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Unformatted text preview: Answers to the Exercise Sets Exercise Set 1 1. (a) 5 − π (b) 2 x + 1 (c) 1 − 2 x (d) | 2 x | − x = { x if x ≥ − 3 x if x < 2. (a) x = a 2 (b) x = 1 (c) x = 1 / 3 (d) x = ± √ 3 2 3. (a) [ − 1 , 0] ∪ [5 , ∞ ) (b) [ − 1 , 3 2 ] (c) ( −∞ , − 7 2 ) ∪ ( 1 2 , ∞ ) (d) ( , 2 3 ] (e) ( −∞ , − 1) ∪ [ − 1 3 , 1 ] (f) ( −∞ , − 1 2 ] ∪ ( 1 5 , ∞ ) 4. 5 5. (1 , − 3) and ( − 5 , − 3) 6. y = − 2 3 x − 7 3 7. y = 2 5 x − 16 5 8.- 3 3 9 x y 9. (a) center (0 , 0), radius 7, x-intercepts ± 7, y-intercepts ± 7 (b) center (3 , − 2), radius 5, x-intercepts 3 ± √ 21, y-intercepts − 6 and 2 10. (a) y = (2 . 2%) t + 5 . 4% (b) 9.8% 11. (b) 5 ≤ C ≤ 45 12. [2 , 3] (in seconds) 13. 11 . 98 ≤ x ≤ 12 . 02 (in inches); Area ∈ [143 . 5204 , 144 . 4804] (in square inches) Exercise Set 2 1. (a) 10 π/ 3 (b) − 105 ◦ 2. (a) 16 π 3 cm (b) 64 π 3 cm 2 3. (a)- 540 ◦ ◦ 90 ◦ (b) 10 π 3 ◦ 90 ◦ 4. (a) sin ( − 5 π 2 ) = − 1, cos ( − 5 π 2 ) = 0, tan ( − 5 π 2 ) does not exist, csc ( − 5 π 2 ) = − 1, sec ( − 5 π 2 ) does not exist, cot ( − 5 π 2 ) = 0 (b) sin ( 11 π 6 ) = − 1 2 , cos ( 11 π 6 ) = √ 3 2 , tan ( 11 π 6 ) = − 1 √ 3 , csc ( 11 π 6 ) = − 2, sec ( 11 π 6 ) = 2 √ 3 , cot ( 11 π 6 ) = − √ 3 5. cos θ = − 2 3 , sin θ = − √ 5 3 , tan θ = √ 5 2 , csc θ = − 3 √ 5 , cot θ = 2 √ 5 6. 9.8506 in 7. (a) true (b) false (c) true 8. (a) 7/25 (b) 6 5 √ 13 10. π/ 3, 5 π/ 6 11. (a) 0, π/ 4, π , 7 π/ 4 (b) π/ 6, 5 π/ 6, 3 π/ 2 (c) π/ 4, 5 π/ 4 (d) π/ 4, 3 π/ 4, 5 π/ 4, 7 π/ 4 12. (a) [ , π 3 ] ∪ [ 2 π 3 , 2 π ) (b) [ , π 4 ) ∪ ( 5 π 4 , 2 π ) 13. [ π 2 ,π ) ∪ [ 3 π 2 , 2 π ) 14. (b) θ = π/ 3, A = 27 √ 3 in 2 Exercise Set 3 1. (a) 5 (b) x ∈ { 5 , 8 } (c) domain [0 , 10], range [ − 2 , 5] (d) true 2. (a) no (b) yes (c) yes (d) no 3. (a) Temperature Time (hours) (b) Score Time (hours) (c) D Hand Position 4. Volume(gallons) Time (minutes) 5. (a) x 2 − 1 x 2 + 1 (b) 2 a 2 a + 2 (c) 2 h 9 + 3 h (d) 2 ( a + 1)( a + h + 1) 6. 3 s 2 + 3 s + 1 7. (a) [ 3 2 , ∞ ) (b) ( −∞ , 0) ∪ (0 , ∞ ) (c) ( −∞ , − 1) ∪ ( − 1 , ∞ ) (d) [0 , 1) ∪ (1 , ∞ ) (e) ( −∞ , 0) ∪ [1 , ∞ ) 8. (b) f ( x ) = { 2 if x > if x < 2 x y (c) f ( x ) = 1 − x , x ̸ = − 1 1 1 (- 1 , 2) x y 9. If A is the area of the pen in square feet, then A ( x ) = x (500 − 2 x ) with domain [0 , 250]. 10. If V is the volume of the can in cubic centimeters, then V ( r ) = 1 2 r (100 − 2 πr 2 ) with domain ( , √ 50 /π ] . 11. If S is the surface area of the can in square centimeters, then S ( r ) = 2 ( πr 2 + 1000 r ) with domain (0 , ∞ )....
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