/*! 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 59 Estimate the length of the equat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 59

Estimate the length of the equator in feet. Assume the radius of the earth to be 4000 miles.

Short Answer

Expert verified
The estimated length of the equator is approximately 132,710,400 feet.

Step by step solution

01

Understand the Formula

To find the length of the equator, or the circumference of Earth, we use the formula for the circumference of a circle: \( C = 2\pi r \), where \( C \) is the circumference and \( r \) is the radius. In this case, \( r = 4000 \) miles.
02

Calculate Circumference in Miles

Substitute \( r = 4000 \) miles into the circumference formula: \( C = 2 \pi \times 4000 \). This gives us \( C = 8000\pi \) miles.
03

Convert Miles to Feet

Since there are 5280 feet in a mile, we convert miles to feet by multiplying the circumference in miles by 5280. So, \( C = 8000\pi \times 5280 \) feet.
04

Estimate Using \( \pi \)

Estimate \( \pi \approx 3.14 \). Then \( C \approx 8000 \times 3.14 \times 5280 \). Performing the multiplication, \( 8000 \times 3.14 = 25120 \), and then, \( 25120 \times 5280 \) gives us \( C \approx 132,710,400 \) feet.

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 91影视!

Key Concepts

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

Radius of the Earth
The radius of the Earth is a crucial measurement when calculating the circumference, which is essentially the boundary length of a circle. Picture this as the Earth is a perfect sphere, though in reality, it's slightly flattened at the poles. The average radius is about 4,000 miles, which has been determined through various methods over time.

When used in calculations, the radius helps in determining key geographical and astronomical dimensions.
  • The Earth's approximate radius simplifies complex calculations in various fields, such as astronomy and geophysics.
  • This estimation is vital because it provides an average measurement useful for all general purposes.
Using the radius, we can derive other measurements, like the circumference, using the formula for the circumference of a circle.
Conversion of Units
Unit conversion is a handy tool in mathematics where one measures quantity in different units. To estimate the circumference of the Earth in feet, you need to convert miles to feet. In this context, knowing that one mile equals 5280 feet is essential.

Here鈥檚 how it works in our calculation:
  • We calculate the circumference in miles first using the formula: \( C = 2\pi r \).
  • Since the circle's radius is in miles, our initial result (8000\( \pi \) miles) gives us the circumference in miles.
  • To convert to feet, multiply by the conversion factor, 5280 feet per mile.
This multiplication allows precision and real-world application, ensuring that the final answer spans the context needed, such as architecture or land surveying.
Mathematical Estimation
Mathematical estimation simplifies complex numbers and is an important skill. Estimations allow us to reach approximate answers quickly once we understand the parameters involved. It is helpful when exact numbers are not needed, or preliminary calculations are required.

In our exercise, estimating \( \pi \approx 3.14 \) makes calculations more straightforward.
  • The number \( \pi \) is an irrational number, so using 3.14 makes it easier to compute multiplication without a calculator.
  • Estimating the final product helps check our result logically, ensuring we understand each step in solving the equation.
Using estimation gives us a ballpark figure, which, in practice, is often sufficiently accurate for many real-world applications, especially when dealing with large measurements like Earth鈥檚 circumference.

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

In Problems \(1-4\), plot the given points in the coordinate plane and then find the distance between them. \((3,1),(1,1)\)

Sketch the graph of \(f(x)=(x-2)^{2}-4\) using translations.

In Problems \(11-16\), find the inverse of the given function \(f\) and verify that \(f\left(f^{-1}(x)\right)=x\) for all \(x\) in the domain of \(f^{-1}\), and \(f^{-1}(f(x))=x\) for all \(x\) in the domain of \(f\). $$ f(x)=\frac{2^{x}}{4+2^{x}} $$

Suppose that a continuous function is periodic with period 2 and is quadratic between \(-0.25\) and \(0.25\) and linear between \(-1.75\) and \(-0.25\). In addition, it has the value 0 at 0 and \(0.0625\) at \(\pm 0.25\). Sketch the function over the domain \([-2,2]\), and give a piecewise definition of the function.

The angle of inclination \(\alpha\) of a line is the smallest positive angle from the positive \(x\)-axis to the line ( \(\alpha=0\) for a horizontal line). Show that the slope \(m\) of the line is equal to \(\tan \alpha\).
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation
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.