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lara [203]
3 years ago
13

The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City, where m is the numb

er of months since January 2001. (m = 0 represents January 2001.)
A sine function is written to represent the data.

What is the amplitude, period, and vertical shift of this equation?

Drag a value into each box to correctly complete the statements.

Mathematics
1 answer:
Bezzdna [24]3 years ago
8 0

Answer:

Part A) The amplitude = 24

Part B) The period = 24

Part C) Vertical shift = 36

Step-by-step explanation:

The general equation of the sine function:

y = A sin (Bx) + C

Where A is the amplitude and B = 360°/Period  and C is the vertical shift

See the attached figure which represents the graph of m and f(m)

So,

<u>Part A:</u>

The function has minimum at 12 and maximum at 60

The difference is = 60 - 12 = 48

So, The amplitude = 48/2 = 24

<u>Part B:</u>

Period: The period of a periodic function is the interval on which the cycle of the graph that's repeated in both directions lies.

We can deduce that the function completes one cycle within 24 months

So, the period = 24

<u>Part C:</u>

Vertical shift is obtained at m = 0

So, f(m) = 36

36 = A sin (0) + C

C = 36 ⇒ Vertical shift

So, The amplitude = 24

The period = 24

Vertical shift = 36

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Answer:

Neither parallel nor perpendicular

Step-by-step explanation:

I'm assuming you meant line k is y = 3x -2. If not, this is wrong.

For this, you need to put both lines in point-slope form, or the form that line k is already in. This means you only need to convert line m.

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v = 2/6r + 18/6

v = 1/3r + 3

Now you can answer the question.

To be parallel, lines must have the same slope (but a different y-intercept). 3 and 1/3 are not the same, so the lines are not parallel.

To be perpendicular, one line must have the opposite reciprocal (fraction flipped and + goes to - or - to +) of the other. While 3 is the reciprocal of 1/3, they are both positive, so they are not perpendicular.

To be the same line, the equations must be absolutely identical, which they aren't.

This leaves the last option: neither.

Let me know if you need a more in-depth explanation of anything here! I'm happy to help!

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Step-by-step explanation:

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Step-by-step explanation:

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A spinner marked A, B, C is spun then a 6-sided die is rolled. What is the probability of getting a B and then a 6.
BigorU [14]

Given:

A spinner marked A, B, C is spun then a 6-sided die is rolled.

To find:

The probability of getting a B and then a 6.

Solution:

We know that,

\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}

Total possible values for a spinner are 3. So, the probability of getting B, we get

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The required probability is \dfrac{1}{18}.

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