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Chapter 1: Problem 4

Suppose a man鈥檚 scalp hair grows at a rate of 0.35 mm per day. What is this growth rate in feet per century?

Short Answer

Expert verified
Approximately 41.917 feet per century.

Step by step solution

01

Convert Daily Growth to Yearly Growth in Millimeters

First, we need to convert the daily growth rate into a yearly growth rate. Since a year typically has 365 days, we calculate:\[0.35 \, \text{mm/day} \times 365 \, \text{days/year} = 127.75 \, \text{mm/year}\]
02

Convert Yearly Growth to Centuries in Millimeters

Next, convert the yearly growth rate to the growth rate over a century (100 years):\[127.75 \, \text{mm/year} \times 100 \, \text{years/century} = 12,775 \, \text{mm/century}\]
03

Convert Millimeters to Feet

Now, we convert millimeters to feet, knowing that 1 foot is equal to approximately 304.8 mm:\[\frac{12,775 \, \text{mm}}{304.8 \, \text{mm/foot}} \approx 41.917 \, \text{feet}\]
04

Conclusion

Therefore, the growth rate of scalp hair is approximately 41.917 feet per century.

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Key Concepts

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

Understanding Growth Rate
A growth rate refers to the amount of increase in a particular quantity over a given period. In simpler terms, it is how fast or slow something is growing. In this case, we are examining the growth rate of a man's scalp hair. The given growth rate is 0.35 mm per day, which means in one day, his hair increases by 0.35 millimeters.
  • To understand growth rates better, you should consider both the rate (how much) and the time period (how often).
  • This information can help predict future growth and make comparisons, like in different units or over time.
Recognizing how to translate this daily growth into another timeframe or measurement type can reveal a deeper understanding of growth patterns, like measuring into feet per century in this math problem.
Exploring Measurement Units
Measurement units are essential in quantifying physical quantities, such as length, mass, and time. In this exercise, we deal with units like millimeters and feet to express hair growth. By comprehending the units, you can accurately transform quantities from one form to another.
  • The original measurement in millimeters is useful for precision over short intervals, making it excellent for daily tracking.
  • Feet are used for larger intervals, especially convenient over long periods such as centuries.
To convert these units properly, numerical relationships are essential. For example, 1 foot is equal to 304.8 millimeters. Knowing these conversions allows us to switch seamlessly between different scales without altering the inherent value of the measurement.
Principles of Mathematical Calculation
Mathematical calculations are the cornerstone of converting, comparing, and understanding different metrics. Here, calculations enable us to adjust the growth rate from millimeters per day to feet per century. Breaking it down:
  • Start by multiplying the daily growth by 365 to find annual growth, using the approximate days in a year.
  • Then, multiply by 100 to convert from a yearly growth rate into a century鈥檚 growth, which is straightforward once you handle annual data.
  • Finally, division translates these values from millimeters into feet, ensuring you always maintain accuracy referencing conversion constants.
These operations illustrate how arithmetic helps us transition between timeframes and spatial scales, providing clarity and context in measurements, vastly expanding numerical data interpretation capabilities.

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Most popular questions from this chapter

A force vector has a magnitude of 575 newtons and points at an angle of \(36.0^{\circ}\) below the positive \(x\) axis. What are (a) the \(x\) scalar component and (b) the \(y\) scalar component of the vector?

\(\mathrm{Mmh}\) On a safari, a team of naturalists sets out toward a research station located \(4.8 \mathrm{km}\) away in a direction \(42^{\circ}\) north of east. After traveling in a straight line for \(2.4 \mathrm{km},\) they stop and discover that they have been traveling \(22^{\circ}\) north of east, because their guide misread his compass. What are (a) the magnitude and (b) the direction (relative to due east) of the displacement vector now required to bring the team to the research station?

Vector \(\overrightarrow{\mathbf{A}}\) has a magnitude of 6.00 units and points due east. Vector \(\overrightarrow{\mathbf{B}}\) points due north. (a) What is the magnitude of \(\overrightarrow{\mathbf{B}},\) if the vector \(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}\) points \(60.0^{\circ}\) north of east? (b) Find the magnitude of \(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}\).

The magnitude of the force vector \(\overrightarrow{\mathbf{F}}\) is 82.3 newtons. The \(x\) component of this vector is directed along the \(+x\) axis and has a magnitude of 74.6 newtons. The \(y\) component points along the \(+y\) axis. (a) Find the direction of \(\overrightarrow{\mathbf{F}}\) relative to the \(+x\) axis. (b) Find the component of \(\overrightarrow{\mathbf{F}}\) along the \(+y\) axis.

Ssm The speed of an object and the direction in which it moves constitute a vector quantity known as the velocity. An ostrich is running at a speed of \(17.0 \mathrm{m} / \mathrm{s}\) in a direction of \(68.0^{\circ}\) north of west. What is the magnitude of the ostrich's velocity component that is directed (a) due north and (b) due west?
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