Answered by Maximillian S. • Maths tutor

3896 Views

A matrix M has eigenvectors (3,1,0) (2,8,2) (1,1,6) with corresponding eigenvalues 1, 6, 2 respectively. Write an invertible matrix P and diagonal matrix D such that M=PD(P^-1), hence calculate M^5.

Without even knowing M, the candidate can calculate M^5. This will follow from the fact that P is the matrix consisting of the eigenvectors of M as columns, and D will have the eigenvalues (in matching co...

Answered by Cameron B. • Maths tutor

2635 Views