It was sunday on Jan 1, 2006. What was the Day of the Week Jan 1, 2010?

It was sunday on Jan 1, 2006. What was the Day of the Week Jan 1, 2010?

The day of the week Jan 1, 2010, was Friday. Let's see how.

• Identify the number of years between 2006 and 2010:
  We are looking at the period from January 1, 2006, to January 1, 2010, which spans 4 years:
  • 2006, 2007, 2008, and 2009.
• Determine the number of odd days in these 4 years:
  • 2006: A regular year (365 days).
    365 ÷ 7 = 52 weeks and 1 extra day → 1 odd day.
  • 2007: A regular year (365 days).
    365 ÷ 7 = 52 weeks and 1 extra day → 1 odd day.
  • 2008: A leap year (366 days).
    366 ÷ 7 = 52 weeks and 2 extra days → 2 odd days.
  • 2009: A regular year (365 days).
    365 ÷ 7 = 52 weeks and 1 extra day → 1 odd day.
• Add up the total number of odd days:
  • 1 odd day (2006) + 1 odd day (2007) + 2 odd days (2008) + 1 odd day (2009) = 5 odd days.
• Calculate the day of the week:
  • Start with Sunday on January 1, 2006.
  • Add the total number of odd days (5) to Sunday:
    • Sunday (0) + 5 odd days = Friday.

How to Solve Math Problems?

1. Understand the Problem

• Read the problem carefully: Ensure you fully understand what is being asked.
• Identify the key information: Look for numbers, variables, and relationships between them.
• Determine what is unknown: Figure out what you need to find or solve for.

2. Devise a Plan

• Decide on the strategy: Choose a method that best fits the problem, such as:
  • Algebra (for equations)
  • Geometry (for shapes, areas, volumes)
  • Arithmetic (for basic calculations)
  • Word problems (for applying math to real-world situations)
• Break down complex problems: If the problem seems complicated, break it into smaller, manageable parts.

3. Translate the Problem into Mathematical Form

• For equations: Write any equations or expressions that represent the situation.
• For word problems: Identify variables for unknown quantities, translate the problem into an equation or set of equations.
• For geometry problems: Draw diagrams to help visualize the problem.

4. Solve the Problem

• Follow through with the chosen method:
  • Algebra: Solve equations step by step, isolate the variable.
  • Geometry: Use formulas for areas, volumes, perimeters, etc.
  • Word problems: Apply the correct mathematical operations to the situation (addition, subtraction, multiplication, division).
• Simplify where necessary: Simplify the expression or solve the equation.

5. Check Your Work

• Substitute the solution back: If possible, substitute your answer back into the original problem to verify it satisfies all conditions.
• Review calculations: Double-check for any mathematical mistakes.

6. Write the Final Answer

• Clearly state your solution: Include the units if applicable (e.g., meters, dollars, etc.).
• Double-check: Ensure the answer is reasonable and makes sense in the context of the problem.

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