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Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
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- Mayor John proposed to utilize a government-ownedland with an area of 12, 150 m2. One-third of the areawill be used to plant mango trees while the rest of the land iswhere an emergency field hospital shall be built. The cityengineer was tasked to determine the following: 1. The dimensions of the land planted with mango trees withthe minimum cost of fencing given that area is to be rectangularand to be fenced off on three sides not adjacent to thehighway. *All derivatives shall be with respect to x, please.Mayor John proposed to utilize a government-ownedland with an area of 12, 150 m2. One-third of the areawill be used to plant mango trees while the rest of the land iswhere an emergency field hospital shall be built. The cityengineer was tasked to determine the following: 1. The dimensions of the land planted with mango trees withthe minimum cost of fencing given that area is to be rectangularand to be fenced off on three sides not adjacent to thehighway. 2. The rate at which the total average of COVID cases isincreasing at x = 10 tents and dx/dt=1 tent per day, given that if 25 tents are built, the average number of COVID cases per tent will be 6 cases, while the average number of cases will increase by 2 per tent for each additional tent in the same area due to overcrowding.The City Council proposed to utilize government-owned land with an area of 15,000 square meters. One-third of the area will be used to plant mango trees while the rest of the land is where an emergency field hospital shall be built. As the city engineer, you were tasked to determine the following: The dimensions of the land planted with mango trees with minimum cost of fencing given that area is to be rectangular and to be fenced off on three sides not adjacent to the highway. Cite other instances aside from the situations given above where optimization (maximization) can be applied.
- The City Council proposed to utilize government-owned land with an area of 12,150 square meters. One-third of the area will be used to plant mango trees while the rest of the land is where an emergency field hospital shall be built. As the city engineer, you were tasked to determine the following: 1. the dimensions of the land planted with mango trees with minimum cost of fencing given that area is to be rectangular and to be fenced off on three sides not adjacent to the highway. A) Illustration and Representation of Variables B) Detailed Solution C) Conclusion D) As an Engineer, cite other instances aside from the situations given above where optimization (one maximization and one minimization) can be applied.The City Council proposed to utilize government-owned land with an area of 12,150 square meters. One-third of the area will be used to plant mango trees while the rest of the land is where an emergency field hospital shall be built. As the city engineer, you were tasked to determine the following: 1. the dimensions of the land planted with mango trees with minimum cost of fencing given that area is to be rectangular and to be fenced off on three sides not adjacent to the highway. A) Illustration and Representation of Variables B) Detailed SolutionThe National Institute of Standards and Technology (NIST) offers Standard Reference Materials to aid in the calibration of measurement instruments and verify the accuracy of measurements. Suppose a medical researcher wants to verify that the distances he measures with his computed tomography machine are not too large, so he orders a Dimensional Standard for Medical Computed Tomography from NIST. This standard consists of 18 plastic balls held in place by a plastic support structure. The certified distance between the balls numbered 2 and 7 is 11.26 mm, and NIST determines that measurement errors are normally distributed with a standard deviation of 0.05 mm. Upon receiving the Standard Reference Material, the researcher measured the distance between balls 2 and 7 six times. Take these six measurements to be a simple random sample of all measurements made on this device under carefully controlled conditions. The researcher then calculated the summary statistics, where ? is the mean…
- The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of 70 modern Italian male skulls and 84 preserved Etruscan male skulls was analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on the WeissStats site. [SOURCE: N. Barnicot and D. Brothwell, “The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones.” In Medical Biology and Etruscan Origins, G. Wolstenholme and C. O’Connor, eds., Little, Brown&Co., 1959] a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples. b. Based on your results from part (a), which would you be inclined to use to…Can you show me your work, caclulations, however you did it please.The City Council proposed to utilize a government-owned land with an area of 9,600 square meters. One-third of it will be used for a picnic area while the rest of the land will be planted by mango trees. As the city engineer, you were tasked to determine thefollowing: 1. the dimensions of the picnic area with a minimum cost of fencing given that area is to be rectangular and to be fenced off on three sides not adjacent to the highway.2. the number of mango trees that leads to a maximum yield given that if 60 trees are planted, the average yield per tree will be 400 kilos while the average yield will decrease by 4 kilos per tree for each additional tree on the same area due to overcrowding.
- The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of 70 modern Italian male skulls and that of 84 preserved Etruscan male skulls were analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on the WeissStats site. [SOURCE: N. Barnicot and D. Brothwell, “The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones.” In a. use the technology of your choice to obtain boxplots for the data sets, using the same scale. b. compare the data sets by using your results from part (a), paying special attention to center and variation.The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of 70 modern Italian male skulls and that of 84 preserved Etruscan male skulls were analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on the WeissStats site. [SOURCE: N. Barnicot and D. Brothwell, “The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones.” In Medical Biology and Etruscan Origins, G. Wolstenholme and C. O’Connor, eds., Little, Brown&Co., 1959] a. use the technology of your choice to obtain boxplots for the data sets, using the same scale. b. compare the data sets by using your results from part (a), paying…The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of 70 modern Italian male skulls and that of 84 preserved Etruscan male skulls were analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on theWeissStats site. [SOURCE: N. Barnicot and D. Brothwell, “The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones.” In Medical Biology and Etruscan Origins, G. Wolstenholme and C. O’Connor, eds., Little, Brown&Co., 1959] a. use the technology of your choice to determine the mean and median of each of the two data sets. b. compare the two data sets by using your results from part (a).