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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1, Problem 22T

(a)

To determine

The proportionality equation through given conditions.

Expert Solution

The equation of proportionality is

**Given:**

The maximum weight *M* is proportional to the width *w* of beam and square height *h* and inversely proportional of length of beam *L*.

**Calculation:**

From given conditions, the maximum weight *M* that supported by a beam is directly proportional to width *w* of beam and square of height so by the definition of direct proportionality the equation is,

For some constant

The weight *w* is inversely proportional to length of beam *L* so by the definition of inverse proportionality the equation is,

For some constant

Combine both equation (1) and (2) to get the proportionality equation,

For some constant

Where,

*k* is constant of proportionality.

In the above equation

Thus, the equation of proportionality is

(b)

To determine

The value of constant of proportionality through given conditions.

Expert Solution

The value of constant of proportionality is 400.

**Given:**

The width of beam is

**Calculation:**

The equation of proportionality from part (a) is,

Substitute 4 for *w*, 6 for *h*, 12 for *l* and 4800 for *M* in the above equation and solve for *k*,

Thus, the value of constant of proportionality is 400.

(c)

To determine

The maximum weight beam can support.

Expert Solution

The value of maximum weight is

**Given:**

The length of beam is

**Calculation:**

The equation of proportionality from part (a) is,

Substitute 3 for *w*, 10 for *h*, 10 for *l* and 400 for *k* in the above equation and solve for *M*,

Thus, the value of maximum weight is