3.10. La revisión

Revisa lo aprendido

Paisaje nevado en la montaña de O Courel

Ahora que ya has adquirido los conocimientos necesarios, solo te queda revisar los últimos detalles.

Repasa las técnicas matemáticas que aplicarás en tu proyecto forestal.

Los datos y cálculos de coordenadas, meteorología, y presupuestos, podrán contener números racionales o irracionales; con potencias y raíces.

Es el momento de ver si lo tienes claro con estas actividades.

Lectura facilitada

Has aprendido lo necesario

Ahora revísalo en un contexto forestal.

Aparecerán números racionales e irracionales.

Con potencias y raíces.

Practícalo en las siguientes actividades.

Resolviendo problemas

Escarabajo Cuando ya tenías todo listo para el estudio de tu parcela, llega un inconveniente.

Una plaga de Gonipterus scutellatus (conocido como "defoliador del eucalipto") empieza en un cierto punto en tu parcela y se extiende de forma circular aumentando cada semana \(\dfrac{2}{3}\) m más el radio.

Este escarabajo vino a Europa desde Australia. El primer espécimen se encontró en 1976 en Italia y en Galicia en 1991.

¿Qué superficie afectó este pequeño escarabajo después de 12 semanas?
En otra parcela afectó a \(113,0973 \ m^2\), ¿cuánto tiempo ha pasado desde que se inició la plaga?

Expansión elíptica

Elipse Ahora, debido a la meteorología adversa, el pequeño escarabajo se extiende de forma elíptica, ocupando un área de \(150,7964 \ m^2\) y extendiendo la elipse en el radio horizontal en 6 metros.

¿Cuántos metros de radio vertical se ha extendido la plaga?

Nueva plaga...

Tabla de madera Para colmo de inconvenientes, un grupo de maderistas se ve afectado por otro insecto que está destruyendo las tablas almacenadas.

La madera se guarda apilada formando un cubo de 8 m³.

¿Cuánto mide la arista del cubo de madera?

Se estima que la fracción de madera afectada es \(\dfrac{37}{64}\) del total.

¿Cuál es la fracción de madera que no está afectada?

Los maderistas vuelven a apilar la madera sana en forma de cubo.

¿Cuál será el volumen de la madera sana?
¿Cuánto mide la arista del nuevo cubo?

Ayuda

El área de un círculo de radio r es: \(\pi\cdot r^2\).
El área de una elipse de radios a y b es: \(\pi\cdot a\cdot b\).
El volumen de un cubo de arista a es: \(a^3\).
Se puede tomar una aproximación como \(\pi=3,141592\).

Aplica tu sabiduría

Parcela de monte con vallado y un árbol al fondo

Has adquirido ya tu finca y decides dividirla en cuatro parcelas con cuatro propósitos específicos:

Parcela de energía limpia (placas solares y alimentación de la finca): representa \(\sqrt{\dfrac{4}{25}}\) de la superficie total de la finca.
Parcela de plantación comestible: representa los \(\dfrac{3}{4}\) de lo que sobra después de haber asignado la zona de energía.
Parcela de plantación maderera: su extensión es igual a la mitad de la diferencia entre la zona de plantación comestible y energía.
Parcela de reserva natural: es el terreno restante destinado a la fauna local.

¿Qué fracción del total de la finca representa cada una de las cuatro parcelas?
Si la parcela de reserva natural tiene una extensión de 340 m2, ¿cuál es la superficie total de la finca y cuánto mide cada una de las otras parcelas?

Apoyo visual

Esquema con el reparto de la finca

Revisión arbórea

Elije la respuesta correcta.

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Su navegador no es compatible con esta herramienta.

Asegura tu monte

Ya tienes tu proyecto casi finalizado.

Antes de continuar, vas a ponerle una clave de seguridad. En todo gran reto y proyecto, debe mantenerse la seguridad y precaución para poder trabajar sin miedo a perder el trabajo ya realizado.

Para obtener la clave óptima, debes calcular las siguientes operaciones que te darán los dígitos para el código:

\(\left( \sqrt{\dfrac{1}{9}} + \dfrac{2}{3} \right) \cdot 2 + \sqrt{\dfrac{121}{100}} : \dfrac{11}{10}\)
\(\left[ \sqrt{\dfrac{64}{16}} \cdot \left( \dfrac{5}{2} - \dfrac{1}{2} \right) \right] : \dfrac{1}{2} - 4\)
\(\dfrac{1}{2} \cdot \left( \sqrt{36} + \dfrac{4}{2} \right) + \sqrt{\dfrac{25}{4}} - \dfrac{3}{2}\)
\(\sqrt{\dfrac{81}{9}} - \left( \dfrac{3}{4} \cdot \dfrac{4}{3} \right) : \sqrt{\dfrac{1}{1}}\)
\(\left( \sqrt{\dfrac{4}{25}} : \dfrac{1}{5} \right) + \dfrac{3}{4} \cdot \left( \sqrt{16} - \dfrac{8}{3} \right)\)
\(\left( \sqrt{\dfrac{49}{4}} - \dfrac{1}{2} \right) : 3 - \sqrt{1}\)

¡Buen trabajo!

Ya dispones de un presupuesto con todas las condiciones y con su código seguro.

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Su navegador no es compatible con esta herramienta.

De la raíz a las alturas

Imagen del diario de aprendizaje en el proxecto cREAgal. Representa un lápiz y un cuaderno con el logotipo del proyecto en la portada.

Después de realizar todas las actividades de la fase 3, has asimilado conceptos nuevos relacionados con los números reales, con los montes gallegos y con el medioambiente.

Todo ello te ayudará en tu proyecto de repoblación forestal.

Reflexiona sobre lo anterior completando en tu diario de aprendizaje las preguntas del bloque 3.