Answer:
53 cm.
Step-by-step explanation:
Circumference = pi times diameter
We are trying to find diameter so rearrange
Circumference/pi = diameter
166.5/pi = 52.998596
Approximately 53 centimeters of lace
We know that
the distance from the centroid of the triangle to one of the vertices is the radius of the circle <span>required to inscribe an equilateral triangle.
[distance </span>centroid of the triangle to one of the vertices]=(2/3)*h
h=the <span>altitude of the equilateral triangle-----> 5.196 in
so
</span>[distance centroid of the triangle to one of the vertices]=(2/3)*5.196
[distance centroid of the triangle to one of the vertices]=3.464 in----> 3.5 in
the radius is equal to the distance of the centroid of the triangle to one of the vertices
hence
the radius is 3.5 in
the answer is
the radius is 3.5 in
Substitute the given point (3, -2) in each condition
(i) y < -3; y ≤ (2/3)x - 4
-2 < -3 → False
Therefore, it is not a solution.
[Since the values of x and y must satisfy both the conditions, if one of them does not satisfy the condition then it is not necessary to check the other one.]
(ii) y > -3; y ≥ 2/3x - 4
-2 > -3 → True
y ≥ 2/3x - 4
-2 ≥ -2 → True
Therefore, it is a solution.
(iii) y < -3; y ≥ 2/3x - 4
-2 < -3 → False
Therefore, it is not a solution.
(iv) y > -2; y ≤ 2/3x - 4
-2 > -2 → False
Therefore, it is not a solution.
Thereofore, the system of linear inequalities having the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4. Hope it helps you.
Step-by-step explanation:
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