What is the midline of this function? y=
What is the amplitude of this function?
Define a function, g, to represent the behavior of the graphed function. g(a)= NO LINKS.
Answers
Answers:
Midline: y = 0Amplitude = 1.5Function: g(x) = 1.5sin(0.5x + pi/4)There are infinitely many possible ways to answer the third part.
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Explanation:
The midline is the horizontal line that goes through the center of the sine curve. Visually we can see that is y = 0. Another way we can see this is to note how y = 0 is the midpoint of y = 1.5 and y = -1.5, which are the max and min respectively.
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The amplitude is the vertical distance from y = 0 to y = 1.5, and it's also the vertical distance from y = 0 to y = -1.5; in short, it's the vertical distance from center to either the peak or valley.
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The general format of a sine curve is
y = A*sin(B(x-C)) + D
where,
|A| = amplitudeB = variable tied with the period T, specifically B = 2pi/TC = handles the left and right phase shiftD = handles the vertical shifting, and y = D is the midline.In this case, we found so far that
|A| = 1.5 which could lead to A = 1.5B = 2pi/(4pi) = 0.5 since T = 4pi is the periodD = 0The only thing we're missing is the value of C, which is the phase shift.
Note the point (pi/2, 1.5) is one of the max points on this curve. Also, recall that sin(x) maxes out at 1 when x = pi/2
This must mean that the stuff inside the sine, the B(x-C) portion, must be equal to pi/2 in order to lead sin(B(x-C)) = 1.
So,
B(x-C) = pi/2
0.5(pi/2-C) = pi/2
pi/4 - C/2 = pi/2
4*( pi/4 - C/2 ) = 4*(pi/2)
pi - 2C = 2pi
-2C = 2pi - pi
-2C = pi
C = pi/(-2)
C = -pi/2
This allows us to update the function to get g(x) = 1.5*sin(0.5(x+pi/2)) which is the same as g(x) = 1.5sin(0.5x + pi/4)
This is one possible answer because we could have infinitely many possible values for C, due to sin(x) = 1 having infinitely many solutions.
Also, you could use cosine instead of sine. Cosine is just a phase shifted version and of sine, and vice versa.
Related Questions
Find mZRTS.
R
112°
S
T
Answers
Answer:
RTS=(180-112)/2
=68/2
=34
Solve the equation for X,
2 (2) + x = 4
A. x=8
B. x=0
C. x= -4
D. x=4
Answers
Answer: x=0
Step-by-step explanation:
2(2)=4
4+x=4
-4 on both sides
so x=0
Answer:
B) x = 0
Step-by-step explanation:
We will get our equation in here first. Our equation is:
2 * 2 + x = 4
We simplify the multiplication giving us:
4 + x = 4
Finally, we subtract 4 from both sides to find the value of x. We get:
x = 0.
So the correct answer is B) x = 0.
Hope this helped!
Helpppp
Due
Rn
Will give brainlist
Answers
Answer:
8ft. 9in.
+13ft. 7in.
_________
22ft. 4in.
because 12 in.= 1 ft. so 9+7=16
16-12=4
so 12in.=1 ft. , as 12 in, got carried by 1ft.
help me pls the question is in the picture
Answers
Answer:
x would be 18
Step-by-step explanation:
180 degrees in a traingle, subtract 90 for the right angle and then you are left with 5x = 90
x = 90/5
x = 18
find each angle using x from here
Answer:
Angle T is 36 degrees
Angle V is 54 degrees
Step-by-step explanation:
x=18
Which statement correctly compares the centers of the distributions?
Answers
Answer:
B
Step-by-step explanation:
Center of the distributions -> mean/median (preferably mean)
The option with range is eliminated
Median might not be accurate as median is the center person, not the center result.
Based on the graphs, identify the graph with the intervals of greatest frequency.
For North Heights -> between 30 and 32 (right-skewed, some higher values)
For Southview -> between 28 and 30 (most concentrated there)
Hence, mean of Southview is lower than North Heights.
60, 80, 100
Right traingle
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which products are purchased only after customer have compared a variety of similar and competitive products
Answers
Function g is a transformation of function f.
What is the equation of function g? I need help please . ASAP.
Answers
Answer:
Solution given:
function of g(x)=?
when
x=0
y=3
so
g(x)=-3f(x) is a function of g.
Let
y=f(x)Face changed to opposite means coefficient is negative
y=-f(x)Streched by 3 [-6/-2=3]
y=-3f(x)An acute angle, θ, is in a right triangle such that sin of theta is equal to 3 over 8 period What is the value of cot θ?
Answers
An acute angle, θ, is in a right triangle such that sin of theta is equal to 3 over 8 period The value of cot θ is (√55)/3.
What is the value of cot θ?To determine the value of cot(θ), Since is an angle in a right triangle and sin() = 3/8, we obtain:
cot(θ) = (√55)/3
In light of the fact that is an acute angle in a right triangle, we may calculate:
sin(θ) = 3/8
Keep in mind:
Hypotenuse = ((opposite cathetus)2 + (adjacent cathetus)2), where sin() = (opposite cathetus)/(hypotenuse)
Next, we have:
contrary cathetus = 3
Using the formula hypotenuse = 8 = (3 + neighboring cathetus)2,
In order to solve this for the nearby cathetus, we obtain:
(82 - 32) = 55 adjacent cathetus
And we are aware of:
(Cot) = (nearby cathetus) (opposite cathetus)
Next, we have:
cot(θ) = (√55)/3
The value of cot θ is (√55)/3.
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A triangle has sides with lengths 8, 15, and 17. approximate the acute angles in this triangle to the nearest degree and list in ascending order
Answers
Answer:
28°, 62°
Step-by-step explanation:
As 8,15,17 is a Pythagorean Triple, the triangle must be a right triangle. Hence, we can use our common trig ratios to solve the problem. Let's assume our right triangle has a base of 8, a height of 15, and a hypotenuse of 17.
Here are all the acute angles in order:
[tex]\cos^{-1}(\frac{15}{17})\approx28^\circ[/tex]
[tex]\sin^{-1}(\frac{15}{17})\approx62^\circ[/tex]
Val had 2 1/2 hours to finish a slide presentation. It takes her 1/6 hour to create each slide. Will Val have enough time to create 12 slides? Explain ur reasoning
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will she have enough time for 12 slides? we dunno, but we know it takes 1/6 hour to make one hmmm for 12 slides that'd be simply their product
[tex]\stackrel{slides}{12}\cdot \stackrel{\textit{it takes one}}{\cfrac{1}{6}}\implies \cfrac{12}{6}\implies 2~hours\qquad \textit{yeap, she has enough time}[/tex]
she even has an extra 30 minutes to check out what's for dinner.
Mr. Smith has 3 packs of pencils with 15 pencils in each pack. There are 32 students in mr.smith's class. He gives each student 1 pencil. How many pencils does mr.smith have left?
Answers
Answer:
13
Step-by-step explanation:
He starts with 45 pencils (3x15) in total. Then he gives 32 to each student. He is left with 13 (45-32) pencils.
In a class of 55 students, 15 students liked Maths but not English and 18 students liked English but
not Maths. If 5 students did not like both, how many students liked both subjects?
Answers
Answer:
17 is the correct answer
Answer:
I think it's the remaining students, 17.
Step-by-step explanation:
15 + 18 = 33 (students that like one subject but not the other)
33 + 5 = 38 ( adding 5 because of the 5 student that dislike both)
38 is the number of students that either don't like both subjects or like one but now the other, so now you would subtract it by the total number of students (55).
55 - 38 = 17
The remaining students are who I believe like both subjects. The remaining number of students are 17.
The probability that a newborn baby at a certain hospital is male is 50%. Find the probability that 7 or 8 out of 10 babies born in the hospital on any day are male. Write your answer rounded to the nearest hundredth if needed.
Answers
Answer:
0.1611
Step-by-step explanation:
Uaing the binomial probability relation :
p = 0.5 ; q = 1 - p = 0.5
n = 10
Using the relation :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 7) = 10C7 * 0.5^7 * 0.5^3
P(x = 7) = 0.1172
x = 8 ;
P(x = 8) = 10C7 * 0.5^7 * 0.5^3
P(x =8) = 0.0439
P(x = 7 or x = 8) = 0.1172 + 0.0439 = 0.1611
Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa. how many dvds does marissa own?
Answers
The number of Dvds owned by Maarissa is 45
How to find the number of dvds?The given parameters that will guide us in finding the number of dvds owned by marissa are
Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa.
Let the number of dvds owned by Marissa be x
Nymber of dvds owned by Kyle be y
This implies that x+y = 66 ............................1
also, 2y + 3 = x ..................................................2
Substitute x = 2y + 3 in equation 1
= 2y + 3+y =66 Collecting like terms
⇒ 3y = 63
Making y the subject of the relation we have y=21
Recall that 2y + 3 = x
That means x = 2(21) + 3
x=45
Therefore Marrissa owns 45 dvds
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A line passes through the points (-2, 9) and (1, 3).
Click “show your work” and provide work for calculating the slope and y-intercept. Then, write the equation for the line in slope-intercept form. Please write your answers on the lines provided in the whiteboard.
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The equation of the line passing through the points (-2,9) and (1,3) is
y = -2x + 11 where the slope is -2 and the y-intercept is +11
What is the Equation of a Line?The equation of a line can be formed with the help of the slope of the line and a point on the line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.
m = (y2 - y1) / (x2 - x1)
y1 = 9
y2 = 3
x1 = -2
x2 = 1
m = (3 - 9) / (1 - (-2))
m = - 6 / 3
m = - 2
The equation of the line;
m = (y - y1) / (x - x1)
-2 = y - 9 / x - 1
y - 9 = -2(x - 1)
y - 9 = -2x + 2
y = -2x + 11
Therefore the y-intercept is +11.
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Help on #8 only please thank you !
Answers
1 yard in 6 minutes
Question 1
Part A
Find the unit rate.
Enter the correct answer in the box.
Answers
Answer: 0.166666667 yards OR 0.1524 meters OR 0.5 feet
Step-by-step explanation:
1 / 6 = 0.166666667 yards
1 yard = 0.9144 meters
0.9144 / 6 = 0.1524 meters
1 yard = 3 feet
3 / 6 = 0.5 feet
A growing amusement park is able to
sell 7 times as many tickets each year
as it did the year before. If you list the
number of tickets sold over time, what
kind of sequence will you see?
Answers
If you list the number of tickets sold over time, the kind of sequence will you see is a geometric sequence.
What is a geometric sequence?
A geometric progression sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Here,
We assume that the variable x represents the number of tickets sold previously (initial year) and it sold 7 times as many tickets each year as it did the year before, a mathematical expression that models this situation is given by geometric sequence:
x, 7x, 49x, 343x, .....
Verification:
7/1 = 49/7 = 343/49 = 7
Hence, this is a geometric sequence.
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1: Find the total cost of 25 pens and 75 books
if each pen costs GH¢0.20 and each book
costs GH¢0.30.
ITI
Answers
Answer:
0.2 x 25 = 5
0.3 x 75=22.5
22.5+5=27.5
Step-by-step explanation:
an open concrete tank is internally 1m wide, 2m long and 1.5m deep, the concrete being 10cm thick. Calculate the capacity of the tank in litres
Answers
The capacity of the tank is 3000 liters
Calculations and ParametersWe would first find the volume of concrete:
(0.1*1.5*1*2)+(0.1*1.5*2(0.1*2))*2)+(0.1*1.2*2.2)
=0.3+0.66+0.264
=[tex]1.224 m^3[/tex] of concrete
The capacity of the tank in liters:
1x2x1.5
=[tex]3m^3[/tex] or 3000 liters
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P
Jimmy tried to solve the system of equations below, but he made an error
S 2.0
y=18
y= 40 +2
His work is shown. Find the error he made. Explain the error and show how to solve the sysm correctly.
1. 2.0 - 4.3 + 2 = 18
2.-2x = 16
3. = -8
4. y=4(-8) + 2
5. Y = -32 +2
6. y=-30
7. Check: 2 (-8) - (-30) = 18
8.
- 16 + 30 = 18
9 14 + 18
His mistake was on Line
because he should have
The correct solution is
Answers
Answer:
"His mistake was on line 1. He didn't distribute the negative sign (indicating a -1) to everything in the equation for y."
The correct solution is: x = -10, y = -38
Step-by-step explanation:
2x - y = 18
y = 4x + 2
Substitute the given value for y into the first equation:
2x - (4x + 2) = 18
2x - 4x - 2 = 18 ** here, he didn't distribute the (-) to everything in the parentheses that represents y
-2x -2 = 18
add 2 to both sides
-2x = 20
divide by -2
x = -10
-------------------
solve for y
y = 4x + 2
y = 4(-10) + 2
y = -40 + 2
y = -38
------------------
Check the math:
2x - y = 18
2(-10) - (-38) = - 20 + 38 = 18
Identify the domain and range of each function
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Answer: A) Domain: All real numbers , Range: All real numbers
Step-by-step explanation: Since the line of the graph continued to infinity, the answer for both domain (goes from Left to right) and range (goes up to down) would be all real numbers
On Wednesday, Isonil earned $21.00 for 3 hours of babysitting. On saturday, she babysat of the same family and earned $56.00. How many hours did she babysit for on saturday? Explain how you determined your answer. (Hint: Think about how much Isonil charge per hour for babysitting.)
Please helppp
Answers
Answer:
8 hours
Step-by-step explanation:
21/3=7 and 56/7=8
Answer:
She worked for 8 hours
Step-by-step explanation:
She earned $21 for 3 hours 21 divided by 3 is 7 so $7 an hour. She made $56 so 56 divided by 7 = 8 hours
Mark has twice as much money as Tamassa. Together they have $630. How much money does Mark have
Answers
Answer:
472
Step-by-step explanation:
630/2= 315 (shared equally)
But 315/2= 157.5
315+157.5= 472.5 (mark)
472.5/2= 157.5
Mark has $472.5
Tamassa has 157.5
All together (472.5+157.5) = $630
Where is the graph of f(x)= 4LX-3]+ 2 discontinuous?
all real numbers
all integers
only at multiples of 3
only at multiples of 4
Answers
Answer:B all integers
Step-by-step explanation: took the test
The option second all integers are correct because for every value of the x the function will always give an integer value.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function
f(x)= 4[X-3]+ 2
f(x) represents the greatest integer function, which means for every value of the x the function will always give an integer value.
The function will be discontinuous for all integers.
Thus, the option second all integers are correct because for every value of the x the function will always give an integer value.
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i need help, i do not understand, this is pythagorean theorem
Answers
Answer:
11.2
Step-by-step explanation:
First draw an imaginary straight line to separate the two shapes.
You will have a side of 10 in the traingle
And a side of 13 - 8 =5
Then
Using pythagoras theorem
Sqrt(10^2+5^2)=11.180
PLEASE HELP ASAP DUE TODAY
Answers
Answer:
y = -3/4x + 52
y + 6 = -3/4(x-8)
Step-by-step explanation:
y = mx + c
as long as the number is -3/4x , it represents slope -3/
Answer:
B. y = -3/4x + 52, C. y + 6 = -3/4(x - 8), and F. 3x + 4y = 9
Step-by-step explanation:
A. -3x + 4y = -34
y = 3/4x - 17/2
Slope = 3/4
INCORRECT
B. y = -3/4x + 52
Slope = -3/4
CORRECT
C. y + 6 = -3/4(x - 8)
y = -3/4x
Slope = -3/4
CORRECT
D. 4x + 3y = -22
y = -4/3x - 22/3
Slope = -4/3
INCORRECT
E. 4x - 3y = 48
y = 4/3x - 16
Slope = 4/3
INCORRECT
F. 3x + 4y = 9
y = -3/4x + 9/4
Slope = -3/4
CORRECT
G. y - 6 = 3/4(x - 8)
y = 3/4x
Slope = 3/4
INCORRECT
In a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
Triangle with vertices labeled golfer and spectator and hole, with the distance from the golfer to the spectator measuring 140 yards and the distance from the golfer to the hole measuring 200 yards and the vertex of the spectator measuring 120 degrees
If the spectator has an angle of 120° between the golfer and the hole, what is the angle that the golfer has between the spectator and the hole?
60.0°
59.6°
37.3°
22.7°
Answers
The angle that the golfer has between the spectator and the hole is 60°. Therefore, option A is the correct answer.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
Given that, in a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
Let the angle that the golfer has between the spectator and the hole be x
Here, sin 120°/200 =sin x/140
0.8660/200 =sin x/140
0.00433 = sin x/140
sin x=0.866
x=60°
Therefore, option A is the correct answer.
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Hi hi! The answer would be 22.7°, I took the test a while ago.
For exponential functions of the form f(x)=a^x which of the fallowing expressions is equal to f(b)*f(c)
A. F(b^c)
B. F(b+c)
C. F(b*c)
Answers
Answer:
B
Step-by-step explanation:
[tex]f(x)=a^x[/tex]
x is the exponent, so [tex]f(b)=a^b \text{ and }f(c)=a^c[/tex].
That makes [tex]f(b) \cdot f(c) =(a^b)(a^c)=a^{b+c}[/tex].
b + c is the exponent, so it takes the place of x.
[tex]a^{b+c}=f(b+c)[/tex]