Practice Problems

# Practice Problems - For the following problems the points A...

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Unformatted text preview: For the following problems, the points A = (37 2), B : (47 7), C’ : (—27 5), D = (O, —3). 1. The vector A33 2 b <\ ) 75> (a) <1g5> (b) <7,9> (c) <—1,—5> (d) <12,14> ‘\ 2‘ The length of BE: (/(91 ’13 (a) x/éngm MK’. (10} M—x/E 0) \f8— m —+ A i 1" 3.1fAE~< 1,2>, thenE~ (Ll, (4,4) (0) (3, 4) (6 4 (d) , ) 4. Are vectors Ab and 0—D orthogonal? < * (2,“) Tie; 5t “V (a) yes “d/ﬂ-l ---- *- ‘ v 1/ w 4;» ~ 00/ 0 rr” A " 3 5. Find the area of triangle ABC: N; I, ‘ {1. HQ, “*2 J x r (a) WW3? Ki 0‘5} 33> ‘ (b) 28 Mm 4,, ﬂ: (C) 7L J. I w» 6. <2,9>-<—4,l>: (§L< —6, —8 > (b) 1} , A O :3 " f‘ L'Ur’Tr’i’r’L, - ’ ’ Q J»? »~ I ‘j | , [J , ‘ /X '2, ,3 _. 13 , gr ' a.) 743 (c) <—8,9> (d) 38 7. Find<3,1,1> >< <2,2,3>: (a) <:1 7,4 >- ”153 l 1Z, 33 (b) <6,2,3> "Vb—Mm“ é£:)-< L-—7,4:> ‘ l w3'ZLIl (d) Si Medan" 8. True or false: Every 3-zonogon can tile the plane. ue g (b) False E 9. A 3-zonogon divides into how many parallelograms? ea n7”? V": 6 (a) 2 9 a 2 (C) 5 ((1) none of the above 10. Which regular polyhedron has exactly 6 vertices? (a) tetrahedron b cube I’ll/{HM @octahedron (d) dodecahedron 1 We J}; (e) icosahedron — ’Kf) SENS 11. If the regular tetrahedron is truncated at the l/3—points of each edge, how many faces does the resulting polyhedron have? (a) 4 (d) 12 12. A semiregular polyhedron has the Schlaﬂi symbol 3.5.3.5. What is the spherical deviation of one vertex? (OOH of Mr! 0% [,3 :5 3 (17» bus/5 3a~waa ( 13. A polyhedron with 10 faces and 36 edges has how many vertices? (a) 24 t: A] «Er/«,7. b 26 LO + \l ‘~ j; z. I; c 8 "’ (d) 44 14. A semiregular polyhedron has 14 faces and the Schlaﬂi symbol 3.4.3.4. Find a module? for this polyhedron: , L> (£31610va if) 1" {l (0% 7a Li L? (a) 1 triangle and 1 square Z; a :3 ,. .3 j: .., b 2 trian les and 2 s uares , ( ) s q 215 T ﬁg (c) 3 triangles and 4 squares 3 @ 4 triangles and 3 squares Ll A “l” (e) 7 triangles and 7 squares l 15, The Schlaﬂi symbol 3.4.4 fails to be a polyhedron for which of the following i‘easonsﬁ/fwtétélj‘fl (EM (a) The spherical deviation at a vertex is not a positive number. l) (b) The spherical deviation is positive, but there are not a whole number of vertices. (c) There is a whole number of vertices but not a whole number of edges. (d) There is a whole number of vertices and edges, but the number of faces is negative. The vertices, edges, and faces are whole numbers, but no module will work. will"; 16. trahedron has an edge length of t and a volume of 5. What is the volume of the octahedron whose edge length is t? __, , 7 , V56, {3 6 5: ,/ ,r i X i Eh I @0 ml}, ,4 .. i j . v. (,7 2/0 (c) 20t (d) 202:3 (e) 125 17. An octahedron has a volume of gg. How long is an edge of this octahedron? A mﬁmk (3‘3) 0 8 r (<93 3 (6)3??? \QLTL "3 «elm ,Ffr_ee..Respon§e,=, The diagram above shows an icosahedron inscribed in a cube. The edges of the icosahedron have length 1. Points A, B, and C are vertices of the icosahedron. Points D and E are the midpoints of the front and top faces of the cube. Point F is the midpoint of the edge shared by the front and top faces of the cube. Complete the following steps to ﬁnd the length of the edges of the cube. ' 1. AC : __l__ (Find the numerical value of this length.) x 2. AD : "/3: (Find the numerical value of this length.) 437 3. CD : "£7." (Find the numerical value of this length.) (Hint: Pythagorean Theorem.) 4. BF : a: (you don’t yet have enough information to ﬁnd this value, so we’ll call it 3:. U . 7, 5. CE : __:‘_2: (Find the numerical value of this length.) V “l3 "1 f E :5 v “N if 6. CF 2%-}; (Find this value in terms of n.3,»- )( 3"" 35%“ ,2 “L 4'» VJ ’L ._ 2.: a -7}. ,é. 7. Use the fact that CFD is a right triangle to solve for x. x = ___ _. 3L 4 I ’ " L; '1' 4v) .1’ / ti 1, 8. How long is an edge of the cube? ls l‘ W 7‘ "Zr “ O ....;,.... r '? "2 . I _ ¢ 1/)“: k 7 “3" w l 'L 0 <3 ( ...
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