Height versus horizontal distance measurements on a hillside are recorded below (in metres):

Distance 0 180 360 540 720 900 1080 1260 1440

Height 0 71 102 130 176 175 130 79 32

All measurements are in the same vertical plane.

Construct a Newton-Gregory Difference table, as far as the fourth difference, for this data. Use Newton-Gregory interpolation to answer the following question:

a) What is the slope of the hill at distance 600m?

b) Where is the highest point on the hillside and how high is it?

c) A construction company would like to flatten the hillside above the height of 130m! In order to estimate the amount of earth they will have to move calculate the cross sectional area of the hill above the height of 130 metres