Could someone help me please
1 answer:
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Answer:
Volume is
Solution:
As per the question:
Diameter, d = 40 m
Radius, r = 20 m
Now,
From north to south, we consider this vertical distance as 'y' and height, h varies linearly as a function of y:
iff
h(y) = cy + d
Then
when y = 1 m
h(- 20) = 1 m
1 = c.(- 20) + d = - 20c + d (1)
when y = 9 m
h(20) = 9 m
9 = c.20 + d = 20c + d (2)
Adding eqn (1) and (2)
d = 5 m
Using d = 5 in eqn (2), we get:
Therefore,
Now, the Volume of the pool is given by:
where
A =
Thus
Answer:
0.20 and 0.36
Step-by-step explanation:
y(t) = 2 sin (4π t) + 5 cos (4π t)
We wish to convert this to:
y = A sin(ωt + φ)
We know that ω = 4π. We also know the following:
5 = A sin φ
2 = A cos φ
Divide the first equation by the second equation:
5/2 = tan φ
φ = tan⁻¹(5/2)
Now, square the two equations and add them together.
5² + 2² = (A sin φ)² + (A cos φ)²
29 = A²
A = √29
The equation of the wave is therefore:
y = √29 sin(4π t + tan⁻¹(5/2))
The maximum negative position is -√29. And half of that is -½√29.
-½√29 = √29 sin(4π t + tan⁻¹(5/2))
-½ = sin(4π t + tan⁻¹(5/2))
7π/6 + 2kπ or 11π/6 + 2kπ = 4π t + tan⁻¹(5/2)
7 + 12k or 11 + 12k = 24t + 6 tan⁻¹(5/2) / π
t = (7 + 12k − 6 tan⁻¹(5/2) / π) / 24 or (11 + 12k − 6 tan⁻¹(5/2) / π) / 24
Trying different integer values of k, we find there are two possible values for t between 0 and 0.5, both when k = 0.
t = (7 − 6 tan⁻¹(5/2) / π) / 24 or (11 − 6 tan⁻¹(5/2) / π) / 24
t ≈ 0.20 or 0.36
