Answers
Answer:
Step-by-step explanation:
Average = (Ymax + Ymin)/2 = (4 + (- 2))/ 2 = 1
Amplitude = (Ymax - Ymin)/2 = (4 - (- 2))/ 2 = 3
y is at a maximum when x = 0, so cosine function is easy.
one cycle (2π radians) is completed in 2π/3
therefore
y = 1 + 3cos(2π(x /(2π/3))
y = 1 + 3cos(3x)
Answer(s):
[tex]\displaystyle y = 3sin\:(3x + \frac{\pi}{2}) + 1 \\ y = 3cos\:3x + 1[/tex]
Step-by-step explanation:
[tex]\displaystyle 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 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{6}} \hookrightarrow \frac{-\frac{\pi}{2}}{3} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{3}\pi \\ Amplitude \hookrightarrow 3[/tex]
OR
[tex]\displaystyle 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 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{3}\pi \\ Amplitude \hookrightarrow 3[/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 cosine graph, if you plan on writing your equation as a function of sine, 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 = 3sin\:3x + 1,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine 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 sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{6}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{6}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{6}} = \frac{-\frac{\pi}{2}}{3}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3sin\:(3x + \frac{\pi}{2}) + 1.[/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 hits [tex]\displaystyle [-\frac{2}{9}\pi, -\frac{1}{2}],[/tex]from there to [tex]\displaystyle [\frac{4}{9}\pi, -\frac{1}{2}],[/tex]they are obviously [tex]\displaystyle \frac{2}{3}\pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{2}{3}\pi.[/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 = 1,[/tex]in which each crest is extended three units 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.
Related Questions
Consider the pattern 24, 33, 42, 51, …. What will the 10th term be?
Answers
Answer:
a₁₀ = 105
Step-by-step explanation:
There is a common difference between consecutive terms , that is
33 - 24 = 42 - 33 = 51 - 42 = 9
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 24 and d = 9 , then
a₁₀ = 24 + (9 × 9) = 24 + 81 = 105
The 10th number of the arithmetic sequence will be 105.
What is an arithmetic sequence?Let a₁ be the first term and d be a common difference. Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The arithmetic sequence is given below.
24, 33, 42, 51, ....
The first term is 24 and the common difference will be
d = 33 - 24
d = 9
Then the 10th term of the arithmetic sequence will be
a₁₀ = 24 + (10 - 1) × 9
a₁₀ = 24 + 9 × 9
a₁₀ = 24 + 81
a₁₀ = 105
The 10th number of the arithmetic sequence will be 105.
More about the arithmetic sequence link is given below.
https://brainly.com/question/12373434
#SPJ2
--8
- 2
4
10
y
8
1
re
-6
—13
Answers
Step-by-step explanation:
sorry I can't find the slope of x y
but I can tell the formula
m=y2-y1/x2-x1
4. How long would it take sound waves traveling through air that is 68°F to
travel 1,372 meters? Use an equation to solve the problem.
Answers
Answer:
2.7 seconds
Step-by-step explanation:
[] Temp of air: 68°F -> 20°C
[] Velocity of sound in air:
[tex]v=331.3\sqrt{1+\frac{T}{273.15} }[/tex]
[tex]v=331.3\sqrt{1+\frac{68}{273.15} }[/tex]
v ≈ 370.25 m/s
[] Last,
t = [tex]\frac{d}{v}[/tex]
t = [tex]\frac{1,372}{370.25}[/tex]
t ≈ 3.7056 ≈ 2.7 seconds
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
There are 10 girls in the class. This is three less thank half the number of boys . How many boys are in the class?
Answers
Answer:
there are 6 boys
Step-by-step explanation:
4
b(x) = 16.22 – 25
bx)
Use the drop-down menus to factor the expression and find the zeros of b(x).
Answers
Answer:
1) (4x)² - (5)²
2) (4x + 5) (4x -5)
3) Zeros of b are [tex]\frac{5}{4}[/tex] and [tex]\frac{-5}{4}[/tex] (can also be 1.25 and -1.25)
what is the percent of change from 5 to 7
Answers
Answer: 40
Step-by-step explanation:
A recipe for cinnamon rolls calls for 3 cups of flour for every cup of water. Using the same recipe, how much water will you need for 5 cups of flour?
How many cups of water will you need for 5 cups of flour?
Answers
Answer:
5/3 cups of flour
Step-by-step explanation:
3/1=5/x x representing the amount of water
cross multiply: 3x=5
divide by 3: x=5/3
Solve for the missing variable
Answers
Answer:
x = 7.5.
The two lines on the side of the triangle in the screenshot show us that the two lines made are the same length. So the difference between the first two values, i.e. 22.3 and 14.9 is the same difference between 14.9 and x.
Step-by-step explanation:
hope this helps. . .<3
good luck! uωu
Answer:
Step-by-step explanation:
14.9 is the middle value of x and 22.3. So your formula looks like this.
(x + 22.3) / 2 = 14.9 Multiply both sides by 2
2(x + 22.3) / 2 = 14.9*2 Remove the brackets.
x + 22.3 = 29.8 Subtract 22.3 from both sides
x = 29.8 - 22.3
x = 7.5
what is the measure of x?
Answers
Answer:
Hello!
After reviewing the problem you have provided I have come up with the correct solution:
x= 9
Step-by-step explanation:
To come up with this solution you have to first realize that the smaller triangle is a proportionally scaled down version of the entire larger triangle! (I will show what I mean in a linked picture)
So after we have realized that the smaller triangle is a scaled down version of the larger one, we can then create a formula or ratio to calculate the value of the missing side of the larger triangle (being x+6=??).
To create the formula/ratio I divided 10inches by 4inches. Thus the larger triangle is 2.5 times larger than the smaller one.
I then use this ratio to figure out the missing length of the larger triangle by doing:
6inches x 2.5 = 15inches.
I then inputed the 15inches into the formula of the missing side:
x+6=15
Subtracted 6 from both sides to simplify, and came up with the solution!
x=9
Let me know if this helps!
find the value of (-7/10)(2/5)
Answers
Answer:
the answer to (-7/10)(2/5) is -7/25.
or if you need decimal form it is -0.28
Step-by-step explanation:
Measure E is equal to?
Answers
Answer:
E =114
Step-by-step explanation:
The two base angles are equal to 33 since it is an isoscles triangle. We know that because the two sides are equal. That means D and F are equal to 33. The sum of the angles of a triangle are 180.
D+E+F = 180
33+E +33=180
66+E = 180
E = 180-66
E =114
Find x intercept
(0, 24) (4,0)
Answers
Answer:
bt.ly/d97sjdu8 there is your answer!
Step-by-step explanation:
Answer:
x-intercept is 0
Step-by-step explanation:
(0, 24) (4,0)
(x, y)
0/4=0
During the 2005 football season,team tackle beat team sack by 10 points. If their combinded scores totaled 36 find the individual team scores
Answers
Answer:
Step-by-step explanation:
t = tackle score
s = sack score
t = s + 10
t + s = 36
s + 10 + s = 36
2s = 26
s = 13 points
t = 13 + 10 = 23 points
Given m\parallel nm∥n, find the value of x. n m (8x+19)° 59°
Answers
50 points! Help (Vectors)
Answers
The magnitude of a vector a is the length of the vector.
We write it ||a||
We can draw a right triangle and apply the pythagoras theorem. The magnitude of a will be the hypotenuse :
||a||² = 3² + 3²
||a||² = 9 + 9
||a||² = 18
||a|| = √18 = √(9*2) = 3√2 ≈ 4.24
So the answeer is 4.24
Good Luck
Good Luck
Look at the angle Z that is marked on the shape. Is this angle less than, more than or equal to a right angle?
Answers
Answer:
Less then a right angle
Step-by-step explanation:
It’s can’t be equal (looks at other examples of a right angle)
It can’t be more since that would bve more then a right angle and it certainly isnt more
it can only be less
What is the slope-intercept equation of the line that includes (0, 12) and
(4,36)?
Answers
Answer:
The slope is 6, but the equation is below.
Step-by-step explanation:
Y2 - Y1/X2 - X1
36-12/4-0
Or
12-36/0-4
=6
You'll get the same answer either way.
here's my question.
Answers
Answer:
use reciprocal
Step-by-step explanation:
Let f(y) = y^4 - 3y^3 + y - 3 and g(y) = y^3 + 7y^2 - 2. Find f(y) + g(y). Write your answer as a polynomial with terms of decreasing degree.
Answers
Work Shown:
h(y) = f(y) + g(y)
h(y) = (y^4 - 3y^3 + y - 3) + (y^3 + 7y^2 - 2)
h(y) = y^4 - 3y^3 + y - 3 + y^3 + 7y^2 - 2
h(y) = y^4 + (-3y^3+y^3) + 7y^2 + y + (-3 - 2)
h(y) = y^4 - 2y^3 + 7y^2 + y - 5
This is a fourth degree polynomial (aka quartic).
Use the clues and each of the numbers on the sign to complete the grid.
Clues
. All four numbers in a row must have a common factor greater than 1.
. Pairs of numbers in a column must have a common factor greater than 1.
Answers
Answer:
prayers lang po katapat nyan
A store sells previously viewed movies. The table shows the cost of buying 1, 2, 3, or 4 movies.
a. Which mapping diagram represents the data in the table
Question 2
b. Is the relation a function? Explain.
Each input has exactly one output. Therefore, the relation is a function.
Question 3
c. Describe the pattern. How does the cost per movie change as you buy more movies?
The pattern is that for each input
increase
of
1
, the output
increases
by $1,2,3,4,6,12
less than the previous increase. For each additional movie you buy, your cost per movie
decreases
by $1,2,3,4,6,12
how much did the output increase in dollars and how much did the movie decrease
Answers
A relation may or may not represent a function.
The relation of the movie and its costs is a function.The pattern is that, as unit cost of each movie decreases as the number of movies increases.The costs are given as:
1 movie costs $102 movies cost $183 movies cost $244 movies cost $28(a) The mapping diagram
To do this, we simply point the number of movies, to the corresponding costs, using arrows
See attachment for the mapping diagram.
(b) Is the relation a function
From the attached mapping, we can see that:
The costs of each movie are different.
This means that: the relation is a function.
(c) Describe the pattern
Notice that as the number of movies increases, the cost also increases;
However, the unit cost decreases.
Hence, the unit cost of each movie decreases as the number of movies increases.
Read more about mappings, functions and relations at:
https://brainly.com/question/8892191
Question 10 of 10 According to this diagram, what is tan 62°? 62 i 7 28° tra OA. A. 15 B. 0 O C. OD D8 O E 17 F
Answers
9514 1404 393
Answer:
B. 15/8
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the tangent relation is ...
Tan = Opposite/Adjacent
The side opposite the 62° angle is marked 15.
The side adjacent the 62° angle is marked 8.
Then the tangent ratio for 62° is ...
tan(62°) = 15/8
If a ≠ 0 and b ≠ 0 which of the following is equivalent to 2/3a 1/b?
Answers
Answer:
58
Step-by-step explanation:
525, 650, 539, 643, 764, 539, 687
What is the interquartile range of these numbers
Answers
Answer:
148
Step-by-step explanation:
sorry, im not sure how to solve it, but its 148
hope this kinda helped :)
mark me brainliest :D
In 1950, the group spent 23% of their budget on food. This has decreased
at an average rate of approximately 0.27% per year since then. Find a
linear function in slope-intercept form that models the percentage of total
spending, p(x), by the group x years after 1950.
Answers
The linear function that can be used to model this relationship is:
y = -0.27x + 23
A linear function is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let P(x) represent the percentage of total spending x years after 1950.
Since In 1950, the group spent 23% of their budget on food, hence b = 23.
Also, this has been decreasing at 0.27% per year. Hence m = -0.27.
The linear function that can be used to model this relationship is:
y = -0.27x + 23
Find out more at: https://brainly.com/question/13911928
PLS HELP I NEED THIS DONE TODAY PLSSS WILL GIVE BRAINLY
Answers
Answer:
You need 6 lbs of red potatoes
32oz of cream cheese
43oz cream of potatoe soup
Step-by-step explanation:
Multiply all by 4
The two parallel sides of a trapezium are 19.8 and 7.2 cm. If the area of the trapezium is 135 sq cm find the distance between its parallel sides
Answers
Answer:
67.72
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
The area of a Trapezium is
(a+b)/2 * h where
a = top
b= bottom
h- height, distance between the two parallel sides (ie the top and bottom)
135 = (19.8+7.2)/2 *h
135=13.5h
h= 10
a car travels at 56 km per hour find the time it takes to travel 300 metres give your answer in seconds correct to the nearest second
Answers
1km = 1000 m , thus 56km = 56000 m
1hr = 60 mins
1min = 60 secs, therefore 60 mins = 60*60 seconds = 3600 seconds = 1hr
so then, we know the car travels 56000 meters in 3600 secs, how many seconds will that be for 300 meters?
[tex]\begin{array}{ccll} meters&seconds\\ \cline{1-2} 56000&3600\\ 300&x \end{array}\implies \cfrac{56000}{300}=\cfrac{3600}{x}\implies \cfrac{560}{3}=\cfrac{3600}{x} \implies 560x=10800 \\\\\\ x = \cfrac{10800}{560}\implies x = \cfrac{135}{7}\implies x \approx 19.286\implies \stackrel{\textit{rounded up}}{x = 19}[/tex]
The circumference of a circle is 28.888 centimeters. What is the circle's radius?
Use 3.14 for pi
Answers
Answer:
4.6
Step-by-step explanation:
28.888 / 3.14 = 9.2
9.2 / 2 = 4.6
Question 3 What is the equation of the parabola that opens up, has a vertex V(5,0), and a y-intercept of 50?
Answers
Answer:
y=2(x-5)^2
Step-by-step explanation:
Vertex form:
y=a(x-p)^2+q
(p,q) = (5,0)
y=a(x-5)^2
y-intercept has coordinates (0,50) so, substitute x=0 and y= 50 in the above equation to find "a"
50=a(0-5)^2
50=25a
a=2
equation
y=2(x-5)^2