113-rosay-07fafin

113-rosay-07fafin - Math 113 FINAL EXAM, Dec. 20th, 2007,...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 113 FINAL EXAM, Dec. 20th, 2007, (2 hours). NAME: ' SECTION: Instructor: lNO CALCULATOR means: NO CALCULATOR.I I. NO CALCULATOR. (20 points) Give the EXACT value of |BD| (the length of the line segment from B to D). B II. (With calculator). Assume that the triangle OAB has an area of 3 sqft, and IOAI = 4 ft. Evaluate the angle 6 in degrees AND in radians. Evaluate the length of the arc of circle from C’ to A, and the area of the shaded region (in terms of 0 if you were not able to find 6). R V (30 points) ANSWERS: 6 = radians 0 Length of arc 2 Area of shaded region : III. No CALCULATOR. ‘ . - ' (25 points) Find all solutions to 1 + tan2 6 = 16 sin2 6, with ~19? g 6 g ' IV. A hiker walks 3 miles in direction of north, then 3 miles east and finally 1 mile in direction of 30° south of east (i.e. a heading of 120°). What is the distance (’as the crOw flies’) from the starting point to the end point? (25 points) r V. Graph 3/ = 2cos 2 7' \I x — —..- ( + 2) 1 3 (30 points) \/ { VI. (20 points) 1). What are all the complex cube roots of —8? 2) Find a complex number 2 such that (1 +2i)z = (1 +32) (2 in Cartesian form a + bi). MM VII. (25 points) 1) Given sing = % and 32'— S 6 S 7r. Evaluate cos 6. Evaluate c053 and sin 3. (NO CALCULATOR) 2) Find a square root of the complex number z = —2\/§ + i. VIII. A river,- flowing south, is .1 mile wide. The speed of the current is 4 mi/h. A swimmer leaves the west bank at point A. Point A’ is straight across the river on the other bank. The swimmer swims at a speed of 1 mi/h. If the swimmer swims with a heading of 400 east of north, how far south of A’ will the swimmer land, and how much time will crossing the river take? ’ I _ (25 points) For 10 points of extra credit ( explanations required): What should the heading be for the swimmer in order to land as close as possible to point A’, and then, how far south of A’ will the swimmer land .9 What should the heading be in order to have the shortest crossing I time, and what would then be the landing point? ...
View Full Document

This note was uploaded on 08/08/2008 for the course MATH 113 taught by Professor Rosay during the Spring '07 term at Wisconsin.

Page1 / 6

113-rosay-07fafin - Math 113 FINAL EXAM, Dec. 20th, 2007,...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online