BuyFind

Precalculus: Mathematics for Calcu...

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

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

Answer to Problem 114E

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_.

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!