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

The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City where m is the number of months since January 2001 m class=

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Matheng

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,

Part A:

The function has minimum at 12 and maximum at 60

The difference is = 60 - 12 = 48

So, The amplitude = 48/2 = 24

Part B:

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

And B = 360/24 = 15

Part C:

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

The equation of is ⇒ f(m) = -24 sin (15m) + 36

Ver imagen Matheng

It can be deduced that the amplitude, period, and vertical shift of this equation will be 24, 24, and 36.

How to solve the equation

It should be noted that the general equation of the sine function will be:

y = A sin (Bx) + C

Where,

A = amplitude

B = 360°/Period

C = vertical shift

The function has a minimum of 12 and a maximum of 60. Therefore, the difference will be:

= 60 - 12 = 48

The amplitude will be:

= 48/2 = 24

Also, the function completes one cycle within 24 months. Hence, the period is 24. The vertical shift is obtained at m = 0. Therefore, f(m) = 36. Then 36 = A sin (0) + C. C = 36.

In conclusion, the vertical shift is 24.

Learn more about equations on:

https://brainly.com/question/13763238

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