The equation of the circle that represents the dartboard is (x - 12)² + (y - 17/3)² = 9/16, where the origin is the lower left corner of the room and the unit of the radius is feet.
The position of Brian's dart is represented by the coordinates (11.5, 5). Brian's dart does land on the dartboard.
What is the equation of a circle?
Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
- h and k represents the coordinates at the center.
- r represents the radius of a circle.
From the question, we have the following information:
The height of this standard dartboard, k = 5 feet, 8 inches.
The diameter of this standard dartboard = 18 inches.
The bull's eye, h = 12 feet.
Next, we would convert the all of the units in inches to feet as follows:
Height, k = 5 + 8/12
Height, k = 5 + 2/3
Height, k = 17/3 feet.
For the diameter, we have:
Diameter = 18/12
Diameter = 3/2 feet.
Also, we would determine the radius as follows:
Radius, r = diameter/2
Radius, r = (3/2)/2
Radius, r = 3/4 feet.
Substituting the parameters into the standard equation, we have;
(x - 12)² + (y - 17/3)² = (3/4)²
(x - 12)² + (y - 17/3)² = 9/16
Next, we would determine whether Brian's dart land on the dartboard:
(x - 12)² + (y - 17/3)² < 9/16
(x - 12)² + (y - 17/3)² < 9/16
(11.5 - 12)² + (5.5 - 5.67)² < 0.5625
0.25 + 0.0289 < 0.5625
0.2789 < 0.5625 (Yes, it does land because it's within the circumference of this standard dartboard).
Read more on equation of a circle here: https://brainly.com/question/18430680
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