/*! 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 49 \(49-52 .\) Use a calculator to ... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 49

\(49-52 .\) Use a calculator to evaluate each expression. Round answers to two decimal places. $$ 7^{0.39} $$

Short Answer

Expert verified
\(7^{0.39} \approx 3.05\)

Step by step solution

01

Understand the Expression

We need to evaluate the expression \(7^{0.39}\) using a calculator. The base is 7, and the exponent is 0.39. This indicates that we need to find the 0.39th power of 7.
02

Input the Expression into the Calculator

Turn on the calculator and enter the base value, which is 7. Then use the exponentiation function (often marked as '^' or 'EXP') and enter 0.39 as the exponent.
03

Calculate the Result

After entering the expression into the calculator correctly as \(7^{0.39}\), press the '=' or 'Enter' key to compute the result. The calculator will output the value of raising 7 to the power of 0.39.
04

Round the Answer

Look at the calculator's output, which is the unrounded result of \(7^{0.39}\). Round this result to two decimal places to get the final answer.

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Key Concepts

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

Calculator Usage
Using a calculator to perform exponentiation is a handy skill, especially when dealing with non-integer exponents like in the expression \(7^{0.39}\). Calculators offer various functions, and knowing how to navigate these features is crucial. To evaluate an exponentiation like \(7^{0.39}\), you first need to:
  • Ensure your calculator is on. This may sound basic, but it helps eliminate any initial confusion.
  • Enter the base number, which in our case is 7.
  • Locate the exponentiation function, often represented as "^" or "EXP". This function allows you to raise the base to any power.
  • Input the exponent, here it is 0.39.
  • Press the equals '=' or 'Enter' to compute the calculated result.
Using these steps ensures that you can efficiently perform calculations with accuracy on your calculator, saving time and reducing errors.
Rounding Numbers
Rounding numbers is crucial for simplifying results and for representation purposes, especially when working with decimals. In scientific calculations, rounded numbers help in presenting an easy-to-understand answer. When a number needs to be rounded to two decimal places:
  • Identify the digit in the third decimal place.
  • If this digit is 5 or higher, round up the second decimal place by adding one to it.
  • If it鈥檚 less than 5, leave the second decimal place as it is.
  • Remove all digits following the second decimal place.
Using this method, you ensure that your mathematical results are precise and presented clearly, even when working with more complex numbers like those resulting from exponentiation.
Decimal Places
Decimal places refer to the numbers after the decimal point in a decimal number. Understanding them is key to precision in math. For example, in the number 3.456, the digits 4, 5, and 6 are in the first, second, and third decimal places, respectively.Choosing how many decimal places to use depends on the required precision:
  • Two decimal places are commonly used for financial calculations, offering a balance between accuracy and simplicity.
  • More decimal places are typically used in scientific calculations to reduce rounding errors.
Ensuring the correct number of decimal places helps maintain accuracy and clarity in mathematical results, particularly in exercises such as evaluating \(7^{0.39}\) and rounding outcomes effectively.

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Most popular questions from this chapter

GENERAL: Impact Velocity If a marble is dropped from a height of \(x\) feet, it will hit the ground with velocity \(v(x)=\frac{60}{11} \sqrt{x}\) miles per hour (neglecting air resistance). Use this formula to find the velocity with which a marble will strike the ground if it is dropped from the height of the tallest building in the United States, the 1776 -foot One World Trade Center in New York City.

93 -94. ALLOMETRY: Heart Rate It is well known that the hearts of smaller animals beat faster than the hearts of larger animals. The actual relationship is approximately (Heart rate) \(=250(\text { Weight })^{-1 / 4}\) where the heart rate is in beats per minute and the weight is in pounds. Use this relationship to estimate the heart rate of: A 16 -pound \(\operatorname{dog}\).

ALLOMETRY: Dinosaurs The study of size and shape is called "allometry," and many allometric relationships involve exponents that are fractions or decimals. For example, the body measurements of most four-legged animals, from mice to elephants, obey (approximately) the following power law: $$ \left(\begin{array}{c} \text { Average body } \\ \text { thickness } \end{array}\right)=0.4 \text { (hip-to-shoulder length) }^{3 / 2} $$ where body thickness is measured vertically and all measurements are in feet. Assuming that this same relationship held for dinosaurs, find the average body thickness of the following dinosaurs, whose hip-toshoulder length can be measured from their skeletons: Triceratops, whose hip-to-shoulder length was 14 feet.

BUSINESS: Break-Even Points and Maximum Profit A company that produces tracking devices for computer disk drives finds that if it produces \(x\) devices per week, its costs will be \(C(x)=180 x+16,000\) and its revenue will be \(R(x)=-2 x^{2}+660 x\) (both in dollars). a. Find the company's break-even points. b. Find the number of devices that will maximize profit, and the maximum profit.

BUSINESS: The Rule of .6 Many chemical and refining companies use "the rule of point six" to estimate the cost of new equipment. According to this rule, if a piece of equipment (such as a storage tank) originally cost C dollars, then the cost of similar equipment that is \(x\) times as large will be approximately \(x^{06} \mathrm{C}\) dollars. For example, if the original equipment cost \(C\) dollars, then new equipment with twice the capacity of the old equipment \((x=2)\) would cost \(2^{0.6} \mathrm{C}=1.516 \mathrm{C}\) dollars - that is, about 1.5 times as much. Therefore, to increase capacity by \(100 \%\) costs only about \(50 \%\) more. \({ }^{*}\) Use the rule of .6 to find how costs change if a company wants to triple \((x=3)\) its capacity.
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