Question

Solve the problem. the following equation is used in meteorology to determine the temperature humidity index t = two-fifths (w 80) 15, where w represents the wet-bulb thermometer reading. for what values of w would t range from 85 to 95? a. 170 less-than-or-equal-to w less-than-or-equal-to 195 c. 95 less-than-or-equal-to w less-than-or-equal-to 120 b. 129 less-than-or-equal-to w less-than-or-equal-to 133 d. 81 less-than-or-equal-to w less-than-or-equal-to 85

Answer 1

The values of w that would make t range from 85 to 95 are 255 less-than-or-equal-to w less-than-or-equal-to 280.

Step-by-step explanation:

The given equation is t = \frac{2}{5}(w-80) + 15, where w represents the wet-bulb thermometer reading. We need to find the values of w that would make t range from 85 to 95.

First, let's substitute the lower limit, t = 85, into the equation to find w:

85 = \frac{2}{5}(w-80) + 15

Simplifying the equation:

85 - 15 = \frac{2}{5}(w-80)

70 = \frac{2}{5}(w-80)

Multiplying both sides by 5 to get rid of the fraction:

70 \times 5 = 2(w-80)

350 = 2(w-80)

Dividing both sides by 2:

175 = w - 80

Adding 80 to both sides:

w = 175 + 80

w = 255

Therefore, the lower limit value of w is 255.

Next, let's substitute the upper limit, t = 95, into the equation to find w:

95 = \frac{2}{5}(w-80) + 15

Simplifying the equation:

95 - 15 = \frac{2}{5}(w-80)

80 = \frac{2}{5}(w-80)

Multiplying both sides by 5:

80 \times 5 = 2(w-80)

400 = 2(w-80)

Dividing both sides by 2:

200 = w - 80

Adding 80 to both sides:

w = 200 + 80

w = 280

Therefore, the upper limit value of w is 280.

So, the values of w that would make t range from 85 to 95 are 255 less-than-or-equal-to w less-than-or-equal-to 280.