Math Problem Statement

Da1×1=√(34,35-32,23)²+(8,1-8,45)²+(14720-1990)²=5270

Solution

Let's break down this equation:

You provided:

1×1=(34.3532.23)2+(8.18.45)2+(147201990)21 \times 1 = \sqrt{(34.35 - 32.23)^2 + (8.1 - 8.45)^2 + (14720 - 1990)^2}

Step-by-step solution:

  1. Calculate each difference:

    (34.3532.23)=2.12(34.35 - 32.23) = 2.12 (8.18.45)=0.35(8.1 - 8.45) = -0.35 (147201990)=12730(14720 - 1990) = 12730

  2. Square the differences:

    (2.12)2=4.4944(2.12)^2 = 4.4944 (0.35)2=0.1225(-0.35)^2 = 0.1225 (12730)2=162,052,900(12730)^2 = 162,052,900

  3. Sum the squared differences:

    4.4944+0.1225+162,052,900=162,053,004.61694.4944 + 0.1225 + 162,052,900 = 162,053,004.6169

  4. Take the square root:

    162,053,004.616912,727.65\sqrt{162,053,004.6169} \approx 12,727.65

Final result:

1×1=12,727.651 \times 1 = 12,727.65

However, the result is not 5270 as you indicated, but rather 12,727.65.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What does this equation represent in geometry or physics?
  2. Would you like to understand the square root process in more detail?
  3. How is this equation used in distance or vector calculations?
  4. What happens if we change the values in the equation?
  5. Why did you expect the result to be 5270?

Tip: Double-checking your calculations step-by-step is crucial to avoid errors, especially when dealing with square roots and large numbers.

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Math Problem Analysis

Mathematical Concepts

Distance Formula
Pythagorean Theorem
Square Roots

Formulas

Distance Formula: d = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 9-12