Answer:
The time it takes for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
Step-by-step explanation:
Given the equation
-----------Equation 1
where d, in inches of the pendulum of a grandfather clock from the center.
Comparing with the standard equation of an oscillating pendulum bob.
----------Equation 2
where ω = angular velocity
t = time taken
α = The angular displacement when t = 0
Comparing equation 1 and 2,
α = 0
Recall that ![w = 2\pi fTherefore,[tex]2\pi f = \frac{8\pi }{5} \\\\f = \frac{4}{5}](https://tex.z-dn.net/?f=w%20%3D%202%5Cpi%20f%3C%2Fp%3E%3Cp%3ETherefore%2C%3C%2Fp%3E%3Cp%3E%5Btex%5D2%5Cpi%20f%20%3D%20%5Cfrac%7B8%5Cpi%20%7D%7B5%7D%20%5C%5C%5C%5Cf%20%3D%20%5Cfrac%7B4%7D%7B5%7D)
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f = 0.8 Hertz
Recall that 
T = 1.25 seconds
Therefore, the time it takes for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
Answer:
Hydrostatic Force = 35.28KN
Step-by-step explanation:
To solve this question, let's consider integrating the hydrostatic force from the top of the triangle to the bottom.
Formula for a thin horizontal slice of the triangle the force is;
δF=ρgxwδx
Where w is width of triangle; ρ is density of water and g is acceleration due to gravity
At depth x, the width of the triangle is w=2/3x.
Thus, F = (3,0)∫)ρgxwδx
=(2/3)ρg[(3,0)∫)x²δx]
= integrating, we have;
F = (2/3)ρg[(3³/3) - (0³/3)]
F = (2/5)ρg [27/3] = (2/5)(1000)(9.8)(9) = 35280 N = 35.28 KN
Hence , the area of circle is 160.66 m²
The answer would be simplified to q-8 after combining the like terms (:
The profit is calculated by subtracting the expenses from the revenue.
For Deal A:
Profit = $100,000 - $10,000
= $90,000
Deal B:
Profit = $50,000 - $20,000 = $30,000
For the percentage of revenue, we divide the revenue by the expense and multiply the quotient by 100%
Deal A: %revenue = $100,000/$10,000 x 100 = 1000%
Deal B: %revenue = $50,000/$20,000 x 100 = 250%
