/*! 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 20 Write an expression that display... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 20

Write an expression that displays the calculation(s) necessary to answer the question. Then use scientific notation and exponent rules to determine the answer. a. Find the number of nickels in \(\$ 500.00\). b. The circumference of Earth is about 40.2 million meters. Find the radius of Earth, in kilometers, using the formula \(C=2 \pi r\)

Short Answer

Expert verified
There are 10000 nickels in \(\$500.00\). Earth's radius is approximately 6400 km.

Step by step solution

01

Find the Number of Nickels

Calculate the number of nickels in \(\$500.00\). Each nickel is worth \(0.05\) dollars. Use the formula \[ \text{Number of Nickels} = \frac{500}{0.05} \].
02

Simplify the Expression

Divide 500 by 0.05: \[ \frac{500}{0.05} = 10000 \]. Thus, there are 10000 nickels in \(\$500.00\).
03

Use Circumference Formula

Given the Earth's circumference is 40.2 million meters, use the formula \[C = 2 \pi r\] and solve for r (radius). \pi \approx 3.14. Substitute \[ C = 40.2 \times 10^6 \] meters.
04

Solve for Radius

Substitute the values into the formula: \[ 40.2 \times 10^6 = 2 \pi r \]. Solve for \text{r}\ by dividing both sides by \2 \pi \: \[ r = \frac{40.2 \times 10^6}{2 \times 3.14} \].
05

Simplify the Radius Expression

Calculate the numerator and denominator separately: \[ 40.2 \times 10^6 \approx 4.02 \times 10^7 \], and \2 \times 3.14 \approx 6.28\. Thus, \[ r = \frac{4.02 \times 10^7}{6.28} \].
06

Final Calculation for Radius

Perform the division: \[ r = \frac{4.02 \times 10^7}{6.28} = \approx 6.4 \times 10^6 \] meters. Convert meters to kilometers: \[ 6.4 \times 10^3 \text{ km}\]. Thus, the Earth's radius is approximately 6400 kilometers.

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.

Exponent Rules
Exponent rules are fundamental for simplifying complex mathematical expressions. They are especially handy when working with powers of ten, which is common in scientific notation. When you multiply two numbers with the same base, you add their exponents, written as: \[ a^m \times a^n = a^{m+n} \].
Conversely, when you divide, you subtract the exponents: \[ \frac{a^m}{a^n} = a^{m-n} \].
Another important rule is power of a power, where you multiply the exponents: \[ (a^m)^n = a^{m*n} \].
Remembering these rules will help you maneuver through equations smoothly, like in Step 5 where we convert and simplify scientific notations.
Circumference Formula
The circumference formula, \[ C = 2 \pi r \], is essential when calculating lengths around circles. In this exercise, you use it to determine Earth's radius given its circumference. Let's break it down:
  • Start by knowing the circumference, which is the distance around the circle鈥攊n this case, Earth's equator.

  • Using the formula, \[ C = 2\pi r \], you can rearrange to solve for radius \[ r \].
  • When given \[ C = 40.2 \times 10^6 \text{ meters} \], replace \[ C \], and solve for \[ r \].
  • Simply follow through with your algebraic manipulation:
    \[ (40.2 \times 10^6)/ (2 \times 3.14) \], leading to \[ r \approx 6.4\times 10^6 \text{ meters} \]
This formula is versatile and used in numerous real-life applications like construction, astronomy, and more.
Unit Conversion
Unit conversion is converting measurements from one unit to another. It is crucial when measurements need consistency. For instance, while Earth's radius is calculated in meters, it鈥檚 more practical to express it in kilometers for simplicity and comprehension. A quick conversion reminder:
  • To convert meters to kilometers, divide by 1000, because there are 1000 meters in 1 kilometer.
  • Using scientific notation simplifies larger numbers: \[ 6.4\times 10^6 \text{ meters} = 6.4\times 10^3 \text{ kilometers} \].
Practice consistently, and conversion will become second nature.

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 the December 1999 issue of the journal Science, two Harvard scientists describe a pair of "nanotweezers" they created that are capable of manipulating objects as small as one- 50,000 th of an inch in width. The scientists used the tweezers to grab and pull clusters of polystyrene molecules, which are of the same size as structures inside cells. A future use of these nanotweezers may be to grab and move components of biological cells. a. Express one- 50,000 th of an inch in scientific notation. b. Express the size of objects the tweezers are able to manipulate in meters. c. The prefix "nano" refers to nine subdivisions by \(10,\) or a multiple of \(10^{-9}\). So a nanometer would be \(10^{-9}\) meters. Is the name for the tweezers given by the inventors appropriate? d. If not, how many orders of magnitude larger or smaller would the tweezers' ability to manipulate small objects have to be in order to grasp things of nanometer size?

A circular swimming pool is \(18 \mathrm{ft}\) in diameter and \(4 \mathrm{ft}\) deep. a. Determine the volume of the pool in gallons if one gallon is 231 cubic inches. b. The pool's filter pump can circulate 2500 gal per hour. How many hours do you need to run the filter in order to filter the number of gallons contained in the pool? c. One pound of chlorine shock treatment can treat 10,000 gal. How much of the shock treatment should you use?

An ant is roughly \(10^{-3}\) meter in length and the average human roughly one meter. How many times longer is a human than an ant?

Write each of the following in standard decimal form: a. \(7.23 \cdot 10^{5}\) d. \(1.5 \cdot 10^{6}\) b. \(5.26 \cdot 10^{-4}\) e. \(1.88 \cdot 10^{-4}\) c. \(1.0 \cdot 10^{-3}\) f. \(6.78 \cdot 10^{7}\)

Describe at least three different methods for entering \(5.23 \cdot 10^{-3}\) into a calculator or spreadsheet.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.