Question

Use the following information. Blotting paper is a thick, soft paper used for absorbing fluids such as water or ink. The distance \(d\) (in centimeters) that tap water is absorbed up a strip of blotting paper at a temperature of \(28.4^{\circ} \mathrm{C}\) is given by the equation \(d=0.444 \sqrt{t}\) where \(t\) is the time (in seconds). How far up the blotting paper would the water be after \(33 \frac{1}{3}\) seconds?

Short answer

The water would be approximately 8.16 cm up the blotting paper after \(33 \frac{1}{3}\) seconds.

Step-by-step solution

Understand the given values

The equation given is \(d=0.444 \sqrt{t}\). In this case, \(t = 33 \frac{1}{3}\) seconds.

Convert the mixed number into a fraction

The mixed number \(33 \frac{1}{3}\) can be converted into an improper fraction to make it easier to work with in the equation. Therefore, \(33 \frac{1}{3} = \frac{100}{3}\) seconds.

Substitute the time value into the equation

Replace \(t\) in the equation with \(\frac{100}{3}\) to calculate the distance. This gives us: \(d=0.444 \sqrt{\frac{100}{3}}\)

Solve the equation

Solve the equation for \(d\), which comes out to be approximately 8.16 cm.