Question

1. Given the following rectangle and circle, at what approximate value of x are the two areas equal?

Answer 1

Answer:

x = 0.86

Step-by-step explanation:

(3x - 1)(x + 6) = 3.14159 × (x + 1)²

3x² + 17x - 6 = 3.14159 × (x² + 2x + 1)

-0.14159x² + 10.7168x - 9.14159 = 0

x² - 75.6875x + 64.5626 = 0

$x = \dfrac{-(-75.6875) \pm \sqrt{(-75.6875)^2 - 4(1)(64.5626)}}{2(1)}$

x = 74.825  or  x = 0.8628

Answer: x = 0.86