What is the general equation of a sine function with an amplitude of 6, a period of StartFraction pi Over 4 EndFraction, and a horizontal shift of StartFraction pi Over 2 EndFraction?
y = sine (8 (x minus StartFraction pi Over 2 EndFraction))
y = 8 sine (4 (x minus StartFraction pi Over 2 EndFraction))
y = 6 sine (8 (x minus StartFraction pi Over 2 EndFraction))
y = 6 sine (8 x) + StartFraction pi Over 2 EndFraction
Answers
Answer:
C: [tex]y = 6 \sin (8(x-\frac{\pi}{2} ))[/tex]
Step-by-step explanation:
Amplitude is changed by multiplying the entire trig function by a number, by default the amplitude is 1, so multiplying by 6 is necessary; eliminate A and B
Horizontal shift is going through the x axis, so it must be subtracted from the x value. This is only seen in choice C of the remaining answers.
Calculating the period isn't necessary because we already found the right answer but in case you need it in the future; the period is by default 2pi, to get to pi/4, it had to be 8 times smaller, so multiplying x and translations on x by 8 will get you the correct period.
The General equation of a sine function is f(x) = 6·sin(8(x -π/2)).
What is Sine Function?The sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function is used to find the unknown angle or sides of a right triangle.
Here, Amplitude = 6, P=π/4, and S=π/2
A transformed sine function with amplitude A, period P, and horizontal shift S can be written as ...
f(x) = A · sin(2π/P(x -S))
f(x) = 6·sin(8(x -π/2))
The horizontal shift is equal to two full periods, so the shifted function is indistinguishable from the unshifted function.
Thus, the General equation of a sine function is f(x) = 6·sin(8(x -π/2)).
Learn more about Sine Function from:
https://brainly.com/question/12015707
#SPJ2
Related Questions
You wonder if weather (rain, cloudy or sunny) makes a difference on mood (happy or not). To determine this, you sample the moods of 200 people on a sunny day, 200 people on a rainy day and 200 people on a cloudy day and record whether they were happy or not. You then want to do a chi square test on this data. What are the degrees of freedom?
Answers
Answer:
2
Step-by-step explanation:
Drawing a table to show the different weather and mood options :
The degree of freedom :
________ WEATHER ________
__________Rain ____ sunny _____ cloudy
Happy
|
Not happy
Here, we have a contingency table formatted in rows and columns
The columns = 3
The rows = 2
Degree of freedom :
(rows - 1) * ( columns - 1)
(2 - 1) * (3 - 1)
1 * 2
= 2
The degree of freedom = 2
f(x) = 3x + 7. What is f(4) ?
Answers
Answer:
I believe the answer is 19.
Ryan has 25 tiles and 12% of them are green. how many tiles are green
Answers
Answer:
208.33. this is it your welcome
WILL MARK BRAINLIEST PLEASE HELP!!!
A right circular cone is intersected by a plane that passes through the cone's vertex and is parallel to its base, as in the picture below. What is produced from this intersection?
A. A Pair of intersecting lines
B. A Parabola
C. A Point
D. A Pair of parallel lines
Answers
Answer:its D. A pair of parallel lines
Step-by-step explanation:
Answer: parallel lines
Step-by-step explanation:
Find the surface area of the prism.
Answers
Answer:
386
Step-by-step explanation:
how many oz do you think this cup is
Answers
Answer:
I'm gonna say 12??
Step-by-step explanation:
Am I close?
Have a nice day! <3
Alice earns M dollars for working 40 hours in a week.Which expression represents the amount of money alice earns each hour?
A.40M
B.40+M
C.40/M
D.M/40
Answers
Answer:
m/40
Step-by-step explanation:
Round two decimal places
729015430.40641995
Answers
Answer:
729015430.40641995 = 729015430.41
Step-by-step explanation:
Since the 3 decimal place is 6, you round up. If you round up for 0 you get 1. Therefore your answer is 729015430.41.
What is m∠G to the nearest tenth?
Answers
Answer:
Step-by-step explanation:
tan(G) = 28.2/45.8
G = arctan(28.2/45.8) = 31.6°
Angle Relationship: Complementary OR Supplementary
Answers
Answer:
supplementary because this is not a 90 degree angle
also i know this person, if anyone want someone to do there homework they can text yktv.sham on insta gram and you can pay her
(X-1)(-5X+1)=0
lesser X=
Greater X=
Answers
Greater X= 1 (x-1)
Hope this helps!
Answer:
lesser x is -5x+1
Greater x is x-1
Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its customers. If a customer's car is not serviced within that period, the customer will receive a 50% discount on the charges. The company wants to limit this discount to at most 8% of the customers. What should the maximum guaranteed waiting time be
Answers
Answer:
The maximum guaranteed waiting time should be of 18.37 minutes.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes.
This means that [tex]\mu = 15, \sigma = 2.4[/tex]
The company wants to limit this discount to at most 8% of the customers. What should the maximum guaranteed waiting time be?
The 100 - 8 = 92th percentile, which is X when Z has a pvalue of 0.92. So X when Z = 1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 15}{2.4}[/tex]
[tex]X - 15 = 1.405*2.4[/tex]
[tex]X = 18.37[/tex]
The maximum guaranteed waiting time should be of 18.37 minutes.
Tasha purchased an iPad for $625. A year later, it was selling for $500. What was the percent of change?
Answers
Answer:
-20
Step-by-step explanation:
i used a percentage calculator
What is the quotient? 2y2-6y-20/4y+12
Answers
Answer:
last 4rd
Step-by-step explanation:
Which is the graph of y= 2 8x - 3?
Graph B.
Graph C
Graph A
Please help!
Answers
Answer:
Graph C
Step-by-step explanation:
We can tell because the equation states that the y intercept is -3 and has a steep slope
An online retailer wants to study whether more lenient return policies increase purchasing behaviors. They
select a random sample of 2000 customers who have made purchases in the past year.
They use a random number generator to select 1000 customer account numbers to assign to the treatment
group. The remaining 1000 customers are assigned to the control group.
What type of experiment design is this?
A) randomized block
B) stratified
C) completely randomized
D) marched pairs
E) cluster
Answers
Answer: Completely Randomized
Step-by-step explanation:
effect of one primary factor rather than many different variables
As per the question the retailer wants to study the return policy that can increase the buying behavior and selects a random sample of 2000.
He uses matched pair of designs in his experiment design in which participants of the same traits get grouped in pairs. After which within each pair, one participant gets randomly allotted to either the treatment, and the other is assigned to the other part.Hence the option D is correct.
Learn more about the study whether more.
brainly.com/question/14894261.
Please Classify ∠1 and ∠2 using all names that apply
Answers
Answer:
if the sum of the two angles is 90°,then they are said to be complementary angles.$500 at 12% for 6 months (0.5 years) Find the interest
Answers
Answer:
Step-by-step explanation:
500(.12)(.5)= $30 interest
Don uses a funnel to pour oil into his car engine. The funnel has a radius of 6 cm and a slant height of 10 cm. How much oil, to the nearest cubic centimeter, will the funnel hold.
Answers
Formulate the null and alternative hypotheses that can be used to determine whether the school is losing money out of the raffle. Note that the issue is whether the school is losing money, not whether the school is breaking even. Please think about what the implication is when formulating the null and alternative hypotheses.
Answers
Answer:
https://brainly.com/question/23195326
Step-by-step explanation:
Quinn and Alexander are painting their bedroom. Quinn has painted 2/5 of his room. Alexander has painted 2/3 of his room. Who has the more left to paint? Explain in a sentence and solve?
Answers
Answer:
Alexander
Step-by-step explanation:
Alexander has painted 2/3 of his room. Quinn has painted 2/5 of his. To find who has painted more, convert both fractions to have the same denominators. An easy way to do this is to multiply the numerator and denominator of one fraction by the denominator of the other, then do the same for the other fraction. So, [tex]\frac{2}{3}[/tex] · 5 = [tex]\frac{10}{15}[/tex] and [tex]\frac{2}{5}[/tex] · 3 = [tex]\frac{6}{15}[/tex].
[tex]\frac{10}{15}[/tex] > [tex]\frac{6}{15}[/tex]. So, Alexander has painted more of his room than Quinn has.
Write a quadratic function f whose only zeros are -3 and -12
Answers
Answer:
Step-by-step explanation:
f(x) = (x + 3)(x + 12)
f(x) = x^2 + 3x + 12x + 36
f(x) = x^2 + 15x + 36
Please help, test due in 2 hours! Will give good review and brainliest.
Answers
Answer:
B. Ellipse
...............................................
In a sequence of numbers, a4=12, a5=14, a6=16, a7=18, and a8=20.
Which equation can be used to find the nth term of the sequence, an?
a) an=2n+4
b) an=2n+12
c) an=3n
d) an=3n+12
I'm pretty sure it's a, but I just wanna check if I did the work right!
Answers
Answer:
you are right, it's a)❤
Step-by-step explanation:
a4=12---> put the formula in it
2×4+4=12
a5=14---> 2×5+4=14
a6=16---> 2×6+4=16
.
.
.
hope it helps❤
Part c Katie started with $40. How much money did she have left after purchasing the supplies? Enter your answer in the box provided.
Answers
Answer:
gotta give me more details here Katie
Graph the equation y=−x²−8x−15 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
Answers
Answer:
Plot these points
(-3,0)
(-5,0)
(-4,1)
(-2,-3)
(-6,-3)
Step-by-step explanation:
Let find the zeros of the equation.
We can factor this equation.
Factor out the -1.
[tex] - 1( {x}^{2} + 8x + 15)[/tex]
Factor using AC method
[tex] - 1(x + 3)(x + 5)[/tex]
Set all the terms equal to zero.
[tex]x + 3 = 0[/tex]
[tex]x + 5 = 0[/tex]
[tex]x = - 3[/tex]
[tex]x = - 5[/tex]
So our x intercepts are -3,0 and -5,0.
To find our vertex, apply the -b/2a.
[tex] \frac{8}{ - 2} = - 4[/tex]
Then
Substitute-4 for x.
[tex]y = - {4}^{2} - 8( - 4) - 15 = 1[/tex]
So our vertex is at (-4,1).
Find some other points like -2 and -6.
To find -2, substitute-2 into the quadratic.
[tex]y = - ( { - 2}^{2}) - 8( - 2) - 15 = - 3[/tex]
So -2,-3.
Since y=-4 is the axis of symmetry
-6,-3
The 5 points which satisfies the quadratic equation y = −x² − 8x − 15 is
( -5 , 0 ) ( -1 , -8 ) , ( -2 , -3 ) , ( 4 , 1 ) , ( -3 , 0 ) and the vertex point is ( 4 , 1 )
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
y = −x² − 8x − 15
On simplifying the equation , we get
y = -1 ( x² + 8x + 15 )
On factorizing the equation , we get
y = -1 ( ( x + 5 ) ( x + 3 )
So , the 2 values for x is -5 , -3
So , the two points are ( -5 , 0 ) and ( -3 , 0 )
The vertex will be -b/2a
Substituting the values in the equation , we get
The vertex = -8/2 = -4
So , when x = -4
y = -1 ( ( x + 5 ) ( x + 3 )
y = -1 ( 1 x -1 )
y = 1
So , the vertex is at the point ( 4 , 1 )
Now , when x = -1
y = -1 ( ( x + 5 ) ( x + 3 )
y = -1 ( 4 x 2 )
y = -8
So , the point is ( -1 , -8 )
Now , when x = -2
y = -1 ( ( x + 5 ) ( x + 3 )
y = -1 ( 3 x 1 )
y = -3
So , the point is ( -2 , -3 )
Hence ,
The 5 points which satisfies the quadratic equation y = −x² − 8x − 15 is
( -5 , 0 ) ( -1 , -8 ) , ( -2 , -3 ) , ( 4 , 1 ) , ( -3 , 0 ) and the vertex point is ( 4 , 1 )
To learn more about quadratic equations click :
https://brainly.com/question/25652857
#SPJ2
there are 125 vehicles in a car dealership's lot. at least 88 of them are hybrid vehicles. write solve an inequality that describes how many vehicles, at most, are not hybrid.
Answers
Answer:
it is 37.
Step-by-step explanation:
125 - 88 is 37
Answer please and explain
Answers
Cómo se formaron los conjuntos numéricos?
Answers
Answer:
Step-by-step explanation:
Los conjuntos numéricos son agrupaciones de números que guardan una serie de propiedades estructurales. Por ejemplo el sistema más usual en aritmética natural está formado por el conjunto de los números naturales, con la suma, la multiplicación y las relaciones usuales de orden aditivo.
helpppppppppppp meee
Answers
Answer:
-8
Step-by-step explanation:
Plz give brainliest
i dont have any
