4x^3-6.68E-7x^2+1.67E-8x-1.04E-10 = 0
What is your question? With two unknowns, cannot solve without more data.
halla el volumen de un barril,si h=80cm,D=65cm y d=50cm
To solve the equation 4x^3 - 6.68E-7x^2 + 1.67E-8x - 1.04E-10 = 0, you can use various methods such as factoring, the quadratic formula, or numerical methods like Newton's method. Since this equation is a cubic equation, factoring might not be the most straightforward method to find the solutions. The quadratic formula is designed for quadratic equations and won't work directly here. Therefore, we will explain how to solve a cubic equation using numerical methods.
One numerical method you can employ to solve cubic equations is the Newton-Raphson method. The steps for using this method to find the roots are as follows:
1. Rewrite the equation in the form f(x) = 4x^3 - 6.68E-7x^2 + 1.67E-8x - 1.04E-10 = 0.
2. Choose an initial guess for the root. Let's start with x = 0.
3. Calculate the derivative of f(x), denoted as f'(x). In this case, f'(x) = 12x^2 - 1.336E-6x + 1.67E-8.
4. Plug the initial guess into both f(x) and f'(x).
f(x) = 0 => f(0) = 4(0)^3 - 6.68E-7(0)^2 + 1.67E-8(0) - 1.04E-10 = -1.04E-10
f'(x) = 0 => f'(0) = 12(0)^2 - 1.336E-6(0) + 1.67E-8 = 1.67E-8
5. Apply the Newton-Raphson formula to update the guess for the root:
x1 = x - f(x) / f'(x)
= 0 - (-1.04E-10) / (1.67E-8)
= 6.227845E-3
6. Repeat steps 4 and 5 using the updated approximation until you reach a desired level of accuracy or convergence.
Note: It is important to keep in mind that solving cubic equations can sometimes be complex, and there might be multiple roots or complex roots. The above method only provides an approach to find one potential root.