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Metodologia de la programación - expresiones

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M
Mar_Angeles

The document contains 6 sections with math word problems and expressions to solve. It begins with evaluating arithmetic expressions and indicating the order of operations. Then it involves deducing values of expressions using given variables. Next it evaluates expressions using variables A, B and C. It continues with converting math expressions to algorithmic expressions. Then it evaluates logical expressions using variables and given values. Finally, it converts language statements to numeric expressions.

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RESUELVE LOS EJERCICIOS QUE ACONTINUACIÓN SE PRESENTAN. EXPRESIONES 1. Evaluar las expresiones aritméticas respetando la jerarquía de operadores. Indicando el orden de ejecución de cada una de ellas. 1. -4 * 7 + 2 ^ 3 / 4 – 5 = -31 = (-4 * 7 + (2^ 3)) / 4 - 5 = (-4 * 7) + ((8 / 4) - 5) = (-28)+ (2 – 5) = -28 + - 3 = -31 2. (7 * (10 - 5) mod 3) + 4 + 9 = 15 = (7 * (10 – 5) mod 3)+ 4+ 9 = (7 * (5) mod 3) + 4 + 9 = (35 mod 3) + 4 + 9 =2+4+9 = 15 3. 10 div 2 * 8 / 4 – 5 = - 2.5 = 10 div (((2 * 8)/ 4) – 5) = 10 div (16 / 4) - 5 = 10 div 4 – 5 = (10 div 4) - 5 = (2.5) - 5 = -2.5 4. (33 + 10 mod 3 * 4) /5 = 1.5 = ((33 + 10) mod (3 * 4)) / 5 = ((33 + 10) mod 12) / 5 = (43 mod 12) / 5 =7/5 = 1.5 1
5. 16 * 12 mod 3 – 3 * 2 = - 6 = ((16 * 12) Mod 3) – (3 * 2) = (192 Mod 3) – 6 = 0–6 = -6 6. ((3 + 2) ^ 2 – 15) / 2 * 5 =1 = (((3 + 2) ^ 2) – 15) / (2 * 5) = (((5) ^2) – 15) / (2 * 5) = (25 - 15) / (10) = 10 / 10 =1 7. Y = (4 * 3 / 2) mod (8 4 + 2) = 2 Y = ((4 * 3)/ 2) mod ((8 4) + 2)) Y = (12 / 2) mod ((2) + 2) Y = 6 mod 4 Y=2 2
2. Deducir el valor de las expresiones siguientes: Siendo: A = 5; B = 25; C = 10 8. X = A + B mod C = 0 X = (5 + 25) mod 10 X = 30 mod 10 X=0 9. X = (A + B) / C = 3 X = (5 + 25) / 10 X = 30 / 10 X=3 10. X = A + (B / C) = 7.5 X = 5 + (25 / 10) X = 5 + 2.5 X = 7.5 11. b ^ 2 - 4 * a * c = -23 a = 2, b = 1, c = 3 = (1^2) – (4 * 2 * 3) = 1 - 24 = -23 12. (X ^ 2 + Y ^ 2) > (30 / 2) = 12 > 15 X = 2, Y = 3, Z = 4 = ((2^2)+ (3^2)) > (30/2) = (4+ 9) > 15 = 13 > 15 3
3. Si el valor de A es 4, el valor de B es 5 y el valor de C es 1, evaluar las siguientes expresiones: 13. B * A - B ^ 2 / 4 * C = -1.25 = (5 * 4 – (5^2)) / (4 * 1) = 20 - (25 / 4) = 20 – 6.25 = 13.75 14. (A * B) / 3 ^ 2 = 2.222222222 = (4 * 5) / (3^2) = (4 * 5) / 9 = 20/ 9 = 2.222222222 15. ( ( ( B + C ) / 2 * A + 10 ) * 3 * B ) - 6 = 416 = (((5 + 4) / 2)* 4 + 10)) * (3 * 5)) -6 = (((9 / 2) * 4) + 10) * (3 * 5) - 6 = (((4.5 * 4)+ 10) * (15)) – 6 = ((18 + 10) * 15) - 6 = (28 * 15) – 6 = 420 - 6 = 416 4
4. Realizar las conversiones de expresiones matemáticas a expresiones algorítmicas. Indicando el orden de ejecución de cada una de ellas. 1. = (m + n) / (p – p) 2. = -b RC ((b^2)- (4 (a)) * c ) / (2 * a) 3. = (m + (n / p)) / (a – (r / s)) 4. P= = P =(A + B + C) / 2 5. = X * (Y ^ 2) 6. + 1 = (m / n) + 1 7. = (m +(n / q)) / (q - (r / s)) 8. (m + n) = (m + n) * (p / q) 9. = (a = RC (b^2) +(c^2)) (b2+ c2 = a2) = (a= ) = a = RC (b^2) +(c^2) 10. = (((3 (x)) – y) /z ) – (((2 (x) )* ( y^2) /( z - 1) + (x / y) 5
5. Evaluar las expresiones lógicas aplicando la jerarquía de operadores. 1. ((A * B) < (B + C)) AND (A = C)= Falso A=3, B=4 y C=2 ((3 * 4) < (4 + 2)) AND (3 = 2) (12 < 6) AND (3 = 2) 2. ((A + B) > C) OR ((B / D > B))= verdadero A=2, B=5, C=3 y D=5 ((2 + 5) > 3) OR ((5 / 5) > 5) (7 > 3) OR (1 >5) 3. X = (A B) * C + (A / B)= X = 8 A = 4, B = 2, C = 3 X = (4 2) * 3) + (4 / 2) X = (2 * 3) + (4 / 2) X= 6+2 X= 8 6
X=1, Y=4; Z=10, PI=3.141592, E=2.718281 4. PI * X^2>Y OR 2* PI * X <=Z Verdadero ((3.141592)*1^2) >4) OR (((2*(3.141592))*1) <= 10 (3.141592 > 4) OR (6.283184 <= 10) 5. X>3 AND Y=4 OR X+Y<=Z Verdadero (1 >3 AND 4 = 4) OR (1 + 4) <=10 (1>3 AND 4 = 4) OR (5<= 10) 6. X>3 AND (Y=4 OR X+Y<=Z) Falso (1 >3) AND (4 = 4 OR (1 + 4) <=10) (1 >3) AND (4 = 4 OR 5<= 10) 7. NOT Y/2=2*X AND NOT Y<(PI-E*Z) Falso NOT ((4 / 2) = (2 * 1) AND NOT (4 < (3.141592 – (2.718281 * 10))) NOT (2 = 2) AND NOT (4 < (3.141592 – (27.18281))) NOT (2 = 2) AND NOT (4 < – 24.041218) NOT (V) AND NOT (F) F AND V F 7
a=5 y b=2 8. a>b = verdadero 5 >2 9. a>=b = Verdadero 5>= 2 10. a<b = falso 5< 2 11. a<=b = falso 5<=2 12. Not a=b = Falso Not 5 = 2 -5 = 2 8
6. Convertir en expresiones numéricas los siguientes enunciados. 1. Elabore una expresión que sólo permita valores entre 1 y 10. (x>=1 and x<=10) 3^2 + 5 – 4 + 7 / 3 = = ((3^2) + 5 – 4) + (7 / 3) = 9 + 5 – 4 + (8 / 2) = (9 + 5) – (4 + 4) = 14 - 8 =6 2. Elabore una expresión que permita valores entre 1 y 3, y 5 a 7 exclusivamente. (v>= 1 AND v<= 3) AND (v>= 5 AND v<= 7) 3. Elabore una expresión que permita edades entre 18 y 25 años. (E>= 18 AND E<= 25) 9

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Metodologia de la programación - expresiones

  • 1. RESUELVE LOS EJERCICIOS QUE ACONTINUACIÓN SE PRESENTAN. EXPRESIONES 1. Evaluar las expresiones aritméticas respetando la jerarquía de operadores. Indicando el orden de ejecución de cada una de ellas. 1. -4 * 7 + 2 ^ 3 / 4 – 5 = -31 = (-4 * 7 + (2^ 3)) / 4 - 5 = (-4 * 7) + ((8 / 4) - 5) = (-28)+ (2 – 5) = -28 + - 3 = -31 2. (7 * (10 - 5) mod 3) + 4 + 9 = 15 = (7 * (10 – 5) mod 3)+ 4+ 9 = (7 * (5) mod 3) + 4 + 9 = (35 mod 3) + 4 + 9 =2+4+9 = 15 3. 10 div 2 * 8 / 4 – 5 = - 2.5 = 10 div (((2 * 8)/ 4) – 5) = 10 div (16 / 4) - 5 = 10 div 4 – 5 = (10 div 4) - 5 = (2.5) - 5 = -2.5 4. (33 + 10 mod 3 * 4) /5 = 1.5 = ((33 + 10) mod (3 * 4)) / 5 = ((33 + 10) mod 12) / 5 = (43 mod 12) / 5 =7/5 = 1.5 1
  • 2. 5. 16 * 12 mod 3 – 3 * 2 = - 6 = ((16 * 12) Mod 3) – (3 * 2) = (192 Mod 3) – 6 = 0–6 = -6 6. ((3 + 2) ^ 2 – 15) / 2 * 5 =1 = (((3 + 2) ^ 2) – 15) / (2 * 5) = (((5) ^2) – 15) / (2 * 5) = (25 - 15) / (10) = 10 / 10 =1 7. Y = (4 * 3 / 2) mod (8 4 + 2) = 2 Y = ((4 * 3)/ 2) mod ((8 4) + 2)) Y = (12 / 2) mod ((2) + 2) Y = 6 mod 4 Y=2 2
  • 3. 2. Deducir el valor de las expresiones siguientes: Siendo: A = 5; B = 25; C = 10 8. X = A + B mod C = 0 X = (5 + 25) mod 10 X = 30 mod 10 X=0 9. X = (A + B) / C = 3 X = (5 + 25) / 10 X = 30 / 10 X=3 10. X = A + (B / C) = 7.5 X = 5 + (25 / 10) X = 5 + 2.5 X = 7.5 11. b ^ 2 - 4 * a * c = -23 a = 2, b = 1, c = 3 = (1^2) – (4 * 2 * 3) = 1 - 24 = -23 12. (X ^ 2 + Y ^ 2) > (30 / 2) = 12 > 15 X = 2, Y = 3, Z = 4 = ((2^2)+ (3^2)) > (30/2) = (4+ 9) > 15 = 13 > 15 3
  • 4. 3. Si el valor de A es 4, el valor de B es 5 y el valor de C es 1, evaluar las siguientes expresiones: 13. B * A - B ^ 2 / 4 * C = -1.25 = (5 * 4 – (5^2)) / (4 * 1) = 20 - (25 / 4) = 20 – 6.25 = 13.75 14. (A * B) / 3 ^ 2 = 2.222222222 = (4 * 5) / (3^2) = (4 * 5) / 9 = 20/ 9 = 2.222222222 15. ( ( ( B + C ) / 2 * A + 10 ) * 3 * B ) - 6 = 416 = (((5 + 4) / 2)* 4 + 10)) * (3 * 5)) -6 = (((9 / 2) * 4) + 10) * (3 * 5) - 6 = (((4.5 * 4)+ 10) * (15)) – 6 = ((18 + 10) * 15) - 6 = (28 * 15) – 6 = 420 - 6 = 416 4
  • 5. 4. Realizar las conversiones de expresiones matemáticas a expresiones algorítmicas. Indicando el orden de ejecución de cada una de ellas. 1. = (m + n) / (p – p) 2. = -b RC ((b^2)- (4 (a)) * c ) / (2 * a) 3. = (m + (n / p)) / (a – (r / s)) 4. P= = P =(A + B + C) / 2 5. = X * (Y ^ 2) 6. + 1 = (m / n) + 1 7. = (m +(n / q)) / (q - (r / s)) 8. (m + n) = (m + n) * (p / q) 9. = (a = RC (b^2) +(c^2)) (b2+ c2 = a2) = (a= ) = a = RC (b^2) +(c^2) 10. = (((3 (x)) – y) /z ) – (((2 (x) )* ( y^2) /( z - 1) + (x / y) 5
  • 6. 5. Evaluar las expresiones lógicas aplicando la jerarquía de operadores. 1. ((A * B) < (B + C)) AND (A = C)= Falso A=3, B=4 y C=2 ((3 * 4) < (4 + 2)) AND (3 = 2) (12 < 6) AND (3 = 2) 2. ((A + B) > C) OR ((B / D > B))= verdadero A=2, B=5, C=3 y D=5 ((2 + 5) > 3) OR ((5 / 5) > 5) (7 > 3) OR (1 >5) 3. X = (A B) * C + (A / B)= X = 8 A = 4, B = 2, C = 3 X = (4 2) * 3) + (4 / 2) X = (2 * 3) + (4 / 2) X= 6+2 X= 8 6
  • 7. X=1, Y=4; Z=10, PI=3.141592, E=2.718281 4. PI * X^2>Y OR 2* PI * X <=Z Verdadero ((3.141592)*1^2) >4) OR (((2*(3.141592))*1) <= 10 (3.141592 > 4) OR (6.283184 <= 10) 5. X>3 AND Y=4 OR X+Y<=Z Verdadero (1 >3 AND 4 = 4) OR (1 + 4) <=10 (1>3 AND 4 = 4) OR (5<= 10) 6. X>3 AND (Y=4 OR X+Y<=Z) Falso (1 >3) AND (4 = 4 OR (1 + 4) <=10) (1 >3) AND (4 = 4 OR 5<= 10) 7. NOT Y/2=2*X AND NOT Y<(PI-E*Z) Falso NOT ((4 / 2) = (2 * 1) AND NOT (4 < (3.141592 – (2.718281 * 10))) NOT (2 = 2) AND NOT (4 < (3.141592 – (27.18281))) NOT (2 = 2) AND NOT (4 < – 24.041218) NOT (V) AND NOT (F) F AND V F 7
  • 8. a=5 y b=2 8. a>b = verdadero 5 >2 9. a>=b = Verdadero 5>= 2 10. a<b = falso 5< 2 11. a<=b = falso 5<=2 12. Not a=b = Falso Not 5 = 2 -5 = 2 8
  • 9. 6. Convertir en expresiones numéricas los siguientes enunciados. 1. Elabore una expresión que sólo permita valores entre 1 y 10. (x>=1 and x<=10) 3^2 + 5 – 4 + 7 / 3 = = ((3^2) + 5 – 4) + (7 / 3) = 9 + 5 – 4 + (8 / 2) = (9 + 5) – (4 + 4) = 14 - 8 =6 2. Elabore una expresión que permita valores entre 1 y 3, y 5 a 7 exclusivamente. (v>= 1 AND v<= 3) AND (v>= 5 AND v<= 7) 3. Elabore una expresión que permita edades entre 18 y 25 años. (E>= 18 AND E<= 25) 9