Using calculus, find the coordinates of the stationary point on the curve with equation y = 2x + 3 + 8/x², x>0 Answer ANSWER Explanation Explanation y = x/√(1 + x) Complete the table...
Find the first 3 terms, in ascending powers of x, in the binomial expansion of (2 − 5x)6 Give each term in its simplest form. (4) Answer ANSWER Explanation Explanation f (x) = ax³...
[In this question i and j are perpendicular unit vectors in a horizontal plane.] A particle P moves in such a way that its velocity v m s–1 at time t seconds is given...
A caravan of mass 600 kg is towed by a car of mass 900 kg along a straight horizontal road. The towbar joining the car to the caravan is modelled as a light rod...
A car of mass 1000 kg moves with constant speed V m s−1 up a straight road inclined at an angle θ to the horizontal, where sin θ = 1/30. The engine of the...
Two uniform rods AB and BC are rigidly joined at B so that ∠ABC = 90°. Rod AB has length 0.5 m and mass 2 kg. Rod BC has length 2 m and mass...
A tennis ball of mass 0.1 kg is hit by a racquet. Immediately before being hit, the ball has velocity 30i m s−1. The racquet exerts an impulse of (−2i − 4j) N s...
A cyclist starts from rest and moves along a straight horizontal road. The combined mass of the cyclist and his cycle is 120 kg. The resistance to motion is modelled as a constant force...
A factory produces components. Each component has a unique identity number and it is assumed that 2% of the components are faulty. On a particular day, a quality control manager wishes to take a...
