The half-angle formula for tangent is:
tan(a/2) = (sin a / (1 + cos a)) = ((1 - cos a) / sin a)
Now we can plug in values:
tan(5π/8) = (sin(5π/4) / (1 + cos(5π/4)) = ((1 - cos(5π/4)) / sin(5π/4)
tan(5π/8) = (-√2/2) / (1 + (-√2/2)) = (1 - (-√2/2)) / (-√2/2)
tan(5π/8) = ((-√2/2)) / ((2 - √2)/2) = ((2 + √2)/2) / (-√2/2)
Now we can solve the first half:
(-√2/2)(2 / (2 - √2))
(-√2/2)((4 + 2√2) / 2)
(-√2/2)(2 + √2)
(-2√2 - 2)/2
-√2 - 1
tan(5pi/8) = -√2 - 1
Answer:
The answer is approximately 5.09 seconds.
Step-by-step explanation:
The given equation is:
f(x) = -5x^2 + 250
To find the elapsed time, x, set the equation equal to 120 and solve for x:
-5x^2 + 250 = 120
-5x^2 = -130
x^2 = -130/-5 = 26
x = Sqrt(26) = 5.09 seconds.
The actual quotient will be greater than 10 because 60 divided by 5 is 12, so the answer will be between 10 and 12, so it will be greater than 10
