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A. Statements a and b are both true. B. Statements a and b are both false. C. Statement a is true, the latter being false. D. Statement a is false, the latter being true. 1. a.In the Theorem of Pappus, the center of mass is always located inside the region or area of the figure. b. In addition, the center of mass is always equal to the geometric centroid. 2. a. For springs obeying Hooke's Law, the work required to compress the material by dx distance is always less than the requirement to stretch it by the same dx distance. b. The spring constant is dependent on the amount of force required to stretch it by some x distance. 3. a. As two objects move farther away from each other, the forceof attraction between them decreases. b. Thus, if the force of attraction decreases with distance, the workshall decrease as well.

A. Statements a and b are both true. B. Statements a and b are both false. C. Statement a is true, the latter being false. D. Statement a is false, the latter being true. 1. a.In the Theorem of Pappus, the center of mass is always located inside the region or area of the figure. b. In addition, the center of mass is always equal to the geometric centroid. 2. a. For springs obeying Hooke's Law, the work required to compress the material by dx distance is always less than the requirement to stretch it by the same dx distance. b. The spring constant is dependent on the amount of force required to stretch it by some x distance. 3. a. As two objects move farther away from each other, the forceof attraction between them decreases. b. Thus, if the force of attraction decreases with distance, the workshall decrease as well.

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A. Statements a and b are both true. C. Statement a is true, the latter being false. B. Statements a and b are both false. D. Statement a is false, the latter being true. 1. a. In the Theorem of Pappus, the center of mass is always locatedinside the region or area of the figure. b. In addition, the center of mass is always equal to the geometric centroid. a. For springs obeying Hooke's Law, the work required to compress the material by dx distance is always less than the requirement to stretch it by the same dx distance. b. The spring constant is dependent on the amount of force required to stretch it by somex distance. 2. a. As two objects move farther away from each other, the forceof attraction between them decreases. b. Thus, if the force of attraction decreases with distance, the workshall decrease as well. 3. a. For a positively charged q, and negatively charged q2, the force will always be positive regardless of the signs. b. Thus, in calculus, the signs of the charges do not affect the work or force between them. 4. 5. a. In evaluating the moment of a planar lamina, a horizontal strip cannot be used as a representative area. b. Themoment of any planar lamina is the product of the mass of the region and its centroid. 6. a.For an object submerged in y distance from the water level, as y increases, the pressure experienced by the object decreases b. The same object placed in containers with three different areas submerging by the same depth will have a varying pressure depending on the containers 7. a. Thereaction kinetics of order 0 cannot be evaluated using the concept of integration. b. If the order of reaction is 1 in PFR, given K, and % conversion, the initial amount is not necessary to find r. 8. a. Infiltration using calculus, the fictitious volume (V.) is considered a variable, like the filtrate (V). b. If the operation is a constant-rate process, the rate is always the ratio of the amount to be filtered and the time elapsed to obtain the necessaryfiltrate. 9. a. In a normal distribution curve, an average of 0 means that any value below 0 shall be located to its left. b. Thus, scores within the 3ơ to the left and right of the mean comprise at least 99% of the population's scores. 10. a. In the Cartesian coordinate plane, single integration produces an area under the curve (or between two curves). b. In a three-dimensional system, singleintegration of an arc produces an area called the line integral.
Transcribed Image Text:A. Statements a and b are both true. C. Statement a is true, the latter being false. B. Statements a and b are both false. D. Statement a is false, the latter being true. 1. a. In the Theorem of Pappus, the center of mass is always locatedinside the region or area of the figure. b. In addition, the center of mass is always equal to the geometric centroid. a. For springs obeying Hooke's Law, the work required to compress the material by dx distance is always less than the requirement to stretch it by the same dx distance. b. The spring constant is dependent on the amount of force required to stretch it by somex distance. 2. a. As two objects move farther away from each other, the forceof attraction between them decreases. b. Thus, if the force of attraction decreases with distance, the workshall decrease as well. 3. a. For a positively charged q, and negatively charged q2, the force will always be positive regardless of the signs. b. Thus, in calculus, the signs of the charges do not affect the work or force between them. 4. 5. a. In evaluating the moment of a planar lamina, a horizontal strip cannot be used as a representative area. b. Themoment of any planar lamina is the product of the mass of the region and its centroid. 6. a.For an object submerged in y distance from the water level, as y increases, the pressure experienced by the object decreases b. The same object placed in containers with three different areas submerging by the same depth will have a varying pressure depending on the containers 7. a. Thereaction kinetics of order 0 cannot be evaluated using the concept of integration. b. If the order of reaction is 1 in PFR, given K, and % conversion, the initial amount is not necessary to find r. 8. a. Infiltration using calculus, the fictitious volume (V.) is considered a variable, like the filtrate (V). b. If the operation is a constant-rate process, the rate is always the ratio of the amount to be filtered and the time elapsed to obtain the necessaryfiltrate. 9. a. In a normal distribution curve, an average of 0 means that any value below 0 shall be located to its left. b. Thus, scores within the 3ơ to the left and right of the mean comprise at least 99% of the population's scores. 10. a. In the Cartesian coordinate plane, single integration produces an area under the curve (or between two curves). b. In a three-dimensional system, singleintegration of an arc produces an area called the line integral.
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