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2 answers:
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Answer:
f(x) = {0, x≤ 1; 4(x -1), 1 < x ≤ 6; 2.5x +5, x > 6}
Step-by-step explanation:
The hourly rate gives you the slope of the function in the relevant interval. The added constant is chosen to make the function continuous.
That is, at 1 hour, the charge is zero, so the next segment (4x+b) must have a value of b that makes the charge for 1 hour be zero. That will be b=-4.
Likewise, for more than 6 hours, the charge will be (2.5x+b), where b is chosen to make this expression match the charge for 6 hours. We know the charge for 6 hours is 4(6) -4 = 20, so b must match ...
2.5(6) +b = 20
b = 20 -15 = 5
The segment from 1 to 6 hours is f(x) = 4x -4.
The segment for more than 6 hours is f(x) = 2.5x +5.
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<em>Alternate solution</em>
Since the charge is zero for the first hour, the first segment could be considered to be charging only for hours after the first. That is, an alternate expression for hours 1–6 could be 4(x -1). Likewise, we could say the expression for hours more than 6 is 2.5(x +2).
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Answer:
The correct option is;
No, the distance from (0, 0) to (2, √6) is not 3 units
Step-by-step explanation:
The given parameters of the question are as follows;
Circle center (h, k) = (0, 0)
Point on the circle (x, y) = (3, 0)
We are required to verify whether point (2, √6) lie on the circle
We note that the radius of the circle is given by the equation of the circle as follows;
Distance² = (x - h)² + (y - k)² = r² which gives;
(3 - 0)² + (0 - 0)² = 3²
Hence r² = 3² and r = 3 units
We check the distance of the point (2, √6) from the center of the circle (0, 0) as follows;
Therefore;
(2 - 0)² + (√6 - 0)² = 2² + √6² = 4 + 6 = 10 = √10²
Which gives the distance of the point (2, √6) from the center of the circle (0, 0) = √10
Hence the distance from the circle center (0, 0) to (2, √6) is not √10 which s more than 3 units hence the point (2, √6), does not lie on the circle.