I’m pretty sure it would be 372.22
Fun, geometry disguised as probability.
That's a pentagon, which we can view as 10 right triangles with legs a and s/2 (half of s) and hypotenuse r. So area of the pentagon is
P = 10 × (1/2) a (s/2) = 10 (1/2) (3.2) (4.7/2) = 37.6
The area of the circle is πr² so the circle area is
C = π (4²) = 50.265482
The white area is the difference, C-P, and the probability we seek is the fraction of the circle that's white, so (C-P)/C.
p = (C-P)/C =1-P/C = 1-37.6/50.265482 = 0.251971
Answer: 0.25
Higher than I would have guessed from the figure.
Answer:
(identity has been verified)
Step-by-step explanation:
Verify the following identity:
sin(x)^4 - sin(x)^2 = cos(x)^4 - cos(x)^2
sin(x)^2 = 1 - cos(x)^2:
sin(x)^4 - 1 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2
-(1 - cos(x)^2) = cos(x)^2 - 1:
cos(x)^2 - 1 + sin(x)^4 = ^?cos(x)^4 - cos(x)^2
sin(x)^4 = (sin(x)^2)^2 = (1 - cos(x)^2)^2:
-1 + cos(x)^2 + (1 - cos(x)^2)^2 = ^?cos(x)^4 - cos(x)^2
(1 - cos(x)^2)^2 = 1 - 2 cos(x)^2 + cos(x)^4:
-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = ^?cos(x)^4 - cos(x)^2
-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = cos(x)^4 - cos(x)^2:
cos(x)^4 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2
The left hand side and right hand side are identical:
Answer: (identity has been verified)
Answer: The answer is (22, 15).
Step-by-step explanation: Given that 'x' represents the number of cars Leonard has and 'y' represents the number of cars Liam has.
Then, according to the given information, we have
Multiplying the first equation by 2 and adding to the second equation, we have
So,
Therefore, Leonard has 22 cars and Liam has 15 cars.
Thus, (22, 15) is the solution to the given system.
