(n-2)*180 =108n
180 n - 108 n = 360
72 n = 360
n = 5
drwls, I had totally misread the problem and thought it said
(n-2)^180 =108n
been working on it for almost an hour, trying Newton's method and all kinds of iteration.
I really have to try to read the questions more carefully, ha ha
You will have to use a graphical or iterative method (like Newton's) to solve that. There is no explicit closed-form answer.
(n-2)^180 =108n
If n = 3.03, you get 204 (left) & 327 (right)
If n = 3.04, you get 1164 (left) and 328 (right)
If n = 3.0326, you get 322 on the left and 327 on the right
The answer is 3.0327...
To solve the equation (n-2)^180 = 108n, you can use an iterative method like Newton's method.
Here's how you can use Newton's method to approximate the value of n:
1. Start with an initial guess for n. Let's say n = 3.
2. Calculate the function value and its derivative at this initial guess.
For the function f(n) = (n-2)^180 - 108n,
f(n) = (3-2)^180 - 108(3) = 1^180 - 324 = -323,
f'(n) = 180(n-2)^179 - 108. Substituting n = 3, we have f'(3) = 180(1)^179 - 108 = 180 - 108 = 72.
3. Use the formula for Newton's method to update the value of n:
n_new = n - f(n)/f'(n).
In this case, n_new = 3 - (-323)/(72) = 3 + 4.49 = 7.49.
4. Repeat steps 2 and 3 using the updated value of n until the value of n converges to a solution.
Keep repeating steps 2 and 3 by substituting the updated value of n into the equation until you get a result that is close enough to the desired accuracy.
It seems that you have been trying to solve a different equation, which is (n-2)*180 = 108n. This equation is linear and can be solved algebraically.
Let's solve it together:
1. Distribute the 180 to both terms on the left side of the equation:
180n - 360 = 108n.
2. Simplify the equation by combining like terms:
180n - 108n = 360.
3. Subtract 108n from both sides to isolate the n term:
72n = 360.
4. Divide both sides by 72 to solve for n:
n = 360/72.
5. Simplify the division:
n = 5.
So, the solution to the equation (n-2)*180 = 108n is n = 5.