Problem no. 1

Find the so-called 5,500 flood control project in entire country using this equation 
(3x4−5x3+2x 2−x+7)⋅log(x)+ x2+1 −sin(2x)=0 

Let "so-called 5,500 flood control project" = X

To solve the equation you provided and find the value of \( x \) that corresponds to the "so-called 5,500 flood control project," we'll need to solve the equation numerically, as it's quite complex and doesn't have a straightforward algebraic solution.

The equation is:

\[
(3x^4 - 5x^3 + 2x^2 - x + 7) \cdot \log(x) + x^2 + 1 - \sin(2x) = 0
\]

Let's proceed with the numerical solution for \( x \).The solution to the equation is approximately \( x \approx 0.878 \).

So, if we interpret the "so-called 5,500 flood control project" as \( X \), then \( X \approx 0.878 \).

Would you like more details on this solution or have any questions?

Here are five related questions you might find interesting:

1. What are the steps involved in solving a non-linear equation numerically?
2. How does the logarithmic function affect the behavior of the equation?
3. What are the challenges of finding roots of complex equations?
4. How can you verify the accuracy of a numerical solution?
5. What are some common methods for solving transcendental equations?

**Tip:** When solving equations numerically, it's important to have a good initial guess, as it can significantly affect the solution's accuracy and convergence.

Learn how to solve the complex non-linear equation (3x^4 - 5x^3 + 2x^2 - x + 7)⋅log(x) + x^2 + 1 - sin(2x) = 0 numerically. Explore the impact of logarithmic and trigonometric functions on equation behavior.

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