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We have our function of y = 1+2x-x² The gradient of a stationary (or turning) point is 0, in essence a peak or a trough. In order to determine the gradient, we need to differentiate our ...

Let's first consider the differential of 2^x. We know that this becomes ln(2)*2^x. We can compare this to the integrand and see that this is very clos...

Coefficient of Restitution (CoR): Speed of Approach x CoR = Speed of Seperation 4 x 0.3 = 1.2 ms^-1 Kinetic Energy (KE) Lost: KE lost = Initial KE - Final KE Initial KE = 1/2mv²      ...

Rearrage equation (1) to make y the subject of the formula. This gives y = -4x -1 .

Substitute this value of y into equation (2). This gives (-4x -1)^2 +5x^2 +2x = 0 . 

Expanding out the bra...

y = x - 2

y² + x² = 10

1. Subsitutute the top equation into the second equation:

     (x-2)² + x² = 10

2. Exp...