exam 2 spring 2008

# exam 2 spring 2008 - Engineering Mathematics(ESE 317 Exam 2...

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Engineering Mathematics (ESE 317) Exam 2 March 5, 2008 This exam contains nine multiple-choice problems worth two points each, 11 true-false problems worth one point each, and two free-response problems worth 11 points altogether, for an exam total of 40 points. Part I. Multiple-Choice Clearly circle the only correct response. Each is worth two points. 1. Let be the angle between the two vectors u and v . Find . # # p p œ Ò"ß #ß #Ó œ Ò\$ß !ß %Ó cos (A) " %& (B) " "& (C) " * (D) " & (E) " \$ (F) \$ (G) & (H) * (I) "& (J) %& 2. Find a vector which is normal to the plane determined by the three points E œ Ð!ß "ß #Ñß F œ Ð%ß #ß "Ñß G œ Ð\$ß #ß %ÑÞ and (A) Ò&ß )ß %Ó (B) Ò&ß )ß %Ó (C) Ò'ß "\$ß #Ó (D) Ò'ß "\$ß #Ó (E) Ò)ß 'ß \$Ó (F) Ò)ß 'ß \$Ó (G) Ò*ß ##ß "!Ó (H) Ò*ß ##ß "!Ó (I) Ò"*ß #(ß &Ó (J) Ò"*ß #(ß &Ó

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3. Identify the segment indicated in the picture below. (A) .B (B) .C (C) ? C (D) 0ÐB  ? (E) 0ÐB BÑ0ÐBÑ B ? ? (F) .C .B 4. What type of curve is represented by the following parametric equations? B œ "  %> C œ #  %> D œ > cos sin (A) line (B) ellipse (including the possibility of a circle) (C) hyperbola (or one branch of a hyperbola) (D) helix 5. Consider the vector function r . Find a , the tangential component of p p Ð>Ñ œ Ò > ß #>ß Ð>Ñ # ln tan acceleration, at the point . Ò"ß #ß !Ó (A) # " # \$ \$ \$ ß  ß  (B) # " \$ \$ ß !ß  (C) # # " \$ \$ \$

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