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.
Simplify 10cm:2m
Ratio
Answer:
1cm:20cm
Step-by-step explanation:
10cm:2m
1m=100cm
10cm:200cm
÷10
1cm:20cm
please help a brotha out and i'll give you brainliest
Answer:
First box: 15 * 10^10.
Second box: 300,000,000 meters per second.
Third box: 48 * 10^-13 meters.
Fourth box: 167 * 10^-29 meters.
Step-by-step explanation:
These should be correct! I put them in order from the top empty box to the bottom empty box!!!
Please mark brainliest if correct!!!
The following data describes weekly gross revenue (), television advertising expenditures (), and newspaper advertising expenditures () for Showtime Movie Theaters.
Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s)
98 5 1.5
90 2 2
95 4 1.5
92 2.5 2.5
95 3 3.3
94 3.5 2.3
94 2.5 4.2
94 3 2.5
Required:
Find an estimated regression equation relating weekdy gross revenue to television advertising expenditures and newspaper advertising expenditures (to 2 decimals).
Answer:
Hope this helps
Step-by-step explanation:
MRK ME BRAINLIEST PLZZZZZZZZZZZZZZ
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
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
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
I NEED HELP ASAP PLEASE HELP ME
Answer:
Can't help you on an ASIT
Step-by-step explanation:
Don invested $ 5 000 in an account paying 5% simple interest per year for 7 years.
Answer:
FV= $6,750
Step-by-step explanation:
Giving the following information:
Initial investment (P)= $5,000
Interest rate (r)= 5% simple interest
Number of periods (t)= 7 years
To calculate the future value of the investment, we need to use the following formula:
FV= (P*r*t) + P
FV= (5,000*0.05*7) + 5,000
FV= 1,750 + 5,000
FV= $6,750
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
What percent of 965 is 193?
No links please
The percentage equivalent is 20.
Given,
Percentage .
Now,
Firstly calculate the fractional form,
193/965 = .2
Now to convert fraction into percentage , multiply by 100.
So,
0.2 * 100
= 20%
Thus 193 is 20% of 965 .
Know more about percentage,
https://brainly.com/question/23418123
#SPJ6
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.
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.
Please help quickly as possible thank you! :)
Answer:
329.5ft
Step-by-step explanation:
First one: ((4+18+26)x10)/2
Second: +(18x4)
Third: (7x5)/2
=240+72+17.5
=329.5
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
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
Use the formula C C = 2pi * r and pi = 3 . 14 to find the circumference of a circle with a radius of 5 meters.
Answer:
Circumference of circle = 31.4 square meter
Step-by-step explanation:
Given:
Radius of a circle = 5 meter
Value of π = 3.14
Find:
Circumference of circle using formula "2πr"
Computation:
Circumference of circle = 2πr
By putting value of 'r' and 'π' in given formula
Circumference of circle = 2(3.14)(5)
Circumference of circle = (6.28)(5)
Circumference of circle = 31.4 square meter
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.
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:
Create the formula for the geometric sequence:
1, 4, 16, 64...
Answer:
since you are helping me with my answer on my other account, cutiepatato about the discrimination
imma try my best to help answer yours <3
the picture is in the box
Step-by-step explanation:
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 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:
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
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:
what is 6 divided by 10 to the second power
Answer:
j
Step-by-step explanation:
h
what is the difference between solid and hollow cone?
Answer:
https://youtu.be/wmQMBJ_ce3k see this video
PLEASE HELP! WILL AWARD BRAINLIEST TO THE FIRST CORRECT ANSWER!
If a/b=6, b/x=36, and a=36, what is the value of 1/x?
A) 1/2
B) 2
C) 3/2
D) 4
E) 6
Answer:
E) 6
Step-by-step explanation:
a/b = 6
36/b = 6
6b = 36
b = 36/6 = 6
b/x = 36
6/x = 36
36x = 6
x = 6/36 = 1/6
hence 1/x = 6
Answer:
E) 6
Step-by-step explanation:
a/b=6, b/x=36, and a=36
=>a = 6b
36 = 6b => b =6
b/x = 36 => x = b/36 = 6/36
so, 1/x = 36/6 = 6
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.
The survey was done to test the suggestion that the proportion of younger adults who use their horn is greater than the proportion of older adults who use their horn. Which of the following represents the hypotheses that we will be testing, assuming that p1 represents the population proportion of all young adults 20-39 who report using their horns and that p2 represents the population proportion of all older adults 60+ who report using their horns?
a. H0: p1=p2 versus Ha: p1>p2
b. H0: p1=p2 versus Ha: p1
c. H0: p1=p2 versus Ha: p2>p1
d. H0: p1=p2 versus Ha: p1=/=p2
Answer:
a. H0: p1=p2 versus Ha: p1>p2
Step-by-step explanation:
Given that
p1 represent the proportion of the population for young allots 20-39
And, p2 denotes the proportion of the population for all older adults that are above 60
So,
We need to find out the hypotheses
The null & alternative hypothesis is
H_o: P_1 = P_2
H_a: P_1>P_2
This shows the right tailed test