Answer:
(x - 1)² + (y + 1/2)² = 65/4
Step-by-step explanation:
Given: the endpoints of the diameter are (3, 3) and (-1, -4). a( To determine the center of this circle, find the midpoint of the line segment connecting these two points:
3 - 1
x = -----------
2
and
-1
y = ----------
2
The center is at x = 1 and y = -1/2: (1, -1/2).
b) The radius is half the diameter. The diameter is the distance between the two endpoints given, that is, the distance between (-1, -4) and (3, 3):
diameter = √(4² + 7²) = √(16 + 49) = √65; therefore,
radius = (1/2)√65.
square of the radius = r² = 65/4
The general equation of a circle with center at (h, k) and radius r is
(x - h)² + (y - k)² = r². In this case, the equation is:
(x - 1)² + (y + 1/2)² = 65/4
Answer:
have you given the solution with questions or not
Answer: 
Step-by-step explanation:
Number of persons said it is legal to text while driving = 8
Number of persons said it is illegal to text while driving = 804
Total persons sampled = 804+8 = 812
Since probability =
The probability of randomly selecting someone who believes it should be legal to text while driving = 
Required probability = 
The given function is
f(x) = x - ln(8x), on the interval [1/2, 2].
The derivative of f is
f'(x) = 1 - 1/x
The second derivative is
f''(x) = 1/x²
A local maximum or minimum occurs when f'(x) = 0.
That is,
1 - 1/x = 0 => 1/x = 1 => x =1.
When x = 1, f'' = 1 (positive).
Therefore f(x) is minimum when x=1.
The minimum value is
f(1) = 1 - ln(8) = -1.079
The maximum value of f occurs either at x = 1/2 or at x = 2.
f(1/2) = 1/2 - ln(4) = -0.886
f(2) = 2 - ln(16) = -0.773
The maximum value of f is
f(2) = 2 - ln(16) = -0.773
A graph of f(x) confirms the results.
Answer:
Minimum value = 1 - ln(8)
Maximum value = 2 - ln(16)