Answer:
The value of w is lie from 95 to 120.
Step-by-step explanation:
The temperature humidity index is given by the equation
\(T=\frac{2}{5}(w+80)+15\)
where w represents the wet-bulb thermometer reading.
We have to find the values of w for which T range from 85 to 95.
\(85\leq T\leq 95\)
\(85\leq \frac{2}{5}(w+80)+15\leq 95\)
Subtract 15 from all the sides.
\(85-15\leq \frac{2}{5}(w+80)+15-15\leq 95-15\)
\(70\leq \frac{2}{5}(w+80)\leq 80\)
Multiply all sides by 5.
\(70\times 5\leq 2(w+80)\leq 80\times 5\)
\(350\leq 2w+160\leq 400\)
Subtract 160 from all the sides.
\(190\leq 2w\leq 240\)
Divide all sides by 2.
\(95\leq w\leq 120\)
Therefore the value of w is lie from 95 to 120.
