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
Lubov Fominskaja [6]
2 years ago
12

The number of daylight hours, D, in the city of Worcester, Massachusetts, where x is the number of days after January 1 (), may

be calculated by the function: What is the period of this function? N/A What is the amplitude of this function? 12 What is the horizontal shift? What is the phase shift? What is the vertical shift? How many hours of sunlight will there be on February 21st of any year?

Physics
1 answer:
mylen [45]2 years ago
7 0

Answer:

a. 365; b. 3; c. 78; d. 1.343 rad; e. 12; f. 10.66

Explanation:

Assume that the function is

D(x) = 3 \sin \left (\dfrac{2\pi}{365}(x - 78) \right ) + 12

The general formula for a sinusoidal function is

      y = A sin(B(x - C))+ D

   |A| = amplitude

     B = frequency

2π/B = period, P

     C = horizontal shift (phase shift)

     D = vertical shift

By comparing the two formulas, we find

|A| = 3

 B = 2π/365

 C = 78

 D = 12

a. Period

P = 2π/B = 2π/(2π/365) = 2π × 365/2π = 365

The period is 365.

b. Amplitude

|A| = 3

The amplitude is 3.  

c. Horizontal shift

C= 78

The horizontal shift is 78.

d. Phase shift  (φ)

Ths phase shift is the horizontal shift expressed in radians.

φ = C × 2π/365 = 78 × 2π/365 ≈ 1.343

The phase shift is 1.343 rad.

e. Vertical shift

D = 12

The vertical shift is 12.

f. Hours of sunlight on Feb 21

Feb 21 is the 52nd day of the year, so x = 51 (the number of days after Jan 1),

\begin{array}{rcl}D(x) &=& 3 \sin \left (\dfrac{2\pi}{365}(x - 78) \right ) + 12\\\\&=& 3 \sin (0.01721(51 - 78) ) + 12\\&=& 3\sin(-0.4648) + 12\\&=& 3(-0.4482) + 12\\\&=& -1.345 + 12\\& = & \textbf{10.66 h}\\\end{array}

There will be 10.66 h of sunlight on Feb 21 of any given year.

The figure below shows the graph of the function from 0 ≤ x ≤ 365.

You might be interested in
Which method is used to separate parts of a solution when the entire solution can pass through a filter?
creativ13 [48]

Answer:

Straining method

Explanation:

Straining method is the method that can be used to separate parts of a liquid mixture when the entire mixture can pass through a filter.

3 0
3 years ago
How many significant figures does 1700000000 have ?
MaRussiya [10]

Answer:

2 sig

Explanation:

1 and 7

3 0
3 years ago
Read 2 more answers
At what temperature will water begin to boil and turn to steam?
butalik [34]

Answer:

100 degrees Celsius

Explanation:

Water starts to boil at 100 degrees celcius or 212 degrees fahrenheit.

5 0
3 years ago
Read 2 more answers
A 1.0-cm-diameter pipe widens to 2.0, then narrows to 0.5. Liquid flows through the first segment at a speed of 4.0. What is the
uysha [10]

Answer:

3.14 ×  10⁻⁴  m³  /s

Explanation:

The flow rate (Q) of a fluid is passing through different cross-sections remains of pipe always remains the same.

Q = Area x velocity

Given:

Diameters of 3 sections of the pipe are given as  

d1  =  1.0  cm,  d2  =  2.0  cm  and  d3  =  0.5  cm.

Speed in the first segment of the pipe is  

v1  =  4  m/s.

From the equation of continuity the flow rate through different cross-sections remains the same.

Flow  rate  =  Q  =  A1  v1  =  A2  v2  =  A3  v3.

Q = A1v1

   =π/4  d²1  v1  =  π/4  * 0.01² ×4.0 m³/s  =  3.14 ×  10⁻⁴  m³  /s

3 0
2 years ago
The sun continuously radiates energy into space in all directions. Some of the sun's energy is intercepted by the Earth. The ave
8_murik_8 [283]

B. The Earth radiates an amount of energy into space equal to the amount it receives.

Part of the solar energy is reflected by the Earth into space, this is known as albedo. The other part of the energy radiated by the Earth in the form of infrared radiation, is absorbed by the greenhouse gases, which cause most of this infrared radiation to be emitted into space. Therefore, the net flow of energy is zero.

7 0
3 years ago
Other questions:
  • Tina and her puppy are tugging on a rope, each pulling on opposite ends.
    13·2 answers
  • 16. A block is sitting on a ramp tilted from horizontal. The block is just about to slide. T he angle of the ramp relative to ho
    15·1 answer
  • A tennis ball is dropped from 1.15 m above the ground. It rebounds to a height of 0.993 m.
    14·1 answer
  • What is true about empirical and molecular formulas?
    7·1 answer
  • A skier weighing 86.2 kg starts from rest and slides down a 32.0-m frictionless slope that is inclined at an angle of 15.0° with
    14·1 answer
  • One safety precaution that you would take when carrying out experiments using resistance wires
    7·1 answer
  • If the gravitational field strength at the top of Mount Everest is 9.772 N/kg, approximately how tall (in feet) is
    8·1 answer
  • 24. A car is travelling along an expressway at 90 km/h. The driver spots a stalled car and some traffic congestion on the road a
    8·1 answer
  • What is usually true about the relationship between the speed mechanical waves travel and the temperature of the medium?
    11·1 answer
  • Rafael is driving his car at 26 m/s. What is the shortest distance in which he can brake and stop if the coefficient of static f
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!