# The formula for the temperature at height h with ground temperature of 20 ° C . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.7, Problem 110E

(a)

To determine

## The formula for the temperature at height h with ground temperature of 20°C.

Expert Solution

The formula for temperature at height h is T=20(h100)_.

### Explanation of Solution

Given:

The air cools at the rate of 1°C for each at 100m height and rise up to a distance of 12km the ground temperature is 20°C.

Calculation:

Since the air cools at the rate of 1°C for each 100m height, at height h=100m the temperature is T=(20100100)°C which is T=(201)°C.

At height h=200m, the temperature will be T=(20200100)°C which is T=(202)°C.

Let the height be h.

At height h, then the value for temperature will be as follows:

T=(20(h100))

Therefore, the formula for temperature at height h is T=20(h100)_.

(b)

To determine

### The range of temperature if the plane takes off and reaches a maximum height of 5km.

Expert Solution

The range for the temperature is 30°CT20°C_.

### Explanation of Solution

From part (a), the formula for temperature at height h is T=20(h100).

It is given that it reaches a maximum height of 5 km. That is, h=5 km.

Convert 5 km to meters as follows:

h=5(1000m)              [1km=1000m]h=5000m

Also, let the minimum height be 0 m. That is, 0h5000.

Simplify T=20(h100) as follows:

T=20(h100)100T=2000hh=2000100T

Substitute h=2000100T in 0h5000 and obtain the range of temperature as follows:

02000100T5000020002000100T2000500020002000100T30002000100100100T300010020T30

Reverse the inequality by diving by –1 as follows:

201T130120T3030T20

Therefore, the range for the temperature is 30°CT20°C_.

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