Answer:
Perimeter = 18(1 + √3 ) cm
Step-by-step explanation:
The radius of each ball = 1/2 * 6 = 3 cm.
Lines drawn from the 2 points of contact for one billiard ball to the center of the ball are at right angles to the sides of the triangle ( Tangent/radius theorem).
If we now draw a line from the vertex of the big triangle to the center of the ball we get 2 right triangles, and they are 30-60-90 triangles.
If the adjacent side of a triangle ( which is part of the side of the big triangle) = x:
tan 30 = 3 / x
x = 3 / tan 30
= 3 / 1/√3
= 3√3 cm.
There are 6 of these sides in the big triangle so their total length =
18√3 cm.
The three 'middle' sides joining 2 billiard balls each have a length of 2 radii = 6 cms ( as they form a rectangle with the radii of 2 billiard balls).
So the perimeter of the triangle = 18√3 + 3(6)
= 18(1 + √3 ) cm
I would have liked to transfer a diagram but I can't get to copy it to this site.
<h3>
Answer: D) 72</h3>
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Work Shown:
Angle PQR = (far arc - near arc)/2
2x+72 = ( (2x+252) - (2x+108) )/2
2x+72 = 144/2
2x+72 = 72
2x = 72-72
2x = 0
x = 0/2
x = 0
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Angle PQR = 2x+72
Angle PQR = 2(0)+72
Angle PQR = 72 degrees
Not quite sure what you are asking...
t stands for time in this formula
if you are trying to solve for t it would be t=d/r or time equals distance divided by rate
hopefully this helps! if not please let me know.
44 students in Mrs. Vitale's class read 11 books
<h3>Ratio and proportions</h3>
Let the number of students that read 11 books in Mrs. Vitale's class be x
If One fourth of the students in Mrs. Vitale's class read 11 books, then
1/4 x = 11 books
x = 11 * 4
x = 44
Hence 44 students in Mrs. Vitale's class read 11 books
Learn more on ratio and proportion here: brainly.com/question/2914376
