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Snowcat [4.5K]
3 years ago
15

On September 17, 2008, high tide in Portland was at midnight. The water level at high tide was 10.3 feet; later, at low tide, it

was 0.3 feet. Assuming the next high tide is exactly at 12 noon and that the height of the water is given by a sine or cosine curve, find a formula for the water level in Portland as a function of time, where y is the water level in feet, and t is the time measured in hours from midnight.
Mathematics
1 answer:
____ [38]3 years ago
7 0
So the problem ask to calculate and formulate a function that could represent the water level in Portland if y is the water level and t is for time in hour so the possible answer would be that y=cosine(t)-0.3. I hope you are satisfied with my answer and feel free to ask for more
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what is a linear function and a nonlinear fuction and how can you tell if the ordered pairs go to them
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Answer:

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Step-by-step explanation:

A function is a linear function if the slope between any two ordered pairs is the same as it is between any other two. That is, the ordered pairs of a linear function will all fall on the same line when they are graphed.

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A nonlinear function is one that is not linear. That is, its points do not all fall on the same line when graphed. Slopes between different pairs of points may differ.

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<em>Detailed Example</em>

If you are given two tables to compare, it is easiest if the x-values (inputs) are separated by a constant amount. For example, x = -2, 0, 2, 4. These all differ by 2. Then the y-values (outputs) of a linear function will all differ by the same quantity. For example, outputs 10, 15, 20, 25 for the above inputs would correspond to a linear function. This one is y = 2.5x +15.

If the output values for that same set of inputs do not have constant differences, then the function is nonlinear. For example, outputs 10, 15, 21, 27 have differences of 5, 6, 7, so correspond to a nonlinear function. This one happens to be y = (x^2 +22x +120)/8.

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If the input values are not uniformly spaced, then you can check to see if the slope between one pair of points is the same as the slope for the next pair, and so on. The slope formula is ...

  m = (y2 -y1)/(x2 -x1)

For our first table, the first pair of points (-2, 10) and (0, 15) are on a line with slope ...

  m = (15 -10)/(0 -(-2)) = 5/2

Of course, when the calculations are repetitive, it is convenient to use a spreadsheet or calculator to do them. See the attachment for the calculations for this example.

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