Warning: This might be rough...
First draw it out. Label the angles at the corners of the triangle 60 (definition of equilateral triangles). Now draw a line from the center of the circle to the corner, splitting the corner in half. Label this line R and a corner as 30 degrees. No to find the height of this triangle, you do rsin(30). The base of this triangle is 2rcos(30). Now find the area of this mini triangle (rsin(30)*2rcos(30)/2=r/2*rsqrt(3)/2=r^2sqrt(3)/4). Now multiply this by 3 because you have 3 mini triangles... to get...
<span>r^2 3sqrt(3)/4</span>
So the first one, 1.2 >11/5. and the second one 1/3> 1/2
The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.
According to the statement
we have given that If 15 actuators have failed and we have to find the probabilities on some conditions.
we know that the formula of probabilities is
probability = possible outcomes / total outcomes
So,
- at least 10 are repairable = 1 - (10 are not repairable)
at least 10 are repairable = 1 - 10/15
at least 10 are repairable = (15 - 10)/15
at least 10 are repairable = (5)/15
at least 10 are repairable = 1/3
- from 3 to 8 are repairable = 3/15 *8/15
from 3 to 8 are repairable = 1/5 *8/15
- exactly 5 are repairable = 5/15
exactly 5 are repairable = 1/3
These are the probabilities of the given conditions.
So, The probabilities of at least 10 are repairable is 1/3. and probabilities of from 3 to 8 are repairable is 1/5*8/15 and probabilities of exactly 5 are repairable is 1/3.
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P1 = 10 m²
P2 = 22 m²
P3 = ?
According to Pythagoras' theorem:
P1 + P2 = P3
P3 = 10 m² + 22 m² = 32 m²
is equal to 16.
