danerape said:Homework Statement
xsin(x)=(x-6)^2
This is for a solid of revolution problem, and I am trying to set these equal to each other to find the points of intersection. How can I solve this equation?
Thanks
Homework Equations
The Attempt at a Solution
The first step is to expand the right side of the equation using the FOIL method: (x-6)^2 = x^2 - 12x + 36. This will give you a quadratic equation in the form of xsin(x) = x^2 - 12x + 36.
To solve for x, you can use the quadratic formula: x = (-b±√(b^2-4ac))/2a. In this case, a=1, b=-1, and c=36. Plug in these values to get x = (-(-1)±√((-1)^2-4(1)(36)))/2(1), which simplifies to x = (1±√(1-144))/2. This will give you two possible solutions for x.
Yes, you can use a calculator to solve this equation. However, be sure to use parentheses when entering the equation to ensure the correct order of operations. Also, be aware that calculators may not give exact solutions for irrational or complex numbers.
Yes, there are restrictions on the values of x. Since the original equation includes the sine function, the solutions for x must also satisfy the domain of the sine function, which is all real numbers. In addition, the solutions must also satisfy the original equation, which may limit the possible values of x.
Yes, there are other methods that can be used to solve this equation, such as factoring or graphing. However, the quadratic formula is often the most efficient method for solving quadratic equations.