Questions: =√(5199.797115)^2(1+255.060/6378137)(1+353.221/6378137)+(353.221-255.060)^2

Solution Steps

To solve the given expression, we need to break it down into smaller parts and compute each part step by step. We will:

1. Compute the squared value of 5199.797115.
2. Compute the fractions \(\frac{255.060}{6378137}\) and \(\frac{353.221}{6378137}\).
3. Add 1 to each of the fractions computed in step 2.
4. Multiply the results from steps 1 and 3.
5. Compute the difference \(353.221 - 255.060\) and then square it.
6. Add the results from steps 4 and 5.
7. Finally, take the square root of the result from step 6.

We start by calculating \( a^2 \) where \( a = 5199.797115 \): \[ a^2 = (5199.797115)^2 = 27037890.037162326 \]

Next, we compute \( 1 + \frac{b}{d} \) where \( b = 255.060 \) and \( d = 6378137 \): \[ 1 + \frac{b}{d} = 1 + \frac{255.060}{6378137} = 1.0000399897336794 \]

Now, we compute \( 1 + \frac{c}{d} \) where \( c = 353.221 \): \[ 1 + \frac{c}{d} = 1 + \frac{353.221}{6378137} = 1.0000553799644003 \]

We multiply the results from Step 1 and Step 2 and Step 3: \[ \text{part4} = a^2 \cdot \left(1 + \frac{b}{d}\right) \cdot \left(1 + \frac{c}{d}\right) = 27037890.037162326 \cdot 1.0000399897336794 \cdot 1.0000553799644003 = 27040468.692450806 \]

Next, we calculate \( (c - b)^2 \): \[ (c - b)^2 = (353.221 - 255.060)^2 = (98.161)^2 = 9635.581921 \]

Finally, we add the results from Step 4 and Step 5, and take the square root: \[ \text{result} = \sqrt{\text{part4} + \text{part5}} = \sqrt{27040468.692450806 + 9635.581921} = \sqrt{27050404.274371827} \approx 5200.971474097104 \]

Final Answer