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S/9 = C/10 = R/(π/20) = k Igualamos cada una a k
S/9 = k , C/10 = k , R/(π/20) = k
S = 9k , C = 10k , R = (π/20)k
En la Pregunta 7:
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Planteando el Problema:
6S + 2C = 222 Reemplazando los valores S = 9k , C = 10k
6(9k) + 2(10k) = 222
54k + 20k = 222
74k = 222
k = 222/74
k = 3
Nos piden el angulo en radianes:
R = (π/20)k
R = (π/20)(3)
R = 3π/20 rad Respuesta
En la Pregunta 8:
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S = 3x - 2 y C = 2x + 4 Reemplazando S = 9k , C = 10k
9k = 3x - 2 10k = 2x + 4
k = (3x - 2)/9 k = (2x + 4)/10
Igualando los valores de k:
(3x - 2)/9 = (2x + 4)/10 multiplicando en aspa
10(3x - 2) = 9(2x + 4)
30x - 20 = 18x + 36
30x - 18x = 36 + 20
12x = 56
x = 56/12 Simplificando 4
x = 14/3
Hallando k:
k = (3x - 2)/9
k = (3(14/3) - 2)/9 Simplificando 3
k = (14 - 2)/9
k = (12)/9 Simplificando 3
k = 4/3
Hallando el angulo en Radianes:
R = (π/20)k
R = (π/20)(4/3) Simplificando 4
R = (π/5)(1/3)
R = π/15 rad
En la Pregunta 9:
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(50S - 20C +40R)/(8S - 22C + 8R) Reemplazando S = 9k , C = 10k
(50(9k) - 20(10k) + 40(π/20)k)/(8(9k) - 22(10k) + 8(π/20)k)
(450k - 200k + 2πk)/(72k - 220k + 2πk/5)
(250k + 2(3,14)k)/(-148k + 2(3,14)k/5)
(250k + 3,28k)/(-148k + 1,256k)
(253,28k)/(-146,744k) Simplificamos k
1,726