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The importance of an army's reserves have always been a part of military planning when it comes to the battlefield. Many military historians and leaders have emphasized their importance, but in different ways. Clearly Carl Von Clausewitz speaks about reserves, and their numbers when a commander is calculating his situation in a battle. He advises field commanders to take note of his own reserves and where possible, a determination of the reserves of an enemy. Depending upon various circumstances, the size of an attacker's reserves may determine whether to retreat or to advance.One of Napoleon's opponents, the Archduke Charles, specifically advises that a commander requires a strong number of reserves to cover a losing army's retreat. Confederate General Robert E. Lee, as one US Civil War example, was successful in using his reserves to thwart an enemies pursuit when Lee was forced to retreat.

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Q: What are two Napoleonic Era responses on the value of an army's reserves?
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1.is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?24.024.324.525.6Grade:0User Responses:Question was not attemptedCorrect Answer:24.0Feedback:2.Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 8, ST = 12, TU = 15, UV = 9, and VR = 12?107141Grade:1User Responses:7Correct Answer:7Feedback:3.is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?19.225.520.221.5Grade:0User Responses:20.2Correct Answer:19.2Feedback:4.A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.17.2 in.6.2 in.11.0 in.4.8 in.Grade:0User Responses:6.2 in.Correct Answer:4.8 in.Feedback:5.A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.12.0 in.6.4 in.1.6 in.9.6 in.Grade:0User Responses:12.0 in.Correct Answer:1.6 in.Feedback:6.Which is an equation of a circle with center (2, -10) and radius 3?(x - 2)2 + (y + 10)2 = 9(x - 2)2 + (y + 10)2 = 3(x + 2)2 + (y - 10)2 = 3(x + 10)2 + (y - 2)2 = 9Grade:0User Responses:(x + 2)2 + (y - 10)2 = 3Correct Answer:(x - 2)2 + (y + 10)2 = 9Feedback:7.What is the standard form of the equation of the circle in the graph?x2 + (y - 4)2 = 16x2 + (y + 4)2 = 16x2 + (y - 4)2 = 4x2 + (y + 4)2 = 4Grade:0User Responses:x2 + (y - 4)2 = 4Correct Answer:x2 + (y + 4)2 = 4Feedback:8.What is the equation of a circle with diameter that has endpoints A(0, 0) and B(8, 6)?(x - 3)2 + (y - 4)2 = 25(x - 4)2 + (y - 3)2 = 5(x - 4)2 + (y - 3)2 = 25(x - 3)2 + (y - 4)2 = 5Grade:1User Responses:(x - 4)2 + (y - 3)2 = 25Correct Answer:(x - 4)2 + (y - 3)2 = 25Feedback:9.What is the circumference of the circle whose equation is (x - 9)2 + (y - 3)2 = 64?64π8π16π4πGrade:1User Responses:16πCorrect Answer:16πFeedback:10.What is the area of the circle whose equation is (x - 9)2 + (y - 3)2 = 64?16π8π4π64πGrade:1User Responses:64πCorrect Answer:64πFeedback:11.What is the value of x to the nearest tenth?9.212.07.24.8Grade:1User Responses:7.2Correct Answer:7.2Feedback:12.What is the value of x to the nearest tenth?20.812.88.09.6Grade:0User Responses:12.8Correct Answer:9.6Feedback:13.Point P is the center of two concentric circles. PQ = 10.5 and PS = 20.9. is tangent to the smaller circle and a chord of the larger circle. What is length of to the nearest tenth?36.141.441.831.4Grade:0User Responses:31.4Correct Answer:36.1Feedback:14.What is the value of x to the nearest tenth?14.110.523.54.8Grade:1User Responses:10.5Correct Answer:10.5Feedback:15.What is the value of x to the nearest tenth?3.14.83.55.4Grade:0User Responses:4.8Correct Answer:5.4Feedback:16.What is ?119197842Grade:1User Responses:119Correct Answer:119Feedback:17.What is the value of x?82685456Grade:0User Responses:68Correct Answer:54Feedback:18.What is the value of d to the nearest tenth?11.216.717.513.8Grade:1User Responses:13.8Correct Answer:13.8Feedback:19.What is the value of d to the nearest tenth?14.326.533.829.3Grade:0User Responses:14.3Correct Answer:26.5Feedback:20.What is the length of ?8.56.512.39.8Grade:0User Responses:6.5Correct Answer:8.5Feedback:21.What is the value of a + b?110135145125Grade:1User Responses:125Correct Answer:125Feedback:22.What is the value of d?508010084Grade:1User Responses:80Correct Answer:80Feedback:23.What is ?102853498Grade:0User Responses:102Correct Answer:34Feedback:24.What is the measure of ?36215130Grade:1User Responses:30Correct Answer:30Feedback:25.What is the value of a + b? You may assume that the ray is tangent to the circle.9012864180Grade:0User Responses:128Correct Answer:90Feedback:1.What is the value of a + b? You may assume that the ray is tangent to the circle.1809012864Grade:0User Responses:128Correct Answer:90Feedback:2.What is the value of d?848050100Grade:1User Responses:80Correct Answer:80Feedback:3.What is the measure of ?85566851Grade:0User Responses:51Correct Answer:68Feedback:4.What is the value of b?541206030Grade:0User Responses:120Correct Answer:30Feedback:5.What is the value of a?96200192101Grade:1User Responses:101Correct Answer:101Feedback:6.Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 8, ST = 12, TU = 15, UV = 9, and VR = 12?101471Grade:0User Responses:10Correct Answer:7Feedback:7., , and are all tangent to circle O. = 13, = 7, and = 10. What is the perimeter of JKL?60 units30 units40 units46 unitsGrade:0User Responses:40 unitsCorrect Answer:60 unitsFeedback:8.is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?20.219.221.525.5Grade:0User Responses:21.5Correct Answer:19.2Feedback:9.is tangent to circle O at B. What is the length of the radius r? Round to the nearest tenth.7.09.913.03.6Grade:1User Responses:7.0Correct Answer:7.0Feedback:10.A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.11.0 in.17.2 in.4.8 in.6.2 in.Grade:1User Responses:4.8 in.Correct Answer:4.8 in.Feedback:11.What is the center and radius of the circle with equation (x + 9)2 + (y + 5)2 = 64?center (-9, -5); radius = 64center (5, 9); radius = 8center (-9, -5); radius = 8center (9, 5); radius = 64Grade:0User Responses:center (5, 9); radius = 8Correct Answer:center (-9, -5); radius = 8Feedback:12.Which point lies inside the circle with equation (x - 2)2 + (y + 3)2 = 4?(0, -3)(2, -4)(2, 0)(2, -5)Grade:0User Responses:(2, -5)Correct Answer:(2, -4)Feedback:13.What is the standard form of the equation of the circle in the graph?x2 + y2 = 9(x + 3)2 + (y + 3)2 =3(x + 3)2 + (y + 3)2 =9x2 + y2 = 3Grade:0User Responses:(x + 3)2 + (y + 3)2 =9Correct Answer:x2 + y2 = 9Feedback:14.Which is an equation of a circle with center (2, 7) and radius 4?(x + 2)2 + (y + 7)2 = 4(x - 2)2 + (y - 7)2 = 16(x - 7)2 + (y - 2)2 = 16(x - 2)2 + (y - 7)2 = 4Grade:1User Responses:(x - 2)2 + (y - 7)2 = 16Correct Answer:(x - 2)2 + (y - 7)2 = 16Feedback:15.What is the center and radius of the circle with equation (x - 5)2 + (y + 3)2 = 16?center (5, -3); radius = 16center (3, -5); radius = 4center (5, -3); radius = 4center (-5, 3); radius = 16Grade:0User Responses:center (-5, 3); radius = 16Correct Answer:center (5, -3); radius = 4Feedback:16.What is the length of ?104711Grade:1User Responses:10Correct Answer:10Feedback:17.What is ?1101206070Grade:1User Responses:60Correct Answer:60Feedback:18.What is the value of d to the nearest tenth?14.326.529.333.8Grade:0User Responses:29.3Correct Answer:26.5Feedback:19.What is ?154112168126Grade:1User Responses:112Correct Answer:112Feedback:20.What is the value of d to the nearest tenth?17.516.711.213.8Grade:0User Responses:11.2Correct Answer:13.8Feedback:21.Point P is the center of two concentric circles. PQ = 4.2 and PS = 8.2. is tangent to the smaller circle and a chord of the larger circle. What is length of to the nearest tenth?16.412.28.114.1Grade:0User Responses:16.4Correct Answer:14.1Feedback:22.What is the value of y?41025Grade:0User Responses:10Correct Answer:4Feedback:23.What is the value of x to the nearest tenth?26.813.430.06.0Grade:0User Responses:6.0Correct Answer:26.8Feedback:24.What is the value of q?4.48.2516.58.8Grade:0User Responses:8.25Correct Answer:16.5Feedback:25.Circle A and circle B are congruent. is a chord of both circles. If AB = 24 in. and the radius is 13 in., how long is ?12 in.26 in.9 in.10 in.Grade:0User Responses:9 in.Correct Answer:10 in.Feedback:1.is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?24.024.324.525.6Grade:0User Responses:Question was not attemptedCorrect Answer:24.0Feedback:2.Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 8, ST = 12, TU = 15, UV = 9, and VR = 12?107141Grade:1User Responses:7Correct Answer:7Feedback:3.is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?19.225.520.221.5Grade:0User Responses:20.2Correct Answer:19.2Feedback:4.A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.17.2 in.6.2 in.11.0 in.4.8 in.Grade:0User Responses:6.2 in.Correct Answer:4.8 in.Feedback:5.A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.12.0 in.6.4 in.1.6 in.9.6 in.Grade:0User Responses:12.0 in.Correct Answer:1.6 in.Feedback:6.Which is an equation of a circle with center (2, -10) and radius 3?(x - 2)2 + (y + 10)2 = 9(x - 2)2 + (y + 10)2 = 3(x + 2)2 + (y - 10)2 = 3(x + 10)2 + (y - 2)2 = 9Grade:0User Responses:(x + 2)2 + (y - 10)2 = 3Correct Answer:(x - 2)2 + (y + 10)2 = 9Feedback:7.What is the standard form of the equation of the circle in the graph?x2 + (y - 4)2 = 16x2 + (y + 4)2 = 16x2 + (y - 4)2 = 4x2 + (y + 4)2 = 4Grade:0User Responses:x2 + (y - 4)2 = 4Correct Answer:x2 + (y + 4)2 = 4Feedback:8.What is the equation of a circle with diameter that has endpoints A(0, 0) and B(8, 6)?(x - 3)2 + (y - 4)2 = 25(x - 4)2 + (y - 3)2 = 5(x - 4)2 + (y - 3)2 = 25(x - 3)2 + (y - 4)2 = 5Grade:1User Responses:(x - 4)2 + (y - 3)2 = 25Correct Answer:(x - 4)2 + (y - 3)2 = 25Feedback:9.What is the circumference of the circle whose equation is (x - 9)2 + (y - 3)2 = 64?64π8π16π4πGrade:1User Responses:16πCorrect Answer:16πFeedback:10.What is the area of the circle whose equation is (x - 9)2 + (y - 3)2 = 64?16π8π4π64πGrade:1User Responses:64πCorrect Answer:64πFeedback:11.What is the value of x to the nearest tenth?9.212.07.24.8Grade:1User Responses:7.2Correct Answer:7.2Feedback:12.What is the value of x to the nearest tenth?20.812.88.09.6Grade:0User Responses:12.8Correct Answer:9.6Feedback:13.Point P is the center of two concentric circles. PQ = 10.5 and PS = 20.9. is tangent to the smaller circle and a chord of the larger circle. What is length of to the nearest tenth?36.141.441.831.4Grade:0User Responses:31.4Correct Answer:36.1Feedback:14.What is the value of x to the nearest tenth?14.110.523.54.8Grade:1User Responses:10.5Correct Answer:10.5Feedback:15.What is the value of x to the nearest tenth?3.14.83.55.4Grade:0User Responses:4.8Correct Answer:5.4Feedback:16.What is ?119197842Grade:1User Responses:119Correct Answer:119Feedback:17.What is the value of x?82685456Grade:0User Responses:68Correct Answer:54Feedback:18.What is the value of d to the nearest tenth?11.216.717.513.8Grade:1User Responses:13.8Correct Answer:13.8Feedback:19.What is the value of d to the nearest tenth?14.326.533.829.3Grade:0User Responses:14.3Correct Answer:26.5Feedback:20.What is the length of ?8.56.512.39.8Grade:0User Responses:6.5Correct Answer:8.5Feedback:21.What is the value of a + b?110135145125Grade:1User Responses:125Correct Answer:125Feedback:22.What is the value of d?508010084Grade:1User Responses:80Correct Answer:80Feedback:23.What is ?102853498Grade:0User Responses:102Correct Answer:34Feedback:24.What is the measure of ?36215130Grade:1User Responses:30Correct Answer:30Feedback:25.What is the value of a + b? You may assume that the ray is tangent to the circle.9012864180Grade:0User Responses:128Correct Answer:90Feedback:1.is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?24.024.324.525.6Grade:0User Responses:Question was not attemptedCorrect Answer:24.0Feedback:2.Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 8, ST = 12, TU = 15, UV = 9, and VR = 12?107141Grade:1User Responses:7Correct Answer:7Feedback:3.is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?19.225.520.221.5Grade:0User Responses:20.2Correct Answer:19.2Feedback:4.A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.17.2 in.6.2 in.11.0 in.4.8 in.Grade:0User Responses:6.2 in.Correct Answer:4.8 in.Feedback:5.A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.12.0 in.6.4 in.1.6 in.9.6 in.Grade:0User Responses:12.0 in.Correct Answer:1.6 in.Feedback:6.Which is an equation of a circle with center (2, -10) and radius 3?(x - 2)2 + (y + 10)2 = 9(x - 2)2 + (y + 10)2 = 3(x + 2)2 + (y - 10)2 = 3(x + 10)2 + (y - 2)2 = 9Grade:0User Responses:(x + 2)2 + (y - 10)2 = 3Correct Answer:(x - 2)2 + (y + 10)2 = 9Feedback:7.What is the standard form of the equation of the circle in the graph?x2 + (y - 4)2 = 16x2 + (y + 4)2 = 16x2 + (y - 4)2 = 4x2 + (y + 4)2 = 4Grade:0User Responses:x2 + (y - 4)2 = 4Correct Answer:x2 + (y + 4)2 = 4Feedback:8.What is the equation of a circle with diameter that has endpoints A(0, 0) and B(8, 6)?(x - 3)2 + (y - 4)2 = 25(x - 4)2 + (y - 3)2 = 5(x - 4)2 + (y - 3)2 = 25(x - 3)2 + (y - 4)2 = 5Grade:1User Responses:(x - 4)2 + (y - 3)2 = 25Correct Answer:(x - 4)2 + (y - 3)2 = 25Feedback:9.What is the circumference of the circle whose equation is (x - 9)2 + (y - 3)2 = 64?64π8π16π4πGrade:1User Responses:16πCorrect Answer:16πFeedback:10.What is the area of the circle whose equation is (x - 9)2 + (y - 3)2 = 64?16π8π4π64πGrade:1User Responses:64πCorrect Answer:64πFeedback:11.What is the value of x to the nearest tenth?9.212.07.24.8Grade:1User Responses:7.2Correct Answer:7.2Feedback:12.What is the value of x to the nearest tenth?20.812.88.09.6Grade:0User Responses:12.8Correct Answer:9.6Feedback:13.Point P is the center of two concentric circles. PQ = 10.5 and PS = 20.9. is tangent to the smaller circle and a chord of the larger circle. What is length of to the nearest tenth?36.141.441.831.4Grade:0User Responses:31.4Correct Answer:36.1Feedback:14.What is the value of x to the nearest tenth?14.110.523.54.8Grade:1User Responses:10.5Correct Answer:10.5Feedback:15.What is the value of x to the nearest tenth?3.14.83.55.4Grade:0User Responses:4.8Correct Answer:5.4Feedback:16.What is ?119197842Grade:1User Responses:119Correct Answer:119Feedback:17.What is the value of x?82685456Grade:0User Responses:68Correct Answer:54Feedback:18.What is the value of d to the nearest tenth?11.216.717.513.8Grade:1User Responses:13.8Correct Answer:13.8Feedback:19.What is the value of d to the nearest tenth?14.326.533.829.3Grade:0User Responses:14.3Correct Answer:26.5Feedback:20.What is the length of ?8.56.512.39.8Grade:0User Responses:6.5Correct Answer:8.5Feedback:21.What is the value of a + b?110135145125Grade:1User Responses:125Correct Answer:125Feedback:22.What is the value of d?508010084Grade:1User Responses:80Correct Answer:80Feedback:23.What is ?102853498Grade:0User Responses:102Correct Answer:34Feedback:24.What is the measure of ?36215130Grade:1User Responses:30Correct Answer:30Feedback:25.What is the value of a + b? You may assume that the ray is tangent to the circle.9012864180Grade:0User Responses:128Correct Answer:90Feedback: