Question

1. which of the following represents the area of a circle with a diameter of 4r - 6?

(a) π(16r² + 36)
(b) π(16r² - 48r + 36)
(c) π(4r² + 9)
(d) π(4r² - 12r + 9)

1. which of the following has a degree of 2?

(a) r + 2
(b) 1 + r + r²
(c) r² + 2r³ - 1 + 3r
(d) 2

Explanation:

Step1: Recall the formula for the area of a circle

The area of a circle is \(A=\pi r^{2}\), and the diameter \(d = 4x-6\), so the radius \(r=\frac{d}{2}=2x - 3\).

Step2: Substitute the radius into the area formula

Substitute \(r = 2x-3\) into \(A=\pi r^{2}\), we get \(A=\pi(2x - 3)^{2}\).
Using the formula \((a - b)^{2}=a^{2}-2ab + b^{2}\) (\(a = 2x\), \(b=3\)), then \((2x - 3)^{2}=(2x)^{2}-2\times(2x)\times3+3^{2}=4x^{2}-12x + 9\).
So \(A=\pi(4x^{2}-12x + 9)\).

Answer:

\(d\)