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Measurement Science - Assignment 4

# Measurement Science - Assignment 4 - SUR 3520 Measurement...

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SUR 3520: Measurement Science Spring 2007 – Section 4218 Assignment No. 4 Due Date: February 12, 2007 Student UFID: 62441221 Student Name: Shane Christy 4.1 Find the inverse of = 10 4 5 3 A - - 3 . 4 . 5 . 1 4.2 Use first-order terms of Taylor’s expansion series to iteratively determine the equation of a circle that passes through the points (9.4, 5.6), (7.6, 7.2), and (3.8, 4.8). Take initial approximation for unknowns of the circle equation: center point (x c ,y c ) = (7, 4.5) and radius (r) = 3; circle equation is 2 2 2 94 . 2 ) 39 . 4 ( ) 72 . 6 ( = - + - y x 4.3 In Problem 1.6 compute the estimated error in the overall distance as measured by both the 100-ft tape. . 0045 . ) 004 (. ) 0021 (. 2 2 ft ± = + 4.4 A slope distance is observed as 1506.843 ± 0.009 m. The zenith angle is observed as 92°37 29 ± 8.8 . What are the horizontal distance and its uncertainty? m ce is HorzontalD S S m S H H H 0095 . 262 . 1505 tan 0095 . ) 00294 (. ) 00899055 (. ) " 8 . 206264 " 8 . 8 ) 29 37 2 sin( 843 . 1506 ( ) 009 . 99895 (. 2 2 2 ± = ± = + = - - - + = 4.5 A rectangular parcel has dimensions of 538.056 ± 0.005 m by 368.459 ± 0.004 m. What are the area of the parcel and the uncertainty in this area? University of Florida Geomatics – SFRC 2 2 2 ) c ( ) ( r y y xc x = - + -

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SUR 3520: Measurement Science Spring 2007 – Section 4218 2 2 2 2 3 198252 068 . 3 ) 004 . 459 . 368 ( ) 005 . 056 . 538 ( m m Area S S A A ± = ± = + = 4.6 A racetrack is measured in three simple components; a rectangle and two semicircles.
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