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Chapter 1: Problem 59

Perform the calculations on a calculator. In 3 successive days, a home solar system produced 32.4 MJ, \(26.704 \mathrm{MJ},\) and \(36.23 \mathrm{MJ}\) of energy. What was the total energy produced in these 3 days?

Short Answer

Expert verified
The total energy produced is 95.334 MJ.

Step by step solution

01

Understanding the Problem

We need to find the total energy produced by the solar system over three days. The amounts of energy produced each day are given in megajoules (MJ). Our task is to sum these values to get the total energy output.
02

Listing the Daily Energy Values

The energy values for the three days are given as follows: Day 1: 32.4 MJ, Day 2: 26.704 MJ, and Day 3: 36.23 MJ.
03

Adding the Energies

Use a calculator to add the energy values for all three days together. This involves simple addition of the listed energy values. Calculate: \[ 32.4 + 26.704 + 36.23 \]
04

Calculating the Sum

Carry out the addition on your calculator: \[ 32.4 + 26.704 + 36.23 = 95.334 \]
05

Writing the Result

The total energy produced over the three days is 95.334 MJ.

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Key Concepts

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

Calculator Usage
Calculators are incredibly helpful tools that can assist us in making complex calculations much easier. They're perfect for when we need fast and accurate results, especially during homework exercises. When using a calculator, the pivotal step is to enter the numbers correctly to avoid errors.

Here鈥檚 a quick guide to using a calculator effectively:
  • Before beginning, check that your calculator is in the correct mode (usually it should be in standard or decimal mode for addition).
  • Clear any previous calculations displayed on the screen to ensure you're starting fresh.
  • Enter each value accurately, maintaining the order given in the exercise, in this case, 32.4, 26.704, and 36.23.
  • After entering each number, use the '+' button to signify addition. Press '=', or 'ENTER,' after adding all values to see the result.
Whenever possible, double-check your final answer. This ensures you've entered each value correctly and that there's no mistake in the addition process.
Energy Measurement
Energy is measured in various units; one such unit is the megajoule (MJ). A joule is a standard way to quantify the amount of energy, in this case, produced by a home solar system.

Understanding this, let鈥檚 break it down:
  • 1 megajoule (MJ) = 1,000,000 joules (J), reflecting a significant amount of energy.
  • Solar panels convert sunlight into electricity, usually providing information in joules or megajoules.
By measuring energy in megajoules, we get a practical sense of how much electricity our systems generate over time. For instance, in our scenario, understanding that producing 95.334 MJ over three days implies consistent energy output. Recognize patterns over time helps in planning the energy needs of your household effectively.
Problem-Solving Steps
Problem-solving in mathematics requires a systematic approach for accuracy and clarity. Let鈥檚 delve into the process used in the exercise:

  • Step 1: Understanding the Problem
    Start by analyzing exactly what the problem is asking. In our case, it鈥檚 to find the total energy output over three days.
  • Step 2: Listing Information
    Once the problem is understood, list out all important information. Write down the energy outputs for each day clearly.
  • Step 3: Performing Calculation
    With values ready, carry out the necessary calculations. Here, we need to add the three individual energy outputs: 32.4 MJ, 26.704 MJ, and 36.23 MJ.
  • Step 4: Validating the Result
    Double-check your arithmetic using a calculator to verify the sum total is correct. The total calculated should be consistent every time.
Following these steps not only helps solve the current problem but also builds skills for tackling other similar problems. By practicing a methodical approach, problem-solving becomes less daunting and more manageable, boosting your confidence with each successful solution.

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Most popular questions from this chapter

Solve the given equations. All numbers are approximate. $$\frac{276 x}{17.0}=\frac{1360}{46.4}$$

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