Question

Suppose we want to add some punch to a partially filled drink dispenser of punch. We know that a 65 ounce bottle of punch will increase the height of the punch in the dispenser by 1.5 inches. Let h represent the varying height of the punch in the dispenser (in inches) and let v represent the varying volume of punch in the dispenser (in ounces).Express the change in height of punch in the dispenser in inches, Δh, in terms of the change in the volume of punch in the dispenser in ounces, Δv. (Use "d" to enter Δ. For example, type dx+5 for Δx+5Δx+5.)

Answer 1

Answer:

dh = 3 *dV / 130

Step-by-step explanation:

Given:

- volume of punch in bottle = 65 ounce

- volume of punch = v

- increase in height of punch level on dispenser = 1.5 in

Find:

- The change in height of punch in the dispenser in inches, Δh, in terms of the change in the volume of punch in the dispenser in ounces, Δv.

Solution:

We will assume a linear relationship between the increase in punch level dispenser and the increase in volume of dispenser.

                   h(v) = m*v + h

Where, m is change of height with respect to volume. Hence,

                   m = dh / dV = 1.5 / 65 = 3 / 130 in / ounce

Hence,

                   dh = 3 *dV / 130