Question

Complete the chart above for the volume of the rectangular package with various widths.

b) Write down the function for the volume V(w).
c) Draw a graph to represent the volumes of the package.
d) Find the domain of the width of the package.
e) Find the width that gives the greatest volume and the maximum volume of the package.

a. Chart:
Width (w) | Volume (V)
10 | 2500
20 | 5000
30 | 7500

b. V(w) = 250w

c. Graph not generatable.

d. Domain: w ≥ 0

e. Width for the greatest volume: 30, Maximum volume: 7500.

Answer 1

The function for the volume of a rectangular package based on the student's chart is V(w) = 250w. The domain for the width is w ≥ 0. The width for the greatest volume based on given data is 30, with a maximum volume of 7500 cubic units.

Step-by-step explanation:

The student is working on a mathematics problem involving volume calculations of a rectangular package. The chart is given with varying widths and corresponding volumes, showing a linear relationship between width and volume.

b) Function for Volume V(w)

The function for the volume V(w) based on the chart is V(w) = 250w.

d) Domain for the Width

The domain for the width of the package is w ≥ 0, since width cannot be negative.

e) Maximum Volume

The width that gives the greatest volume is 30, with the maximum volume being 7500 cubic units. This relationship assumes that the trend in the chart continues linearly and there are no constraints on the width beyond what's observed in the data.