A circle’s area is represented by A = π(x2 − 22x + 121). What expression represents the radius of the circle?
A. x + 11
B. x − 11
C. x − 22
D. x + 22
I got B. please correct me if I am wrong/ Thank You sir
you are correct.
You are correct, the expression that represents the radius of the circle is B. x - 11.
In the equation A = π(x^2 - 22x + 121), the expression inside the parentheses (x^2 - 22x + 121) represents the square of the radius. To find the radius, we need to take the square root of this expression.
Taking the square root of (x^2 - 22x + 121), we get √(x^2 - 22x + 121).
Simplifying further, we get √((x - 11)(x - 11)).
Finally, simplifying one more time, we get (x - 11), which is the expression that represents the radius of the circle.
To find the expression that represents the radius of the circle, we need to recognize that the formula for the area of a circle is A = πr^2, where r represents the radius of the circle.
Given that A = π(x^2 − 22x + 121), to find the expression representing the radius, we need to rewrite the equation in the form A = πr^2.
So, we have:
πr^2 = π(x^2 − 22x + 121)
Next, we need to isolate the term representing the radius. To do this, we divide both sides of the equation by π:
r^2 = x^2 − 22x + 121
Finally, to find the expression representing the radius, we take the square root of both sides of the equation:
√(r^2) = √(x^2 − 22x + 121)
Simplifying this, we get:
r = x − 11
Therefore, the expression that represents the radius of the circle is x − 11, which is option B. You are correct!