   Chapter 14.5, Problem 36E

Chapter
Section
Textbook Problem

Modeling DataA company builds a ware house with dimensions 30 feet by 50 feet. The symmetrical shape and selected heights of the roof are shown in the figure. (a) Use the regression capabilities of a graphing utility to find a model of the form z = a y 3 + b y 2 + c y + d for the roof line.(b) Use the numerical integration capabilities of a graphing utility and the model in part (a) to approximate the volume of storage space in the ware house.(c) Use the numerical integration capabilities of a graphing utility and the model in part (a) to approximate the surface area of the roof.(d) Approximate the are length of the roof line and find the surface area of the roof by multiplying the arc length by the length of the ware house. Compare the results and the integrations with those found in part (c). (a)

To determine

To calculate: The modal of the form z=ay3+by2+cy+d with the help of graphing utility by the use of regression capabilities..

Explanation

Given:

The given modal of the form is z=ay3+by2+cy+d.

Calculation:

The provided modal is in the form z=ay3+by2+cy+d.

From the figure, the points can be considered as (0,0,25),(0,5,22),(0,10,17) and (0,15,0).

And it can be seen that points lies in z-y plane.

Then with the use of Ti-83 use the regression capabilities

(b)

To determine

To calculate: The volume of storage space in warehouse, z=0.013333y3+0.16y21.0667y+25 with the use of graphing utility for the modal obtained in the above part..

(c)

To determine

To calculate: The surface area, z=0.013333y3+0.16y21.0667y+25 with the use of graphing utility for the modal obtained in above part.

(d)

To determine

To calculate: The arc length of modal of the form z=ay3+by2+cy+d and then find the surface area and then compare it with that in part (c).

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