Answer: 5
Step-by-step explanation: You can write out any division problem this way. 5 divided by 14 is the same as 5/14, for example.
In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The longest and the shortes 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 trigonamic function to model the hours of daylight hours on certain days of the year in New York City
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]
3y + 7 =28 how do I solve
Answer:
y= 7
Step-by-step explanation:
3y+7=28
subtract 7 from both sides
3y=21
divide each side by 3
y/3=21/3
y=7
Answer:
y=7
Step-by-step explanation:
3y+7=28
Move the constant to the right
3y=28-7
Calculate
3y=21
divide both sides to get y=7
Can you make a triangle?
8, 2,8
Answer:
Step-by-step explanation:
yep
Always true, sometimes true, never true.
1) the centroid of a triangle is a point where the medians intersect.
2) a line of reflection is also a line of symmetry
3) a figure with rational symmetry can be rotated x degrees about a one of its vertices and the resulting image lines up perfectly with the original image.
4) the centroid of a triangle is located inside the triangle
5) all points on the angle bisector of
6) if there exists a transformation that takes triangle QRS to triangle XYZ then the triangles are congruent
7) the inscribed circle of a triangle intersects all three of the triangles vertices.
_______________________
TRUE OR FALSE:
8) the base is the length of the altitude
9) a median of a triangle cuts the original triangle into two smaller triangles, each of whose area is half of the original triangle
10) the circumscribed circle lies inside the triangle and touches each of the sides
11) the incenter of a triangle is a point where the angle bisectors intersect
I really need help on these ASAP, thank you!!
Answer: the answers for numbers 1,2 and 4 are all true :)
1: True
2: True
4: True
In the evenings, Jake and his friends would cookout and make s'mores for dessert. the ratio of chocolate squares to Graham crackers that they used is shown in the graph below. (repost)
Answer:
(2,3) also love your profile pic :)
( 2,3 ) I hope this helped you!~ have a great day~
~Keiji❤
Treat yourself well, remember to eat. You are valid. Love you!~
1) Mike invests $2,316 in a retirement
account with a fixed annual interest rate of
3% compounded continuously. What will
the account balance be after 17 years?
Answer:
$3828 approx
Step-by-step explanation:
Given data
Principal=$2316
Rate= 3%
Time= 17 years
The compound interest formula is
A=P(1+r)^t
substitute
A=2316(1+0.03)^17
A=2316(1.03)^17
A=2316*1.652847
A=$3827.99
Hence the account balance after 17 years is $3828 approx
Ben has 43 coins belonging to dimes or quarters. If he has
$8.80, how many dimes does he have?
dimes
Answer:
7 dollars and 50 cents of quarters. That right there equals 30 coins
He has a dollar and thirty cents in dimes and that equals 13 coins
Together that is $8.80. with 43 coins.
Step-by-step explanation:
A triangular wall decoration on Kelsey's wall has vertices M4-1), (3, -4), and R(1, -2). The triangle is translated 5 units left and 4 units up. What are the coordinates of N' after the translation
N(-1,0)
N(-2,0)
N(0,0)
N(-2,3)
Answer:
N’ is (-2,0)
Step-by-step explanation:
Here, we want to find coordinates after translation
mathematically, a translation of 5 units left means we are to subtract 5 from the coordinate of the x point
Also, 4 units up means we are to add the value 4 to the value of the y coordinate
Thus, for N, we have the image after translation as:
(3-5, 4 + (-4))
= (-2, 0)
Answer:
2,0
Step-by-step explanation:
Thus is because 2,0 = 180 + 90 degrees into the ferhinite
Cameron surveys every tenth student who walks into school to determine the favorite type of movie of students in his school. what is the population,sample,random and representative.
A swimmming pool with cylindrical base has a diameter of 21 feet and a depth of 5 feet. Find the volume of the pool
Answer: V = 1731.8Ft³
Step-by-step explanation:
v = πr²h
Radius is half of the diameter ⇒ 21/2 = 10.5
V = π(10.5)²(5)
V=π(110.5)(5)
V = π(551.25)
V = 1731.8Ft³
The solution is : the volume of the pool is V = 1731.8Ft³.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
Here, we have,
we know that,
the volume of the cylinder is:
v = πr²h
Radius is half of the diameter
⇒ 21/2
= 10.5
so, we get,
V = π(10.5)²(5)
V=π(110.5)(5)
V = π(551.25)
V = 1731.8Ft³
Hence, The solution is : the volume of the pool is V = 1731.8Ft³.
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wich is the correct?
Answer:
c
Step-by-step explanation:
A circular plate has circumference 32 inches. What is the area of this plate? Use 3.14 for pi. The area of this plate is about nothing square inches.
Answer: The area of the plate is 81.67 in^2
Step-by-step explanation:
If we have a circle of radius R, the area of this circle can be computed as:
A = pi*R^2
where pi = 3.14
And the circumference is:
C = 2*pi*R
and we know that this is equal to 32 in, then:
32in = 2*pi*R
Now we can isolate R, and we get:
32in/(2*pi) = R
32in/(2*3.14) = R = 5.1 in
Then the area of the plate is:
A = 3.14*(5.1in)^2 = 81.67 in^2
Find the value of the variables in the table.
x
n
4
6
10
12
y
1
9
m
21
25
Answer:
n=0 , m= 13 A
Step-by-step explanation:
simplify 32q2r2/4q3r
Answer: 16q5r2
Step-by-step explanation:
Which is greater
30% of 30 or 28% of 32 ?
You must show your working.
Answer:
30% of 30 = 9
28% of 32 = 8.96
Step-by-step explanation:
0.30 x 30 = 9
0.28 x 32 = 8.96
Answer:
30% of 30 > 28% of 32
Step-by-step explanation:
30% of 30:
0.3 x 30 = 9
28% of 32:
0.28 x 32 = 8.96
9 > 8.96
What percent of 15y is 75?
Answer:
20%
Step-by-step explanation:
because 15/75×100 =1/5×100=20%
Answer:
Step-by-step explanation:
x% of 15y = 75
x% =75/(15y) = 5/y
x = 500/y
State the slope and y-intercept of the graph of y = 1/5x – 7.
Answer:
The slope is 1/5 and the y-intercept is -7
Step-by-step explanation:
In point-slope form (y = mx + b), m is the slope and b is the y-intercept.
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 10% are pennies and 36% are dimes. There are 4 more nickels than pennies. How much money does the bag contain?
Find the missing angle of the parallelogram.
V
52°
?
60
Answer:
3120
Step-by-step explanation:
52x60=3120
Answer:68
Step-by-step explanation:
Do 52 plus 60 then subtract it by 180 and you get 68
i need help with this
Answer:
the second one
Step-by-step explanation:
When subtracting a negative, the negative turns to a positive, so in this case, -14- -8 would be the same as -14 + 8
20 POINTS!!!!!! HELP PLEASE!!!!!!!
Answer:
umm???????????? let me try doin it
A circle and a regular pentagon can intersect in
A. 5 triangles
B. A circle
C. A square
D. 5 points
Answer:
I think it is option D,
hope it helps
For f(x) = x3 – x2, which gives an output of 48?
O f(-8)
O fl-4)
O f(4)
O f(8)
Answer:
f(4)
Step-by-step explanation:
The output is the value of f(x) for a given value of x ( the input )
Substitute the given values of x into f(x) to determine the output, that is
f(- 8) = (- 8)³ - (- 8)² = - 512 - 64 = - 576 ≠ 48
f(- 4) = (- 4)³ - (- 4)² = - 64 - 16 = - 80 ≠ 48
f(4) = 4³ - 4² = 64 - 16 = 48
Thus f(4) gives an output of 48
Which of the following is a solution to the equation x^3=1/49? x=7^−2/3 x = 7^-3/2 X=7 2/3 This equation has no solution x=7 3/2
Step-by-step explanation:
x³=1/49
x= third root of 1/third root of 49
x=1/square root of 7
2(3x-5)+2y=12 find the slope intercept form
Answer: y=-3x+11
Step-by-step explanation:
According to a survey of workers, 5/50
of them walk to work, 4/50
bike, 20/50
carpool, and 9/50
alone. What percent of workers walk or bike to work?
Answer:
45 percent like to walk or bike
Step-by-step explanation:
Which has opposite sides parallel and congruent?
9514 1404 393
Answer:
(d) parallelogram, rectangle, rhombus, and square
Step-by-step explanation:
Any form of parallelogram has opposite sides parallel and congruent. A trapezoid does not match that description.
A rectangle, rhombus, or square will be a parallelogram.
Alanna went for a run. She ran d kilometers at an average speed of v kilometers per hour, and then walked to cool down for 0.25 hours. The total duration of the trip was t hours.
Write an equation that relates d, v, and t.
Answer:
t=d/v +0.25
Step-by-step explanation:
If the speed is v, distance is d and time is t then the equation that shows the total time taken by Alanna in run is t=d/v+0.25.
What is equation?Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.
How to form equation?We have been given distance d , speed v and time t that Alanna takes and we have to form an equation that shows the total time taken by Alanna in run. We know that,
Speed=Distance/time
We have to just put the values given to us:
v=d/t
t=d/v
But she cools down for 0.25 hours so the above equation will increase by 0.25.
t=d/v+0.25.
Hence the equation that shows the total time taken by Alanna in run is t=d/v+0.25.
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Solve the following equation 2x
2
−3=0
1
Answer:
true
Step-by-step explanation:
Which of the following inequalities represent the number line below?
I NEED HELPPPPPPPPPPPPP