Question

Scientists are studying the temperature on a distant planet. they find that the surface temperature at one location is 45 Celsius. they also find that the temperature decreases by 7 Celsius for each kilometer you go up from the surface.

let T represent the temperature (in Celsius), and let H be the height above the surface (in kilometers). write an equation relating T to H, and then graph your equation using the axes.

Answer 1

answer is A

Step-by-step explanation:

Answer 2

The equation
`\(T = 45 - 7H\)` represents the relationship between temperature (T) and height above the surface (H) on the distant planet, where the surface temperature is 45 Celsius, decreasing by 7 Celsius for each kilometer of height. Graphing this equation reveals a linear line with a negative slope, portraying the systematic decrease in temperature as one moves higher above the planet's surface.

Step-by-step explanation:

The equation
`\(T = 45 - 7H\)` is derived from the given information about the distant planet's temperature. The surface temperature is 45 Celsius, and for each kilometer above the surface (represented by H), the temperature decreases by 7 Celsius.

The equation reflects this linear relationship. The term 45 is the starting temperature at the surface, and the term -7H represents the decrease for each kilometer above.

For example, let's substitute H = 1 into the equation to find the temperature at a height of 1 kilometer:

`\[ T = 45 - 7(1) = 45 - 7 = 38 \]`

This calculation shows that at a height of 1 kilometer, the temperature is 38 Celsius. Similarly, for H = 2:

`\[ T = 45 - 7(2) = 45 - 14 = 31 \]`

This process can be repeated for different values of H to create a set of coordinates (H, T) that form a linear relationship. Graphing these points produces a straight line with a negative slope, illustrating the temperature decrease with increasing height.

In essence, the detailed calculation demonstrates how the equation captures the specified temperature-height relationship on the distant planet. It provides a mathematical representation of the observed data and allows scientists to predict temperatures at various heights above the surface.