Jun 07, 9:22:26 AM
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Write a sine function that has an
amplitude of 2, a midline of 3 and a period of 3/2.
Answers
Answer:
[tex]\displaystyle y = 2sin\:1\frac{1}{3}\pi{x} + 3[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{y = 2cos\:(1\frac{1}{3}\pi{x} - \frac{\pi}{2}) + 3} \\ \\ 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 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{3}{8}} \hookrightarrow \frac{\frac{\pi}{2}}{1\frac{1}{3}\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{2}} \hookrightarrow \frac{2}{1\frac{1}{3}\pi}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[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 3 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{1\frac{1}{2}} \hookrightarrow \frac{2}{1\frac{1}{3}\pi}\pi \\ Amplitude \hookrightarrow 2[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although the exercise told you to write the sine equation based on the speculations it gave you, if you plan on writing your equation as a function of cosine, 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 = 2cos\:1\frac{1}{3}\pi{x} + 3,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine 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 cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{3}{8}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{3}{8}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{3}{8}} = \frac{\frac{\pi}{2}}{1\frac{1}{3}\pi}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2cos\:(1\frac{1}{3}\pi{x} - \frac{\pi}{2}) + 3.[/tex]Now, with all that being said, in this case, sinse you ONLY have the exercise to wourk with, take a look at the above information next to [tex]\displaystyle Wavelength\:[Period].[/tex]It displays the formula on how to define each wavelength of the graph. You just need to remember that the B-term has [tex]\displaystyle \pi[/tex]in it as well, meaning both of them strike each other out, leaving you with just a fraction. Now, the amplitude is obvious to figure out because it is the A-term, so this is self-explanatory. 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 = 3,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter what the vertical shift is, that will ALWAYS be the equation of the midline, and if viewed from a graph, no matter how far it shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Related Questions
A skateboarding ramp is 13in. high and rises at an angle of 13°. How long is the base of the ramp? Round to the nearest inch.
Answers
===========================================================
Explanation:
The diagram is shown below. We know the vertical part of the triangle is 13 inches, which is the side opposite the reference angle 13 degrees. The adjacent side is unknown. We'll call it x. This is how long the base of the ramp is, which is the horizontal distance along the entire ramp. This distance is on the ground. The ramp itself is the hypotenuse but it seems like your teacher isn't wanting to know this value. So we'll ignore the hypotenuse.
We'll use the tangent rule to connect the opposite and adjacent sides.
tan(angle) = opposite/adjacent
tan(13) = 13/x
x*tan(13) = 13
x = 13/tan(13)
x = 56.309186365694
x = 56 inches is the approximate horizontal distance underneath the ramp
The base of the ramp is 57 inches long.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The tangent function relates the opposite side (height) and adjacent side (base) of a right triangle to the angle of elevation.
We know the opposite side is the height of the ramp, which is 13 inches, and the angle of elevation is 13 degrees.
Let the adjacent side (the base of the ramp) be "x".
The tangent of 13 degrees is equal to the opposite side divided by the adjacent side:
tan(13) = 13/x
To solve for x, we can multiply both sides by x:
x × tan(13) = 13
Then, we can divide both sides by tan(13):
x = 13 / tan(13)
x = 13 / 0.228
x= 56.99
Therefore, the base of the ramp is 57 inches long.
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If x=4 and y=5. The value of 3x-5y
Answers
Answer:
13, I believe :)
Step-by-step explanation:
3(4)-5(5)
multiply by the coefficient
=12-25
=-13
Four expressions are written in the table.
What value of n makes all of the expressions equivalent?
0
1
10
100
Answers
y = 3 sine (one-third x)
Answers
a
sin
(
b
x
−
c
)
+
d
a
sin
(
b
x
-
c
)
+
d
to find the variables used to find the amplitude, period, phase shift, and vertical shift.
a
=
3
a
=
3
b
=
1
3
b
=
1
3
c
=
0
c
=
0
d
=
0
d
=
0
Find the amplitude
|
a
|
|
a
|
.
Amplitude:
3
3
Find the period using the formula
2
π
|
b
|
2
π
|
b
|
.
Tap for more steps...
Period:
6
π
6
π
Find the phase shift using the formula
c
b
c
b
.
Tap for more steps...
Phase Shift:
0
0
Find the vertical shift
d
d
.
Vertical Shift:
0
0
List the properties of the trigonometric function.
Amplitude:
3
3
Period:
6
π
6
π
Phase Shift:
0
0
(
0
0
to the right)
Vertical Shift:
0
0
Select a few points to graph.
Tap for more steps...
x
f
(
x
)
0
0
3
π
2
3
3
π
0
9
π
2
−
3
6
π
0
x f
(
x
)
0 0
3
π
2
3 3π 0
9
π
2
-3 6π 0
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude:
3
3
Period:
6
π
6
π
Phase Shift:
0
0
(
0
0
to the right)
Vertical Shift:
0
0
x
f
(
x
)
0
0
3
π
2
3
3
π
0
9
π
2
−
3
6
π
0
x f
(
x
)
0 0
3
π
2
3 3π 0
9
π
2
-3 6π 0
y
=
3
s
i
n
(
1
3
x
)
y
=
3
(
1
3
x
)
Answer:
B on edge
Step-by-step explanation:
please help! (listing BRAINLIST and giving points) :)
Answers
Answer:
sin∅ = 12/13
Step-by-step explanation:
use pythagorean theorem to find the missing side
a² + 5² = 13²
a² = 13² - 5²
a² = 169 - 25
a² = 144
a = 12
-----------------------------
Sin∅ = opp/hyp
sin∅ = 12/13
Can y’all help me on question 13?!
Answers
Answer:
90 cm²
Step-by-step explanation:
The shape can be divided in three rectangles.
Area = area of rectangle 1 + area of rectangle 2 + area of rectangle 3
✔️Area of rectangle 1 = L*W
L = 5 cm
W = 3 cm
Area = 5*3 = 15 cm²
✔️Area of rectangle 2 = L*W
L = 6 + 5 + 1 = 12 cm
W = 5 cm
Area = 12*5 = 60 cm²
✔️Area of rectangle 3 = L*W
L = 5 cm
W = 3 cm
Area = 5*3 = 15 cm²
✅Area of the shape = 15 + 60 + 15 = 90 cm²
can someone answer this i’ll give u a cookie PLEASE I NEED IT NOW
Answers
Answer:
its c
Step-by-step explanation:
What is the sum of the interior angle measures of a polygon that has 11 sides?
HINT: Sum= (n-2)180
Answers
Answer:
Step-by-step explanation:
no of sides (n)=11
sum=(n-2)180
=(11-2)180
=9*180
=1620
therefore sum of the interior angles of a polygon having 11 sides id 1620°.
Answer:
n= 1620
Step-by-step explanation:
I know the answer is correct I got the exact same question during the lessons.
What's the surface area of this figure? Pick one of the options.
Answers
Just find the area of each face in the figure.
These are the formulas I used:
Formula for area of trapzoid:
(a + b/ 2) x height
Formula for area of rectangle:
length x width
Formula for area of square:
Length x width
Hope this helps!
Second, What do you do to find the area of a surface? (Square or rectangle)
Third, Add up all of the sides.
1: 6
2: multiply the length and width
(I am just doing the sides in a random order)
Top side: 5 x 5 = 25
Left side: 5 x 5 = 25
Right side: 6.4 x 5 = 32
Bottom side: 9 x 5 = 45
Front side: (14 x 5) divided by 2 = 35
Back side: (14 x 5) divided by 2 = 35
3: 25 + 25 + 32 + 45 + 35 + 35 = 197
Answer: 197
Hope this helps :D
HELP ME PLEASEEEEEEEEEEEEEEEE
Answers
Answer:
[tex] \frac{2}{3} a - \frac{1}{6} = \frac{1}{3} \\ \frac{2}{3} a = \frac{1}{2} \\ 4a = 3 \\ a = \frac{3}{4} [/tex]
The probalityof raining today is 30% what is the probality tha it will nat rain?
Answers
Choose the solution set represented by the following graph.
{x | x R, x ≤ -2}
{x | x R, x > -2}
{x | x R, x < -2}
{x | x R, x ≥ -2}
Answers
Answer:
{x|x rx>-2}
Step-by-step explanation:
hope helpful answer
Suri and Carter want to start saving for the future. they each invest $4,000 into a certificate of deposit account. suri's investment earns 3% interest compounded annually. Carter's investment is 3% simple interest.
Answers
Two formulas:
Compound interest - A = P(1 + r/n)^nt
Simple interest = A = P(1 + rt)
A - final amount
P - initial principal balance
r - interest rate
n - number of times interest applied per time period
t - number of time periods elapsed
Suri --
A = 4,000(1+0.03/1)^5
A = $4,637.09
Carter --
A = 4,000(1+0.03*5)
A = $4,600
In 5 years, Suri makes $37.09 more than Carter
Will mark brainlest
find the domain and range of following
Answers
Answer:
Result:
{0, 3/7}
Decimal approximation:
{0, 0.428571}
Step-by-step explanation:
Find the norm...
and you know I wanna speedrun
An auto repair shop charged a customer $496 to repair a car. The bill listed $96 for parts and the remainder for labor. If the cost of labor is $40 per hour, how many hours of labor did it take to repair the car?
Answers
Get brainly if right?
10 points!
Answers
Answer:
Tn = -13n +37
ordered list is 24, 11 , -2 , -15, -28 ,-41
What is the slope of the line represented by the equation y =4/5x-3?
A. -3
B. - 4/5
C. 4/5
D. 3
Answers
Answer:
4/5
Step-by-step explanation:
y =4/5x-3
The equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 4/5
Answer:
4/5
Step-by-step explanation:
The slope will be in front of the x in slope intercept form.
ASAP:
Consider the word pROPOSITION. How many five letter words can be formed if two letters are alike and three letters are different? Consider the cases.
Answers
Answer:
The letters M, N, A , E appear twice and G, T appear once.
So, the first case was where all the letters were different, thus, the number of words formed were:
6C5 . 5!(further permutation) = 720
the second case was where there were two groups of two alike letters and one different letter. Thus, the number of words formed were:
2C1 . 4C2 . 3! = 72
the third case was where there were one group of two alike letters and three different letters.
Thus, the number of words formed were:
4C1 . 5C3 . 4!= 960
thus, the total number of words were:
720 + 72 + 960 = 1752
but this answer is wrong as the Real answer is 1824.
Step-by-step explanation:
A woman when working with her takes 2 hours to complete the housework, and takes 3 hours when working alone How long would it take the daughter to complete the housework if working alone?
Answers
The daughter will take 6 hours to complete the housework if working alone.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
A woman when working with her takes 2 hours to complete the housework and takes 3 hours when working alone.
Let's suppose y minutes taken by the daughter to complete the housework:
Rate for daughter = 1/x
1/3 + 1/x = 1/2
2x + 6 = 3x
x = 6 hours
Thus, the daughter will take 6 hours to complete the housework if working alone.
Learn more about the linear equation here:
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The managers of a fast food chain want their products to be as similar as possible across locations. They suspect that the burgers at their Albuquerque branch have bigger parties than the burgers at the Santa Fe branch, so they take a sample of 7 patties from each restaurant and measure their weights in gransk
Albuquerque 11011 110 110 111 112 106
Santa Fe 107 111 110 108 109 110 109
The managers want to test if the parties in the Albuquerque branch have a higher average weight than the patties in the Santa Fe branch. Assume that all conditions for inference have been met
Which of these is the most appropriate test and alternative hypothesis?
a. Pairedt test with H>0 3
b. Pairedt test with H > 0
c. Pairedt test with Ht0
d. Two-sample t test with H. > 0
Answers
Answer:
H0 : μd = 0
H1 : μd > 0
Step-by-step explanation:
The scenario described above can be compared statistically using a paired test mean as the mean if the two groups are dependent, the two restaurants, Albuquerque and Santa Fe are both restaurant locations of a single restaurant company. Hence, to test the mean difference, we use the paired test statistic. Defined thus `
Null hypothesis ; H0 : μd = 0 and the Alternative hypothesis ; H1 : μd > 0
Answer:
Two Sample T test with Ha = Albernuque>Santa Fe
Step-by-step explanation:
Khan
Help please ASAP ASAP ASAP
Answers
Answer:
13A
Step-by-step explanation:
The distance between two points P=(px,py) and Q=(qx,qy) is d=(qx−px)2+
Help plz I’m so confused
Answers
u never multiply the bottoms only the top so it will give u 6 since theyre both negatives
-
answer = 6/7
Answer and Step-by-step explanation:
Simply multiply the numerator by the numerator, and the denominator by the denominator.
[tex]-\frac{2}{7}[/tex] × [tex]-\frac{3}{7}[/tex] = [tex]\frac{6}{49}[/tex]
#teamtrees #PAW (Plant And Water)
The following cylinder has a height of 7.2 in. and diameter of 6.8 in.
Cylinder with measures described in text.
What is the volume of the cylinder? Remember, the diameter of a circle is two times its radius.
Use 3.14 for π and round your answer to the nearest tenth.
Answers
Answer:
598.16
Step-by-step explanation:
Eh you should have the formula if not I can't really type it but ,trust, the answer is 598.16 in²
Answer:
261.3 in.
Step-by-step explanation:
HELPPPP I need help with this question!!!!
Answers
I think the 4th one but Im not too sure please forgive me if I'm wrong.
A collection of 39 coins consists of dimes and nickels. The total value is $2.75. How many dimes and how many nickels are there?
Answers
Answer:
23 nickels and 16 dimes
Step-by-step explanation:
16 dimes = 1.60
23 nickels = 1.15
1.60 + 1.15 = 2.75
help me plz plz!! It's due tomorrow will Mark u as BRAINLIEST
Answers
Answer: Mean(Mia)=34.33 Mean(Sophia)=35.667
Sophia's phone calls on average, are longer in length than Mia's phone calls.
Step-by-step explanation:
Need help if anyone can help me that’ll be nice
Answers
i hope this helped and let me know if you need help with any other questions:)
ALSO, PLS MARK THIS BRAINLIEST IF YOU CAN!!
Answer:
times up the outside bc we know the outside is the area
HELP PLEASE!!!!
By which rule are these triangles congruent?
A) AAS
B) ASA
C) SAS
D) SSS
Answers
Answer:
ASA
Step-by-step explanation:
Both triangles contains two angles which indicate that it can only be the top 2 options.
Write the number 2.4 in the form
A/B, using integers,
Answers
Answer:
[tex] \frac{12}{5} [/tex][tex]2 \frac{2}{5} [/tex]Step-by-step explanation:
Convert to simplified fraction:
Convert to a mixed number by placing the numbers to the right of the decimal over 10. Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.
Convert to Mixed fraction:
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over 10[tex] ^{1} [/tex](10). Next, add the whole number to the left of the decimal.
[tex]2 \frac{4}{10} [/tex]
Reduce the fractional part of the mixed number.
[tex]2 \frac{2}{5} [/tex]
Hope it is helpful...you spend $40 on a meal for you and your friends. Sandwiches cost $5 and beverages cost $2 each. Write and equation in standard form where x is the number of sandwiches purchased and y is the number of beverages posted.