By Allen J. Baldwin P.E., Karen M. Hess Ph.D. (auth.)

Engineering registration is accelerating at a speed unmatched due to the fact establishment of registration legislation within the Nineteen Twenties and Thirties. This phenomenon isn't because of an easing of front require ments, due to the fact that in simple terms vestiges of "grand fathering" and eminence exist in so much states. neither is it because of a lessening within the trouble of the registration examinations. actually, it really is as a rule agreed that the Engineering basics exam has considerably elevated in trouble during the last fifteen years. Why then the elevated curiosity in registration between working towards engineers? traditionally the pro engineer has been in inner most perform providing consulting providers on to the general public. Registration legislation have been handed to guard the general public from incompetent, untrained practioners in any engineering zone. despite the fact that, the registration legislation transcend estab lishing an individual's credentials. One explanation for the recent curiosity in engineering registration is the proliferation of recent task parts equivalent to toxins regulate and effort conservation the place the general public is keenly conscious of and insistent upon caliber technological inputs.

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D. Triangle B is not a right triangle, so the Pythagorean Theorem does not apply, but one can construct a right triangle and apply the Pythagorean Theorem to it: This is one method of operating on oblique triangles. 27 I / MATHEMATICS AND SCIENCE 2. b. Area of triangle 1bh = 7000. This is one equation in two unknowns. The Pythagorean Theorem provides another equation in the same two unknowns: = (172)2. b2 + h2 Solve these two simultaneously. If you had difficulty with this problem, review p. 10.

PROBLEM The distance between P(2,3) and P( -1,2) is: a. b. c. d. e. 41. 83. 89. 00. 16. Check your answer. Answer e. If you had trouble with this problem, you probably (a) were not consistent in defining point 1 and point 2, OR (b) made an error in the sign of a number during manipulation. C. LOCI The Latin word locus is the root of the English word location. A moving point has a location in Cartesian coordinates at any point in time. If these locations were plotted, the result would be a line; therefore, a locus is a line in space.

42 ANALYTIC GEOMETRY Example Find the locus of a point (P) which moves so that it is always equidistant from two fixed points, A(1,2) and B(-l,O). y B --_""""'-----+------- x From the statement we know that Dl always equals D2 : Reducing this results in the following: x 2 - 2x + I + y2 - 4y + 4 = x 2 + 2x + I + y2 or x+y-l=O the equation of a straight line. PROBLEMS 1. What is the locus of a point which is always equidistant from the point P( 1,1) and the line x =O? a. b. c. d. e. Circle. Ellipse.