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  • Dashboard
Topics
Exponents & LogarithmsRounding & ErrorSequences & SeriesFinancial MathematicsMatricesComplex Numbers
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2D & 3D GeometryVoronoi DiagramsTrig equations & identitiesVectorsGraph Theory
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DifferentiationIntegrationDifferential Equations
Paper 3
Plus
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IB Math AIHL
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Bivariate Statistics
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Problem Bank
IB Math AIHL
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Bivariate Statistics
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Problem Bank

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[Maximum mark: 5]

The depth ​H​ meters of water in Boston's harbor can be modeled by the function ​H(t)=asin(bt+c)+12, where ​a,b>0​ and ​t​ is the time in hours after midnight on a particular day.


On this day, the minimum depth observed was ​9.3​ meters.

  1. Determine the maximum observed depth.

    [2]
    Enter your answer for (a):
    m

The following table shows the depth of water at various times throughout the day.

​t​

​2​

​7​

​14​

​18​

​H​

​9.426​

​13.60​

​9.71​

​11.68​

Ocean tides, which are due to the orbit of the moon, have a period slightly greater than ​12​ hours.

  1. Estimate the value of ​b​ and the value of ​c​ in radians, giving your answers to ​1​ significant figure.

    [3]
[Maximum mark: 5]

The depth ​H​ meters of water in Boston's harbor can be modeled by the function ​H(t)=asin(bt+c)+12, where ​a,b>0​ and ​t​ is the time in hours after midnight on a particular day.


On this day, the minimum depth observed was ​9.3​ meters.

  1. Determine the maximum observed depth.

    [2]
    Enter your answer for (a):
    m

The following table shows the depth of water at various times throughout the day.

​t​

​2​

​7​

​14​

​18​

​H​

​9.426​

​13.60​

​9.71​

​11.68​

Ocean tides, which are due to the orbit of the moon, have a period slightly greater than ​12​ hours.

  1. Estimate the value of ​b​ and the value of ​c​ in radians, giving your answers to ​1​ significant figure.

    [3]