Calculus

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What would the values of A, B, and C be in this problem?

The tides in a particular bay can be modeled with an equation of the form d= A cos (Bt) + C, where t represents the number of hours since high-tide and d represents the depth of water in the bay. The maximum depth of water is 36 feet, the minimum depth is 22 feet and high-tide is hitting every 12 hours.

  • Calculus -

    max - min = 36-22 = 14
    so the amplitude is 7
    what do we have to add to 7 to get 36 ? ----- 29
    period of cosine curve = 2π/k
    12 = 2π/k
    k = π/6

    so d = 7 cos (πt/6) + 29

    check:
    at t=0 , d = 7cos 0 + 29 = 36 ---> high tide
    at t=3 , d = 7cos π/2 + 29 = 29 ---> makes sense
    at t=6 , d = 7cos π + 29 = -7+29 = 22 ---> low tide
    at t=9 , d = 7cos 3π/2 + 29 = 29 --->makes sense
    at t=12, d = 7cos 2π + 29 = 7(1)+29 = 36 ---> back to high tide

  • Calculus -

    What will the graph look like for two full periods?

  • Calculus -

    first period:
    mark off from 0 to 12, with marks at 0, 3, 6, 9, and 12
    at 0 , d=36
    at 3, d= 29
    at 6, d = 22
    at 9, d = 29
    at 12, d = 36 --- end of first period, now repeat that
    draw a smoth cosine curve .

    (I am somewhat surprised you even asked that question)

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