Matematicaa
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This document provides formulas for calculating interest, discount rates, present and future values for loans and investments. It includes formulas to calculate interest rates, loan balances over time, present and future values, discounts, and compound interest with up to 3 periods of growth. Key variables included are principal (C), interest rate (R or i), time in months, years or days (T, Tm, Td).
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Formulario Trigonometria
1. The document contains formulas and definitions related to trigonometry, including definitions of trigonometric functions, identities, right triangles, laws of sines and cosines for oblique triangles, trigonometric functions of vectors, and hyperbolic trigonometry.
2. Key concepts covered include definitions of trigonometric functions, complementary and supplementary angles, trigonometric ratios in right triangles, trigonometric identities, laws of sines and cosines, vector dot and cross products, and hyperbolic trigonometric functions.
3. The document provides over 75 formulas and definitions in both text and mathematical notation to comprehensively cover topics in plane and vector trigonometry.
Examen final
The document contains 4 problems:
1) Calculating the isothermal work done on a gas compressed from 23L to 3L.
2) Interpolating viscosity data to find viscosity at 7.5°C.
3) Solving a system of 3 equations.
4) Approximating the solution to a differential equation.
数式処理ソフトMathematicaで数学の問題を解く
平成27年度(第49次)第7回算数・数学教育研修会
平成28年6月12日(日) @ 代々木ゼミナール福岡校
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Wolfram Programing Lab: https://lab.open.wolframcloud.com/app/
印刷配布用のスライドのコピーは qmath4in1.pdf です.
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Measures of dispersion - united world school of business
Here are the key steps to solve this problem:
1. Calculate the coefficient of variation for each factory:
Factory A:
Coefficient of variation = Standard deviation/Average
= 6.5/19.7 = 33%
Factory B:
Coefficient of variation = Standard deviation/Average
= 8.64/21 = 41%
2. The factory with the lower coefficient of variation has more consistent profits.
Factory A has a coefficient of variation of 33%, lower than Factory B's 41%. Therefore, the profits of Factory A are more consistent.
The coefficient of variation allows us to compare the extent of variability in relation to the average of the data set. A lower coefficient
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Matematicaa
- 5. R = I x 100 x 12 C x Tm R = I x 100 C x T R = I x 100 x 360 C x Td I = C x R x Tm 100 x 12 C = I x 100 x 12 R x Tm Tm = I x 100 x 12 C x R I = C x R x T 100 T= I x 100 C x R I = C x R x Td 100 x 360 C = I x 100 x 360 R x Td Td = I x 100 x 360 C x R C = I x 100 R x T Tiempo Expresado en Meses Tiempo Expresado en Años Tiempo Expresado en Días
- 6. C = I i x T I = C x i x T I = C x R x T 100 i = R 100 T = I C x i I = I C x T
- 7. M = C + I M = C+ C x R x T 100 C = FACTOR COMUN M = C ( 1 + R x T ) 100 R = ( M -1) x T C 100 C = M 1 + R x T 100 T = ( M -1) x 100 C R
- 9. D = Vn - Va D = N - A Va = Vn - D A = N - D D: Descuento Vn o N: Valor Nominal Va o A: Valor Actual R: Razón Td: Tempo en Días
- 10. I C R Td A D N Td M R Interés Descuento Interés Descuento R = I x 100 x 360 C x Td I = C x R x Td 100 x 360 C = I x 100 x 360 R x Td Td = I x 100 x 360 C x R R = D x 100 x 360 N x Td D = N x R x Td 100 x 360 N = D x 100 x 360 R x Td Td = C x 100 x 360 N x R
- 11. D = N x i x Td 360 N = D x 360 I x Td D = N x R x Td 100 x 360 i = R 100 Td = D x 360 N x i i = D x 360 N x Td
- 12. M = C + I M = C ( 1 + R x T ) 100 x 360 A = N ( 1 – R x Td ) 100 x 360 C = M 1 + R x T 100x360 A = N - D Monto Valor Actual N = A 1 + R x T 100 x 360
- 14. M3 = M2 + I = C ( 1 x i )^2 + C ( 1 x i )^2 C (1 + i )^2 x (1 + i) C = ( 1 + i )^3 M1 = C x I = C + C x i x T = C + C x R = C + C x i = C x (1 + i ) 100 x Ut 100 M2 = M1 + I = ( C + C x i ) + ( C + C x i ) x i ( C + C x i ) x ( 1 + i ) = C ( 1 + i ) x ( 1 + i ) C (1 + i )^2 MT = C ( 1 + i )^r
- 15. Bibliografía • Apuntes de clase • Internet (páginas varias)