Math Problem Statement

d $$$$ ^2=890^2+2670^2

Solution

Let's solve the equation for dd using the Pythagorean theorem:

d2=8902+26702d^2 = 890^2 + 2670^2

First, calculate the squares of 890 and 2670:

8902=792,100890^2 = 792,100 26702=7,128,9002670^2 = 7,128,900

Now, sum the two values:

d2=792,100+7,128,900=7,921,000d^2 = 792,100 + 7,128,900 = 7,921,000

Finally, take the square root of both sides to find dd:

d=7,921,0002,814.42d = \sqrt{7,921,000} \approx 2,814.42

Thus, d2,814.42d \approx 2,814.42.

Would you like more details or have any questions?

Here are some related questions:

  1. What is the Pythagorean theorem used for?
  2. How do you approximate square roots without a calculator?
  3. How is the distance formula related to the Pythagorean theorem?
  4. Can this problem be solved in three dimensions?
  5. What is the significance of the square root in geometry?

Tip: When solving for a distance, always check that your inputs are squared correctly before summing them.

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Math Problem Analysis

Mathematical Concepts

Geometry
Pythagorean Theorem

Formulas

d^2 = a^2 + b^2
Square root formula

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10