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Given that k is a real number and that A = ((1+k k)(k 1-k)) find the exact values of k for which A is a singular matrix.

okay so A is a 2x2 matrix.for it to be singular its determinate has to equal 0.a 2x2 matrix's determinate is equal to m 1,1 m 2,2 - m 1,2 m 2,1 for this example:det(A) = (1+k)(1-k) - (k)(k) = 0multiplying ou...
KY
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The function f is given by f(x) = SQRT(2x − 5). Work out x when f(x) = 1.2

1.2 = SQRT(2x-5)square both sides1.2^2 = 2x -5 add 5 to both sides 1.2^2 + 5 = 2xdivide both sides by 2(1.2^2 + 5)/2 = x
KY
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A rectangular hyperbola has parametric equations x = 4t, y = 4/t , (z non 0). Points P and Q on this hyperbola have parameters t = 1/4 and t = 2. Find the equation of the line l which passes through the origin and is perpendicular to the line PQ.

Since we are told that the line l is perpendicular to the line PQ, we first need to find out the gradient of PQ. To do this, it is easiest to find out the co-ordinates of points P and Q in terms of their car...
ZE
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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
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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
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