59. Nautical Distance A close estimate of the radius of Earth's equator is 3960 mi.
    1. Write the equation of the equator with the center of Earth as the origin.
    2. Find the length of a 1 ° 1 degrees  arc on the equator to the nearest tenth of a mile.
    3. History Columbus planned his trip to the East by going west. He thought each 1 ° 1 degrees  arc was 45 mi long. He estimated that the trip would take 21 days. Use your answer to part (b) to find a better estimate.

Standardized Test Prep

SAT/ACT

60. What is an equation of a circle with radius 16 and center ( 2 , − 5 ) ? open 2 comma negative 5 close question mark
    1. ( x − 2 ) 2 + ( y + 5 ) 2 = 16 open x minus . 2 , close squared , plus , open y plus . 5 , close squared . equals 16
    2. ( x + 2 ) 2 + ( y − 5 ) 2 = 4 open x plus . 2 , close squared , plus , open y minus . 5 , close squared . equals 4
    3. ( x + 2 ) 2 + ( y − 5 ) 2 = 256 open x plus . 2 , close squared , plus , open y minus . 5 , close squared . equals 256
    4. ( x − 2 ) 2 + ( y + 5 ) 2 = 256 open x minus . 2 , close squared , plus , open y plus . 5 , close squared . equals 256

61. What can you NOT conclude from the diagram below?

    
    Image Long Description

    6. c = d c equals d
    7. c 2 + e 2 = b 2 c squared , plus , e squared , equals , b squared
    8. a = b eh equals b
    9. e = d e equals d

Short Response

62. Are the following statements equivalent?
    • In a circle, if two central angles are congruent, then they have congruent arcs.
    • In a circle, if two arcs are congruent, then they have congruent central angles.

Mixed Review

See Lesson 12-4.

Find the value of each variable.

See Lesson 8-5.

For the given vectors a ⇀ modified a with right harpoon up above  and C ⇀ , c with right harpoon up above , comma  write the sum a ⇀ + C ⇀ modified a with right harpoon up above , plus , c with right harpoon up above  as an ordered pair.

65. a ⇀ = 〈 − 2 , 5 〉 modified a with right harpoon up above , equals left pointing angle bracket negative 2 comma , 5 right pointing angle bracket  and C ⇀ = 〈 8 , 7 〉 c with right harpoon up above , equals left pointing angle bracket 8 comma 7 right pointing angle bracket
66. a ⇀ = 〈 − 3 , − 4 〉 modified a with right harpoon up above , equals left pointing angle bracket negative 3 comma negative , 4 right pointing angle bracket  and C ⇀ = 〈 − 2 , 6 〉 c with right harpoon up above , equals left pointing angle bracket negative 2 comma 6 right pointing angle bracket
67. a ⇀ = 〈 3 , 1 〉 modified a with right harpoon up above , equals left pointing angle bracket 3 comma , 1 right pointing angle bracket  and C ⇀ = 〈 1 , 3 〉 c with right harpoon up above , equals left pointing angle bracket 1 comma 3 right pointing angle bracket
68. a ⇀ = 〈 9 , − 6 〉 modified a with right harpoon up above , equals left pointing angle bracket 9 comma negative , 6 right pointing angle bracket  and C ⇀ = 〈 2 , − 1 〉 c with right harpoon up above , equals , left pointing angle bracket 2 comma minus , 1 right pointing angle bracket

See Lessons 1-2 and 1-5.

Get Ready! To prepare for Lesson 12-6, do Exercises 69–71.

Sketch each of the following.

69. the perpendicular bisector of B C ¯ b c bar
70. line k parallel to line m and perpendicular to line w, all in plane N
71. ∠ E F G angle e f g  bisected by F H → f h vector

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