Determine whether or not the given set is open, connected, and simply-connected. (Select all that apply.) (x, y) | 16 ≤ x2 + y2
≤ 25, y ≥ 0 open connected simply-connected
1 answer:
Answer:
The set is closed, connected and simyple connected
Step-by-step explanation:
A set is closed if contains all the point in its boundaries. A set is open if it doesn't contain any of the points in its boundaries. In this set, all the points of the boundaries are included because it is using the less than or equal to and greater than or equal to define the set.
The set is connected if you can find a path inside the set to connect any two points of the set. If you make the graph of the set you would see the set covers this condition because the set hasn't any division.
The set is simply connected if you can draw a closed curve inside the set and in the interior of the curve there are only points of the set. In other words, if the set has holes is not simply connected. This set doesn't have holes, it's simply connected.
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From the time you see the first beacon, you have to wait for the lighthouse to make 120°, i.e. 1/3 of a whole turn.
So, if T is the time it takes for the lighthouse to make a whole turn, the interval between the first and the second beacon is T/3.
The interval between the second and third beacon is the amount of time it takes to the lighthouse to make the remaining 2/3 of a turn, so that you'll see the first beacon again. So, this time is 2T/3
So, the ratio is
So, the time between the second and third beacon is twice as much the time between the first two.
Answer:
The distance between two points ( -1,1) and (2,-4) is:
or d = 5.8 units.
Step-by-step explanation:
Given the points
- (-1, 1)
- (2, -4)
Finding the distance between (-1, 1) and (2, -4) using the formula
substitute (x₁, y₁) = (-1, 1) and (x₂, y₂) = (2, -4)
units
or
units
Therefore, the distance between two points ( -1,1) and (2,-4) is:
or d = 5.8 units.
<h3>The perimeter of circle = 17.6 cm</h3><h3>Perimeter of square = 22.4 cm</h3>
Step-by-step explanation:
The total length of the wire = 40 cm
Let us assume the circumference of the circle = k cm
So, the circumference of the square = ( 40 - k) cm
Now,as circumference of circle = 2πR
⇒2πR = k cm or, R =
Area of the circle = πR²
or, A =
....... (1)
Similarly , perimeter of square = 4 x Side
⇒ 4 x Side = ( 40 - k) cm ⇒ S =
Area of the square = (Side)² =
Solving, we get: ....... (1)
So, combining (1) and (2), total area A is
or, we get: A = 0.07962 k² + 0.0625 k² + 100 - 5 k
A = 0.1422 k² - 5 k + 100
For axis of symmetry :
⇒ k = 17.6 inches
So, the perimeter of circle = 17.6 cm
Perimeter of square = (40 - 17.6 ) = 22.4 cm