the question was:
(225^2 - 2*225*16π + 256π^2)/(16π^2) = 16+h^2
The Bots all missed it, since the solution is as follows:
(225 - 16π)^2 /(16π)^2 = h^2 + 16
h^2 = 50625/(16π^2) - 450/π
or, (225/4π)^2 - 2*225/π
*π + 256 = h^2 + 16
To solve the given equation: (225^2 - 2*225*16π + 256π^2)/(16π^2) = 16+h^2, we can follow these steps:
Step 1: Simplify the expression on the left-hand side:
- Distribute the square in the numerator: (225 - 16π)^2
- Expand to get: 50625 - 7200π + 256π^2
Step 2: Divide the numerator by the denominator:
- We have: (50625 - 7200π + 256π^2)/(16π^2)
Step 3: Simplify the fraction:
- Divide each term in the numerator by the denominator: 50625/(16π^2) - 7200π/(16π^2) + 256π^2/(16π^2)
- Simplify: 3164.06/π^2 - 450/π + 16
Step 4: Match the equation given: 16+h^2
- Set up the equation to solve for h^2: 3164.06/π^2 - 450/π + 16 = 16 + h^2
Therefore, the equation can be rewritten as: h^2 = 3164.06/π^2 - 450/π
Note: The last part of the equation, (225/4π)^2 - 2*225/π, was not explained further, as it is different from the given equation and seems to be unrelated.
To solve the equation (225^2 - 2*225*16π + 256π^2)/(16π^2) = 16+h^2, we can follow these steps:
1. Simplify the numerator: (225^2 - 2*225*16π + 256π^2) becomes (225 - 16π)^2.
2. Simplify the denominator: (16π^2) remains as it is.
3. Rewrite the equation: (225 - 16π)^2 /(16π)^2 = h^2 + 16.
4. Divide both sides of the equation by (16π)^2: (225 - 16π)^2 /(16π)^2 = h^2 + 16.
5. Simplify the expression on the left side by cancelling out common factors: (225/16π - 16)^2 = h^2 + 16.
6. Square root both sides of the equation to solve for h: √((225/16π - 16)^2) = √(h^2 + 16).
7. Simplify the right side: √(h^2 + 16) = √(h^2 + 16).
Therefore, the equation is already simplified as (225/4π)^2 - 2*225/π.