# The formula for the temperature at height h.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter A, Problem 29E

(a)

To determine

## To write: The formula for the temperature at height h.

Expert Solution

The formula for the temperature is T=2010h,0h12.

### Explanation of Solution

Given:

The ground temperature is 20°C.

For each 100 m rise up, the temperature is increased by 1°C.

Calculation:

Let the temperature is denoted by T and the height is denoted by h.

From the given information, it is observed that T=20 when h=0.

Since the temperature is increasing by 1°C, T=2010h,0h12.

(b)

To determine

### To find: The range of temperature of plane at height 5 km.

Expert Solution

The range of temperature of plane at height 5 km is [30,20].

### Explanation of Solution

Calculation:

From part (a), the temperature is given by the formula, T=2010h,0h12.

Re write this as,

T=2010h,0h5T20=10h,0h5T2010=h,0h5h=2T10,0h502T105

Simplify further as,

2T10320T30T[30,20]

Thus, the range of the temperature of plane at the height of 5 km is [30,20].

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