A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t) = 7 sin t where s is measured in centimeters andt is measured in seconds. Find the rate at which the mass is moving at t = 9 s. Round your answer to four decimal places. 9 s. cm/s

Q: . During a rainfall, the depth of water in a rain gauge increases at a rate modeled by R(t) = 0.5 +…

A: Given:  dh(t)dt = R(t) = 0.5 + tcosπt380                                 (1) R(t) = rate of change…

Q: (a) Find the average velocity during each time period.

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Q: A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t) = 2…

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Q: The acceleration of an object (in m/s?) is given by the function a(t) = 9 sin(t). The initial…

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Q: A vehicle : travel S in a stenght Tine for :timinutes with a velociti of v(t) =180t feet per.…

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Q: A drag racer accelerates at a(t) = 96 ft/s2. Assume that v(0) = 0 and s(0) = 0. a. Determine the…

A: To find out the distance/position function.

Q: The acceleration of an object (in m/s2) is given by the function a(t) = 9 sin(t). The initial…

A: To find  The total distance travelled by the object from time 0 to time 3.

Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

A: Given,The depth is modeled by the function : D(t) = 2 cosπ6t+7π6+5Asked Depth changing rate at…

Q: A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t) = 2…

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Q: The displacement (in centimeters) of a particle moving back and forth along a straight line is given…

A: Given:- Displacement  S = 3sin(πt)+5cos(πt) To find:- Average velocity in intervals [1,2] ,[1,1.1],…

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Q: The acceleration of an object (in m/s2) is given by the function a(t) = 5 sin(t). The initial…

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Q: A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t) = 3…

A: Given query is to find the rate of oscillation at t=4 second.

Q: 34. The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth 7n is…

A: Given, the depth Dt=5sinπ6t-7π6+8, where t is the number of hours after 6 a.m. To find the rate of…

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Q: The acceleration of an object (in m/s²) is given by the function a(t) = 8 sin(t). The initial…

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Q: A drag racer accelerates at a(t) = 88 ft/s. Assume that v(0) = 0 and s(0) = 0. a. Determine the…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: A tidal pool has a volume of 120 m³ at t = 0, at t hrs the rate (m³ /hr) that a tidal pool fills is…

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Q: If a cup of coffee has temperature 93°C in a room where the ambient air temperature is 23°C, then,…

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Q: The displacement (in centimeters) of a particle moving back and forth along a straight line is given…

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Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is…

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Q: 15. The height above the ground of a Ferris wheel car is modelled with the equation h(t) = -15 cos +…

A: (a) The height is modeled by a cosine function and we know cos 0°= 1, cos 90° = 0 and cos 180° = -1…

Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

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Q: For a person at rest, the velocity v (in liters per second) of air flow into and out of the lungs…

A: Explained below

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Q: onsider the position function s(t) =8 sin 5t that describes a block bouncing vertically on a spring.…

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Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

A: The depth is modeled by function  Dt=2cosπ4t+3π4+3 where t is the number of hours after midnight.

Q: Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of…

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Q: 2. During a rainfall, the depth of water in a rain gauge increases at a rate modeled by R(t) = 0.5 +…

A: Given: Rt=0.5+tcosπt380 We have to find that how much did the depth of water in the rain gauge…

Q: A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t) = 5…

A: Given:         st=5cos t, t=8s To find the speed take the derivative of the S(t) equation wrt to t…

Q: The rate at which sand is removed from the beach of a water park wave pool is modeled by the…

A: The rate at which sand is removed from the beach of a water park wave pool is modeled by the…

Q: A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t)=6sin…

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Q: A damping force affects the vibration of a spring so that the displacement of the spring is given by…

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Q: A ladder inclined at 60 ° with the horizontal is leaning against a vertical wall. The foot of the…

A: Given that angle is 60. The foot of the ladder is 3 meters. So, this can be written as, It is known…

Q: 5 y In the triangle shown above, if 0 increases at a constant rate of 3 radians per minute, at what…

A: In the triangle, θ increases at a constant rate of 3 radians per minute. To determine the rate at…

Q: You are studying the impacts of rising sea levels on an estuary, and are modeling how the salinity…

A: Given that st=12sin3π25tcosπ25t+15St=14sin3π25tcosπ25t+17 Here S(t), s(t) gives the salinity level…

Q: The displacement (in centimeters) of a particle moving back and forth along a straight line is given…

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Q: Suppose a damping force affects the vibration of a spring so that the displacement of the string is…

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Q: A buoy bobs up and down on ocean waves. It’s heigh is measured by the function h(t)= 3 cos (t) where…

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Q: A graphing calculator is recommended. The displacement (in centimeters) of a particle s moving back…

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Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

A: The given function which models the depth function is - D(t) = 4cosπ4t + 9π4 + 5 Where t represents…

Q: A Sliding Ladder A 26 ft ladder leaning against a wall begins to slide. How fast is the top of the…

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Q: The displacement (in centimeters) of a particle moving back and forth along a straight line is given…

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Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

A: We solve the above question.

Q: The displacement from equilibrium of an oscillating weight suspended by a spring is given by y(t) =…

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Q: A ladder, inclined at 60 with the horizontal is leaning against a vertical wall. The foot of the…

A: Given that,  A ladder inclined at 60° the foot of the ladder is 3 meters away from the foot of the…

Q: The displacement (in centimeters) of a particle moving back and forth along a straight line is given…

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Q: A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t) = 2…

A: The equation of distance S(t) as a function of time t is given asS(t) = 2 sin t , To find the…

Q: The displacement from equilibrium of an oscillating weight suspended by a spring is given by y(t) =…

A: