Question

temperature suppose there is a 1.3°f drop in temperature for every thousand feet that an airplane climbs into the sky. if the temperature on the ground is 61.8°f, what will be the temperature when the plane reaches an altitude of 5,000 ft? the temperature will be 55°f. (type an integer or a decimal )

Explanation:

Step1: Find total temperature drop

First, determine how many thousand - foot intervals are in 5000 feet. Since 5000 feet divided by 1000 feet per interval gives 5 intervals. The temperature drop per thousand feet is \(1.3^{\circ}\text{F}\), so the total temperature drop is the number of intervals times the drop per interval. Let \(n = \frac{5000}{1000}=5\) and the drop per interval \(d = 1.3^{\circ}\text{F}\). The total drop \(D=n\times d=5\times1.3\).
\(5\times1.3 = 6.5\)

Step2: Calculate the temperature at 5000 ft

The ground temperature \(T_{ground}=61.8^{\circ}\text{F}\). The temperature at 5000 ft \(T = T_{ground}-D\). Substitute \(T_{ground}=61.8\) and \(D = 6.5\) into the formula: \(T=61.8 - 6.5\).
\(61.8-6.5 = 55.3\) (Wait, the original answer in the box is 55, but let's check the calculation again. Wait, maybe I made a mistake. Wait, \(5\times1.3 = 6.5\), \(61.8-6.5=55.3\). But the box has 55. Maybe there is a miscalculation in the problem's given box? Wait, let's re - do the steps.

Wait, maybe the problem expects a different approach? Wait, no. Let's check:

Number of 1000 - foot increments in 5000 ft: \(5000\div1000 = 5\)

Temperature drop: \(5\times1.3=6.5\)

Ground temperature: \(61.8\)

Temperature at 5000 ft: \(61.8 - 6.5=55.3\). But the box has 55. Maybe there is a rounding error? If we round 55.3 to the nearest integer, we get 55. So perhaps the problem expects rounding.

Answer:

\(55.3\) (or 55 if rounded to the nearest integer)