@DrAviLoeb Probably not...it's just a rock. Think, the closest possible life-sustaining planet if at Proxima Centauri (4.2 light years away) would take a spacecraft over 75000 years to reach us. So the return journey is say 150000 years. That's a long wait for a scout report....
@itvnews Page 8:
Which is equivalent to the Pythagorean Theorem:
b² + a² = c²
Thus, we have proven the Pythagorean Theorem using trigonometry without using the identity cos²(θ) + sin²(θ) = 1.
@itvnews Page 7:
Squaring both sides, we get:
b * a = c² / 2 * sin(2θ)
Substituting in the identity sin(2θ) = 2 sin(θ) cos(θ), we get:
b * a = c² * sin(θ) * cos(θ)
@itvnews Page 6:
Since θ is the angle between the hypotenuse and leg a, it must be less than 90 degrees, so sin(2θ) is positive. Therefore, we can take the square root of both sides of the equation without changing the sign:
sqrt(b * a) = (c / sqrt(2)) * sqrt(sin(2θ))
@itvnews Page 5:
b * (a/c) = h = c * cos(θ)
Simplifying and rearranging terms, we get:
b * a = c² * sin(θ) * cos(θ)
Using the identity sin(2θ) = 2 sin(θ) cos(θ), we can rewrite the above equation as:
b * a = (c² / 2) * sin(2θ)
@itvnews Page 4:
Multiplying both sides by b and substituting in the expression for sin(θ) from above, we get:
h = (a/c) * b
From the smaller triangle on the right, we get:
cos(θ) = h/c
Multiplying both sides by c and substituting in the expression for h from above, we get:
@itvnews Page 3:
Using basic trigonometric functions, we can write:
sin(θ) = opposite/hypotenuse = a/c
cos(θ) = adjacent/hypotenuse = b/c
tan(θ) = opposite/adjacent = a/b
From the smaller triangle on the left, we get:
sin(θ) = h/b
@itvnews Page 2:
Now, draw a perpendicular line from the right angle to the hypotenuse, creating two smaller triangles within the original triangle. Let's label the length of the segment connecting the right angle to the point where the perpendicular line intersects the hypotenuse as h.
@itvnews That's easy - but is this really a proof?
Page 1:
Consider a right triangle with legs of length a and b and a hypotenuse of length c. Let's label the angle between the hypotenuse and leg a as θ.
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From the European Commission:
The conclusion is clear.
Fully vaccinated people are less likely to die with Covid19 than those who are not vaccinated.
The higher the vaccination rate, the lower the death rate.
From the European Commission:
The conclusion is clear.
Fully vaccinated people are less likely to die with Covid19 than those who are not vaccinated.
The higher the vaccination rate, the lower the death rate.