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
Please any math experts helps thank you
Answers
Answer:
[tex]\frac{t^2-16}{t^2-8t+16}[/tex]
We can factorise the numerator which the difference of squares formula:
[tex]x^2-y^2=(x+y)(x-y)[/tex]
---------------------------------
[tex]\frac{t^2-4^2}{t^2-8t+16} =\frac{(t+4)(t-4)}{t^2-8t+16}[/tex]
Next, factorise the denominator:
[tex]\frac{t^2-4^2}{t^2-8t+16} =\frac{(t+4)(t-4)}{(t-4)^2}[/tex]
[tex]\frac{(t+4)(t-4)}{(t-4)(t-4)}[/tex]
Cancel out the common factor of (t-4):
[tex]\frac{t+4}{t-4}[/tex]
What's the constant in 12n + 7 +13k⁴ + 4+ 39z
Answers
Answer:
7, 4 or 11
Step-by-step explanation:
No matter what n, k, or z is, 7 + 4 will always be constant. If you need to go farther, 7 + 4 is 11.
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
Math test urgent & any help would be greatly appreciated thank you the question is attached in the photo below
Answers
Answer:
Good luck on the test <333
Step-by-step explanation:
m<1 = ? // m<2 = ? // m<3 = ? // m<4 = ?
First I want to find the third angle because I see 93 degrees + 3 equals 180, so angle 3 is 87.
Now I find angle 2, because it seems as angle 2 is the same as 49 degrees.
Now for angle 1 and 4, we now that angles in a triangle sum to 180°. So for angle 1 the equation is 180 - (49 + 68), which is 63.
For angle 4 the equation is 180 - (49 + 87), which is 44.
Write an equation in slope-intercept form of the line shown.
Answers
Answer:
y=-3/2x+5
Step-by-step explanation:
The line intersects with points (2,2) and (4,-1). Slope intercept form is y=mx+b, where m is slope and b is the y intercept. The y intercept appears to be at (0,5), so b=5. As for the line, the formula for calculating slope is y2-y1/x2-x1 (the order of the points you use actually does not matter; you just have to make sure both coordinates from the same point are placed in the same part of the formula). -1-2/4-2=-3/2. Therefore, the slope is -3/2 (or -1.5 if you want a decimal).
What is -3/2 as a decimal
Answers
Answer:
-1.5
Step-by-step explanation:
To convert a fraction to a decimal number divide the numerator (-3) by denominator (2)
Answer:
-1.5
Step-by-step explanation:
Hai has 1 gallon jug of water. He drinks 1/8 gallons of water before lunch and 2/3 gallons of water after lunch. How much water did Hai drink all day?
Answers
Hai drink 11/24 gallons of water in all day
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Hai has 1 gallon jug of water.
Drinks 1/8 gallons of water before lunch
2/3 gallons of water after lunch.
We need to find how much water did Hai drink all day.
Now we have to add the water he drink.
1/8+2/3
LCM of 8 and 3
3+8/24
11/24
Hence, he drink 11/24 gallons of water in all day.
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right ANSWERS only plz i need help on how to do it also not just the answer plz and thank u
Answers
Answer:
option c
Step-by-step explanation:
because 2x +1= 0
2x/2= -1
x= -1/2
help !! giving brainliest.
Answers
Answer:
i guess the 2nd one
.
.........
Calculate the volume of a cuboid whose dimensions are 3.6cm 8.2cm 11cm
Answers
Answer:
[tex] 324.72 {cm}^{3} [/tex]Step-by-step explanation:
Given,
Dimensions of a cuboid = 3.6cm, 8.2cm and 11cm
As we know,
Volume of a cuboid = length × breadth × height
Therefore,
Volume of the given cuboid
= 3.6cm × 8.2cm × 11cm
(On multiplying)[tex] = 3.6cm \: \times 90.2 {cm}^{2} [/tex]
(On further multiplying)[tex] = 324.72 {cm}^{3} (ans)[/tex]
Hello there! :)
V=lwh (length times width times height)
We are given that:
Length=3.6 cm
Width=8.2 cm
Height=11 cm
Plug the values into the formula for volume:
V=lwh
V=(3.6)(8.2)(11)
Multiply:
V=324.72 cm³ (cubic centimeters)
Remember, volume is measured in cubic centimeters.
Hope it helps. Please let me know if you have any questions.
~A smiley teen who adores helping others
[tex]MagicalNature :)[/tex]
How do I do this problem?
Answers
Answer:
hey you can use scan and search
Answer:
I got : 0.42264973
Step-by-step explanation:
1/ -√3 + 1
-√3 = -1.73 ( 2 decimal place )
1/ -1.73 + 1
and found the answer
What is the scale factor of the dilation?
Answers
Step-by-step explanation:
Scale Factor (Dilation) The scale factor in the dilation of a mathematical object determines how much larger or smaller the image will be (compared to the original object). When the absolute value of the scale factor is greater than one, an expansion occurs. Hope this helps :)
Suppose that each of the numbers 0,1,2,3,4,5,6,7,8,9 is written on a piece of paper in a jar. If each number is equally likely, and x is the value of the number on the piece of paper, what is P(x < 6)
Answers
Answer:
10
Step-by-step explanation:
The value of P(x<6) is 1/2.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
The numbers 0,1,2,3,4,5,6,7,8,9 is written on a piece of paper in a jar.
So, P(x<6)
= P(x=5)+ P(x = 4)+ P(x=3) + P(x=2) + P(x=1)
= 1/10 + 1/10+ 1/10 + 1/10 + 1/10
= 5/10
= 1/2
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can you please help out my daughter on this...
Answers
Answer:
d
Step-by-step explanation:
What function is graphed below?
Answers
what is 1/5 divided by 9?
Answers
Answer:
9/5
Step-by-step explanation:
Just divide the 9 by 1 so it'll be 9/5 hope it helps
My Kotwica is baking a few cakes for the bake sale for her school. Each cake requires 2
cups of sugar. How many cakes cun she bake if she has 7 1/3 cups of sugar?
Answers
Given that 6 >-2, which statements are true? Check all that apply. (2)(6)>(-2)(2) 6 --2 2 2. 0 (-2)(6)>(-2)(-2) 6 -2 -2 -2 (2)(6)
Answers
Answer:
Gogogigi
Step-by-step explanation:
A BIOCHEMICAL RESEARCH COMPANY PRODUCES 50% OF ITS INSULIN AT A PLANT IN KANSAS CITY, AND THE REMAINDER IS PRODUCED AT A PLANT IN JEFFERSON CITY. QUALITY CONTROL HAS SHOWN THAT.5% OF THE INSULIN PRODUCED AT THE PLANT IN KANSAS CITY IS DEFECTIVE, WHILE 1.35% OF THE INSULIN PRODUCED AT THE PLANT IN JEFFERSON CITY IS DEFECTIVE. WHAT IS THE PROBABILITY THAT A RANDOMLY CHOSEN UNIT OF INSULIN CAME FROM THE PLANT IN JEFFERSON CITY GIVEN THAT IT IS DEFECTIVE?
Answers
The probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that is defective is 72.97%.
Given that a biochemical research company produces 50% of its insulin in Kansas and the rest in Jefferson, and 0.5% of Kansas's insulin is defective, while 1.35% of Jefferson's also is defective, to determine what is the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that it is defective, the following calculation must be performed:
0.5 + 1.35 = 1.85 1.85 = 100 1.35 = X 1.35 x 100 / 1.85 = X 72.97 = X
Therefore, the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that is defective is 72.97%.
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Write the equation of the line that passes through the points (-9,9) and (8, -2).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answers
Answer:
y + 2 = (11/17)(x - 8)
Step-by-step explanation:
Working with the x- and y-components of the given points, we see that the x component increases by 17 and the y-component decreases by 11. Thus, the slope of this line is m = rise / run, or 11/17.
Start with the general point-slope form: y - k = m(x - h) and use the coordinates of the 2nd point for h and k in this equation:
y + 2 = (11/17)(x - 8)
This is based on the point (-2, 8)
and the slope 11/17.
This result is the desired equation in point-slope form. If we wish to reduce this, proceed as follows:
17(y + 2) = 11x - 88, or 17y + 34 = 11x - 88
This last result simplifies to 17y = 11x - 54, or y = (11/17)x -54/17 (which is in slope-intercept form).
toby used 4 inches of tape to wrap a gift how much tape will he need to wrap 5 more of the same gift?
Answers
Answer:
20
Step-by-step explanation:
4*5 = 20%
Help help help please good luck be honest
Answers
Answer:
A'(-6,4) B'(2,2) C'(-2,-2)
Step-by-step explanation:
The dilation is by 2. This just means you multiply each number by two. FOr example, for point a, multiply -3 by 2 and 2 by 2 to get (-6, 4).
Select the geometric figure that correctly matches with the following formula:
A=LW
Answers
Answer:
Square because the area of a square is length times width.
The formula matches with square.
What is Geometry?A branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids
As,
First, Area of circle = πr²
Hence, it is not possible.
Second, square
Area of square = l * b = LW
Similarly for trapezium
Area= 1/2( a+ b)* h
Hence, the formula matches with square figure.
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00.5 divide 53.342 give solution right answer=brainliest=10 points
☢️⚠☢️nonsense report☢️⚠☢️
Answers
Answer:
Iᖴ 00.5÷53.342=0.009373476
Iᖴ 53.342÷00.5=106.684
Step-by-step explanation:
ᕼOᑭᗴ IT ᑕᗩᑎ ᕼᗴᒪᑭ YOᑌ ᒪOᐯᗴᒪOTՏ
The radius of a circle is constantly increasing. At a certain moment, the rate of increase of the circumference is the same as the rate of increase of the area. At that moment, what is the area of the circle?
a. 1/pi
b.pi/4
c.4pi
d.pi
e.4/pi
Answers
I need help. Im in 6th grade and I'm so confused. IT IS SAYING I NEED TO UPGRADE TO SEE THE ANSWER> NOO
Answers
Answer:
i can help with the problem
Simplify: 8√3 + 12√3
Answers
Answer:
20√3
Step-by-step explanation:
10
Find the area of the shape.
Either enter on exact answer in terms of it or use 3.14 for it and enter your answer as a decimal.
units
Show Calculator
Answers
Answer:
(4-x)(x-4)=16-x2 help me please
Expand and simplify.
(x + 1)(2-6)
Answers
:(x+1)(4)
(X+1)
-4x+1)
-4x-4 answer correct.
Dita adds 2 oz of milk to an 18 oz cup of coffee that is 10% milk. What is the percentage of milk in the resulting mixture?
SHOW YOUR WORK!
Answers
Increasing the amount of milk in the coffee increases the percentage of milk in the cup of coffee.
The resulting mixture is 19% milkReasons:
The known quantities are;
The volume of milk Dita adds to an cup of coffee = 18 oz
The percentage of milk in the cup of coffee = 10%
Required:
The percentage milk in the resulting mixture.
Solution:
Initial amount of milk initially in the cup of coffee = 10% × 18 oz = 1.8 oz
The total amount of milk in the resulting mixture = 2 oz + 1.8 oz = 3.8 oz
Volume of the resulting mixture = 2 oz + 18 oz = 20 oz
The percentage of milk in the resulting mixture is therefore;
[tex]\displaystyle \mathrm{Percentage \ of \ milk = } \frac{3.8}{20} \times 100 = 19\%[/tex]
The resulting mixture is 19% milk.
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On a very hot summer day, 5% of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism. Assuming a binomial distribution, what is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent
Answers
Answer:
Answer:
60
Step-by-step explanation:
Given : On a very hot summer day, 5 percent of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism.
To find : What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?