Mathematics, 19.10.2019 01:30, levicorey846

Over the past several years, the owner of a boutique on aspen avenue has observed a pattern in the amount of revenue for the store. the revenue reaches a maximum of about $ 42000 in april and a minimum of about $ 25000 in october. suppose the months are numbered 1 through 12, and write a function of the form f(x)=asin(b[x-c])+d that models the boutique's revenue during the year, where corresponds to the month.

Answers: 1

Show answers

Answers

answered: briannahernand2

The sinusoidal function that models the revenue, in thousands, is given by:

$f(x) = 8.5\sin{\left(\frac{\pi}{6}\right[x - 1])} + 33.5$

The standard form of the function is:

$f(x) = A\sin{(B[x - C])} + D$

In which:

The amplitude is

.The period is $\frac{2\pi}{B}$ .The horizontal shift is C.The vertical shift is D.

In this problem, first, we consider that the revenue is between $25,000 and $42000, thus, the amplitude is of $17,000, then:

2A = 17

$A = \frac{17}{2}$

A = 8.5

In a standard equation, this means that the function would assume values between -8.5 and 8.5. We want them to be between 25 and 42, thus, a vertical shift of D = 25 - (-8.5) = 33.5 is used.

We want a period of 12 months, which is 1 year, thus:

$\frac{2\pi}{B} = 12$

$12B = 2\pi$

$B = \frac{2\pi}{12}$

$B = \frac{\pi}{6}$

Using a graphing calculator, the maximum revenue is for x = 3 and the minumum revenue is for x = 9 . We want it for x = 4 and x = 10 , so a shift to the right of 1 unit, thus the horizontal shift is C = 1

Then, the equation is:

$f(x) = 8.5\sin{\left(\frac{\pi}{6}\right[x - 1])} + 33.5$

Which graph is sketched at the end of this answer.

A similar problem is given at link

answered: kad3n

$f(x)=8500\sin\left(\frac{\pi}{6}\left(x-1\right)\right)+33500$

Step-by-step explanation:

Given information:

Maximum revenue = 42000

Minimum revenue = $25000

Time period = 12 months

We need to write a function that models the boutique's revenue during the year, where corresponds to the month.

f(x)=Asin(B[x-C])+D .... (1)

where, A is amplitude, $\frac{2\pi}{B}$ is period, C is phase shift and D is midline.

$A=Amplitude =\frac{Maximum-Minimum}{2}\Rightarrow \frac{42000-25000}{2}=8500$

$D=midline =\frac{Maximum+Minimum}{2}\Rightarrow \frac{42000+25000}{2}=33500$

$Period=\frac{2\pi}{B}$

$12=\frac{2\pi}{B}\Rightarrow B=\frac{\pi}{6}$

Substitute the value of A, B and D in equation (1).

$f(x)=8500\sin\left(\frac{\pi}{6}\left(x-C\right)\right)+33500$ ..... (2)

In April, revenue of the store is $42000. So, the graph passes through the point (4,42000).

$42000=8500\sin\left(\frac{\pi}{6}\left(4-C\right)\right)+33500$

$42000-33500=8500\sin\left(\frac{\pi}{6}\left(4-C\right)\right)$

$8500=8500\sin\left(\frac{\pi}{6}\left(4-C\right)\right)$

Divide both sides by 8500.

$1=\sin\left(\frac{\pi}{6}\left(4-C\right)\right)$

$\sin \frac{\pi}{2}=\sin\left(\frac{\pi}{6}\left(4-C\right)\right)$

On comparing both sides we get

$\frac{\pi}{2}=\frac{\pi}{6}(4-C)$

3=4-C

C=4-3

C=1

Substitute the value of C in equation (2).

Therefore, the required function is $f(x)=8500\sin\left(\frac{\pi}{6}\left(x-1\right)\right)+33500$ .

Over the past several years, the owner of a boutique on aspen avenue has observed a pattern in the a

answered: Guest

answer: 180

step-by-step explanation:

12-2=10

20-2=18

10x18=180

answered: Guest

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 19:00, kayranicole1

The weekly revenue for a company is r = 3p^2 + 60p + 1060, where p is the price of the company's product. what price will result in a revenue of $1200.

Answers: 1

continue

Mathematics, 21.06.2019 22:20, jlo15

The coordinates of vortex a’ are (8,4) (-4,2) (4,-,4) the coordinates of vortex b’ are (6,6)(12,-,12)(12,12) the coordinates of vortex c’ are(-2,,12)(4,12)(12,-4)

Answers: 3

continue

Mathematics, 22.06.2019 00:30, breroyalee2584

Fixed rate mortgage offer: purchase price: $170,000 down payment ($34k): 20% term: 30 years interest rate: 4.25% property tax (yearly): $1,500 homeowner’s insurance (yearly): $1,000 use this example from a fixed-rate mortgage calculator to you answer the questions. keep the page open after you complete this question. according to the calculator, the monthly payment demarco and tanya should anticipate paying for principal and interest is $208. $877. $669. $1,200.

Answers: 1

continue

Mathematics, 22.06.2019 03:30, ggcampos

Arectangular lawn is 65 m long and 34 m wide. over time, people have walked along a diagonal as a shortcut and have created a straight path. what is the length of the path, to the nearest tenth of a meter? enter your answer as a deicmal in the box. m

Answers: 2

continue

Do you know the correct answer?

Over the past several years, the owner of a boutique on aspen avenue has observed a pattern in the a...