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12 days ago

13. En un pueblo, 5 personas escucharon una noticia. En una hora, cada una de ellas

Mathematics

1 answer:

Leona [4.1K]12 days ago

7 0

Answer:

En un lapso de 5 horas, la noticia habrá llegado a toda la comunidad.

Step-by-step explanation:

Iniciamos con 5 individuos que conocieron la noticia.

Transcurrida una hora, cada uno de ellos comunicó la noticia a 5 más.

Las nuevas 5 personas luego se la contaron a otras 5, continuando este ciclo.

Cada persona escucha y narra la noticia solo una vez y la población del pueblo es un poco superior a 19000.

La fórmula que utilizamos para resolver este problema es la siguiente:

Empezamos con 5 personas que supieron de la noticia en el tiempo 'hora 0'.

Después de una hora, cada uno transmitió la noticia a 5 personas adicionales, lo que significa que después de la primera hora tendremos:

$5+5^{2}=30$ (I)

Esto incluye las 5 originales de la 'hora 0' más 25 que se enteraron en la primera hora. La fórmula que formulamos es esta:

$5^{1}+5^{2}+5^{3}+...+5^{x}>19000$ (II)

Debemos hallar el valor de $x$ que cumpla con la ecuación (II).

Al calcular y sumar, descubrimos que:

$5^{1}+5^{2}+5^{3}+5^{4}+5^{5}+5^{6}>19000$

$19530>19000$

El valor de $x$ que satisface (II) es $x=6$ .

Para determinar el número de horas, observamos que en (I) el mayor exponente del 5 es 2. Por ese exponente, ha pasado una hora.

Así que para nuestro $x=6$ , las horas transcurridas son 5 horas (una menos que el valor de $x$ ).

El pueblo entero conocerá la noticia a las 5 horas.

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for the level 3 course, examination hours cost twice as much as workshop hours and workshop hours cost twice as much as lecture

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Answer:

The hourly rate for lectures is $7.33

Step-by-step explanation:

* Let's break down how to tackle the problem.

- For the level 3 course, examination hours are priced at double that of workshop hours.

- Workshop hours cost twice the rate of lecture hours.

- The total includes examination, workshop, and lecture hours.

- Examination lasts 3 hours, workshops 24 hours, and lectures 12 hours.

* Let’s denote the cost of lecture hours as $x per hour.

∴ The lectures cost $x per hour.

∵ Workshop charge is twice that of lectures

∴ Workshop hours cost 2(x) = 2x per hour.

∵ Examination fees are double that of workshop hours

∵ The workshop cost is 2x

∴ Examination fees are 2(2x) = 4x per hour.

- Combining costs for level 3 gives us the total of lecture, workshop, and examination hours.

∵ 12 hours for lectures

∵ 24 hours for workshops

∵ 3 hours for examinations

∵ Thus the total cost for level 3 = 12(x) + 24(2x) + 3(4x).

∴ Total cost for level 3 = 12x + 48x + 12x.

∵ Therefore, total cost = $528.

∴ 12x + 48x + 12x = 528.

∴ 72x = 528; hence we divide both sides by 72.

∴ x = 7.33.

∵ x represents the cost of lecture hours per hour.

∴ Therefore, the hourly price for lectures is $7.33.

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