/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 A gry is an old English measure ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

A gry is an old English measure for length, defined as \(1 / 10\) of a line, where line is another old English measure for length, defined as \(1 / 12\) inch. A common measure for length in the publishing business is a point, defined as \(1 / 72\) inch. What is an area of \(0.50\) gry \(^{2}\) in points squared (points \(\left.^{2}\right)\) ?

Short Answer

Expert verified
0.50 gry \(^2\) is approximately 0.18 points \(^2\).

Step by step solution

01

Understand the Relationship

First, we need to understand the relationship between gry, line, and inch. A gry is equal to \( \frac{1}{10} \) of a line. A line, in turn, is \( \frac{1}{12} \) of an inch.
02

Convert Gry to Inches

Calculate the length of one gry in inches. Since one gry is \( \frac{1}{10} \) of a line and a line is \( \frac{1}{12} \) of an inch, we have:\[ \text{1 gry} = \frac{1}{10} \times \frac{1}{12} \text{ inch} = \frac{1}{120} \text{ inch} \]
03

Convert Square Gry to Square Inches

To convert an area of 0.50 gry\(^2\) to square inches, we use the conversion:\[ \text{Area in inches}^2 = 0.50 \times \left( \frac{1}{120} \right)^2 = 0.50 \times \frac{1}{14400} = \frac{0.50}{14400} \text{ inch}^2 \]
04

Convert Square Inches to Square Points

Since 1 point is \( \frac{1}{72} \) inch, 1 inch equals 72 points. Therefore, to convert the area from square inches to square points, we square the conversion factor 72:\[ \text{Area in points}^2 = \frac{0.50}{14400} \times 72^2 \]Calculating further:\[ \frac{0.50}{14400} \times 5184 = \frac{0.50 \times 5184}{14400} = \frac{2592}{14400} \approx 0.18 \text{ points}^2 \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Old English Measurements
Old English measurements are units of measurement that were used historically in England before the adoption of the metric system. These measurements include unique units such as the "gry" and the "line," among others. Understanding these measurements requires a bit of historical knowledge, as they evolved from systems used in medieval times.

The gry, for instance, is a tenth of a line, which is another old measurement. The line is equal to one-twelfth of an inch. These types of measurements were commonly used in everyday life, before standardization efforts made more consistent units like the inch, foot, and yard prevail.

The use of such measurements was practical back then for everyday tasks like measuring cloth and land, yet they are mainly of historical interest now.
Area Conversion
Area conversion deals with changing an area from one set of units to another. It's a fundamental concept in geometry and measurement systems. When we talk about converting square grys to square points, for instance, we need to understand the size of each unit and how they relate to each other.

In many real-world scenarios, area conversion is needed to make measurements universally understandable. If you have an area measured in an old English unit and need it in a modern unit, you must multiply by the conversion factor. For example, to convert gry to inches, we find the equivalent in inches, and then the same logic is applied to square units. This ensures accurate and consistent area measurement across different systems.
Length Units Conversion
Length units conversion is the process of converting a measurement from one unit of length to another. This can be particularly important when comparing measurements from different regions or times. For the exercise described, converting gry to inches is a key step.

To perform this conversion, you determine the equivalent length in the desired units by using conversion factors. A gry, as described, is one-tenth of a line, and a line is one-twelfth of an inch. Thus, one gry corresponds to \( \frac{1}{120} \) of an inch. This type of conversion is essential for ensuring that lengths are accurately measured and communicated, whether using historical or modern units.

Mastering these conversions allows a better understanding of diverse measurement units and more precise scientific calculations.
Measurement Systems
Measurement systems provide a framework for quantifying physical properties, like length and area. Different systems have evolved over time to suit the needs of societies that used them. In the context of the exercise, we see a comparison between old English measurement systems and modern systems.

Old English systems included unique units such as grys and lines. Modern systems often use more standardized measurements like inches and points. Each system reflects different needs and technological abilities of its time. Modern measurement systems, like the metric system, offer a universal standard based on consistent, reproducible measures.

Understanding measurement systems involves knowing their history, usage, and conversion methods. This helps in translating and communicating measurements effectively in various fields like science, engineering, and commerce.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel con- sumption was at the rate of 40 miles per gallon on the open road. The tourist does not realize that the U.K. gallon differs from the U.S. gallon: $$ \begin{gathered} \text { 1 U.K. gallon }=4.5460900 \text { liters } \\ \text { 1 U.S. gallon }=3.785411 \text { 8 liters. } \end{gathered} $$ For a trip of 750 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?

Water is poured into a container that has a small leak. The mass \(m\) of the water is given as a function of time \(t\) by \(m=5.00 t^{0.8}-3.00 t+20.00\), with \(t \geq 0, m\) in grams, and \(t\) in seconds. (a) At what time is the water mass greatest, and (b) what is that greatest mass? In kilograms per minute, what is the rate of mass change at (c) \(t=2.00 \mathrm{~s}\) and \((\) d \() t=5.00 \mathrm{~s}\) ?

The description for a certain brand of house paint claims a coverage of \(460 \mathrm{ft}^{2} /\) gal. (a) Express this quantity in square meters per liter. (b) Express this quantity in an SI unit (see Appendices \(\mathrm{A}\) and D). (c) What is the inverse of the original quantity, and (d) what is its physical significance?

Gold, which has a density of \(19.32 \mathrm{~g} / \mathrm{cm}^{3}\), is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold, with a mass of \(27.63 \mathrm{~g}\), is pressed into a leaf of \(1.000 \mu \mathrm{m}\) thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius \(2.500\) \(\mu \mathrm{m}\), what is the length of the fiber?

Suppose that, while lying on a beach near the equator watching the Sun set over a calm ocean, you start a stopwatch just as the top of the Sun disappears. You then stand, elevating your eyes by a height \(H=1.70 \mathrm{~m}\), and stop the watch when the top of the Sun again disappears. If the elapsed time is \(t=11.1 \mathrm{~s}\), what is the radius \(r\) of Earth?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.