Answers
The cosine model is y = - 7 + 10 · cos (π · x/30 - π).
The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).
How to find sinusoidal functions from a given graph
Sinusoidal functions are periodic trascendent expressions which involves trigonometric functions. There are two kinds of sinusoidal functions:
[tex]y = A \cdot \cos (B\cdot x + C) + D[/tex] (1)
[tex]y = A\cdot \sin (B\cdot x + C) + D[/tex] (2)
Where:
A - AmplitudeB - Angular frecuencyC - Angular phaseD - MidpointFirst, we find the amplitude and the midpoint:
A = [3 - (- 17)]/2
A = 10
D = [3 + (- 17)]/2
D = - 7
Now we find the angular phase and the angular frequency for each model:
Cosine model (x, y) = (0, - 17), (x, y) = (30, 3)
- 17 = 10 · cos C - 7 (3)
3 = 10 · cos (30 · B + C) - 7 (4)
By (3):
- 10 = 10 · cos C
cos C = - 1
C = acos(- 1)
C = - π
And by (4):
3 = 10 · cos (30 · B - π) - 7
10 = 10 · cos (30 · B - π)
cos (30 · B - π) = 1
30 · B - π = acos 1
30 · B - π = 0
30 · B = π
B = π/30
The cosine model is y = - 7 + 10 · cos (π · x/30 - π).
Sine model
Obtain the sine model by using trigonometric expressions:
cos θ = sin (θ + π/2) (5)
By (5):
y = - 7 + 10 · sin (π · x/30 - π + π/2)
y = - 7 + 10 · sin (π · x/30 - π/2)
The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).
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Related Questions
a square room has a area of 49 square feet the height of the room is 4 feet. what is the area of one wall
Answers
Answer:
28 ft^2
Step-by-step explanation:
The room is in the shape of a square. That means the base of the room (width and length) will have the same dimensions.
Length x Width = 49 ft^2
Length = Width
Length^2 = 49 ft^2
Length = 7 feet
Width is also 7 feet
The height of the room is 4 feet, plenty for non-humans. One wall area would be (7 ft)*(4 ft) = 28 ft^2
the milligrams of aspirin in a persons body is given by the equation a=500x(3/4)t, where t is the number of hours since the patient took the medicine.
A. how much aspirin will bein the patients body after two hours?
B. in the equation, about what does the 500 tell us the situation
C. in the equation, what does the 3/4 tells us about the situation.
Answers
The amount of aspirin that would be in the patient's body is; 281.25.
What is the amount of aspirin in the patient's body after 2 hours?A) The amount of aspirin in the patient's body after 2 hours can be evaluated as follows;
a = 500×(3/4)² = 4500/16 = 281.25.
B) The number 500 as used in the equation represents the amount of aspirin in the patient's body prior to taking the medicine, at time, t= 0.
C) The fraction 3/4 as used in the task content is the factor of change in aspirin content in the patient's body.
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Solve each triangle – find any missing side and angle measures. Round answers to the nearest tenth.
Answers
Step-by-step explanation:
Match each formula on the left with an equivalent formula on the right.
W = X-Y
W = X - //
W = 4 - Y
W = XY
Y
X =W₁ + ½
X = Z(W + Y)
X = WZ+Y
X = // +Y
Answers
The formulas and the equivalent formulas are
W = X - Y X = W +Y
W = X/Z - Y X = Z(W + Y)
W = (X - Y)/Z X = WZ+Y
W = XY X =W/Y
How to match the formulas?To do this, we simply make X the subject of the formula in expressions on the left.
So, we have:
W = X - Y
This gives
X = W + Y
W = X/Z - Y
This gives
X/Z = W + Y
X = Z(W + Y)
W = (X - Y)/Z
This gives
X - Y = WZ
X = WZ + Y
W = XY
This gives
X =W/Y
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Complete question
Match each formula on the left with an equivalent formula on the right.
W = X - Y X =W/Y
W = X/Z - Y X = Z(W + Y)
W = (X - Y)/Z X = WZ+Y
W = XY X = W +Y
In a group of 60 students, 18 students take Algebra I, 20 students take
Algebra II, and 10 students take both subjects. How many students don't take
either of these subjects?
A. 12
B. 32
C. 34
D. 36
Answers
Answer:
32...................
The following figure shows a square-based pyramid.
5
6
Which expression represents the surface area of the pyramid?
Choose 1 answer:
Answers
The expression that shows the surface area of the pyramid is (2 * 2) + 4(0.5 * 2 * 3)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The surface area of pyramid = sum of individual area of the surface
Surface area = (2 * 2) + 4(0.5 * 2 * 3)
The expression that shows the surface area of the pyramid is (2 * 2) + 4(0.5 * 2 * 3)
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A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles
Answers
A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles.
----------------------
The car is 120 miles away when the motorcycle starts.
The bike gains on the car at 30 mph (70-40).
It takes 4 hours for the bike to close the gap (120/30).
In 4 hours, the bike and the car are 280 miles from the starting point.
---------
4*70 = 280
7*40 = 280
Since Distance = Speed x Time, and in this case, the distances are equal, we, therefore, have: 70T = 40(T + 3)
70T = 40T + 120
30T = 120
T=4, which makes the distance that both vehicles traveled, highlight_green280miles, calculated as (70 * 4), or (40 * 7).
It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance.
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(−7)^-2 and more letters cause needed
Answers
Answer:
1/49.
Step-by-step explanation:
(−7)^-2
= 1 /(- 7)^2
= 1/49.
look at image............
Answers
Answer:
f(x)=2x-3
Step-by-step explanation:
cause fir example if you put x=2 the y became 1.
Let $m$ be a positive integer such that $m$ has exactly 5 positive divisors. How many distinct prime factors does $m$ have
Answers
If m has exactly 5 positive divisors then there can only be one prime factor.
According to statement
m has exactly 5 positive divisors AND
Let A^p,B^q,.... are the possible factors of integer m then
assume that p and q ≥ 1.
then the number of possible divisors cannot be 5 because there are no two integers p, q ≥ 1, such that (p +1)(q + 1) = 5
So, If m has exactly 5 positive divisors then there can only be one prime factor.
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Can someone pls help me?
Answers
Answer:
[tex] \frac{8}{24} [/tex]
Step-by-step explanation:
If Adam's family uses 8lb of apples to make pie. We know that 3 x 8 = 24, so it's probably approximately 3 out of 18.
Please help ill give whoever answers the best the brainliest answer
Answers
Please help! I can't figure this out, i'll give a brainliest
Answers
The linear equation that best fits the data is: y = 10x + 15.
How to Write the Linear Equation of a Data?First, find the slope/unit rate (m) and the y-intercept/starting value, then substitute the values into y = mx + b.
Using two points on the graph, (1, 25) and (2, 35), find the slope (m):
Slope (m) = (35 - 25)/(2 - 1)
Slope (m) = 10/1
Slope (m) = 10
Substitute (x, y) = (1, 25) and m = 10 into y = mx + b to find b
25 = 10(1) + b
25 - 10 = b
b = 15
Substitute m = 10 and b = 15 into y = mx + b
y = 10x + 15
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Name the ordered pair that would be a reflection of (9, 2) over the y axis
Answers
Answer:
(- 9, 2 )
Step-by-step explanation:
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
(9, 2 ) → (- 9, 2 )
A room has a length of 8 m. A scale diagram is drawn of the room. In the diagram, the room has a length of 1 cm. What is the scale of the diagram? Give your answer as a ratio in the form 1 : k , where k is an integer.
Answers
The scale of the diagram as described in the task content is; 1: 8 where k= 8.
What is the scale of the diagram?It follows from the task content that the original length of the room in discuss is 8cm. It therefore follows that the length of the room in the scale diagram is 1cm. On this note, the scale of the diagram in discuss is; 1 : 8 as 1cm on the diagram corresponds to 8cm actual length.
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Which ratio is equivalent to 4:5 ?
Answers
Answer:
Step-by-step explanation:
Maybe..
8/10
12/15
16/20
20/25
24/30
28/35
32/40
36/45
40/50
Any one of these is equal to the ratio of 4 over 5.
Answer:
No, the person who answered first is wrong
I'll give you the correct answer
Step-by-step explanation:
He the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.
thank you, this is the correct answer
hope that hepls
4
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Answers
X= 1
The answer will have to be 1
The following table shows a proportional relationship between jjj and mmm.
jjj mmm
444 333
121212 999
202020 151515
Write an equation to describe the relationship between jjj and mmm.
Answers
Answer:
The equation representing the proportional relationship between j and m is m = 3j/4 .
Step-by-step explanation:
Writing an Equation to Represent a Proportional Relationship
What is proportional relationship?
A proportional relationship between two quantities is when the two quantities vary directly with one and other. Meaning if one item is doubled, the other item is also doubled.
Going back to the given problem above, we have the table showing the proportional relationship between j and m.
j | 4 | 12 | 20 |
m | 3 | 9 | 15 |
Solution:
Step #1
The proportional relationship can be written as:
m/j = ¾ = 9⁄12 = 15⁄20 = ¾
Step #2
So, the equation representing this proportional relationship is:
m = ¾ × j/1 = 3j/4
Final Answer:
The equation representing the proportional relationship between j and m is m = 3j/4 .
Step-by-step explanation:
HELP QUICKKK What is the difference between –4 and 6?
–10
–2
2
10
Answers
Answer:
10
Step-by-step explanation:
Plugin your answer: -4 + 10 = 6
Answer:
10
Step-by-step explanation:
PLEASE HELPPPP!
Susan's calculator has a key that replaces the number displayed with its cube. If a² is displayed, how many times must Susan press the " cubing" key to display a number that is greater than 10?
Please explain it step-by-step! Also, I will give you a brainlist!!
Answers
Answer:
10
Step-by-step explanation:
This is because you would have to start with 109 = 23x
then solve it using logarithms
Then once you get the x value, it becomes
X>_10__(whatever number you found)
Look at this table.
Hours of Monthly
Pay
1220
1420
1620
1820
2020
2220
2420
Training
10
20
30
40
50
60
70
According to the table, how many hours of training would you need to have a
monthly pay of $1500?
Answers
Using a linear function, it is found that you would need roughly 24 hours of training to have a monthly pay of $1500.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Looking at the table, the pay increases $200 each 10 hours of work, hence the slope is:
m = 200/10 = 20
Then:
y = 20x + b
When x = 10, y = 1220, hence:
y = 20x + b
1220 = 20(10) + b
b = 1020.
Then the pay for x hours of training is:
y = 20x + 1020.
For a pay of $1500, we have that:
y = 20x + 1020.
1500 = 20x + 1020.
20x = 480
x = 24
You would need roughly 24 hours of training to have a monthly pay of $1500.
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Translate into an algebraic expression:
How much 50% of sugar syrup can you make if you have x grams of sugar?
(Need Urgent Help)
Answers
Answer:
Que is talking about a syrup which contains 50% of sugar .
Que asked : amount of sugar syrup from X grams of sugar.
Explanation :
if a sugar syrup contains 50% of sugar , that means that the half of the solution contains sugar and half is solvent .
means , 2 × amount of sugar = solution (syrup)
now , we are given x grams of sugar
then , solution can be made with x grams of sugar = 2 × (X grams) = 2X gram of solution or sugar syrup.
.
.
Mark BRAINLIEST!
What are the two binomial factors for x2 – 25? (x – 5)(x – 5) (x 5)(x 5) (x – 20)(x 5) (x – 5)(x 5)
Answers
Answer:
(x - 5)(x + 5)
Step-by-step explanation:
x² - 25 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
x² - 25
= x² - 5²
= (x - 5)(x + 5)
Answer:
Step-by-step explanation:
(x-5) +(x+5)
Members of the band sold juice and popcorn at a college football game to raise money for an
upcoming trip. Each juice bottle sold costs $2.50, and each container of popcorn sold costs
$1.25.
a. write an equation to represent how much money was made
b. be sure to specify what the variables represent.
Answers
Answer:
2.50x+1.25y=z
Step-by-step explanation:
Let the number of juice bottles = x
And the number of containers of popcorns=y
And the total number of juice bottles and containers of popcorns=z
Total number of juice bottles=x times $2.50
Total number of containers of popcorn= y times $ 1.25
equation; 2.50x+1.25y=z
Which of the following situations involve opposite quantities combining to make 0?
·Krista has a new piggy bank. She adds 3 quarters on Tuesday, and then adds another 3 quarters on Thursday.
·Carlyns opens a new checking account with $30. His first purchase, made with his new debit card, totals $28.
·Bekzod makes 1.5 liters of lemonade and drinks it all during the afternoon.
·Daisy is writing a novel. She wrote 4 new pages to finish Chapter 1. When she reviews Chapter 1, she discards these 4 pages and an additional 4 pages.
Answers
CAN ANYONE HELP PLSS
Answers
Answer:
CD = 13
Step-by-step explanation:
since Δ ABD and Δ CBD are congruent , then corresponding sides are congruent, so
CD = DA = 13
Answer:
13
Step-by-step explanation:
We know that if two triangles are congruent, the corresponding element of those are also equal.
Given that,
ABD Δ ≡ CBD Δ
Therefore, the corresponding elements are also equal.
AD = CD
AD = 13 units
∴ CD = 13 units
number 8. use the Steps in the construction to determine which statement is true
Answers
Answer:
choice C
Step-by-step explanation:
The circle is circumscribed because circles drawn on the outside is known as circumscription. The circle is clearly outside touching the three vertices of the triangle.
Please help ASAP
Please help ASAP
Please help ASAP
Please help ASAP
Answers
Substituting L = 7.29,
[tex]t = 2.01 \sqrt{7.29} \approx \boxed {5.4}[/tex]
Given that
x
= 8 cm and
y
= 23 cm, work out
∠
BCA rounded to 3 SF.
Answers
The value of the angle ∠BCA when approximated to 3 significant figures is; 20.4°
How to use Trigonometric Ratios?From the attached image of the triangle ABC showing the side lengths x and y, we can see clearly that it is a right angle triangle.
Now, since we want to find the value of the angle ∠BCA, then it means we have to use trigonometric ratio to get;
x/y = sin BCA
Plugging in the relevant values gives us;
8/23 = sin BCA
∠BCA = sin⁻¹(8/23)
∠BCA = 20.355
Approximating to 3 significant figures gives us;
∠BCA = 20.4°
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7. A student on the cross-country team runs 30 minutes a day as a part of her training.
Write an equation to describe the relationship between the distance she runs in miles, , and her running speed, in miles per hour, when she runs:
a. at a constant speed of 4 miles per hour for the entire 30 minutes.
Answers
The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The distance travelled in 30 minutes is:
Distance = speed * time = 4 mph * 0.5 h = 2 miles
The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time
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