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