19 resultados para Trigonometry Formulas


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This is a work involving fundamental studies of chemistry where the synthesis and structural characterization, as well as a possible future application of these new compounds as luminescent sensors or sunscreen agents, complexes with 4,4 diaminostilbene-2,2-disulfonic (DSD) and trivalent lanthanide ions La3+, Nd3+, Eu3+, Gd3+ and Yb3+, were synthesized in the ratio of 3 mmol: 1 mmol (DSD: lanthanides). The complexes obtained with these ions were present in powder form and were characterized by complexometric titration with EDTA CHN Elemental analysis, molecular absorption spectroscopy in the ultraviolet region, the absorption spectroscopy in the infrared, thermal analysis (TG / DTG), Nuclear Magnetic Resonance - NMR 1H and Luminescence Spectroscopy. The complexometric titration and CHN analysis, confirmed the TG / DTG which suggest that these complexes have the following general chemical formulas: [La2(C14H12S2O6N2)2(H2O)2Cl2].7H2O,[Nd2(C14H12S2O6N2)2(H2O)2Cl2].6H2O,[Eu2(C14 H12S2O6N2)2(H2O)2Cl2].7H2O,[Gd2(C14H12S2O6N2)2(H2O)2Cl2].4H2O e [Yb2(C14H12S2O6N2)2(H2O)2].6H2O. The disappearance of the bands in the infrared spectrum at 2921 cm-1 and 2623 cm-1 and the displacement of the bands in the spectra of the amine complex indicate that the lanthanide ion is coordinated to the oxygen atoms and the sulfonate groups of the nitrogens amines, suggesting the formation of the dimer. The disappearance of the signal and the displacement signal SO3H amines in the 1H NMR spectrum of this complex are also indicative coordination and dimer formation. The Thermogravimetry indicates that the DSD is thermally stable in the range of 40º to 385°C and their complexes with lanthanide ions exhibit weight loss between 4 and 5 stages. The Uv-visible spectra indicated that the DSD and complexes exhibit cis isomers. The analysis of luminescence indicates that the complexes do not exhibit emission in the region of the lanthanides but an intense emission part of the binder. This is related to the triplet states of the ligand, which are in the lowest energy state emitting lanthanide ions, and also the formation of the dimer that suppress the luminescence of ion Eu3+. The formation of dimer was also confirmed by calculating the europium complex structure using the model Hamiltonian PM6 and Sparkle

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In general, the study of quadratic functions is based on an excessive amount formulas, all content is approached without justification. Here is the quadratic function and its properties from problems involving quadratic equations and the technique of completing the square. Based on the definitions we will show that the graph of the quadratic function is the parabola and finished our studies finding that several properties of the function can be read from the simple observation of your chart. Thus, we built the whole matter justifying each step, abandoning the use of decorated formulas and valuing the reasoning

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Generally, arithmetic and geometric progressions are taught separately from ane and exponential functions, only by the use of memorized formulas and without any concern of showing students how these contents are related. This paper aims at presenting a way of teaching such contents in an integrated way, starting with the definition of ane and exponential functions relating them to situations from the daily life of the students. Then, characteristics and graphics of those functions are presented and, subsequently, arithmetic and geometric progression are shown as a restriction of the ane and exponential functions. Thus, the study of the progressions is introduced based on the functions mentioned above using situations from students daily lives as examples

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In this dissertation, we present a study on the teaching of volume of the sphere and the area of spherical surface. On this topic, a quali-quantitative was taken survey with the objective of identifying how these topics are addressed. For this, we made 14 questions to 30 teachers of Natal and the results of this survey are presented and discussed. After that, we present alternative ways to derive the formulas of the volume of a sphere and the are of a spherical surface