BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 22T

(a)

To determine

The proportionality equation through given conditions.

Expert Solution

Answer to Problem 22T

The equation of proportionality is M=kwh2/L .

Explanation of Solution

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,

M=k1wh2 . (1)

For some constant k10 .

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

M=k2L . (2)

For some constant k20

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

M=k1k2wh2L=kwh2L

For some constant k0

Where,

k is constant of proportionality.

In the above equation k1 and k2 are constant so the product of constant is a constant.

Thus, the equation of proportionality is M=kwh2/L .

(b)

To determine

The value of constant of proportionality through given conditions.

Expert Solution

Answer to Problem 22T

The value of constant of proportionality is 400.

Explanation of Solution

Given:

The width of beam is 4in , height of beam is 6in and length of beam is 12ft that support a weight of 4800Ib .

Calculation:

The equation of proportionality from part (a) is,

M=kwh2/L

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

4800=k(4)(6)212k(4)(6)2=480012k=57600144k=400

Thus, the value of constant of proportionality is 400.

(c)

To determine

The maximum weight beam can support.

Expert Solution

Answer to Problem 22T

The value of maximum weight is 12,000Ib .

Explanation of Solution

Given:

The length of beam is 10-ft , width of beam is 3in and height of beam is 10in because the beam is made of same material that means the value of constant of proportionality is k=400 same for this beam obtained from part (b).

Calculation:

The equation of proportionality from part (a) is,

M=kwh2/L

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

M=(400)(3)(10)2/10M=12,0000/10M=12,000

Thus, the value of maximum weight is 12,000Ib .

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