Math Problem Statement

Unos científicos miden la temperatura de un planeta distante. El gráfico muestra la temperatura (en °C) respecto a la altura (en kilómetros) sobre la superficie del planeta. Responder a las siguientes preguntas: (a) ¿Cuál es la temperatura a 0 kilómetros? (b) Elegir el enunciado que mejor describa cómo se relacionan la altura y la temperatura y luego dar el valor solicitado.

Solution

Let's analyze the graph and the questions:

  1. The graph shows the relationship between "Temperatura" (Temperature in °C) and "Altura" (Height in kilometers).
  2. It appears to be a linear relationship, where the temperature decreases as the altitude increases.

Let's answer the questions based on the graph:

(a) ¿Cuál es la temperatura a 0 kilómetros?

At 0 km on the x-axis, the temperature on the y-axis is 40°C, so:

  • Respuesta: 40°C

(b) Elegir el enunciado que mejor describa cómo se relacionan la altura y la temperatura.

From the graph, as altitude increases, the temperature decreases. Therefore, the correct statement is:

  • A medida que la altura aumenta, la temperatura disminuye.

¿A qué tasa disminuye la temperatura?**

To find the rate at which temperature decreases (slope), we can use two points from the graph:

  • At 0 km, the temperature is 40°C.
  • At 8 km, the temperature is 0°C.

The slope is calculated as: slope=ΔTΔh=0°C40°C8km0km=40°C8km=5°Cpor kiloˊmetro\text{slope} = \frac{\Delta T}{\Delta h} = \frac{0°C - 40°C}{8 \, \text{km} - 0 \, \text{km}} = \frac{-40°C}{8 \, \text{km}} = -5°C \, \text{por kilómetro}

So, the temperature decreases at a rate of 5°C por kilómetro.

Would you like more details or have any further questions?

Here are some related questions:

  1. How do we calculate the slope of a line from a graph?
  2. What is the equation of the line based on this graph?
  3. How could we interpret the y-intercept in this case?
  4. What would the temperature be at 10 kilometers if the trend continued?
  5. How would this graph change if the planet had a thinner atmosphere?

Tip: The slope of a line is crucial for understanding the rate of change between two variables.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope
Graph Interpretation

Formulas

Slope formula: (change in y) / (change in x)

Theorems

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Suitable Grade Level

Grades 6-8