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torisob [31]
3 years ago
11

What are the amplitude, period, and midline of f(x)=-4 cos (2x-n)+3?

Mathematics
1 answer:
tangare [24]3 years ago
7 0
To find the amplitude and period you need to be familiar with the following equation. Also you need to know that the standard cos has a period of 2\pi and the midline is a line that runs between the max and min of the y-values of the function.

Equations:
f(x) = A cos(Bx +C) + D
f(x) = -4 cos(2x -n) + 3

A = amplitude = |-4| = 4
B = 2
C = phase shift = n = 0 
D = vertical shift = midline = 3

Amplitude = 4

Find the period:
Period = \frac{2\pi}{B} = \frac{2\pi}{2} = \pi

Find the midline:
We know that the amplitude is 4  so we have a range from -4 to 4. The standard y = cos(x) has its midline at 0 so y = 0. This is also true for y = -4 cos(x). In your equation though, you have a vertical shift of +3 so this changes our midline. With an amplitude of 4, which gives us a range from -4 to 4(our y-values), the shift moves this up by 3 so that means we will have new y-values and a range of -1 to 7. Now we need to find the midline(the middle of our y-values) of our new range. We can find this by using the following formula
Midline = \frac{Y_1 + Y_2}{2} = \frac{-1+ 7}{2} = \frac{6}{2} = 3

Midline:
y = 3

Note, in the following equations that D = 3 = midline

y = A (Bx+C) + D
y = -4 (2x + n) + 3

Also, the picture that is attached is what your equation looks like when graphed.


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a = d + r + c

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6 0
3 years ago
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frutty [35]
The correct answer is B: f=4.5n
5 0
2 years ago
Read 2 more answers
FIRST QUESTION!!!!
aleksley [76]

Option B: 1088 is the next term in the geometric sequence.

Explanation:

The sequence is 17,68,272

We need to determine the next term.

To determine the next term, let us find the common ratio between the terms.

r=\frac{68}{17} =4

r=\frac{272}{68} =4

Thus, the common ratio is r=4

And the given sequence is a geometric sequence.

To determine the next term in a geometric sequence, we always multiply the common ratio to the current term.

Hence, the current term is 272 and the common ratio is 4.

Next term = Current term × Common ratio

                =272\times4

                =1088

Thus, the next term of the geometric sequence is 1088

Therefore, Option B is the correct answer.

6 0
3 years ago
According to the graph what is the value of the constant in the equation below?<br> Answer:0.5
worty [1.4K]
Constant=2 you can try this method with the other points

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