a. Find the amplitude.
b. Find the period.
c. Find the vertical shift.
d. Find the horizontal shift.
e. Find the number of cycles between 0 and 2π.
f. Find the equation of the graph.
You must show all of your work to receive credit.
Answers
Answers:
a) Amplitude = 2b) Period = pic) Vertical shift = -2, which means it has been shifted down 2 units.d) Horizontal shift = 3pi/8, this shifting is to the right.e) There is one cycle between 0 and 2pi.f) The equation of the graph is y = 2*sin(2(x-3pi/8))-2========================================================
Explanations:
Part (a)
The highest point is when y = 0 and the lowest point is when y = -4. The vertical distance between the peak and valley is 4 units, which cuts in half to 2. This is the amplitude. It's the vertical distance from the center to either the peak or valley.
Note: Amplitude is always positive as it measures a distance.
---------------------
Part (b)
For x > 0, the first valley or lowest point occurs between 0 and pi/4. It appears to be the midpoint of the two values. So that would be (0+pi/4)/2 = pi/8.
The next valley occurs between pi and 5pi/4. Compute the midpoint to get (pi+5pi/4)/2 = (4pi/4+5pi/4)/2 = (9pi/4)/2 = 9pi/8
So we have the graph go from one valley x = pi/8 to the next valley over x = 9pi/8. This is a distance of pi units because 9pi/8-pi/8 = 8pi/8 = pi
The graph repeats itself every pi units, so the period is pi.
---------------------
Part (c)
The midline is normally through y = 0, aka the x axis. However, the graph shows the midline is through y = -2. This means the graph has been shifted down 2 units.
---------------------
Part (d)
This will depend on whether you use sine or cosine. This is entirely because cosine is a phase-shifted version of sine, and vice versa. I'll go with sine.
The parent sine function y = sin(x) goes through the origin (0,0)
However, as part (c) mentioned, we shifted the graph 2 units down. So we have y = sin(x)-2. But plugging x = 0 into this leads to the point (0,-2)
This doesn't match what the graph says. The graph shows the point (3pi/8, -2) on the red curve. The x coordinate 3pi/8 is the midpoint of pi/4 and pi/2
This must mean we need to shift the sine graph 3pi/8 units to the right.
---------------------
Part (e)
Start at the lowest point when x = pi/8. If you start the cycle here, then it ends when x = 9pi/8. See part (b).
So far we've completed one cycle. If we start at x = 9pi/8, then the next valley or lowest point is slightly beyond or to the right of x = 2pi. This means we run out of room and we haven't completed a full cycle.
Overall, one full cycle is between 0 and 2pi.
---------------------
Part (f)
Again I'm going to use sine instead of cosine. Refer back to part (d).
The general sine curve equation is
y = A*sin(B(x-C))+D
where
|A| = amplitudeB handles the period, specifically T = 2pi/B where T is the period. We can solve for B to get B = 2pi/TC = horizontal phase shiftD = vertical shift, and ties together with the midline equationIn this case, we found that
|A| = 2T = pi leads to B = 2pi/T = 2pi/pi = 2C = 3pi/8D = -2So,
y = A*sin(B(x-C))+D
will update to
y = 2*sin(2(x-3pi/8))-2
which is one way to express the equation of the red curve. Optionally you can distribute the 2 through to (x-3pi/8).
Related Questions
i need help now its due right now can anyone help me
Answers
Answer:
(2,-3)
Step-by-step explanation:
I thought you'd actually have to calculate it but I guess they just wanted to give you guys a graph lol
Chase caught 2/3 of the balls hit to left field. Ryan caught 3/5 of the balls hit to right field. Which pair of equivalent fractions will help them find the total amount of the balls they both caught?
Answers
Answer:
1 4/15 balls
Step-by-step explanation:
From the question, we are told that:
Chase caught 2/3 of the balls hit to left field.
Ryan caught 3/5 of the balls hit to right field.
The Lowest common denominator for both fraction is given as 15
Hence, the equivalent fractions for each boy is calculated such that the denominators of both fraction is 15
For Chase:
We Multiply both numerator and Denominator by 5
2 × 5 /3 × 5 = 10/15
2/5 = 10/15
For Ryan
We Multiply both numerator and Denominator by 3
3 × 3 /5 × 3 = 9/15
3/5 = 9/15
The total amount of the balls they both caught is:
10/15 + 9/15
= 19/15 = 1 4/15
Where to finds test answers on mathspace before you do the test?
Answers
Step-by-step explanation:
You can use web browser to type your answer into mathspace. The following browsers supports mathspace.
Chrome, MacOS safari, Microsoft edge .
1.) Which of the following is closest to 1?
A.
B.
9
10
C.
D. 98%
99
E.
100
8
Answers
Answer:
Step-by-step explanation:
98% it is the only percent and it is close to one
Here is a set of signed numbers: 7, -3, LaTeX: \frac{1}{2}1 2, -0.8, 0.8, LaTeX: -\frac{1}{10}− 1 10, -2 Order the numbers from least to greatest. Group of answer choices 7, 0.8, 1/2, -1/10, -0.8, -2, -3 -3, -2, -0.8, -1/10, 1/2, 0.8, 7 -1/10, 1/2, -0.8, 0.8, -2, -3, 7
Answers
Answer:
[tex]-3, -2, -0.8, -\frac{1}{10} ,\frac{1}{2}, 0.8, 7[/tex]
Step-by-step explanation:
Given
[tex]7, -3, \frac{1}{2}, -0.8, 0.8, -\frac{1}{10}, -2[/tex]
Required
Order from least to greatest
[tex]7, -3, \frac{1}{2}, -0.8, 0.8, -\frac{1}{10}, -2[/tex]
Convert 1/2 and -1/10 to decimals
[tex]7, -3, 0.5, -0.8, 0.8, -0.1, -2[/tex]
Negative numbers are always the least of all numbers.
In the given list, the negative numbers are:
[tex]-3, -0.8, -0.1, -2[/tex]
The higher the magnitude of a negative number, the smaller it is.
--------------------------------------------------------------------------------------------
Take for instance: -7 and -8.
-8 has a magnitude of 8 and -7 has a magnitude of 7.
Because 8 > 7 (the magnitudes), then
-8 < -7
--------------------------------------------------------------------------------------------
Using the above analysis:
[tex]-3, -0.8, -0.1, -2[/tex] from least to greatest is:
[tex]-3, -2, -0.8, -0.1[/tex]
Considering the positive numbers:
[tex]7, 0.5, 0.8[/tex]
From least to greatest, it is:
[tex]0.5, 0.8, 7[/tex]
Merge the negative and the positive numbers:
[tex]-3, -2, -0.8, -0.1,0.5, 0.8, 7[/tex]
Convert 0.5 and -0.1 back to fractions
[tex]-3, -2, -0.8, -\frac{1}{10} ,\frac{1}{2}, 0.8, 7[/tex]
Fill in the blanks needs to be done by 9:30!!
Answers
Answer:
1. Straight line
2. mx+b
3. slope , y intercept
4. dont know sorry
Step-by-step explanation:
•Straight Line
•Mx+b
• (not sure)
• (not sure)
•constant
can you help me the first person will get brainliest
Answers
Answer:
put the equations in tiger math
Step-by-step explanation:
but other than that have a good day !! goodluck with everything
3 balloon + 2 cakes = £19
9 balloon + 3 cakes = £42
work out:
1 balloon in £
1 cake in £
Answers
Step-by-step explanation:
3 balloons + 2 cakes = £19
=> 9 balloons + 6 cakes = £57 (multiply by 3)
9 balloons + 6 cakes = £57
- (9 balloons + 3 cakes = £42)
=> 3 cakes = £15, 1 cake = £5.
Therefore 3 balloons + 2(£5) = £19,
3 balloons = £9, 1 balloon = £3.
Hence each balloon is £3 and each cake is £5.
Number Lines
F is between E and G. EF= 9 and FG= 11. what is the length of EG?
Answers
Answer:
20
Step-by-step explanation:
EG = EF + FG
Its given in the question that -
• EF = 9
• FG = 11
So,
EG = 9 + 11 = 20
Can somebody plz help solve for each question what x =?(only if u know how to do it) thanks :)
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DD!!
Answers
Answer:
7)x=11
8)x=16
9)n=12
10)m=13
11)n=8
12)m=3
Step-by-step explanation:
Answer:
7= 11. 8=16. 9=12. 10=13 11=8. 12=3
Step-by-step explanation:
7= 9+2=11
8=12+4=16
9=9+3=12
10=8+5=14
11=7+1=8
12=3+0=3
Andy found these used cars prices in the newspaper.
Answers
Answer:
11,000
Step-by-step explanation:
Average or Mean= sum of goods/ total number of goods
Average= 6,000+12,000+20,000+8,000+9,000/5
= 55,000/5
= 11,000
Last month, a car dealer sold 50 cars. This month, 60 cars were sold. Find the percent increase in sales.
Answers
Answer:
the sale is an increase of 10 cars. 10 is 20% of 50 so therefore the dealer had an increase of 20% in sales.
this is the choices
88
70
110
120
Answers
Answer:
110
Step-by-step explanation:
Y and X have to equal 180
70+x+180
=110
find the probability that a number chosen at random from the integers between 5 and 16 inclusive is a multiple of 3 or a mutiple of 2
Answers
Answer: Numbers between 5 and 16 are:-
6, 7, 8, 9, 10, 11, 12, 13, 14 , 15 and 16.
Therefore, total number of outcomes =11
Numbers inclusive between 5 and 16 which are divisible by 2 or 3 are-
6 , 8, 9 ,10 ,12, 14 and 15.
Number of favourable outcomes = 7
Therefore, probability of getting a number which is either a multiple of 2 or 3 is:
p(e) = \frac{7}{11}p(e)=
11
7
HENCE, THE REQUIRED PROBABILITY IS = 7 / 11.
Step-by-step explanation: does this help?
HElP MEh PleZ
A scuba diver descends below the surface of a lake at a rate of 12 feet per minute. What integer represents the depth of the diver after 4 minutes?
Answers
Since this scuba diver descends below the surface of a lake at a rate of 12 feet per minute, an integer which represents the depth of the diver after four (4) minutes is 48 feet.
What is the rate of change?The rate of change can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.
Mathematically, the rate of change for the depth covered by this scuba can be calculated by using this formula;
Rate of change = Depth/time
Making depth the subject of formula, we have:
Depth = Rate of change × time
Substituting the given parameters into the formula, we have;
Depth = 12 × 4
Depth = 48 feet.
Read more on rate of change here: brainly.com/question/15648128
#SPJ1
What is the slope of the linear equation y=x+10
a. Slope=m=10
b. Slope=m=1
c. Slope=m=5
d. Slope=m=11
Answers
Answer:
slope = 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x + 10 ← is in slope- intercept form
with slope m = 1
Help and you shall receive 20 points
Answers
Answer:
its D 7 2/5
Step-by-step explanation:
Acela Express, the fastest train between Washington D.C and Boston covers a distance of 455 miles in 7 hours. How many miles will the train travel in 4 hours?
Answers
Answer:
260 miles
Step-by-step explanation:
Given that:
Distance covered in 7 hours = 455 miles
Number of miles train will travel in 4 hours
Average travel speed per hour :
Distance traveled / time taken
455 miles / 7 hours
= 65 miles per hour
Number of miles traveled in 4 hours :
Average Speed per hour * time
(65 * 4) = 260 miles
Please answer correctly !!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!
Answers
Answer: c
Step-by-step explanation: a parrelagram has each side parrel
Answer:
B. - it has four right angles
PLS HELP ME WITH THIS !!
Answers
180 = 5p+98 + 9p-2
180 = 14p + 96
84 = 14p
6 = p
part 2:
angle S will be the same as angle Q, so:
9p-2
9(6)-2
54-2
M
Clear selection
If I double a number, subtract 3 and the answer is 7, what number did I start 1 point
with?
10
5
4
6
Answers
Answer:
5
Step-by-step explanation:
if you double 5 you get 10 and if you remove 3 you get 7
Answer:
5
Step-by-step explanation:
since 5 +5 = 10 then you'd subtract 3 u would end up with 7
To the nearest millimeter, a cell phone is 135 mm long and 51 mm wide. What is the ratio of the width to the length?
Answers
Answer:
51:135
common factor is 3
51/3 = 17
135/3 = 45
17:45
A plane can travel 640 miles against the wind in the same time it can travel 800 miles with the wind. If the plane can fly 180 mph in calm air, what is the speed of the wind? If x represents the speed of the wind, which expression represents the time it takes for the plane to travel the 640 miles against the wind?
1. 640/x
2. 640/(x+180)
3. 640/(180-x)
Answers
A 25 foot ladder leans against a house. How far
is the foot of the ladder from base of the building
if the top of the ladder is 20 feet from the ground?
A. 20 ft
B. 15 ft
C. 18 ft
D. 10 ft
Answers
Answer:
x=15
Step-by-step explanation:
Wilson is 6 years older than Mary. Wilson's age is 10 years less than five times Mary's age. The equations below model the relationship between Wilson's age (w) and Mary's age (m):
w = m + 6
w = 5m − 10
Which is a possible correct method to find Wilson's and Mary's ages?
Solve w + 6 = 5w − 10 to find the value of w.
Write the points where the graphs of the equations intersect the x axis.
Solve m + 6 = 5m − 10 to find the value of m.
Write the points where the graphs of the equations intersect the y axis.
Answers
Answer:
no 4=f
Step-by-step explanation:
dwfn sdv and it appers to be marys age ;)
think before you do something rude
Answer:
C. Solve m + 6 = 5m - 10
Step-by-step explanation:
Wilson is 6 years older than Mary.
(MARY's age + 6 = WILSON's age)
Wilson's age is 10 years less than five times Mary's age.
(MARY's age * 5 - 10years = WILSON's age)
(Mary is 4 years old and Wilson is 10:
4 + 6 = 10
4(5) = 20 - 10 = 10
just in case you were curious)
Good luck!!
3. Abdoul has $100 in his bank account and he adds $50 each month.
Answers
Answer:
$600
Step-by-step explanation:
Multiply 50, 12 times, you get 600. Add 100, and you get 700.
Answer is $700
A jar contains 21 marbles: 8 white, 3 green, and 10 red. Write the described ratio in simplest form.
A. number of white marbles to number of green marbles.
Answers
Answer:
The question you posted was a bit confusing for me, but I'm assuming that you want the simplified ratio of the number of white marbles to the number of green marbles.
The answer would be 8:3.
Step-by-step explanation:
There are 8 white marbles and 3 green marbles, so you get 8:3. And since 8 and 3 are relatively prime, no simplifying is needed.
The answer is 8:3.
Need a little help here.
Answers
Answer:
sorry i will answer if you make me branlyist
Step-by-step explanation:
How many solutions are there to the following equation?
5 ( x-3 ) - 3x = 8x - 15 - 6x
A) exactly two solutions
B) exactly one solution
C) no solution
D) infinitely many solutions
Answers
Answer:
D) infinitely many solutions
Step-by-step explanation:
5 ( x-3 ) - 3x = 8x - 15 - 6x
5x - 3x - 15 = 8x - 6x - 15
2x - 15 = 2x - 15
2x = 2x
Since, equations of both lines are same. Therefore, there are infinitely many solutions.
Answer:
D
Step-by-step explanation:
Given
5(x - 3) - 3x = 8x - 15 - 6x
5x - 15 - 3x = 2x - 15
2x - 15 = 2x - 15
Since both sides are the same then any real value of x will be a solution.
That is there are infinitely many solutions
49x + 9 = 49x + 83
PLEASE quickkkk i need a specific explanation on how to do this
Answers
Answer:
Step-by-step explanation:
49x + 9 = 49x +83
-49x -9
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