# The range of the distances from the fire’s center where the temperature is less than 500 ° 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 114E
To determine

## The range of the distances from the fire’s center where the temperature is less than 500°C.

Expert Solution

The temperature is less than 500°C if the distance from the fire’s center is more than 30m_.

### Explanation of Solution

Given:

The temperature T in °C at a distance of x meters from the center of the fire was given by T=600,000x2+300.

Calculation:

To obtain the range of the distances from the fire’s center where the temperature is less than 500°C, set T<500 and solve this inequality.

That is, solve the inequality 600,000x2+300<500.

Simplify the above inequality as follows.

600,000<500(x2+300)[Multiply both sides by (x2+300)]1200<x2+300[Divide both sides by 500]900<x2[Subtract 300 from both sides]x2>900

Simplify further as follows.

x2>900|x|>900|x|>30x>30or x<30[|x|>ax>aor x<a]

Since x represents the distance, x will be positive.

Hence, the temperature is less than 500°C if the distance from the fire’s center is more than 30m_.

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