Write the equation of a sine or cosine function to describe the graph.
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.
Use the table below to answer the following question,
2:
хо 1 2 3 4 5 6
y 100 200 400 800 1,600 3,200 6,400
Which equation BEST fits the data given in the table?
se 3:
Of(x) = { (200)*
Of(x) = 100(2)*
uge 4
f(x) = 200)
age 5
Of(x) = 200(2)*
5
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Answer Of(x) = 200(2)
Step-by-step explanation:
Of(x) = 200(2)
If an object's position over time is given by the function d(t)=(t^2 +3)e^-1/2 for greater than 0 , on what interval is the object's position increasing and concave down ?
Answer:
Step-by-step explanation:
[tex]d(t)=(t^2+3)e^\frac{-1}{2} \\d'(t)=2t e^{-\frac{1}{2} }\\it~ is~ increasing ~if~d'(t)>0\\e^{-\frac{1}{2} } =\frac{1}{e^\frac{1}{2} } >0\\so~t>0\\and~decreasing~if~t<0\\[/tex]
so it is concave upward at t=0
A submersible is a type of underwater vessel. Suppose a submersible starts at a depth of 40 feet below sea level, represented by –40 feet. The table shows the submersible's change in depth from one minute to the next.
Answer the questions to find the depth of the submersible after 3 minutes.
1. Write and evaluate a subtraction expression to find the depth of the submersible at 2:16 p.m. (2 points)
2. Write and evaluate a subtraction expression to find the depth of the submersible at 2:17 p.m. (2 points)
3. Write and evaluate a subtraction expression to find the depth of the submersible at 2:18 p.m. (3 points)
4. If the submersible dove straight down, what is the distance between the submersible's starting position at 2:15 and its position at 2:18? Show your work. (3 points)
1. -40 - 180 = -220
2. -40 - 175 = -135
3. -40 - 185 = -225
4. 2:15 = -40
2:18 = 185
distance b/w them is = -40 - 185 = - 225
hope this answer helps you dear! btw I'm not sure but hope so this helps...!!
I agree with the first person that answered.
evaluate the expression 5+3
some one answer me with a question not a link
Answer:
8
Step-by-step explanation:
Add 5 and 3
-Lexi
Tp 3 Work Backwards
1. Bowser, Abby, and Chuckles are 3 dogs with a
combined age of 44. Bowser is 6 years older than
Abby. Abby is 2 years younger than Chuckles, c.
Which expression could be used to find the age of
Chuckles?
Answer:
Your equation option is possibly in here somewhere.
Step-by-step explanation:
A = C - 2
B = A + 6 → A = B - 6
C - 2 = A = B - 6 → B = C + 4
44 = C + B + A
44 = C + (C + 4) + (C - 2)
44 = 3C + 2
42 = 3C
C = 7
Dylan had 300 5p coins in a box last month. He now has 360 5p coins. Find the percentage increase.
Therefore the percentage increase is 72
72Can you help please?
Answer:
Step-by-step explanation:
Simplify.
81‾‾‾√
18
9
−3
−18
9514 1404 393
Answer:
(b) 9
Step-by-step explanation:
Maybe you want to simplify ...
[tex]\sqrt{81}=\sqrt{9^2} =\boxed{9}[/tex]
which is the correct answer??
geometry
Answer:
SAS || Side - Angle - Side
Step-by-step explanation:
You have 2 sets of congruent sides, and one set of congruent angles between them. (SAS)
That angle is congruent because ∠QRP and ∠TRS are vertical angles, and vertical angles have the same measurement.
Please answer and show your work
Answer:
check online for more information
Due Tomorrow: Answer question 21 with steps
[tex]\\ \sf\longmapsto tan28=\dfrac{BC}{AC}[/tex]
[tex]\\ \sf\longmapsto 0.5317=\dfrac{BC}{29.3}[/tex]
[tex]\\ \sf\longmapsto BC=29.3(0.5317)[/tex]
[tex]\\ \sf\longmapsto BC=15.5mi[/tex]
Now
[tex]\\ \sf\longmapsto AB^2=29.3^2+15.5^2[/tex]
[tex]\\ \sf\longmapsto AB^2=848.49+240.25[/tex]
[tex]\\ \sf\longmapsto AB^2=1088.74[/tex]
[tex]\\ \sf\longmapsto AB=32.9mi[/tex]
Given the function h (x) = –22 - 4, the value of h(-5) would be?
Answer:
At the value of x = 3 the function H(x) is undefined. (answer is 3)
Step-by-step explanation:
h (x) = 1/(x-5)2 + 4 (x-5) +4
Solution :
We know that for the values of x where denominator is zero the function H(x) is not define.
(x -5)2 +4 (x -5 ) +4 = 0
x2 -6x +9 =0
x2 - 3x - 3x +9 = 0
(x - 3)2 = 0
So x= 3
At x = 3 the function H(x) is undefined. (3 is your answer)
Rachel invests $25,000 at age 25. She hopes the investment will be worth $125,000 when she turns 50. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
The rate of growth will she need to achieve her goal is 2.8%
The formula for finding the compound amount is expressed as:
[tex]A =P(1+\frac{r}{n} )^{nt}[/tex]
P is the amount invested = $25000
t is the time in years = 25 years
A is the amount = $125000
r is the rate in %
Substitute the given parameters into the formula to have:
[tex]125000 =25000(1+r )^{25}\\5 =(1+r)^{25}\\log5=25log(1+r)\\log(1+r)=\frac{log5}{25} \\log(1+r)=0.02796\\1+r = e^{0.02795}\\1+r=1.0283\\r = 1.0283 -1\\r = 0.0283\\[/tex]
Hence the rate of growth will she need to achieve her goal is 2.8%
Learn more about compound amount here: https://brainly.com/question/18442810
Javier worked 45 hours last week. His hourly rate for hours worked is $ 8.75 . After his 40 hour work week, he is paid time and a half for overtime. What is Javier’s gross pay for last week?
The gross pay that Javier gets for last week is $415.625.
What is rate?Rate is a measurement to determine the change in one quantity with respect to another quantity.
Given that,
Rate for 1 hour = $8.75,
Since, Javier worked 45 hours last week,
So total amount got by Javier = 45×8.75=393.75
According to condition,
Last 5 days Javier is paid half more amount for overtime,
Therefore,
Javier amount of overtime gets by Javier in last 5 days
=8.75×5/2
=21.875
Total amount = 393.75+21.875=415.625
So the gross pay for last week is $415.625.
To know more about Rate on :
https://brainly.com/question/28580620
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an alloy is 70% iron. How much of this alloy do you need if you want to obtain 50.35 lb of iron?
Answer:
1007/20
Step-by-step explanation:
You helped me so i help you. Here you go my friends sorry i dont have an explanation. Good luck !
Use proportions. X is what you want.
70 50.35lb
__ = _____
100 x
Cross multiply to get 70x = 5035
Solve to get about 71.93 lbs of the alloy.
Skip count by 100 starting with 95.
95, ____, ____, ____, ____
Answer:
195, 295, 395, 495?
Step-by-step explanation:
10% of $70 = what is the answer i do not now it.
Answer:
10% 0f 70 is 7
Step-by-step explanation:
70÷10=7
10%=7
what if 5476 divided by 74? i need the working out too please!
I hope that the attachment helps you..
Show all work to identify the asymptotes and zero of the function f of x equals 3 x over quantity x squared minus 9.
Answer:
Asymptotes: x = -3, x = 3, y = 0Step-by-step explanation:
Given function:
f(x) = 3x / (x² - 9)Zero of the function:
f(x) = 03x / (x² - 9) = 0x = 0, x ≠ -3; 3Vertical asymptotes:
x² - 9 = 0x² = 9x = √9x = -3; x = 3Horizontal asymptotes:
The horizontal asymptote is y = 0, since the degree of the numerator is 1, while the degree of the denominator is 2.The graph with asymptotes and zero is attached
Today only, a sofa is being sold at a 32% discount. The sale price is $289.
What was the price yesterday?
Answer:
425$Step-by-step explanation:
Today only, a sofa is being sold at a 32% discount. The sale price is $289.
What was the price yesterday?
289 is 68% (100% - 32% = 68%)
289 : 68 * 100 =
425
--------------------------
check
425 - 32% = 289
the answer is good
Can someone please help me I will mark u brilliant
Answer:
the whole number 5 goes to the left of the decimal
Step-by-step explanation:
so think about it this way...
I have 10 dots .......... that is 1.0 but if I only have 5 of the 10 I have 0.5. if you have anymore questions just ask and ill help
A shoe store uses a 40% markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of $71?
Answer:
40% * 71 = Markup price
40% of 71 is 28.4, so i added the two together and got 99.4
so...
$28.4 + $71 = $99.40
Solve for k:
k + 6 > -37
Answer:
[tex]\sf k + 6 > -37[/tex]
[tex]\sf k+6-6>-37-6[/tex]
[tex]\boxed{\sf k>-43}[/tex]
Answer:
Subtract 6 from both sides:
K +6 - 6 > - 37 - 6
Simplify the arithmetic:
k > - 37 - 6
Simplify the arithmetic
k > - 43
Solve the equation.
2x - 3 + 4x = 21
A)x = -12
B)x= -6
C)x= 4
D)x = 6
Answer:
C. X=4
Step-by-step explanation:
Hello everybody! Can anybody help me out with this fairly simple multiple choice algebra problem? Thanks!
Answer:
l = P -2w
________ D is the correct choice
2
Today only, a table is being sold at a 33% discount. The sale price is 201.
What was the price yesterday?
if someone helps me with dis ill def give em brainliest
Answer:
with what?
Step-by-step explanation:
I think you forgot to attach something.
Josh volunteers at a library. One weekend, he put 234 returned books back on the shelves. Of those books 2/3 were hardcover books and the rest were paperback books. How many paperback books did Josh put back on the shelves?
Answer: 78 paperback books.
Step-by-step explanation:
1. Since 2/3 of the books are hardcover books, then 1/3 of the books are paperback books.
2. 234/3 = 78 books.
Answer:
78 paperback books
Step-by-step explanation:
234 x (2/3) = 156
234 - 156 = 78
Find complex numbers z=(x,y) such that
[tex]z ^{2} = - 5 - 12i[/tex]
Answer:
I don't know..,.............,,.,.......,