A pendulum is swinging next to a wall. The distance from the bob of the swinging pendulum to the wall varies in a periodic way t
hat can be modeled by a trigonometric function.
The function has period 0.80.80, point, 8 seconds, amplitude 6 \text{ cm}6 cm6, start text, space, c, m, end text, and midline H = 15 \text{ cm}H=15 cmH, equals, 15, start text, space, c, m, end text. At time t = 0.5t=0.5t, equals, 0, point, 5 seconds, the bob is at its midline, moving towards the wall.
Find the formula of the trigonometric function that models the distance HHH from the pendulum's bob to the wall after t seconds. Define the function using radians.
The function has period 0.80.80, point, 8 seconds, amplitude 6 \text{ cm}6 cm6, start text, space, c, m, end text, and midline H = 15 \text{ cm}H=15 cmH, equals, 15, start text, space, c, m, end text. At time t = 0.5t=0.5t, equals, 0, point, 5 seconds, the bob is at its midline, moving towards the wall.
Find the formula of the trigonometric function that models the distance HHH from the pendulum's bob to the wall after t seconds. Define the function using radians.
1 answer:
Answer:
H(t) = 15 -6sin(2.5π(t -0.5))
Step-by-step explanation:
For midline M, amplitude A, period T and time t0 at which the function is decreasing from the midline, the function can be written as ...
H(t) = M -Asin(2π/T(t -t0))
Using the given values of M=15, A=6, T=0.8 and t0 = 0.5, the equation is ...
H(t) = 15 -6sin(2.5π(t -0.5))
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Answer:
a ) See Annex
b) P₁ = 0,0464 or P₁ = 4,64 %
c) P₄ = 0,92 or P₄ = 92 %
Step-by-step explanation:
b) P₁ [ X being defective ] = P₂ + P₃
Where P₂ is the probability of X rays machine detects a weld defective and the weld is really defective
And P₃ is the probability of X rays machine detects a weld defective and the weld is not defective
Then
P₂ = 0,04 * 0,92 = 0,0368
P₃ = 0,96 * 0,01 = 0,0096
Then P₁ = 0,0368 + 0,0096
P₁ = 0,0464 or P₁ = 4,64 %
c) P₄ = 0,04 *0,92
P₄ = 0,92 or P₄ = 92 %
Answer:
Step-by-step explanation:
By the tangent ratio, . Substituting the given values into this equation gives us:
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(Multiply both sides of the equation by
)
(Divide both sides of the equation by
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