A power station A and sub-station B are separated by hills. The shortest distance through the hills is 12.0 km due north. The distance from A to this point is 18.0 km due west over level ground. Underground power cabling is needed to connect A and B. At some stage the cable must run through the hills to get to B which is located immediately on the other side of the hills. The cost of laying the cable on level land is £175,000 per km. The cost of tunnelling it through hill is £550,000 per km. a. Using differential calculus find the most economical way of laying the pipeline from A to B and the length of tunnelling required. Verify that it is a minimum value by used of a calculus method. b. Check your solutions in a by using a graphical method and compare your answers.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.