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I don't know what I am doing when I solve differential equations using the integrating factor and why does this give us the solutions it does?

Start by looking at the form of equation where we can use the integrating factor:y' + f'(x) y = g(x) The general principle of this method is that by multiplying our expression by some function of x it become...
OB
2818 Views

A 1kg ball is dropped of a 20m tall bridge onto tarmac. The ball experiences 2N of drag throughout its motion. The ground has a coefficient of restitution of 0.5. What is the maximum height the ball will reach after one bounce

Energy GPE of the ball on the bridge: MGH = 1 * 9.81 * 20 =196 J energy lost to drag = F * D = 2 * 20 = 40 J Velocity of the ball just before impact =sqr(2*(196-40)/1) =17.66 m/s Velocity of the ball just af...
MD
2766 Views

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
3470 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
3017 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
3097 Views