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Irregular areas and volumes and mean values
Published in John Bird, Bird's Basic Engineering Mathematics, 2021
A planimeter is an instrument for directly measuring small areas bounded by an irregular curve. There are many different kinds of planimeters but all operate in a similar way. A pointer on the planimeter is used to trace around the boundary of the shape. This induces a movement in another part of the instrument and a reading of this is used to establish the area of the shape.
Pre-service mathematics teachers using Geogebra to learn about instantaneous rate of change
Published in International Journal of Mathematical Education in Science and Technology, 2023
Vilmar Gomes da Fonseca, Ana Cláudia Correia Batalha Henriques
For Arzarello and Manzone (2017), who developed a virtual planimeter1 in GeoGebra and used it to simulate and explore the notion of infinitesimals in the calculation of area measurements, the use of this software facilitates the proof of mathematical conjecture supported by the concept of limit. In the view of these authors, GeoGebra’s resources that enabled experimental tests of area measurement approximations, allowing the increased decimal extension of the calculated area value and zoom increase/decrease in the graph visualization, were fundamental for the students to be able to prove the area measurement and conclude on the root of the limit definition and infinitesimal. Finally, Ocal (2017) also states that the students were able to formulate algebraic generalizations by analyzing geometric and algebraic records of functions and their derivatives, in GeoGebra, which made it possible to mathematically model and solve optimization problems of area.
Functional and physical properties of oil-in-water emulsion based on sodium caseinate, beef rumen and sunflower oil and its effect on nutritional quality of forcemeat
Published in Journal of Dispersion Science and Technology, 2023
Eleonora Okuskhanova, Nicola Caporaso, Zhanibek Yessimbekov, Bahytkul Assenova, Farida Smolnikova, Maksim Rebezov, Mohammad Ali Shariati, Muhammad Usman Khan, Muthu Thiruvengadam
Forcemeat weighing 0.3 g was placed on a polythene circle with a diameter of 15–20 mm, then it was transferred to an ashless filter that was placed on a glass or plexiglass plate. The minced meat was covered with the same plate as the lower one. Then the load of 1 kg was loaded on it and kept for 10 min. After that, removed the load and the bottom plate. Then outlined the contour of the spot around the compressed meat. The outer contour was drawn when the filter paper dried out in the air. The area of the spots formed by compressed meat and adsorbed moisture was measured with a planimeter. The size of the wet spot (external) was calculated by the difference between the total spot area and the area of the spot formed by the meat. It was determined experimentally that 1 cm3 of the wet spot area of filtrate corresponds to 8.4 mg of moisture.[36,37]
Development of Integrated Renewable Energy System Based on Optimal Operational Strategy and Sizing for an Un-Electrified Remote Area
Published in IETE Journal of Research, 2021
Dixitkumar P. Pathak, Dheeraj Kumar Khatod
Micro-hydro generators with turbines can execute low elevation heads or low volumetric flow rate situations, eventually supporting the small water streams. Considering the survey, the discharge was estimated based on monthly average rainfall data and topography collected closer to the gauge station. Area, elevation difference of the stream and length of the watershed were calculated based on planimeter and topo-sheet drawings of the concerned environmental region. Collected data examined for preferred frequency and discharge was estimated employing the curve number method [35]. The power generation of the micro-hydro generator (MHG) system has been estimated established on the head, reliability, and flow speed. The output of MHG can be determined according to the expression given in (4) [20]. where is the rated power output, Q is discharged in m3/s, is head in m, is the whole effectiveness of micro-hydro unit, and is the density of water.