Does anyone know the equation to this trigonometric function? Step by step?
A general cosine function (we could also use a sine function) is written as:
y = A*cos(k*x + p) + M
We will find that the function of the graph is:
f(x) = 2*cos(2*x + 2.09) - 2
Let's return to the general function:
y = A*cos(k*x + p) + M
A is the amplitude, it defines the distance between the value of a maximum and the value of the minimum, such that A is exactly half of that difference.
Here we can see that the maximum is 0, and the minimum is -4
The differene is: 0 - (-4) = 4
Then:
A = 4/2 = 2
f(x) = 2*cos(k*x + p) + M.
M is the midline, this is, the horizontal line that cuts the graph in two halves. Here we can see that the midline is x = -2, then:
M = -2
f(x) = 2*cos(k*x + p) - 2
p is the phase shift.
In the graph, we can see that f(0) = -3, so we have:
f(0) = 2*cos(0 + p) - 2 = -3
cos(p) = -1/2
p = Acos(-1/2) = 2.09
Then we have:
f(x) = 2*cos(k*x + 2.09) - 2
Finally, k is related to the frequency of the function.
We can see that the function does a complete cycle at x = pi
This means that:
f(x) = f(x + pi)
Knowing that the period of a cosine function is 2*pi, then:
k*(x + pi) = k*x + 2*pi
k = 2
Then the equation of the graph is:
f(x) = 2*cos(2*x + 2.09) - 2
If you want to learn more, you can read:
https://brainly.com/question/24372261
Answer(s):
[tex]\displaystyle y = 2sin\:(2x + 1\frac{1}{4}\pi) - 2 \\ y = 2cos\:(2x - 1\frac{1}{4}\pi) - 2[/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 -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{5}{8}\pi} \hookrightarrow \frac{-1\frac{1}{4}\pi}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/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 -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{5}{8}\pi} \hookrightarrow \frac{1\frac{1}{4}\pi}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/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 by all means, go for it, but be careful and follow what is explained here. Now, as you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2sin\:(2x - 1\frac{1}{4}\pi) - 2,[/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}{4}\: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}{4}\:unit,[/tex] which means the C-term will be negative. Now, BEFORE we go any further, we must remember that this particular cosine graph [thank goodness it is a cosine graph we are working with] ALREADY has a horisontal shift and does not have a single crest oscıllαtıng about any endpoint on the y-axis. So, in this case we need to figure out how far the FIRST oscıllαtıng crest is from the origin, and that obviously would be [tex]\displaystyle \frac{5}{8}\pi\:units.[/tex] Though, sinse we want the sine equation of this graph, it must be “negative”; so, by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{5}{8}\pi} = \frac{-1\frac{1}{4}\pi}{2},[/tex] in which the value of C is [tex]\displaystyle -1\frac{1}{4}\pi.[/tex] So, the sine equation of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2sin\:(2x + 1\frac{1}{4}\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 hits [tex]\displaystyle [\frac{7}{8}\pi, -2],[/tex] from there to [tex]\displaystyle [-\frac{\pi}{8}, -2],[/tex] they are obviously [tex]\displaystyle \pi\:units[/tex] apart, telling you that the period of the graph is [tex]\displaystyle \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 = -2,[/tex] in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
**As you can see, this is one of those moments where you will really need to be careful because if you notised, both equations have OPPOCITE horisontal shifts and C-values. Now, the ONLY TIME this occurs is when all crests in a SINUSOIDAL graph cycle half-way in between endpoints. Your best bet is to jot this down for when you see graphs like these in the future.
I am delighted to assist you at any time.
PLEASE HELP IM ON A TIMER: I WILL GIVE 5 STARS AND BRAINLIEST!!
f) Create a residual plot for your data.
13.8 1.42
18 3.7
16.7 3.21
18 4
0.7 1.11
21.9 3.69
18 3.8
18 4
19.7 3.5
16.7 3.21
g) Does your residual plot show that the linear model from the regression calculator is a good model? Explain your reasoning.
a) Using your equation from step 2d, estimate the GPA of a student who studies for 15 hours a week. Justify your answer.
Answer:
y = 0.1491x + 0.7556
R² = 0.6943
r^2 at .69 ≅ .7 is somewhat strong
y = 0.1491(15) + 0.7556
GPA= 2.2365
Step-by-step explanation:
Somebody can help me please
The graph of h(x) = (x - 3)2 is a translation of the
graph of f(x) ….. blank
by
…. Blank units.
Answer:
right by 3 I think
Step-by-step explanation:
Answer: Right by 3 Units
Step-by-step explanation:
Right on edge 2021
what is the perimeter
A) 20.3
B)18.3
C)24.3
D)22.3
Answer:
b
Step-by-step explanation:
cuz u add them all
can somene explain this to me please?
Answer:
10/3
Step-by-step explanation:
rate of change = gradient
(17-7)/(6-3) = 10/3
basically difference of y values / difference of x values
Which expression is equivalent to −24x+72?
−24(x−72)negative 24 times open paren x minus 72 close paren
−24(x−3)negative 24 times open paren x minus 3 close paren
24(x+3)24 times open paren x plus 3 close paren
24(x+72)
Answer:-24(x-3) = -24x (-24)(-3)
Step-by-step explanation:
Answer:
eat my hand where the pic
Step-by-step explanation:
yeah
-(2x +y) - 2 ( -x - y)
....................
Answer:
First, we apply the Distributive property and then we combine like terms,
To combine like terms, we add or subtract.
[tex]-(2x +y) - 2 ( -x - y)[/tex]
[tex]=-2x-y+2x+2y[/tex]
[tex]=(-2x+2x)+(-y+2y)[/tex]
[tex]=0+y[/tex]
[tex]=y[/tex]
OAmalOHopeO
Answer:
y is the simplest result here.
Step-by-step explanation:
Perform the indicated multiplication as a first step towards simplifying this expression:
-2x - y + 2x + 2y
-2x and 2x cancel each other out, leaving 2y - y, or just y
What is the length of AC?
Because all the angles are congruent (the same), this is an equilateral triangle. All equilateral triangles have congruent angles and congruent sides, so all sides has to be 14.
write following ratio in simplest form :
125 g : 1 kg
Answer:
125g:1Kg
=> 125g : 1000g
=> 1:4Answer:
1:8
Step-by-step explanation:
125 g:1 kg
125g:1000 g
1 g:8 g
Keep smiling and hope u will be satisfied with my answer.Have a good day :)
find out 6 rational numbers between 3 and 4
Answer:
22/7, 23/7, 24/7, 25/7, 26/7, and 27/7.
Step-by-step explanation:
Write the fraction or mixed number as a decimal.
The water level of a river is 170feet. The river recedes 4 feet each year. Ingrid claims that the equation that represents this scenario is y=170x-4. Is her equation correct?
Answer:
Step-by-step explanation:
In the equation y = mx + b, which is the form Ingrid's equation is in, the m stands for the rate of change. If the water level is decreasing, the rate at which it is decreasing is what goes in for m. The "b" of that equation indicates the starting height of the water, which is 170. The equation should be:
y = -4x + 170, negative because the water is decreasing.
HELP ME SOLVE THIS PLEASE
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Answer:
J'(3 , 5)
Step-by-step explanation:
Rule for reflection over x-axis,
Original point(x , y) After reflection (x, -y)
After reflection, there will be no change in the x-coordinate and y - coordinate will the change the sign
So, J(3,-5) After reflection J'(3,5)
A car travels 52/5 kilometers in 23/4 minutes. What is the unit rate in kilometers per minute?
The unit rate of the car that travels 5 2/5 km in 2 3/4 mins is: 1.96 km/min.
What is Unit Rate?Unit rate can be defined as the ratio of one quantity in comparison to another.
Distance travelled by a car = 5 2/5 km = 5.4 km
Time travelled = 2 3/4 mins = 2.75 mins
Unit rate in km/min = 5.4/2.75
Unit rate in km/min = 1.96 km/min.
Learn more about the unit rate on:
https://brainly.com/question/19493296
#SPJ1
find the 80th term following arithmetic sequence 8,14,20,26
Answer:
The 80th term is 482
Step-by-step explanation:
8,14,20,26
This is an arithmetic sequence
Find the common difference by taking the second term and subtracting the first term
14-8 = 6
We are adding 6 each time
The formula for an arithmetic sequence is
an =a1+d(n-1) where a1 is the first term, d is the common difference and n is the term we are looking for
a80 = 8+6(80-1)
= 8 + 6*79
= 8+474
= 482
The 80th term is 482
Answer: 482
Step-by-step explanation:
[tex]\displaystyle\ \Large \boldsymbol{Rule:} \\\\\boxed{ \huge \boxed{a_n=a_1+(n-1)d }} } \ \ \\\\\\ 8 \underbrace{}_6 14 \underbrace{}_620\underbrace{}_626 ......a_{80}=? \\\\\\a_1=8 \ \ ; \ \ d=6 \\\\\\ a_{80}=8+(80-1)\cdot 6=480+8-6=482 \\\\\\\\ Answer: \boxed{\boldsymbol{ a_{80}=482}}[/tex]
A table is made using the following two patterns.
Pattern 2: Starting number: 5, Rule: Multiply by 3
1
Pattern y: Starting number: 20, Rule: Multiply by
2
Complete the table for the given patterns.
C
y
5
20
Answer:
x y
5 20
15 10
45 5
Step-by-step explanation:
Pattern x:
Start with 5.
Multiply by 3: 5 * 3 = 15
Multiply by 3: 15 * 3 = 45
Pattern x:
Start with 20.
Multiply by 1/2: 20 * 1/2 = 10
Multiply by 1/2: 10 * 1/2 = 5
x y
5 20
15 10
45 5
5(x+6=50
x=
Ty you for helping
Answer:
[tex] \frac{5(x + 6)}{5} = \frac{50}{5} \\ x + 6 = 10 \\ x = 10 - 6 \\ x = 4[/tex]
Answer:
x=4
Step-by-step explanation:
5(x+6)=50
First expand the brackets:
5 times x equals 5x
5 times 6 equals 30
Form an equation:
5x+30=50
Do inverse operations to "undo" the equation:
50-30=20
5x=20
20÷5=4 (We divide 20 by 5 because when a number is next to a letter, it means times so we do the inverse and divide).
x=4
We can check our answer by substituting in 4:
5(4+6)
Do brackets first:
4+6=10
5(10)
Then as the 5 is next to the bracket on the outside we times everything on the inside by 5:
5 times 10 equals 50
Hope this helps :)
there are nickels, dimes, and quarters in a piggy bank. altogether, the coins are worth $3.65. the number of dimes is three times greater than the number of nickels, and the number of quarters is one greater than double the number of nickels. how many quarters, nickels, and dimes are there?
Answer:
4 nickels
12 dimes
9 quarters
Step-by-step explanation:
x = number of nickels
y = number of dimes
z = number if quarters
0.05×x + 0.1×y + 0.25×z = 3.65
y = 3x
z = 2x + 1
0.05x + 0.1×3x + 0.25×(2x + 1) = 3.65
5x + 30x + 25×(2x + 1) = 365
35x + 50x + 25 = 365
85x = 340
x = 340/85 = 4
y = 3×4 = 12
z = 2×4 + 1 = 9
What is the domain of the function graphed below?
Answer:
(-2,4] and [7,α)
Step-by-step explanation:
the domain is open at -2 but closed at 4 and also closed at 7 but open till infinity..
The domain of the given function is (-2,4] U [7, ∞), which is the correct option (B).
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
f(x) = x²+1 if (-2,0]
This the sub-function define between the interval (-2,0].
f(x) = -1 if (0, 4]
This the sub-function define between the interval (0, 4].
f(x) = -(x-7)² if [7, ∞)
This the sub-function define between the interval [7, ∞).
Thus, the domain of the given function is (-2,4] U [7, ∞).
Learn more about the piecewise function here:
https://brainly.com/question/12700952
#SPJ7
If sin A= 0.8, find the positive value of cos A
Answer:
cosA = 0.6
Step-by-step explanation:
Using the Pythagorean identity
sin²A + cos²A = 1 ( subtract sin²A from both sides )
cos²A = 1 - sin²A ( take the square root of both sides )
cosA = ± [tex]\sqrt{1-sin^2A[/tex]
Since only the positive value is required , then
cosA = [tex]\sqrt{1-(0.8)^2}[/tex]
= [tex]\sqrt{1-0.64}[/tex]
= [tex]\sqrt{0.36}[/tex]
= 0.6
Answer:
Answer:
Answer:x = 25°
Answer:x = 25°Step-by-step explanation:
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2}
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 2
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2}
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 2
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )x = 25°
math help please help please my parents are going to hit me
Answer:
2.1
Step-by-step explanation:
Angle Q of the triangle, SRQ is 47. Let find Length of RQ of SRQ.
If we apply tangent ratio, we get
[tex]x = 5.9[/tex]
Now let find the measure of RP of Triangle SRP.
If we apply tangent ratio, we get
[tex]x = 3.8[/tex]
We can find PQ by Subtraction Poustulate.
[tex]5.9 - 3.8 = 2.1[/tex]
so
Pq=21
Answer:
PQ ≈ 2 cm
Step-by-step explanation:
We know that SRQ is 47.
Next we apply the tangent ratio. We get x = 5.9
Now we find the measure of RP of the triangle SRP.
If we apply tangent ratio, we get x = 3.8
We can find PQ with this:
5.9 - 3.8 = 2.1 ≈ 2 cm
Rewrite in simplest radical form the problem in the image below. Show and explain each step. Thank you for your time and help.
Answer:
Hello,
Step-by-step explanation:
[tex]\dfrac{x^{\frac{5}{6}} }{x^{\frac{1}{6}} } \\\\=x^{\frac{5}{6} -\frac{1}{6} }\\\\=x^{\frac{4}{6} }\\\\=x^{\frac{2}{3} }\\\\=\sqrt[3]{x^2}[/tex]
Hi there!
Look the picture for your answer.
Hope it helps!
Describe the symmetry of the figure. Identify lines of symmetry, if any. Find the angle and the order of any
rotational symmetry.
Answer:
No symmetry
Step-by-step explanation:
The shape cannot be folded over any line to be equally matched up to the other side
mΖΗ - 67
pleas please please help!! i’m doing angles
Answer:
could u take a picture of the angles please
Step-by-step explanation:
Need help asapppppppppp
If the mean of a normal distribution is 210, what is the median of the
distribution?
210
B. 315
C. 105
D. 420
Answer:
210
Step-by-step explanation:
In a normal distribtuion mean=mode=median
so 210=median
juan analyzes the amount of radioactive material remaining in a medical waste container over time. He writes the function f(x)=10(0.98)x to represent the amount of radioactive material that will remain after x hours in the container.
Rounded to the nearest tenth, how much radioactive material will remain after 10 hours?
0.8 units
1.3 units
8.2 units
9.8 units
Answer:
8.2 units
Step-by-step explanation:
For radioactive decay, the amount should decrease over time. Given the function:
f(x) = 10(0.98[tex])^{x}[/tex]
We substitute the time of x = 10 hours:
f(10) = 10(0.98[tex])^{10}[/tex]
f(10) = 8.17
Round 8.17 to 8.2.
Therefore 8.2 units will remain after 10 hours.
17. DEFG is a square. Find the value
of x.
Answer:
x = 3
Step-by-step explanation:
All the angles of a square are 90°
The diagonals bisect the angles , then
5x² = 45 ( divide both sides by 5 )
x² = 9 ( take the square root of both sides )
x = [tex]\sqrt{9}[/tex] = 3
