Math Problem Statement

Study the problem and proposed solution below. Is the final answer correct? Then click the No mistakes button. Is the final answer wrong? Then click the button in front of the line with the first mistake and correct the mistake.

Solution

To help you determine if the final answer is correct, I'll first transcribe and analyze the content of the image.

Problem Statement:

A problem regarding the calculation of speed is given, which involves the formula:

v=dtv = \frac{d}{t}

Where:

  • vv is the speed.
  • dd is the distance.
  • tt is the time.

Provided Values:

  • Distance (dd): 55m55 \, \text{m}
  • Time (tt): 3.6s3.6 \, \text{s}

Solution Steps:

  1. Write down the definition of speed: v=dtv = \frac{d}{t}
  2. Substitute the given values: v=553.6v = \frac{55}{3.6}
  3. Calculate the quotient: v15.2777778v \approx 15.2777778
  4. Round to the correct number of significant digits: v15.28m/sv \approx 15.28 \, \text{m/s}

Analysis:

  1. Step 3 Calculation:
    The division 553.6\frac{55}{3.6} gives approximately 15.277777815.2777778, which is correctly calculated.

  2. Rounding:
    The value 15.277777815.2777778 is rounded to 15.2815.28. Both the original distance and time have two significant digits (since 55 has two and 3.6 has two as well). Thus, the final answer should also be rounded to two significant digits. The correct rounding of 15.277777815.2777778 to two significant digits is 1515.

Conclusion:

The final answer should be rounded to 15 m/s instead of 15.28 m/s. The mistake occurred in the rounding step. Therefore, you should click the button in front of the line with the mistake and correct the final answer to 15m/s15 \, \text{m/s}.

Would you like further details or have any questions? Here are five related questions you might consider:

  1. What is the rule for rounding numbers based on significant digits?
  2. How do you determine the number of significant digits in a measurement?
  3. Why is it important to match the number of significant digits in your final answer to the given data?
  4. What would the calculation look like if the time were given as 3.60 seconds instead of 3.6?
  5. How would the procedure change if the distance were given as 55.0m55.0 \, \text{m} instead of 55m55 \, \text{m}?

Tip: Always match the number of significant digits in your final result to the least precise measurement in the data.

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Math Problem Analysis

Mathematical Concepts

Physics
Kinematics

Formulas

Speed formula v = d / t

Theorems

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Suitable Grade Level

Grades 9-12