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.
Answer:
12.1
Step-by-step explanation:
Answer:
y = -40*x + 170
Step-by-step explanation:
Data
When price is $1.50 per banana, sales reach 110 per day
When price is $2.50 per banana, sales reach 70 per day
Calling y the number of deep fried bananas on a stick per day the vendor sells and x its price in dollars per banana; the above data can be expressed as points (x1, y1) and (x2, y2), i. e., (1.5, 110) and (2.5, 70). The question asks for a linear expression to represent given points. General linear formula is:
y = m*x + b
where m is the slope and b is the y-intercept.
Slope is computed as follows
m = (y2 -y1)/(x2 -x1) = (70 - 110)/(2.5 - 1.5) =-40
y-intercept is computed replacing general formula with a known point and the slope, as follows
y1 = m*x1 + b
110 = -40*1.5 + b
110 + 60 = b
170 = b
Therefore, the linear equation is: y = -40*x + 170
