10.1 Exercises Do the exercises, and check your work. *Additional answers can be found in the Answers to Exercises appendix. Objective 1: Solve an Equation of the Form x2 k 1) What are two methods that can be used to solve x2 81 0? Solve the equation using both methods. 2) If k is a negative number and x2 k, what can you conclude about the solution to the equation? Solve using the square root property. 3) b2 16 {4, 4} 4) h2 100 {10, 10} 5) w2 11 {111, 111} 6) x2 23 {123, 123} 7) p2 49 8) s2 81 {513, 513} {212, 212} {212, 212} {10, 10} {2 113, 2 113} {5 17, 5 17} {10 315, 10 315} {4 215, 4 215} {3 2117, 3 2117} {5 612, 5 612} SECTION 10.1 Solving Quadratic Equations Using the Square Root Property 611 9) x2 25 9 e 5 3 , 5 3 f 10) m2 16 121 e 4 11 , 4 11 f 11) y2 0.04 {0.2, 0.2} 12) d 2 0.25 {0.5, 0.5} 13) r2 144 0 {12, 12} 14) a2 1 0 {1, 1} 15) c2 19 0 {119, 119} 16) a2 6 0 {16, 16} 17) v2 54 0 {316, 316} 18) g2 75 0 19) t2 5 64 0 20) c2 14 81 0 21) z2 5 19 22) x2 9 17 {114, 114} 23) n2 10 6 24) y2 11 9 25) 3d 2 14 41 {3, 3} 26) 2m2 5 67 {6, 6} 27) 4p2 9 39 28) 3j2 7 31 {213, 213} 29) 3 35 8h2 { 2, 2}30) 145 2w2 55 31) 10 14 2x2 32) 6 24 3k2 33) 4y2 15 24 e 3 2 , 3 2 f 34) 9n2 17 18 35) 9w2 5 5 36) 16a2 2 13 37) 7 4 5b2 38) 1 13 6t2 Objective 2: Solve an Equation of the Form (ax b)2 k Choose from always, sometimes, or never. 39) The solutions of (ax b)2 k (where k 0) are always, sometimes, or never positive. sometimes 40) The equation (ax b)2 0 will always, sometimes, or never have exactly one solution. always Solve using the square root property. 41) (r 6)2 25 {11, 1} 42) (x 1)2 16 {3, 5} 43) (q 8)2 1 {7, 9} 44) (c 11)2 49 {18, 4} 45) (a 2)2 13 46) (t 5)2 7 47) (k 10)2 45 48) (b 4)2 20 49) (m 7)2 18 50) ( y 3)2 100 51) 0 ( p 3)2 68 52) 0 (d 5)2 72 53) (2z 1)2 9 {1, 2} 54) (5h 9)2 36 55) 121 (4q 5)2 56) 64 (3c 4)2 57) (3g 10)2 24 58) (2w 7)2 63 59) 125 (5u 8)2 60) 44 (4a 5)2 61) (2x 3)2 54 0 62) (6t 1)2 90 0 63) (7h 8)2 32 0 64) (2b 9)2 18 0 65) (5y 2)2 6 22 66) 29 4 (3m 1)2 67) 1 (6r 7)2 8 68) (3 4k)2 18 2 69) (2z 11)2 3 17 70) (5x 8)2 2 6 71) a1 1 2 cb 2 6 5 72) a2 3 p 5b 2 7 56 Objective 3: Solve a Formula for a Specific Variable Solve each problem. 73) The area of a circle is 81 cm2. Find the radius of the circle. 9 cm 74) The volume of a right circular cylinder is 28 in3. Find the radius of the cylinder if it is 7 in. tall. 2 in. 75) The surface area, S, of a sphere is given by S 4r2, where r is the radius. Find the radius of the sphere with a surface area of m2. 1 2 m 76) The surface area, S, of a cube is given by S 6L2, where L is the length of one of its sides. Find the length of a side of a cube with a surface area of 150 in2. 5 in. 77) The illuminance E (the measure of light emitted, in lux) of a light source is given by E 1 d 2, where I is the luminous intensity (measured in candela) and d is the distance, in meters, from the light source. Find the distance, d, from the light source when E 300 lux and I 2700 candela. 3 m e3, 3 5 f e4, 3 2 f e 4 3 , 4 f {0, 4} {18, 3} factoring and the square root property; {9, 9} There is no real number solution. The solution set is . e 15 8 , 15 8 f e 114 9 , 114 9 f e 1 3 , 1 3 f www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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