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How would you show the equation f(x) = 2x – 10 sin x – 2 has a root between 2 and 3 (where x is measured in radians)

With these kind of problems you are looking to find 2 values with which the output of the function is positive for one and negative for the other. In this scenario they have given 2 values 2 and 3 so the fir...
KN
3490 Views

express z(2+i)=(1+2i)^2 in the form z=x+iy

rearrange gives z = [(1+2i)^2]/(2+i)expanding (1+2i)^2 gives 4i-3 therefore this becomes (4i-3)/2+i multiply that by the conjugate (2-i)/(2-i) to give (11i-2)/5therefore z= -2/5 + 11i/5
HH
3162 Views

Find the determinant of matrix M. [3]

Markscheme:[M1] correct expansion shown, allowing sign slips.[A1] correct (unsimplified) expression obtained [A1] correct answer obtained (this can also earn both A1 marks if correct expression is not shown)...
AS
3065 Views

Find the eigenvalues and eigenvectors of A = ([2, 0 , 0], [0, 1, 1], [0, 3, 3])

We can use the characteristic equation, det(A - k I) = 0 to find the eigenvalues of A. Performing this, we see that(2-k) * ( (1-k) (3-k) - 3 ) = 0.Immediately, we can see a root is k = 2, which is our first ...
CT
3120 Views

Differentiate w.r.t x the expression arccos(x).

Using implicit differentiation, let y equal arccos(x) : y=arccos(x). So x = cos(y), and dx/dy = -sin(y). dy/dx is therefore -1/sin(y). from trig indentities: sin(y) = sqrt(1-cos^2(y)). Substituting gives dy/...
DP
5326 Views