By de Francoise Demengel, Gilbert Demengel

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**Additional info for Espaces fonctionnels : Utilisation dans la résolution des équations aux dérivées partielles (Broché) **

**Sample text**

C) Find C for u = 15° (to the nearest hundred dollars). (D) The following table from a graphing calculator display shows the various costs for u from 15° to 45° (X represents u and Y1 represents C). Explain the behavior of C relative to u. For what value of u in the table is the total cost C minimum? What is the minimum cost (to the nearest hundred dollars)? 42Њ x Figure for 37 38. Surveying Standing on one bank of a river, a surveyor measures the angle to the top of a tree on the opposite bank to be 23°.

Coastal Piloting A boat is cruising along the coast on a straight course. A rocky point is sighted at an angle of 31° from the course. 8 mi, another sighting is taken and the point is found to be 55° from the course (see Fig. 5). How close will the boat come to the point? 8 mi Solution x Referring to Figure 5, y is the closest distance that the boat will be to the point. To ﬁnd y we proceed as follows: From the small right triangle we note that x cot 55° = Solve for x. 8 + x cot 31° = Multiply both sides by y .

Explain. ) 35. Precalculus: Pipeline An island is 4 mi offshore in a large bay. A water pipeline is to be run from a water tank on the shore to the island, as indicated in the ﬁgure. Island 4 mi u P (E) How many miles of pipe (to two decimal places) should be laid on land and how many miles placed in the water for the total cost to be minimum? 36. Precalculus: Pipeline Refer to Problem 35. (A) Express the total length of the pipeline L in terms of u. (B) Find L (to two decimal places) for u = 35°.