1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sertanlavr [38]
3 years ago
7

The number of hours of daylight measured in one year in Ellenville can be modeled by a sinusoidal function. During 2006, (not a

leap year), the longest day occurred on June 21 with 15.7 hours of daylight. The shortest day of the year occurred on December 21 with 8.3 hours of daylight. Write a sinusoidal equation to model the hours of daylight in Ellenville.
Mathematics
1 answer:
Kamila [148]3 years ago
8 0

Answer:

f ( t ) = 3.7*sin ( 0.01736*t ) + 12

Step-by-step explanation:

Solution:-

- We are to model a sinusoidal function for the number of hours of daylight measured in one year in Ellenville.

- We will express a general form of a sinusoidal function [ f ( t ) ] as follows:

                                f ( t ) = A*sin ( w*t ) + c

Where,

                  A: The amplitude of the hours of daylight

                  w: The angular frequency of occurring event

                  c: The mean hours of daylight

                  t: The time taken from reference ( days )

- We are given that the longest day [ f ( t_m_a_x ) ] occurred on June 21st and the shortest day [ f ( t_m_i_n ) ] on December 21st.

- The mean hours of daylight ( c ) is the average of the maximum and minimum hours of daylight as follows:

                              c = \frac{f(t_m_a_x ) +f(t_m_i_n )  }{2} \\\\c = \frac{15.7 + 8.3}{2} = \frac{24}{2} \\\\c = 12

- The amplitude ( A ) of the sinusoidal function is given by the difference of either maximum or minimum value of the function from the mean value ( c ):

                              A = f ( t_m_a_x ) - c\\\\A = 15.7 - 12\\\\A = 3.7

- The frequency of occurrence ( w ) is defined by the periodicity of the function. In other words how frequently does two maximum hours of daylight occur or how frequently does two minimum hours of daylight occur.

- The time period ( T ) is the time taken between two successive maximum duration of daylight hours. We were given the longest day occurred on June 21st and the shortest day occurred on December 21st. The number of days between the longest and shortest day will correspond to half of the time period ( 0.5*T ):

                              0.5*T = 7 + 31 + 31 + 30 +31 +30 +21\\\\T = 2* [ 181 ] \\\\T = 362 days

- The angular frequency ( w ) is then defined as:

                              w = \frac{2\pi }{T} = \frac{2\pi }{362}  \\\\w = 0.01736

- We will now express the model for the duration of daylight each day as function of each day:

                              f ( t ) = 3.7*sin ( 0.01736*t ) + 12

               

You might be interested in
PLZ HELP ILL MARK U BRAINLIEST
Dafna11 [192]
30 b/c 60 x 1/2= 30

Answer= 30
7 0
3 years ago
Read 2 more answers
Which method listed below could not be used to prove that two triangles are congruent? a. Prove all three sets of corresponding
Maurinko [17]

Answer:

All corresponding sides and angles will be congruent

Step-by-step explanation:

7 0
3 years ago
Pleasee help me i will give you 40 points. in the boxes it says amount of money or amount of houses.
Montano1993 [528]

Answer: type it in quizlet

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Calculate x Give your answer correct to 1 d.p. Х 35° 15 cm<br> it is a trigonometry question.​
OlgaM077 [116]

Here we are finding x, given the angle and adjacent side. To find x we will use the function cos as cos = a/h.

So let's do cos(35°) = 15cm / x

cos(35°) = 0.8 (1 dp)

x = 15 cm / cos(35°)

x = 18.3 cm (1 dp)

6 0
2 years ago
PLEASE HELP ME ILL GIVE 5 STARS ASAP PLEASE
kicyunya [14]

16 wide

Step-by-step explanation:

because i do 8 x 2

8 0
2 years ago
Read 2 more answers
Other questions:
  • Which of the following are arranged in order from least to greatest?
    15·2 answers
  • A salesperson earns $320 per week plus 8% of her weekly sales. The expression representing her earnings is 320 + 0.08x. Which of
    13·1 answer
  • The histogram represents the number of gallons of gasoline that drivers purchase weekly. Which bar represents the number of gall
    5·1 answer
  • Can someone help me with this? please​
    7·1 answer
  • In western Kansas, the summer density of hailstorms is estimated at about 2.6 storms per 5 square miles. In most cases, a hailst
    8·1 answer
  • What is 7/9 ÷ 1/3 plz help ​
    11·2 answers
  • 8cm<br> 20cm<br> What is the volume of this cylinder?
    14·1 answer
  • In the expression (44 ÷ 4 + 10) - 20 , with which operation should we start?
    13·2 answers
  • Compare these ratios <br><br> 1.2:5 and 1:1<br><br> 2. 0:5 and 100:1<br><br> 3: 100:1 and 1:100
    9·1 answer
  • I need help on this to bring my grade up
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!