A system of equations is given below. y = negative 2 x + one-fourth and y = negative 2 x minus one-fourth Which of the following
1 answer:
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Response-
(78,104) represents the point closest to the interior.
Explanation-
The equation defining the circle,
Since the point lies on the circle, its coordinates must be,
The distance "d" from the point to (30,40) can be calculated as,
Next, we need to determine the value of x for which d is minimized. The minimum distance occurs when is at its lowest value.
Let’s set up the equation,
We find the critical points,
Then,
Since f''(x) is positive, the function f(x) achieves its minimum at x=78
When x is set to 78, the corresponding y value will be
This leads us to conclude that the closest point is (78,104)
