Question

At what altitudes does the dew point range from 31.7°F to 31.3°F, given that the dew point on the ground is 40°F and the dew point x miles high is given by d(x) = 40 - 5.8x?

Options:
A) 0.7 miles to 0.8 miles
B) 0.8 miles to 0.9 miles
C) 0.9 miles to 1.0 miles
D) 1.0 miles to 1.1 miles
E) 1.1 miles to 1.2 miles

Answer 1

The dew point ranges from 31.3°F to 31.7°F at altitudes between 1.43 miles and 1.5 miles.

Step-by-step explanation:

To find at what altitudes the dew point ranges from 31.7°F to 31.3°F, we need to find the values of x that satisfy the given condition. The dew point x miles high is given by the equation d(x) = 40 - 5.8x. We can set up the inequality 31.3 ≤ 40 - 5.8x ≤ 31.7 and solve for x.

First, subtract 40 from all three parts of the inequality to get -8.7 ≤ -5.8x ≤ -8.3. Then, divide all three parts of the inequality by -5.8 (remember to reverse the inequality signs when dividing by a negative number) to get 1.5 ≥ x ≥ 1.43. Therefore, the altitudes where the dew point ranges from 31.7°F to 31.3°F are between 1.43 miles and 1.5 miles high.