Answer:
470.89%
3.72 divided by 0.79 = 4.70886076
470.89%
Step-by-step explanation:
Answer:
ENGLISH
One of the angles must equal 90 degrees and the other two angles must add up to 90 degrees.
SPANISH TRANSLATION
Uno de los ángulos debe ser igual a 90 grados y los otros dos ángulos deben sumar 90 grados.
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.
The tetrahedron passes through the intercepts (5, 0, 0), (0, 2, 0), and (0, 0, 10). Parameterize the surface (call it 
) by
with 
and 
. Take the normal vector to to be
Then the flux of 
across is
If the cosine is 1/2, and the angle is acute, then the angle is 60 degrees. Using the rules for a 30-60-90 right triangle, hyp=2 times the short leg. So 7/2= 3.5.
