Chapter 3, Problem 20E

Interpretation Introduction

(a)

Interpretation:

The equivalency and both conversion factor a) hours and days is to be stated.

Concept introduction:

Equivalency is defined as the two quantities that are equivalent in value. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

Answer to Problem 20E

The equivalency of a) hours and days is $24\mathrm{ }\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{ }=\mathrm{ }1\mathrm{ }\mathrm{d}\mathrm{a}\mathrm{y}$

Conversion factor of a) hours and days is given by;

$\frac{\text{24 hour}}{\text{1}\text{day}}\text{ and }\frac{1\text{day}}{\text{24 hour}}$

Explanation of Solution

The two quantities that are equivalent in value is denoted as equivalence. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

$\begin{array}{l}\text{0}\text{.025 furlong = 1 rod (and)}\\ \frac{\text{0}\text{.025 furlong}}{\text{1 rod}}\text{ (and) }\frac{\text{1 rod}}{\text{0}\text{.025 furlong}}\mathrm{...}(1)\end{array}$

In the expression (1), the conversion factor 1 rod / 0.025 furlong is used to convert a length expressed in furlongs to a length expressed in rods. Two variable, x and y are directly proportional if there is a non-zero constant k which connect them in the form of $y = kx$. Besides, the relationship is expressed as y α x. In the expression the symbol α is called as ‘is proportional to’.

A proportionality constant, m is inserted to convert a proportionality into an equality. Such as,

$\text{y = m}\cdot \text{x}\mathrm{...}\text{(2)}$

Given expression;

a) hours and days

Based on the above discussion the equivalency and conversion factors are states as follows;

The equivalency of a) hours and days is $24\mathrm{ }\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{ }=\mathrm{ }1\mathrm{ }\mathrm{d}\mathrm{a}\mathrm{y}$

Conversion factor of a) minutes and seconds is given by;

$\frac{\text{24 hour}}{\text{1}\text{day}}\text{ and }\frac{1\text{day}}{\text{24 hour}}$

Conclusion

Thus, the equivalency and both conversion factor a) hours and days is stated.

Interpretation Introduction

(b)

Interpretation:

The equivalency and both conversion factor b) gallons and quarts is to be stated.

Concept introduction:

Equivalency is defined as the two quantities that are equivalent in value. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

Answer to Problem 20E

The equivalency of b) gallons and quarts is $1\mathrm{ }\mathrm{g}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{ }=\mathrm{ }4\mathrm{ }\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{t}$

Conversion factor of b) gallons and quarts is given by;

$\frac{1\text{ gallon }}{4\text{ quart}}\text{ and }\frac{\text{4 quart }}{\text{1 gallon}}$

Explanation of Solution

The two quantities that are equivalent in value is denoted as equivalence. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

$\begin{array}{l}\text{0}\text{.025 furlong = 1 rod (and)}\\ \frac{\text{0}\text{.025 furlong}}{\text{1 rod}}\text{ (and) }\frac{\text{1 rod}}{\text{0}\text{.025 furlong}}\mathrm{...}(1)\end{array}$

In the expression (1), the conversion factor 1 rod / 0.025 furlong is used to convert a length expressed in furlongs to a length expressed in rods. Two variable, x and y are directly proportional if there is a non-zero constant k which connect them in the form of y = kx. Besides, the relationship is expressed as y α x. In the expression the symbol α is called as ‘is proportional to’.

A proportionality constant, m is inserted to convert a proportionality into an equality. Such as,

$\text{y = m}\cdot \text{x}\mathrm{...}\text{(2)}$

Given expression;

b) Gallons and quarts

Based on the above discussion the equivalency and conversion factors are states as follows;

The equivalency of b) gallons and quarts is $1\mathrm{ }\mathrm{g}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{ }=\mathrm{ }4\mathrm{ }\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{t}$

Conversion factor of b) gallons and quarts is given by;

$\frac{1\text{ gallon }}{4\text{ quart}}\text{ and }\frac{\text{4 quart }}{\text{1 gallon}}$

Conclusion

Thus, the equivalency and both conversion factor b) gallons and quarts is stated.

Interpretation Introduction

Interpretation:

(c)

The equivalency and both conversion factor c) quarters and dollars is to be stated.

Concept introduction:

Equivalency is defined as the two quantities that are equivalent in value. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

Answer to Problem 20E

The equivalency of c) quarters and dollars is $1\mathrm{ }\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{ }=\mathrm{ }0.25\mathrm{ }\mathrm{d}\mathrm{o}\mathrm{l}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{s}$

Conversion factor of c) quarters and dollars is given by;

$\frac{1\text{ quarters }}{0.25\text{ dollars}}\text{ and }\frac{\text{0}\text{.25 dollars }}{\text{1 quarters}}$

Explanation of Solution

The two quantities that are equivalent in value is denoted as equivalence. For example: 0.025 furlong is equal to 1 rod. In this case, furlong and rod represent the same physical length but expressed in various units. When an equivalency is denoted as a fractional value it is called ‘conversion factor’. Moreover, two conversion factors result from each equivalency.

$\begin{array}{l}\text{0}\text{.025 furlong = 1 rod (and)}\\ \frac{\text{0}\text{.025 furlong}}{\text{1 rod}}\text{ (and) }\frac{\text{1 rod}}{\text{0}\text{.025 furlong}}\mathrm{...}(1)\end{array}$

In the expression (1), the conversion factor 1 rod / 0.025 furlong is used to convert a length expressed in furlongs to a length expressed in rods. Two variable, x and y are directly proportional if there is a non-zero constant k which connect them in the form of y = kx. Besides, the relationship is expressed as y α x. In the expression the symbol α is called as ‘is proportional to’.

A proportionality constant, m is inserted to convert a proportionality into an equality. Such as

$\text{y = m}\cdot \text{x}\mathrm{...}\text{(2)}$

Given expression;

c) quarters and dollars

Based on the above discussion the equivalency and conversion factors are states as follows;

The equivalency of c) quarters and dollars is $1\mathrm{ }\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{ }=\mathrm{ }0.25\mathrm{ }\mathrm{d}\mathrm{o}\mathrm{l}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{s}$

Conversion factor of c) quarters and dollars is given by;

$\frac{1\text{ quarters }}{0.25\text{ dollars}}\text{ and }\frac{\text{0}\text{.25 dollars }}{\text{1 quarters}}$

Conclusion

Thus, the equivalency and both conversion factor c) quarters and dollars is stated.