Determine the amplitude of the trigonometric function: *attached image*
Answer:
[tex]\displaystyle 2[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{y = -2cos\:(\frac{\pi}{3}x - \frac{2}{3}\pi) + \frac{1}{2}} \\ \\ 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 \frac{1}{2} \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{2} \hookrightarrow \frac{\frac{2}{3}\pi}{\frac{\pi}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6} \hookrightarrow \frac{2}{\frac{\pi}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle \boxed{y = -2sin\:(\frac{\pi}{3}x - \frac{\pi}{6}) + \frac{1}{2}} \\ \\ 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 \frac{1}{2} \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{1}{2}} \hookrightarrow \frac{\frac{\pi}{6}}{\frac{\pi}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6} \hookrightarrow \frac{2}{\frac{\pi}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]
As you can see, the right-centred photograph displays the trigonometric graph of [tex]\displaystyle y = -2cos\:\frac{\pi}{3}x + \frac{1}{2},[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will horisontally shift and map the graph onto the sine graph [photograph farthest to 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 be very careful with your calculations. So, between the two photographs, we can tell that the cosine graph [centre right photograph] is shifted [tex]\displaystyle 2\:units[/tex]to the left, which means that in order to match the sine graph [photograph farthest to the left], we need to shift the graph FORWARD [tex]\displaystyle 2\:units,[/tex]which means the C-term will be positive, and by perfourming your calculations, you get [tex]\displaystyle \boxed{2} = \frac{\frac{2}{3}\pi}{\frac{\pi}{3}}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = -2cos\:(\frac{\pi}{3}x - \frac{2}{3}\pi) + \frac{1}{2}.[/tex]Intermediate, we have two sine graphs to deal with [centre left photograph and the photograph farthest to the left]. The left-centred photograph displays the trigonometric graph of [tex]\displaystyle y = -2sin\:\frac{\pi}{3}x + \frac{1}{2}.[/tex]So, just like before, we need to figure out the appropriate C-term that will horisontally shift the graph back into position ["position", meaning shifting this sine graph back in plase (matching the sine graph in the photograph on the left)]. So, between the two photographs, we can tell that the left-centred sine graph is shifted [tex]\displaystyle \frac{1}{2}\:unit[/tex]to the left, which means that in order to match the leftward sine graph, we need to shift the graph FORWARD [tex]\displaystyle \frac{1}{2}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you get [tex]\displaystyle \boxed{\frac{1}{2}} = \frac{\frac{\pi}{6}}{\frac{\pi}{3}}.[/tex]So, when shifted back into original position, the sine graph is [tex]\displaystyle y = -2sin\:(\frac{\pi}{3}x - \frac{\pi}{6}) + \frac{1}{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 WILL hit [tex]\displaystyle [-2\frac{1}{2}, \frac{1}{2}],[/tex]from there to [tex]\displaystyle [3\frac{1}{2}, \frac{1}{2}],[/tex]they are obviously [tex]\displaystyle 6\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 6.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, and to be certain, 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 = \frac{1}{2},[/tex]in which each crest is extended two units beyond the midline, hence, your amplitude. Now... the sine graph in the photograph farthest to the right is the OPPOCITE of the sine graph in the photograph farthest to the left, and the reason for this is because of the negative inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of any trigonometric equation, the whole graph reflects over the midline. Keep this in mind moving forward. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
BEEN ASKING FOR AN HOUR PLEASE! a rectangle's area is 336 mm Its height is 16 mm. What is its bases?
Answer:
Base is 21
Step-by-step explanation:
I'm gonna be honest, just divide 336 by 16.
However just in case you meant volume instead of area because you said (bases), they would be 5 and 4.2
How much water is needed to completely fill up a swimming pool with dimensions of 18 ft by 36 ft by 5 ft?
Answer:
i think 648
Step-by-step explanation:
Area = Length times width
18 times 36 = 648
But It could be 3,240
18 times 36 times 5
24 mi
32 mi
c
What is the length of the hypotenuse?
c =
miles
Answer:
40 mi
Step-by-step explanation:
a² + b² = c²
24² + 32² = c²
1600 = c²
√1600 = c
c = 40
What is the value of
0 4,194,304
020
O 1,024
O 625
Answer:
1024
Step-by-step explanation:
4^8/4^3=4^8-3=4^5=1024
PLEASE ANSWER I DON'T HAVE ALL DAY WILL MARK BRAINLIEST
Mr. Smith took his car to an auto shop for repairs. The shop
charged him $75 per hour plus $10 for parts. The equation
C = 75h+ 10 represents the total cost, c, of the repairs takin
h hours. How much did Mr. Smith pay if the repairs took
2 hours?
A $85
B $235
$160
$150
Answer:
$160
Step-by-step explanation:
you replace h with 2 and then add 10 so the equation would look like 75 times 2 plus 10 then you would get 160
Evaluate F(x)=4x+5 when x=4
f(4)=
Answer:
F(4) = 21
Step-by-step explanation:
[tex]F(4)=4(4)+5\\F(4)=16+5\\F(4)=21[/tex]
Answer:
21
Step-by-step explanation:
F(X) = 4x + 5
One is asked to find (F(4)), substitute (4) in place of (x) and solve,
F(4) = 4(4) + 5
= 16 + 5
= 21
Eight hundred dentists were surveyed about the toothpaste they would recommend to their patients. The survey results are shown in the table below.
Dentists Survey Results
Toothpaste Number Recommended
W 280
X 165
Y 210
Z 145
Which of these could a commercial accurately state about the results of the survey?
Select one:
More than half of the dentists recommended toothpaste W and Y.
More than twice as many dentists recommended toothpaste W over Z.
More dentists recommended toothpaste Z over Y.
Four out of five dentists recommended one of the toothpastes.
Answer:
[tex] \huge \sf \underline { \orange{AnSwEr : }}[/tex]
More dentists recommended toothpaste Z over Y.~
Large Small
Blue 17 3
Red 8 12
?
Find: P(Red and Small)
Remember to reduce your answer.
Answer:
Step-by-step explanation:
20
The probability of red to small will be equal to 12 / 20.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
It is given that there are 20 blue numbers large are 17 and small are 3. Similarly, there are 20 red numbers large are 8 and small are 12.
The probability of getting a small red number will be calculated as below:-
Probability = Number of favorable outcomes / Number of sample
Number of favorable outcomes = 12
Number of samples = 20
Put the value in the formula above.
Probability = 12 / 20
Therefore, the probability of red to small will be equal to 12 / 20.
To know more about probability follow
https://brainly.com/question/24756209
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help!! please answer this easy math <3 :)
Answer:
y = x - 10
Step-by-step explanation:
slope intercept form is
y = mx + b
m is the slope = 1
b is the y intercept = -10
Therefor
y = x - 10
A rectangular prism with a square base has a volume of 980 inches. If the height of this rectangular prism is 5 inches, what are the dimensions of its base?
Answer:
14 inches
Step-by-step explanation:
Since the rectangular prism has a square base, we know that the width and length are equal.
Using the formula for calculating the volume of a rectangular prism, we can set up an equation:
(width^2)*height = 980 cubic inches or
(width^2)*5 in. = 980 cubic inches, simplify the equation by dividing each side by 5 inches, and the result is:
width^2 = 196 sq.in., simply by taking the square root of each side of the equation, and the result is:
√width (inches) = √196 square inches = width = 14 inches
each side of the prism's base is 14 inches
Answer:
980 in
Step-by-step explanation:
How many children would you need to invite to the party for the cost to be the same both places
Answer:
4 children
Step-by-step explanation:
Let the number of children = c.
The cost of the pizza place for c children (without the fee) = 8c
The cost of the pizza place for c children (with the fee) = 8c+30
The cost of the taco place for c children (without the fee) = 12c
The cost of the taco place for c children (with the fee) = 12c+14
To find c when the totals are equal, set 8c+30 equal to 12c+14 and solve:
8c+30=12c+14
8c-12c=14-30
-4c=-16
c=4
correct answer gets brainlisted and a like
An arena charged $119.49 for 4 tickets. This price included a $9.49 service fee What was the cost of one ticket?
Enter your answer in the box.
$
Answer: $27.50
Step-by-step explanation: So first off you would subtract the service fee from the total amount to get $110.00 then you would divide that by four to get $27.50 per ticket.
A fish tank holds approximately how much water?
Answer:
Fish tanks come in all different sizes. I can't answer unless you tell me the dimensions (Length, width, height)
Step-by-step explanation:
If you can paint 75 square feet every 45 minutes how long will it take to paint a 8 by 5
Answer:
24 minutes
Step-by-step explanation:
The Dimensions of the wall are given as:
8ft × 5ft = 40ft² or 40 square feet
Step-by-step explanation:
Answer:
24 minutes
Step-by-step explanation:
8 * 5 = 40 ft²
---------------------------
Method I: Use a proportion
x/40 = 45/75
multiply both sides by 40
x = 45/75 * 40
x = 24
24 minutes
---------------------------
Method II: Use the rate
45/75 = 0.6min/ft²
40 * 0.6 = 24
24 minutes
The base of a pyramid is a rectangle with a length of 3 centimeters and a width of 6 centimeters. If the height of the pyramid is 12 centimeters, what is the volume of the pyramid?
Answer:
Step-by-step explanation:
okay so if the centimeter is 3 you would multiply it by 6 cm and that
18 and then mulitiply that by 12 and your answer is
216
Susan is making a large batch of salsa. She can spend no more than $30 on ingredients. She buys all of the ingredients except for tomatoes for $6.50. Tomatoes cost $2 per pound. How many pounds of tomatoes, x, can she buy?
I'll give you the answer :)
Step-by-step explanation:
sorry I don't know the answer
Answer: 3 Pounds
Step-by-step explanation: Limit = 30 - 6.50 / 2 = 3.25. Limit = 30, she wouldn't be able to go over 6.50 so it would be 3.
In clinical trials of a newly developed cold medicine, it was found that 45 out of 200 individuals that took the new medicine (Group 1) experienced an upset stomach as a side effect and 33 out of 150 individuals that took a placebo (Group 2) experienced an upset stomach. Test to see if the new drug produced a significantly higher proportion of individuals experiencing upset stomach. Use a 0.01 level of significance. Select the correct alternative hypothesis and decision.
a. H: Pi≠P2; Do not reject the null hypothesis.
b. H1: p1>P2; Do not reject the null hypothesis.
c. H: Pi > p2; Reject the null hypothesis.
d. H1: p. e.) Hi: p1≠P2; Reject the null hypothesis.
f. H: P1
Answer:
Step-by-step explanation:
Group 1 Information:
sample size : n₁ = 200
individuals with stomach as a side effect x₁ = 45
p₁ = 45 / 200 p₁ = 0,225 then q₁ = 1 - p₁ q₁ = 0,775
Group 2 Information:
sample size : n₂ = 150
individuals with stomach as a side effect x₂ = 33
p₂ = 33/150 p₂ = 0,22 q₂ = 0,78
Hypothesis Test:
Null Hypothesis: H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ > p₂
The alternative hypothesis indicates that the test is a one-tail test to the right
Significance level is α = 0,01 ( confidence interval 99%)
From z-table we get z(c) for that α z(c) = 2,32
To calculate z(s)
z(s) = ( p₁ - p₂ ) / EED
EED = √ ( p₁*q₁)/n₁ + ( p₂*q₂)/n₂
EED = √ ( 0,225*0,775)/200 + (0,22*0,78)/150
EED = √ 0,0008718 + 0,001144
EED = 0,045
z(s) = ( 0,225 - 0,22 ) / 0,045
z(s) = 0,005 / 0,045
z(s) = 0,11
Comparing z(s) and z(c)
z(s) < z(c) 0.11 < 2.32
Then z(s) is in the acceptance region. We accept H₀ . We don´t have evidence to support differences between the two groups.
Two shops, Lidal and Oldi, sell the same brand of toilet rolls but with different package sizes.
Calculate the price per 72 rolls for each shop.
Write which shop is the best value for money in the comment box.
Lidal's price is better
Step-by-step explanation:
Lidal
4 for £2.04
1 for £2.04/4= £0.51= 51 p
Oldi
9 for £4.68
1 for £4.68/9= £0.52= 51 p
Lidal offers better price per roll
evaluate the expression for x = 6
3 x + 5 =
Answer:
23
Step-by-step explanation:
6x3=18
18+5=23
Answer
this is wrong
Step-by-step explanation:
this is an equation not an expression. Equations have = and expressions dont. Please rewrite this and I will help.
Walker invests $4,200 in a savings account earning 8% interest compounded yearly. What will the account balance be after 7 years?
Answer:
2,562
Step-by-step explanation:
8% of 4,200 is 366, 366×7=2,562
Hope This Helps!
PLEASE HELP
there were 16 more nickels than dimes in the purse. if there were a hundred coins total how many nickels were there?
Answer:
58
Step-by-step explanation:
There would be 58 nickels and 42 dimes. This can be found out by
1. 100 - 16 = 84
2. 84/2 = 42
3. 42 + 16 = 58
making 42 dimes and 58 nickels.
Two rectangular picture frames have the same area of 45 square inches but have different side lengths. Frame A has a length of 6 3/4 inches, and Frame B has a length of
7 1/2 inches.
WITHOUT CALCULATING, predict whicb frame has the SHORTER WIDTH. Explain you reasoning.
Pleaseee HELP!! Pls support your answer by reasoning
Question:
Two rectangular picture frames have the same area of 45 square inches but have different side lengths. Frame A has a length of 6 3/4 inches, and Frame B has a length of 7 1/2 inches.
Answer:
1. the longer frame (B) has the shorter width
2. the shorter width is 6 3/7 inches, area divided by length
Step-by-step explanation:
The relation between area, length, and width is ...
A = LW
Then the width is ...
W = A/L . . . . . inversely proportional to length
1. Since length and width are inversely proportional (when area is constant), the shorter width will be associated with the longer length. Frame B will have the shorter width.__
2. The width of frame B is ...
W = A/L = (45 in²)/(7 in) = 45/7 in = 6 3/7 in
-Alan Becker
what is the difference between solid and hollow cone?
Answer:
https://youtu.be/wmQMBJ_ce3k see this video
in a class of students, the following data table summarizes how many students have a brother or sister. What is the probability that a student chosen from randomly from the class does not have a sister?
Answer:
Step-by-step explanation:
The fact that the student does not have a brother either only means that you have chosen an only child. So there are 13 people that do not have a sister. The 13 comes from the bottom row. 9 + 4 = 13
What is the total number of people in the class? There must be 15 more who do have a sister.
15 + 13 = 28
So the answer should be 13 / 28 or 0.464
The ratio of Alex's toy cars to Jim's is 8:3. How many toy cars do they have altogether, if Alex has 40 more cars than Jim?
Answer:
88
A:J
8:3
a - 40 = j
8y - 40 = 3y
5y = 40
y = 8
8 *11 = 88
Step-by-step explanation:
Hope i helped! have a nice day
Answer:
88
Step-by-step explanation:
I know this because I used a secret method my parents told me that I can't tell anyone.
Re write this expression 4(6 x +12)
Answer:
24 (x + 2)
24x + 48
these are two ways to rewrite the expression
Answer:
24x+48
Step-by-step explanation:
I NEED HELP ASAP PLEASE HELP ME
Answer:
Can't help you on an ASIT
Step-by-step explanation:
Consider the function g (x) = StartFraction x squared + 7 x minus 18 Over x squared + 2 x minus 8 EndFraction. Which type of discontinuity does the function have at x = –4? jump mixed infinite removable
Answer:
D. Removeable
Step-by-step explanation:
ed2021
Answer:
It's actually C, infinite!
Step-by-step explanation: