The compound inequality can be rewritten as two separate inequalities. Use the table to solve for these inequalities separately.
24.46≤ P≤ 28.62
Practice makes perfect
We have to find the pressure experienced when traveling from Phoenix to Denver, represented by the compound inequality 1117≤ A(P)≤ 5280. This means we need to solve the following two inequalities.
1117 ≤ & 90 000-26 500ln(P)
& 90 000-26 500ln(P)≤ 5280
Let's revisit the table we created in a previous exercise.
We will start by finding the corresponding pressure to A(P)=1117. To find more precise values, we change the table settings to show decimal values of P. Push 2nd and WINDOW, then change â–³ Tbl to - 0.01. Note that 1117 is somewhere in the interval 28
The function's value is about 1117 at P≈ 28.62. Since we want the pressures to be greater than 1117, our inequality becomes P≤ 28.62. Note that the table is decreasing as you move down the list. We want to know when y is less than or equal to 5280.
y≤ 5280
To determine this, we change the table setup once more. From the original table we see that 5280 lies in the interval 24 < P < 25. Therefore, we will choose 24.5 as the table's starting point.
The function's value is about 5280 at P≈ 24.46. Since we are looking for altitudes less than 5280, and as altitude increases pressure decreases, our inequality becomes P≥ 24.46. Combining our inequalities, we get a compound inequality.
24.46≤ P≤ 28.62
