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Manual del detective: capítulo 1

 

Glosario

Alicatado

Alicatado

Definición:

Efecto de revestir algo de azulejos, embaldosado.

Ejemplo:

El alicatado de la pared del baño está roto.

Allanamiento

Persona intentando forzar una puerta

Definición:

Delito que consiste en entrar en un recinto o casa ajena sin el consentimiento del propietario.

Ejemplo:

Se produjo un allanamiento de morada la pasada madrugada en mi edificio.

Capítulo 1

Libro antiguo con el título

Como ya te habrás dado cuenta, en tu carrera como detective te encontrarás con muchas incógnitas e información que no conoces.

Esto tiene cierta similitud con el álgebra, que usa letras para representar cantidades desconocidas.

A partir de estos símbolos se construyen expresiones que permiten modelar y resolver situaciones cotidianas.

En este capítulo te iniciarás en este nuevo lenguaje que sirve de apoyo en la investigación de casos reales.

Lectura facilitada

En tu carrera como detective te encontrarás con muchas incógnitas.

Esto tiene cierto parecido con el álgebra.

En este capítulo te iniciarás en este nuevo lenguaje.

Lenguaje algebraico

Mujer científica

Aquí tienes algunas definiciones que debes conocer para adentrarte en el mundo del álgebra.

Variable
Son las letras que representan cantidades desconocidas. Su valor cambia según el contexto.
Monomio

Es una expresión algebraica formada solo por el producto de números y letras (variables). Los exponentes de las letras deben ser números naturales.

Partes de un monomio

Todo monomio está formado por:

- Coeficiente: parte numérica del monomio.
- Parte literal: parte que incluye las letras con sus exponentes.
- Grado: es la suma de los exponentes de todas las variables que forman el monomio

Polinomio

Es la suma o resta de varios monomios. Cada uno de los monomios que lo forman también se pueden llamar términos.

El grado del polinomio es el grado más alto de los términos que lo forman.

Por ejemplo, la expresión \(A(x)=-x^4+x^2-4x+2\) es un polinomio de grado 4.

Valor numérico

Es el resultado de sustituir en una expresión algebraica las letras por números.

Por ejemplo, para el polinomio \(P(x)=x^3-5x\) el valor numérico si \(x=2\) es

\[P(2)=2^3-5\cdot 2=8-10=-2\]

Clasifica expresiones

Clasifica cada una de las siguientes expresiones algebraicas 

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Su navegador no es compatible con esta herramienta.

Partes de un monomio

Completa la siguiente tabla en tu cuaderno

Monomio Coeficiente Parte literal Grado
\(-2x^2y\)

\(\dfrac{ab}{3}\)

\(-\sqrt{5}x^6\)

\(x^3z^2\)

Practica el valor numérico

Calcula los siguientes valores numéricos de polinomios

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%E1%B2%FF%F3%E6%F7%FFs%E6%FB%F1%FD%E1%B0%EF%EF

\(P(x)=2x^2+3x+1\)

P({x})=

P(x)=2x

P({x})=

\(P(x)=x^2+3\)

P({x})=

\(P(x, y)=5xy+y^2\)

P({x}, {y})=

\(P(x)=x^2+5x+1\)

P({x})=

\(P(x)=3x^2+7x+9\)

P({x})=

\(P(x)=5x^2-3\)

P({x})=

\(P(x)=2x^2+x-5\)

P({x})=

\(P(x)=x+x^3+7\)

P({x})=

\(P(x)=6x^2-3\)

P({x})=

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Comprando piso

Suelo de baldosas rectangulares con alfombra al fondo

Una página web anuncia la venta de una vivienda con un dormitorio para dos personas y María está pensando en comprarla. Sin embargo, le da la impresión de que es demasiado pequeña.

En España, los dormitorios dobles han de tener un tamaño mínimo de 10 m2 y María tiene miedo de que la vivienda no cumpla la normativa.

María es una persona muy observadora y se da cuenta de que la alfombra de la foto es un modelo muy conocido de la tienda Zaska. Tras una pequeña búsqueda averigua que las medidas de la alfombra son 230 cm x 160 cm.

Rápidamente se pone a hacer cálculos:

El ancho de la habitación es de cm = m

La longitud de cada baldosa es de cm =   m.

Llamándole x al ancho (en metros) de una baldosa, el largo de la habitación es + x .

La superficie de la habitación medirá · ( +  x) m2.

Unos días más tarde va a ver el piso con una regla. La baldosa de la habitación mide 20 cm de ancho (0,20 m).

¡Ahora sí que puede averiguar cuánto mide la superficie de la habitación!: m2 .

¿Es una buena idea que compre la casa? 

NOTA: escribe todos los números decimales con 2 cifras.

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Prueba 1.1. Medidas del ladrón

Como investigador o investigadora en formación creemos que es importante tener una buena base teórica pero también experiencia práctica. La policía local de A Guarda ha recurrido a nuestra agencia de detectives y te hemos elegido para ayudarlos con su caso. Te ponemos en contexto:

Ladrón con pasamontañas cerca de pared alicatada.

Está habiendo una oleada de allanamientos en los domicilios de la zona. Por suerte, una cámara de seguridad ha conseguido registrar una instantánea del sospechoso antes de ser desconectada. Necesitan una descripción detallada para poder atraparlo, y su altura resulta clave en la investigación. ¿Cómo puedes saber cuánto mide?

Si observas el alicatado que se ve al fondo, te darás cuenta de que puedes escribir la altura del sospechoso utilizando como referencia el lado del azulejo.

Altura sospechoso = 9 · x

Utilizando una notación más matemática: P(x) = 9x

Ahora solo tendrás que desplazarte hasta el lugar donde fue tomada la foto y medir el lado de un azulejo.

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Si el lado de la baldosa mide 20 cm, entonces la altura del sospechoso sería de @@180@@cm.

Guarda la clave de acreditación que obtienes al resolver correctamente esta prueba. La necesitarás más adelante para resolver el caso Muerte en el hotel.

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