/*! 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 58 Use your calculator and evaluate... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 58

Use your calculator and evaluate each of the algebraic expressions for the indicated values. Express the final answers to the nearest tenth. $$ \pi r^{2}, \quad \pi=3.14 \text { and } r=2.1 $$

Short Answer

Expert verified
13.8

Step by step solution

01

Substitute Values into the Expression

First, substitute the given values into the algebraic expression \(\pi r^2\). Replace \(\pi\) with 3.14 and \(r\) with 2.1. The expression becomes: \(3.14 \times (2.1)^2\).
02

Calculate the Square of the Radius

Now, calculate \((2.1)^2\). This means multiplying 2.1 by itself: \(2.1 \times 2.1 = 4.41\).
03

Multiply by Pi

Next, multiply the square of the radius by \(\pi\). So, multiply 3.14 by 4.41: \(3.14 \times 4.41\).
04

Use Calculator and Round the Answer

Use a calculator to find \(3.14 \times 4.41 = 13.8474\). Round this result to the nearest tenth to get 13.8.

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.

Substitution in Algebra
Substitution is a fundamental concept in algebra, where you replace variables in an expression with given numerical values. This technique is especially useful in evaluating expressions like \(\pi r^2\). It involves the following steps:
  • Identify the variables in the expression. For \(\pi r^2\), \pi\ and \r\ are the variables.
  • Substitute each variable with its given value. In this exercise, replace \pi\ with 3.14 and \r\ with 2.1. This changes the expression to \(3.14 \times (2.1)^2\).
Remember, proper substitution allows for accurate calculations, making it a crucial skill when working with algebraic formulas.
Calculating Squares
Calculating squares is all about multiplying a number by itself. When the problem gives you \(r = 2.1\), and asks for \(r^2\), you need to perform the operation:
  • Multiply the radius (2.1) by itself: \(2.1 \times 2.1 = 4.41\).
Understanding squares is essential because it appears frequently in algebra, especially in formulas involving areas, like \[\pi r^2\], which is used to find the area of a circle. The square of a number gives you the area of a square with sides equal to that number, which helps in visualizing the magnitude of squares.
Being comfortable with squaring numbers helps simplify many algebraic expressions and is a stepping stone to more complex calculations.
Rounding Numbers
Rounding is a method of reducing the digits in a number while keeping its value close to the original. This process makes calculations simpler and results easier to communicate. To round a number to the nearest tenth, follow these steps:
  • Identify the hundredths place. For the number 13.8474, 4 is in the hundredths place.
  • If the hundredths digit is 5 or greater, round the tenths digit up. Otherwise, keep the tenths digit the same.
In our example, since 4 is less than 5, we keep the tenths digit as it is. Thus, 13.8474 rounds to 13.8.
Rounding values is useful in making numerical answers more manageable and is a standard step in presenting numerical results, ensuring your calculations maintain clarity and precision.

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

Simplify the algebraic expressions by removing parentheses and combining similar terms. $$ -7(2 x-3 y)+9(3 x+y) $$

Evaluate the algebraic expressions for the given values of the variables. $$ (x-y)^{2}, \quad x=5 \text { and } y=-3 $$

Evaluate the algebraic expressions for the given values of the variables. $$ 7 a-2 b-9 a+3 b, \quad a=4 \text { and } b=-6 $$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Twelve times the sum of a number and 7

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. The quotient of a number and 8
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

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.