Q49. - Algebra 2

Question

The atmosphere of Earth is divided into four layers based on temperature variations. The troposphere is the layer closest to the planet. The average upper boundary of the layer is about 13 kilometres above Earth’s surface. This height varies with latitude and with the seasons by as much as 5 kilometres. Write and solve an equation describing the maximum and minimum heights of the upper bound of the troposphere.

Step-by-Step Solution

Answer

If the upper bound of the troposphere be x kilometres.

Absolute value equation is $\left|x-13\right|=5$

On solving equation maximum upper bound of troposphere is 18 kilometres and minimum upper bound of troposphere is 8 kilometres

Step 1 - Define variable

Let the upper bound of the troposphere be x kilometres.

Step 2 - Write absolute equation

As the average upper boundary of the layer is about 13 kilometres above Earth’s surface plus minus five kilometres. So absolute value equation is obtained by subtracting 13 from x inside the absolute vale symbol and equating it to 5 as shown below

$\left|x-13\right|=5$

Step 3 - Simplify x - 13 = 5

For any real number $a\text{ and }b$ with $b\ge 0$, if $\left|a\right|=b$ then either a=b or a=-b

So given equation can be written as

$\begin{array}{c}x-13=5\text{ or }x-13=-5\\ x=5+13\text{ or }x=-5+13\\ x=18\text{ or }x=8\end{array}$

So maximum upper bound of troposphere is 18 kilometres and minimum upper bound of troposphere is 8 kilometres.