Answers
Answer:
[tex]f(x)= \sin(6x)+3[/tex]
Step-by-step explanation:
The parent function of this graph is: y = sin(x)
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function:
[tex]f(x) = \sf A \sin (B(x + C)) + D[/tex]
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftThe parent function y = sin(x) has the following:
Amplitude (A) = 1Period = 2πPhase shift (C) = 0Vertical shift (D) = 0Mid-line: y = 0From inspection of the given graph:
Amplitude (A) = 1[tex]\sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}[/tex]Phase shift (C) = 0Vertical shift (D) = +3 (as mid-line is y = 3)[tex]\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6[/tex]
Substituting the values into the standard form:
[tex]\implies f(x) =1 \sin (6(x + 0)) + 3[/tex]
[tex]\implies f(x) = \sin (6x) + 3[/tex]
Therefore, the equation of the given trigonometric graph is:
[tex]f(x)= \sin(6x)+3[/tex]
Answer(s):
[tex]\displaystyle y = cos\:(6x - \frac{\pi}{2}) + 3 \\ y = -sin\:(6x \pm \pi) + 3 \\ y = sin\:6x + 3[/tex]
Step-by-step explanation:
[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 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{12}} \hookrightarrow \frac{\frac{\pi}{2}}{6} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{3}} \hookrightarrow \frac{2}{6}\pi \\ Amplitude \hookrightarrow 1[/tex]
OR
[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 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{3}} \hookrightarrow \frac{2}{6}\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\:6x + 3,[/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 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 cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{12}\:unit[/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 \frac{\pi}{12}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{12}} = \frac{\frac{\pi}{2}}{6}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = cos\:(6x - \frac{\pi}{2}) + 3.[/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 [-\frac{5}{12}\pi, 2],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{12}, 2],[/tex]they are obviously [tex]\displaystyle \frac{\pi}{3}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{3}.[/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 = 3,[/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.
Related Questions
Describe how you would simplify the given expression.
(20x^5y^2/5x^-3y^7)^-3
Answers
Answer:
hope you can understand
Please help me 35 points and Brainliest if your right
Answers
Answer:
y = - 2 | x - 2 | + 4
Step-by-step explanation:
the general equation of an absolute value function is
y = a|x - h| + k
where (h, k ) are the coordinates of the vertex and a is the stretch factor
here (h, k ) = (2, 4 ) , then
y = - 2|x - 2| + 4
Answer:
See below ~
Step-by-step explanation:
Formula for absolute value function :
y = a |x - h| + k
==============================================================
Given :
⇒ a = -2
⇒ Vertex = (h, k) = (2, 4) [based on graph]
=============================================================
Solving by substitution :
⇒ y = -2|x - 2| + 4
HUGE POINTS
PLEASE ANSWER
BE INFORMATIVE AS POSSIBLE
Question:
A parallelogram fencing area is to be constructed for a general swimming pool area. The total perimeter of the parallelogram fence is 220m. If one of the lengths is 50m, determine the dimension of the other length and draw it out.
If you want more information let me know
Answers
Answer:
The other length is 60m.
Step-by-step explanation:
If you look at the shape of a parallelogram, you will see that a parallelogram has two parallel sides. So, if the total perimeter is 220m, then 50m and 50m together would be 100m, so 220- 100= 120m left to fill in both sides left. so, 120÷2= 60m. 60m is the other length.
how do we solve this I need a quick answer please :)
Answers
Sorry don't no the answer
sorry if I kwon the answer
I telling u the answer
Explanation: Key word, boundary. Meaning its perimeter of the field. Find the perimeter then multiply by 3. inches
what types of angles are in these quadrilaterals iready level d
Answers
Based on the quadrilaterals given, the types of angles that we see are Acute and Obtuse.
Which angles are shown in these quadrilaterals?Acute angles are those that are less than 90° and these are shown in the trapezium quadrilateral.
Obtuse angles are higher than 90° and so are drawn outwards as seen in the parallelogram.
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Solve the system of equations.
Answers
Answer:
The answer is the third bullet. (number 3)
13 - r < 82
PLA I NEED THIS
Answers
Answer:
r > -69
Step-by-step explanation:
13 - r < 82
subtract 13 from both sides
13 - r - 13 < 82 - 13
- r < 69
to flip the inequality sign, multiply both side by -1 to make r positive:
- r (-1) < 69 (-1)
r > -69
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
13-r<82
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
First of all, we need to isolate r (get r by itself). What I Mean by that is
We need to get r by itself on one side of the inequality.
So it should look something like this:-
r<___
So r is all by itself.
How will we get r by itself? Well, First of all, we need to subtract 13 on both sides:-
[tex]\longmapsto\bf{-r < 82-13[/tex]
Simplifying,
[tex]\longmapsto\bf{-r < 69}[/tex]
Now, is r by itself? Nopes, There's also a minus sign next to it , which indicates that r is multiplied by -1.
So we do the opposite operation and divide both sides by -1:-
(watch what happens)
[tex]\longmapsto\bf{r > -69}[/tex]
The inequality sign changed from "less than" to "greater than".
This happened because we divided by a negative number on both sides.
Good luck with your studies. [tex]\ddot\smile[/tex]#TogetherWeGoFar
[tex]\rule{300}{1}[/tex]
Please i really need help!
Answers
Answer:
21.25=4.25
Ms. Diaz buys 5 pounds of strawberrys
Step-by-step explanation:
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.4, with a standard deviation of 2.3.
(a) What response represents the 86th percentile? (Round to two decimal places as needed).
(b) What response represents the 55th percentile? (Round to two decimal places as needed).
(c) What response represents the first quartile? (Round to two decimal places as needed).
Answers
The response that represents the 86th percentile is 7.884
The response that represents the 55th percentile is 5.69
The response that represents the first percentile 3.85
How to solve for the 86th percentilemean = 5.4
sd = 2.3
p(X>x) = 0.86
find the value of z using the NORMSINV function in excel with a probability of 0.86
z = 1.080
x = mean + sd*z
= 5.4 + 2.3 * 1.080
= 7.88
How to solve for the 55th percentilemean = 5.4
sd = 2.3
p(X>x) = 0.55
find the value of z using the NORMSINV function in excel with a probability of 0.55
z = 0.1257
x = mean + sd*z
= 5.4 + 2.3 * 0.1257
= 5.69
c. The first quartile is 25%
z = -0.6745
5.4 + 2.3 * -0.6745
= 5.4-1.551
= 3.85
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Y’all pls help I’m gunna cry
Answers
First Quartile = 57
Third Quartile = 62
What method can be used?
Answers
Answer:
'''
Step-by-step explanation:
How many lines of symmetry does this figure have?
1
2
4
3
Answers
The number of lines of symmetry for the given figure will be 4.
What is symmetry?Symmetry is described in geometry as a balanced and proportionate likeness between two halves of an object.
As we know that similarity is defined as when the image is divided into two halves and one portion is completely overlapped by the other.
So in the given figure, the figure can be divided into two halves by drawing four lines along with the arrows and along with the corners. In all cases, the two halves overlap with the other.
Therefore the number of lines of symmetry for the given figure will be 4.
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The top four teams in a local tournament move onto the playoffs. if 7 teams enter the tournament how many different
combination of teams can make it to the playoffs?
Answers
Using the combination formula, it is found that 35 different combination of teams can make it to the playoffs.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 4 students are taken from a set of 7, hence the number of combinations is given by:
[tex]C_{7,4} = \frac{7!}{4!3!} = 35[/tex]
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through: (-3, 4), slope
1
4
Answers
Answer:
y = (-1/4)x + (13/4)
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
Remember that in a point (-3,4) you have an "x" and "y" value. As such, you have been given values for the "x", "y", and "m" variables. Therefore, you can plug these values into the general structure to find the value of "b".
y = mx + b <---- General structure
y = (-1/4)x + b <---- Plug (-1/4) in "m"
4 = (-1/4)(-3) + b <---- Plug in values from point
4 = (13/4) + b <---- Multiply (-1/4) and -3
(13/4) = b <---- Subtract (13/4) from both sides
Now that you know the value of "m" and "b", you can determine the formula.
y = (-1/4)x + (13/4)
the diagram is not drawn to scale!!
pls
Answers
Answer:
135°
Step-by-step explanation:
That triangle in the corner is an right angle isosceles triangle as that line the midpoint of both sides :
the base angle of this triangle (x) will be :
180 = 90 + 2x
90 = 2x
x= 45
Angles on a straight line add up to 180. So to work out a :
180 = 45 + a
135 = a
Hope this helped and brainliest please
here is the histogram of a data distribution. All class widths are 1.
what is the median of the distribution?
Answers
The median of the data is 5 if the all class widths are 1, option (C) is correct.
What is the median?A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.
In the histogram, 15 data values are given:
1, 2, 2, 3, 3, 3, 4, 5, 6, 6, 7, 7, 7, 8, 9
The mid-value is 5 which is on the 8th place
Thus, the median of the data is 5 if the all class widths are 1, option (C) is correct.
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Given that the measure of ∠x is 66°, and the measure of ∠y is 66°, find the measure of ∠z
Answers
Answer:
48
Step-by-step explanation:
66*2=132
180-132=48
Hope this helps!
If not, I am sorry.
These tables represent a quadratic function with a vertex at (6, 8). Which is the average rate of change for the interval from x = 13 to x = 14?
Answers
The average rate of a function is 81 if a quadratic function with a vertex at (6, 8).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
Quadratic function with a vertex at (6, 8).
It is required to find the average rate of the function:
Here the data table is not given, so we are assuming the value of a function:
At x = 13 is 196
f(13) = 144
At x = 14 is 225
f(14) = 225
The average rate of a function:
= [f(14) - f(13)]/(14 - 13)
= [225 - 144]/(1)
= 81
Thus, the average rate of a function is 81 if a quadratic function with a vertex at (6, 8).
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can anyone help? Need expert advice
Answers
Answer:
C (3,6)
Step-by-step explanation:
So the zeroes are the points that the loop goes through on the x-axis
so three and six
2. Draw a diagram to show that 5(x + 2) = 5x + 10.
Answers
Step-by-step explanation:
5(x+2)
1. Distributive property
2. Multiply
(5*x) + (5*2)
(5x)+(10)
Remove parenthesis
5x+10 ;
Therefore, 5(x+2) = 5x+10
Hopefully this helps! :3
Give the prime factorization of 28.
Answers
i need help with the area only for 7 8 and 9
Answers
We will get the areas of each one of the given triangles:
7) A = 12.69 mm²
8) A = 19.21 in²
9) A = 16.81 yd²
How to get the area of the given triangles?
7) First, we have an equilateral triangle, where all the sides measure 5.4mm
For an equilateral triangle of side length S, the area is:
[tex]A = \frac{\sqrt{3} }{4}S^2[/tex]
In this case, S = 5.4 mm, replacing we get:
[tex]A = \frac{\sqrt{3} }{4}(5.4mm)^2 = 12.62 mm^2[/tex]
8) Now we have two equal sides and one different. The general area of a triangle of base B and height H is:
A = B*H/2.
In this case, the base measures 3.4 in.
To get the height, let's divide the triangle into two right triangles, such that one cathetus is 3.4in/2 = 1.7 in.
The hypotenuse measures 5.9 in
And the other cathetus is the height of the triangle.
Then, by using the Pythagorean theorem, we see that the height is:
[tex]H = \sqrt{(5.9 in)^2 - (1.7in)^2} = 5.65 in[/tex]
Then the area of this triangle is:
[tex]A = (3.4 in)*(5.65 in)/2 = 19.21 in^2[/tex]
9) Here the base measures 8.2 yds, and the height 4.1 yds, so the area is just:
[tex]A = (4.1 yd)*(8.2 yd)/2 = 16.81 yd^2[/tex]
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Factorize the following perfectly:
1) 9x^4-16y^439
2) 64x^4+y^4
Answers
Answer:
neither can be factored any further but if it is (9x^4) - (16y^4) it can be factored down to ((3x^2)+(4y^2)) ((3x^2)+(4y^2))
Step-by-step explanation:
Which of the expressions are equivalent to the one below? (5x1)-7
Answers
Answer:
-2
Step-by-step explanation:
[tex](5 \times 1) - 7 \\ 5 - 7 \\ - 2[/tex]
-8x - 5y = 12
8x - y = 12
Answers
Natalie wants to use a sheet of fiberboard 30 inches long to create a skateboard ramp with a 28 angle of elevation from the ground
Answers
Answer:
You should raise one side 14 inches
Step-by-step explanation:
I used a right angle triangle calculater at this sight
https://www.calculator.net/right-triangle-calculator.html
State the various transformations applied to the base function f(x)=|x| to obtain a graph of the function g(x) = |x| − 2.
Horizontal shift of 1 unit to the right and a vertical shift upward of 2 units.
Horizontal shift of 1 unit to the right and a vertical shift downward of 2 units.
Horizontal shift of 1 unit to the left and a vertical shift downward of 2 units.
Horizontal shift of 1 unit to the left and a vertical shift upward of 2 units.
Answers
Horizontal shift of 1 unit to the left and a vertical shift downward of 2 units.
Transformation of functionTransformation technique is a way of changing the position of an object on an xy-plane.
Given the parent function of a modulus function f(x) = |x|, the graph of the function g(x) = |x| - 2 shows a vertical translation of the parent function down by 2 units.
The resulting graph of the translated function is as shown below
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Question
What expression represents the area of the square?
Answers
(3x-2)^2
squares area is 2 times its side length, since all the sides are the same. if the side length is 3x-2, take its second power
The area of a square is the product of the length of each side with itself. That is, Area A = s x s where s is the length of each side of the square.
A brand of cereal had 1.2 milligrams of iron per serving. Then they changed their recipe so they had 1.8 mg of iron per serving.
Answers
Using it's concept, it is found that the percent increase in the amount of iron per serving was of 50%.
What is the percentage increase of a value?It is given by the increase divided by the initial value, and subtracted by 100%.
In this problem:
The initial value is of 1.2 mg.The increase was of 1.8 mg - 1.2 mg = 0.6 mg.Hence the percent increase is given by:
P = 0.6/1.2 x 100% = 50%.
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!!!!! determine the function being differentiated, and the number at which its derivative is being evaluated. Where possible, evaluate the limits using differentiation.
Answers
Recall that the derivative of a function f(x) at a point x = c is given by
[tex]\displaystyle f'(c) = \lim_{x\to c} \frac{f(x) - f(c)}{x - c}[/tex]
By substituting h = x - c, we have the equivalent expression
[tex]\displaystyle f'(c) = \lim_{h\to0} \frac{f(c+h) - f(c)}h[/tex]
since if x approaches c, then h = x - c approaches c - c = 0.
The two given limits strongly resemble what we have here, so it's just a matter of identifying the f(x) and c.
For the first limit,
[tex]\displaystyle \lim_{h\to0} \frac{\sin\left(\frac\pi3 + h\right) - \frac{\sqrt3}2}h[/tex]
recall that sin(π/3) = √3/2. Then c = π/3 and f(x) = sin(x), and the limit is equal to the derivative of sin(x) at x = π/3. We have
[tex](\sin(x))' = \cos(x)[/tex]
and cos(π/3) = 1/2.
For the second limit,
[tex]\displaystyle \lim_{a\to0} \frac{e^{2a} - 1}a[/tex]
we observe that e²ˣ = 1 if x = 0. So this limit is the derivative of e²ˣ at x = 0. We have
[tex]\left(e^{2x}\right)' = e^{2x} (2x)' = 2e^{2x}[/tex]
and 2e⁰ = 2.