Question:
In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The longest and the shortest days of the year vary by 2 hours 53 minutes from the equinox. In this year, the equinox falls on March 21. In this task, you'll use a trigonometric function to model the hours of daylight hours on certain days of the year in New York City.
- Find amplitude and the period of the function
- Create a trigonometric function that describes the hours of sunlight for each day of the year
- Then use the function you built to find how fewer daylight hours February 10 will have then March 21
Answer:
(a)
[tex]A = 2.883[/tex] --- Amplitude
[tex]T = 365[/tex] ---- Period
(b) Trigonometry function
[tex]f(x) = 12.133 + 2.883sin(\frac{2\pi}{365}[x - 80])[/tex]
(c) [tex]Hours= 1.794[/tex]
Step-by-step explanation:
Given
[tex]Average\ Sunlight = 12hr\ 8 min[/tex]
[tex]Variance = 2hr\ 53min[/tex]
Solving (a): Amplitude (P) and Period (T)
The amplitude is the amount of time the longest and the shortest day vary.
So
[tex]A = 2\ hr\ 53\ min[/tex]
Convert to hours
[tex]A = 2\ + \frac{53}{60}[/tex]
[tex]A = 2+0.883[/tex]
[tex]A = 2.883[/tex]
The period (T) is the duration i.e 1 year
[tex]T = 1\ year[/tex]
Assume no leap year
[tex]T = 365[/tex]
Solving (b): Trigonometry function
The function follows a sinusoidal pattern and the general form is:
[tex]f(x) = \mu+ Asin(\frac{2\pi}{T}(x -n))[/tex]
Where
[tex]\mu = Average\ Value[/tex]
[tex]\mu = 12\ hr 8\ min[/tex]
Convert to hours
[tex]\mu = 12 + \frac{8}{60}[/tex]
[tex]\mu = 12 + 0.133[/tex]
[tex]\mu = 12.133[/tex]
[tex]A = 2.883[/tex] --- Amplitude
[tex]T = 365[/tex] ---- Period
[tex]n = Equinox[/tex]
[tex]n = March\ 21[/tex]
[tex]March\ 21st = 80th\ day[/tex]
So:
[tex]n= 80[/tex]
The function becomes:
[tex]f(x) = \mu+ Asin(\frac{2\pi}{T}(x -n))[/tex]
[tex]f(x) = 12.133 + 2.883sin(\frac{2\pi}{365}[x - 80])[/tex]
Solving (c): Fewer daylight hours will Feb. 10 have.
[tex]Feb\ 10 = 41st\ day[/tex]
So:
[tex]f(x) = 12.133 + 2.883sin(\frac{2\pi}{365}[x - 80])[/tex]
[tex]f(41) = 12.133 + 2.883sin(\frac{2\pi}{365}[41 - 80])[/tex]
[tex]f(41) = 12.133 + 2.883sin(\frac{2\pi}{365}[-39])[/tex]
[tex]2\pi = 360^\circ[/tex]
So:
[tex]f(41) = 12.133 + 2.883sin(\frac{360}{365}[-39])[/tex]
[tex]f(41) = 12.133 + 2.883sin(-38.466)[/tex]
[tex]f(41) = 12.133 - 2.883*0.6221[/tex]
[tex]f(41) = 10.339[/tex]
The fewer daylight hours is the calculated as:
[tex]Hours= Average - f(41)[/tex]
[tex]Hours= \mu - f(41)[/tex]
[tex]Hours= 12.133 - 10.339[/tex]
[tex]Hours= 1.794[/tex]
which translation below translates the figure according to the rule (x,y) -> (x, y-3)
What is the equation of the following line? Be sure to scroll down first to see
all answer options,
(0,0) (7,2)
Given the function f(x)= -3(x)^2 , find the value of f(4).
Step-by-step explanation:
f(x) = -3x²
f(4) = -3(4²)
= -48
15 POINTS 15 POINTS !5 POINTS
Answer:
I AM SO SORRY but I need that point soo plsss Im sooo sorry
Answer:
The answer is (x+2)²+(y-3)²=29.
Hope it helps uh
expression equivalent to -4(7 + 2m)
Answer:
Use the distributive property -28-8m
Step-by-step explanation:
-4(7+2m)
-28-8m
you don't have to do all of them
Answer: lol your using canvas
1. 63
2. D
3. B
4. A
Sorry for the bland explinations havin a bad day.
Step-by-step explanation:
1. The way we solve this is by adding the degrees 72 and 45. then we subtract it by 180. this is because in all triangles the angles always add up to 180 degrees.
2. Like question one what set of angles measures to 180 degrees.
3. The sides of a triangle should define the angle measurements. you can also see if its a triangle if the numbers are continues like 3,4,5 or in this case 4,5,6
4. like in questions 1 and 2 the angles of a triangle has to equal 180 degrees so 60 times 3 is 180 so each angle would have to be 60 degrees.
Bob, a lawyer, used to charge his clients $220 per hour Recently, he reconsidered his rates and ultimately decided to charge 30% more. Now how much does Bob charge per hour?
Answer:
The Poisson probability distribution gives the probability of a number of events occurring in a fixed interval of time or space if these events happen with a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on the average, there are five words spelled incorrectly in 100 pages. The interval is the 100 pages.
Answer:
$286 per hour
Step-by-step explanation:
first we have to find out what 30% of $220 is
we do this by multiplying $220 by 0.3
We get $66
then we add the markup value to the initial value
$66 + $220= $286
bob's a scu.mbag
hope this helps chu babe <3
simplify (n+1)!/(n+3)!
Answer:
Step-by-step explanation:
[tex]\frac{(n + 1)!}{(n+3)!}=\frac{(n + 1)!}{(n+3)*(n +2)*(n+1)!}\\\\= \frac{1}{(n+3)(n+2)}\\[/tex]
Solve for y. 1) 5x + 4= - 4y
Answer:
y = -5x/4 - 1
Step-by-step explanation:
A square has one
side that measures
6 inches. What is
the perimeter of
the square?
Answer:
24 inches
Step-by-step explanation:
a square has 4 equal sides. if one side is 6, the rest of the sides are also six. perimeter is all the sides added. so 6+6+6+6, or 6*4, equals 24 inches as perimeter.
Figure with four equal sides and four right (90°) angles. If a square has one side that measures 6 inches then perimeter of square is 24 inches.
What is Square?a figure with four equal sides and four right (90°) angles.
We know that in a square all the sides will measure equal length. So the formula for perimeter of square is P=4a or p equal to four times of a.
Where p is the perimeter and a is the measurement of a side.
It is given that measure of one side of square is 6 inches.
So value of a is 6.
Substitue the value of a in the perimeter formula.
Perimeter=4×6
When four is multiplied with six we get twenty four.
=24 inches.
Hence perimeter of the square with one side measure 6 inches is 24 inches.
To learn more on Perimeter of square click:
https://brainly.com/question/11495285
#SPJ2
Find the area of the shape.
Answer:
[tex] area \: of \: trapezium = \: \frac{1}{2} (a + b) \times h[/tex]
Therefore, 1/2 (9 +17)*8
Therefore, 1/2(26)*8
Therefore, 13*8
Therefore, 104
Your answer is 104ft²
In a recent election, there were six candidates and 4700 total votes. The circle graph below summarizes the votes by candidate.
The central angle for the Bowerman slice is 36º. What percentage of the votes did Bowerman get? Do not round.
The circle is 360 degrees so,
360 degrees --> 4700 votes
36 degrees ---> x
4700*36 = 360*x
169,200 = 360*x
x= 169,200/360
x= 470
[tex] \frac{470}{4700} = 0.1 = 10\%[/tex]
Find the value of each variable. Write your answers in simplest radical form.
A rock is dropped down from the top of a 500-foot cliff. After 1 second, the rock is traveling 32 feet per second. After 5 seconds, the rock is traveling 160 feet per second.
a. Assume that the relationship between time, t, and speed, s, is linear, and write an equation describing this relationship. Use ordered pairs of the form (time, speed).
b. Use this equation to determine the speed of the rock 7 seconds after it is dropped.
Answer:
A) s=32t
B) 224 ft/s
Step-by-step explanation:
A)
In the form (time, speed), the question gives us the following data: (1,32) and (5,160). Since we are told that the relationship between time, t, and speed, s, is linear, we know the equation will fit the formula y=mx+c, where m is slope c is the y-intercept and y and x are the co-ordinate values. Plug in (1,32) and (5,160) to find the formula:
y=mx+c
s=mt+c
32=1m+c
c=32-m
160=5m+C
160=5m+32-m
128=4m
m=32
c=32-m
=32-32=0
So our equation is s=32t
B)
s=32t
s=32(7)=224 ft/s
6) All chords are diameters.
True
or
False
2(a-3)
Expand please
Answer:
2a-6
Step-by-step explanation:
2(a-3)
2*a-(2*3)
2a-6
Please help!
Passes through (- 1, - 8) and perpendicular to x + 3y = - 6
What is the equation?
Answer:
y = 3x - 5
Step-by-step explanation:
1) First, place the given equation in slope-intercept form, represented by the formula [tex]y = mx +b[/tex], to find the slope. Whatever [tex]m[/tex] or the coefficient of x-term is will be the slope. Isolate y in the equation:
[tex]x + 3y = -6\\3y = -x -6\\y = -\frac{1}{3}x-2[/tex]
So, the slope of that line is [tex]-\frac{1}{3}[/tex]. Lines that are perpendicular have slopes that are opposite reciprocals, thus the slope of the new line will be 3.
2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to find the equation of the new line. Substitute real values for the [tex]m[/tex], [tex]x_1[/tex] and [tex]y_1[/tex] in the equation.
Since [tex]m[/tex] represents the slope, substitute [tex]-\frac{1}{3}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represents the x and y values of one point the line passes through, substitute the x and y values of (-1,-8) into the formula as well. Then, isolate the y in the resulting equation to put the equation in slope-intercept form and find an answer:
[tex]y-(-8) = 3 (x-(-1))\\y + 8 = 3(x+1)\\y + 8=3x + 3\\y = 3x -5[/tex]
2. How would you say 406,762?
Four hundred six thousand, seven hundred sixty-two
Four hundred sixty thousand, seven hundred sixty-two
Forty-six thousand, seven hundred sixty-two
Four thousand, six hundred seventy-two
Answer:
A- Four hundred six thousand, seven hundred sixty-two
Hope this helps!
Answer:
A. Four hundred six thousand, seven hundred sixty-two
Step-by-step explanation:
Sound out the number before the comma first:
You would read it as four hundred six, not four hundred sixty (That would mean 460 and not 406.)
Sound out the number after the comma next:
You would read that as seven hundred sixty-two.
So combine them to say:
four hundred six thousand, seven hundred sixty-two. Choose A
There are twenty-two more chickens than cows. The number of cows and chickens combined is 98. How many are chickens? There are 60 chickens. There are 38 chickens. There are 38 cows.
Answer:
Step-by-step explanation:
chicken=x+22
cow=x
chicken+cow=98
x+22+x=98
2x+22=98
2x=76
x=38
chicken =x+22=38+22=60
There are 60 chickens
Answer:
chicken=x+22
cow=x
chicken+cow=98
x+22+x=98
2x+22=98
2x=76
x=38
Step-by-step explanation:
Complete the proof that △FGH isn't similar to △JIH
Answer:
step 2: (FH)/(JH)=5/6
step 3: (GH)/(IH)=(FH)/(JH)
Step-by-step explanation:
this is right
The △FGH isn't similar to △JIH.
What is a Triangle?A triangle is a polygon with three sides, angles and vertices.
The triangle is classified into various types on the basis of the angle and on the basis of the equality of the length of the sides, as obtuse , acute and right angled triangle and scalene, isosceles and equilateral triangle.
Two triangles are said to be similar when the sides of both the triangle are in proportion.
Two triangles FGH and IJH are given and have to be proved that they are not similar
The step 1 is GH/IH = 10/10 = 1 ( By substituting given values)
The step 2 is GF/IJ = 8 /8 = 1 ( By substituting given values)
The step 3 is FH/HJ = 1
FH = HJ ( ( By substituting values from 1 and 2)
This is not true, FH = 5 and HJ = 6
As the corresponding sides of the triangles are not equal so they are not similar.
To know more about Triangle
https://brainly.com/question/2773823
#SPJ5
Find the equation of the line
perpendicular to 3x + 5y = 15 with an
x-intercept 6.
Maya is 14 years old. Her brother Jorge is 3 years more than half her age. Which of the following is the correct expression for Jorge's age?
(7 x 2) + 3
7 − (2 + 3)
(14 ÷ 2) + 3
14 ÷ (7 − 3)
Answer:
7 x 2 + 3 = 17
7 - 2 + 3= 8
14 ÷ 2 + 3 = 10
14 ÷ 7 - 3 - 1
Step-by-step explanation:
what is
Evaluate the expression 120n+160,500 when n=32
Answer:
164,340
Step-by-step explanation:
Plug in 32 as n into the expression
120n + 160,500
120(32) + 160,500
3,840 + 160,500
= 164,340
So, the expression is equivalent to 164,340
PLEASE HELP IVE BEEN STUCK ON THIS ONE FOR QUITE A WHILE.
Someone help it's due today!!
Answer:
can you like zoom the question because i cannot find it.
need help with surface area
Which of the following equations shows how to correctly calculate the volume, V, in cubic centimeters, of the prism below?
A.V = (9)(12) × 18
B.V = × 9
C.V = × 12
D.V = × 18
Answer:
A
Step-by-step explanation:
WILL GIVE BRAINLIEST
Answer:
A
Step-by-step explanation:
JK is longer than JL and isn't 9 units long
Identify the type of triangle by looking at the sum of the angle
measures.
145 + 20 + 15 = 180°
Answer:
Scalene triangle because it's all sides are unequal
Answer:
Scalene triangle
Step-by-step explanation:
1.02 sinusoidal graphs
Answer:
The answer is 20
Step-by-step explanation:
The wave starts at the origin and doesn't complete the cycle until unit 20.
Answer:
[tex]\displaystyle 20[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{y = cos\:(\frac{\pi}{10}x - \frac{\pi}{2})} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{5} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{\pi}{10}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{20} \hookrightarrow \frac{2}{\frac{\pi}{10}}\pi \\ Amplitude \hookrightarrow 1[/tex]
OR
[tex]\displaystyle \boxed{y = sin\:\frac{\pi}{10}x} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{20} \hookrightarrow \frac{2}{\frac{\pi}{10}}\pi \\ Amplitude \hookrightarrow 1[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = cos\:\frac{\pi}{10}x,[/tex] in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle 5\:units[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle 5\:units,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{5} = \frac{\frac{\pi}{2}}{\frac{\pi}{10}}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = cos\:(\frac{\pi}{10}x - \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-15, 1],[/tex]from there to [tex]\displaystyle [5, 1],[/tex]they are obviously [tex]\displaystyle 20\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 20.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.