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Cerrena [4.2K]
3 years ago
13

The height of the tide over time is shown on the graph. Which of the following equations can be used to reasonably model the dat

a represented in the graph? Select two of the following that apply. There needs to be two selections!

Mathematics
2 answers:
Ne4ueva [31]3 years ago
7 0

Answer:

The correct options are the first and the fourth

f(x) = -3sin(\frac{\pi}{6}x) + 3

and

f(x) = 3cos(\frac{\pi}{6}x+\frac{\pi}{2}) + 3

Step-by-step explanation:

We can observe in the graph that when x = 0 then y = 3. Therefore f(0) must be equal to 3.

We also observe in the graph that f(x) = 0 when x = 3+12k, {3, 15, 27...}

where k is a Whole number k : {0, 1, 3, 4, 5....n}

The function that meets these two conditions is

f(x) = -3sin(\frac{\pi}{6}x) + 3

and

f(x) = 3cos(\frac{\pi}{6}x+\frac{\pi}{2}) + 3

We can check it by substituting x = 3+12k and verifying that f(x) = 0

f(3+12k) = -3sin(\frac{\pi}{6}(3+12k)) + 3

f(3k) = -3sin(\frac{\pi}{2} + 2\pi(k)) + 3

We know that sin(\frac{\pi}{2})) = 1 and sin(2k\pi) = 0

Then

f(3+12k) = -3+ 3 = 0

Also

f(3+12k) = 3cos(\frac{\pi}{6}(3k) + \frac{\pi}{2})+ 3

We know that cos(\frac{\pi}{2}k) = -1  and cos(2k\pi) = 1

f(3+ 12k) = -3 +3 = 0

Therefore The correct options are the first and the fourth

polet [3.4K]3 years ago
7 0

Answer:

Option 1 and 4 are the two functions.

Step-by-step explanation:

The given graph may be of sine function or cosine function.

So we start with sine function first.

f(x) = asin(bx+c) +d

Here the features of given graph are

1). Amplitude a = (6-0)/2 =3

2). Period = 12 therefore b = 2π/period = 2π/12 = π/6

3). Midline is y = 3

4). Horizontal shift c = 0

5). vertical shift d = 3 in upward direction

5). Since graph starts below the midline means the function will start with negative notation

So we design the function as y = -3sin(π/6+0)+3

Now for cosine function f(x) = a cos(bx+c)+d

1). Amplitude a = 3

2). Midline is y = 3

3). period = 2π therefore b = 2π/period = 2π/12 = π/6

4). Horizontal shift which is in right side, c = +(π/2)

5). Vertical shift d = 3

Therefore the cosine function will be f(x) = 3cos(π/6+π/2)+3

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