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]
3 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]3 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
When two systems in contact are not at the same temperature, _____ occurs.expansionheat flowfrictionevaporation
Murljashka [212]

Heat flow occurs when two systems in contact are not at the same temperature.

What is heat flow?

  • when two bodies of different temperatures are in contact, heat flow takes place.
  • Heat flows till the two bodies in contact achieve equilibrium.
  • To achieve equilibrium, heat flows from hotter bodies to colder bodies.
  • There is no heat flow after achieving the state of equilibrium because the amount of heat flow from one body to the other is the same.

For more information, please visit: brainly.com/question/11297584?referrer=searchResults

#SPJ4

8 0
1 year ago
If a speeding train hits the brakes and it takes the train 39 seconds to go from 54.8 m/s to 12 m/s what is the acceleration?
jekas [21]

Answer:

-1.09m/sec^2

Explanation:

Acceleration= (Vf-Vi)/Time

=12-54.8

= -42.8

= -42.8/39

=-1.09

-ve sign is due to recoil of train

as it suddenly hits brakes.

8 0
3 years ago
Read 2 more answers
Atoms in a solid are not stationary, but vibrate about their equilibrium positions. Typically, the frequency of vibration is abo
hoa [83]

To develop this problem it is necessary to use the equations of description of the simple harmonic movement in which the acceleration and angular velocity are expressed as a function of the Amplitude.

Our values are given as

f = 4.11 *10^{12} Hz

A = 1.23 * 10^{-11}m

The angular velocity of a body can be described as a function of frequency as

\omega = 2\pi f

\omega = 2\pi 4.11 *10^{12}

\omega=2.582*10^{13} rad/s

PART A) The expression for the maximum angular velocity is given by the amplitude so that

V = A\omega

V =( 1.23 * 10^{-11})(2.582*10^{13})

V =  = 317.586m/s

PART B) The maximum acceleration on your part would be given by the expression

a = A \omega^2

a =( 1.23 * 10^{-11})(2.582*10^{13})^2

a= 8.2*10^{15}m/s^2

4 0
3 years ago
75kg man climbs a mountain 1000m high in 3hrs and uses 4100 joulse/min. (a) calculate the power consumption in watt, (b) what is
mr Goodwill [35]

Answer:

Explanation:

a) Power consumption is 4100 J/min / 60 s/min = 68.3 W(atts)

work done raised the potential energy

b) 75(9.8)(1000) / (3(3600)) = 68.055555... 68.1 W

c) efficiency is 68.1 / 68.3 = 0.99593... or nearly 100%

Not a very likely scenario.

3 0
3 years ago
A projectile is launched
Flauer [41]

The vertical component of the velocity after the given time is -9.8 m/s while the horizontal component of the velocity is 16 m/s.

The given parameters;

  • initial horizontal velocity, vₓ = 16 m/s
  • initial vertical velocity, v_y =0
  • time interval 1 seconds

The components of the velocity can be horizontal or vertical velocity.

The vertical component of the velocity is affected by acceleration due to gravity while the horizontal component of the velocity is not affected by gravity.

The vertical component of the velocity is calculated as;

v_y = v_0_y -gt\\\\v_y = 0 - (1\times 9.8)\\\\v_y = -9.8 \ m/s

The horizontal component of the velocity is constant since it is not affected by gravity.

The horizontal component of the velocity = 16 m/s

Thus, the vertical component of the velocity after the given time is -9.8 m/s while the horizontal component of the velocity is 16 m/s.

Learn more here:brainly.com/question/20349275

4 0
3 years ago
Other questions:
  • If an object starting from rest and position d o = 0 attains a velocity of 20 m/s at d = 50 m, calculate the acceleration requir
    9·1 answer
  • 8. A car travels from Town A to Town B on one road at different speeds and stops at red lights. If you know the distance between
    14·1 answer
  • A light bulb radiates 110 nW of single-frequency sinusoidal electromagnetic waves uniformly in all directions. Calculate the ave
    5·1 answer
  • Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth a
    7·1 answer
  • An object has a mass of 20 grams and a volume of 5 cubic centimeters what is the object density
    12·1 answer
  • State two environmental problems caused by coal fired power stations
    8·1 answer
  • (1 point) Unknown resistor in voltage divider Suppose that a power supply is connected across two resistors R1 and R2 that are c
    8·1 answer
  • In your own words, describe how matter is identified.
    8·2 answers
  • What is the difference between a mineral, glass, and a rock?
    15·1 answer
  • A large tank is filled with water to a depth of 38 m. An opening is located 14 m
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!