The distance, d metres, of a moving object from an observer after t minutes is given by d = t² + (48/t) - 20.

1. (a)Some values of t and d are given in the table. The values of d are given to the nearest whole number where appropriate. Complete the table.[1]
2. (b)On the grid, plot the points given in the table and join them with a smooth curve.[2]
3. (c)(i)By drawing a tangent, calculate the gradient of the curve when t = 4.[2]
4. (c)(ii)Explain what this gradient represents.[1]
5. (d)For how long is the object less than 10 metres from the observer?[2]
6. (e)(i)Using your graph, write down the two values of t when the object is 12 metres from the observer. For each value of t, state whether the object is moving towards or away from the observer.[2]
7. (e)(ii)Write down the equation that gives the values of t when the object is 12 metres from the observer.[1]
8. (e)(iii)This equation is equivalent to t³ + At + 48 = 0. Find A.[1]

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