A contestant on a game show spins a wheel that is located on a plane perpendicular to the floor. He grabs the only red peg on the circumference of the wheel, which is 1.5 m above the floor (the peg is) and pushes it downward. The peg reaches a min height of 0.25 m and a max height of 2.75 m above the floor. Sketch two cycles of the graph representing the height above the ground as a function of the total distance moved. Then determine the equation of the sine function
Answers
The spin of the wheel by the contestant is an illustration of a sine function whose equation is [tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]
The wheel is 1.5 m above the floor, and the peg reaches a maximum height of 2.75 m.
So, the amplitude is:
[tex]\mathbf{A = 1.5 - 2.75}[/tex]
[tex]\mathbf{A = -1.25}[/tex]
The vertical shift is the minimum height of the peg.
So, we have:
[tex]\mathbf{D = 0.25}[/tex]
The period (T) equals one circumference.
So, we have:
[tex]\mathbf{T = (max-min)\pi}[/tex]
This gives
[tex]\mathbf{T = (2.75-0.25)\pi}[/tex]
[tex]\mathbf{T = 2.5\pi}[/tex]
The frequency (B) is then calculated as:
[tex]\mathbf{B = \frac{2\pi}{T}}[/tex]
This gives
[tex]\mathbf{B = \frac{2\pi}{2.5\pi}}[/tex]
Divide
[tex]\mathbf{B = 0.8}[/tex]
A sine function is represented as:
[tex]\mathbf{y =A sin(B(x + C)) + D}[/tex]
Substitute the calculated values
[tex]\mathbf{y =-1.25 sin(0.8(x + C)) + 0.25}[/tex]
The horizontal shift (C) is 0.
So, the function becomes
[tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]
See attachment for the graph of the equation
Read more sine function at:
https://brainly.com/question/11904902
Related Questions
The FAA tracks average flight delays. It found that, last year, a particular airline had an average flight delay of 20 minutes. So far this year, the airline has an average that is 45% shorter. What is the current year's average?
Answers
Answer:
11 minutes
Step-by-step explanation:
45% of 20 can be found by multiplying 20 and 0.45
which equals 9
so if the average delay was 20 but is now 9 minutes shorter then the current year's average is 11 minutes
The average delay in the current year is 11 minutes.
Given that, last year, a particular airline had an average flight delay of 20 minutes.
This year the airline has an average that is 45% shorter.
We need to find what is the current year's average.
What is average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Now, 45% of 20=45/100×20=9
So,20-9=11
Hence, the average delay in the current year is 11 minutes.
To learn more about the average visit:
https://brainly.com/question/24057012.
#SPJ2
Alex borrowed 12.50 from his friend. He paid him back 8.75. How much does he still owe?
Answers
Answer:
3.75
Step-by-step explanation:
If Alex borrowed 12.50 and paid him back only 8.75, that means he still owes him 3.75. 12.50 - 8.75 = 3.75
help please and thank u
Answers
Answer:
The line is y = (1/2)x + 3
Step-by-step explanation:
We can calculate a slope. I'll use the two points (-4,1) and (-1,2.5).
Rise = (2.5-1) = 1.5
Run = (-1-(-4)) = 3
Rise/Run = Slope = (1.5/3.0) = 1/2
Find b, the y-intercept, by using point (-4,1) in the equation y = (1/2)x + b
y = (1/2)x + b
1 = (1/2)*(-4) + b
1 = -2 + b
b=3
The line is y = (1/2)x + 3
Which expression represents the area of this figure in square feet?
Answers
Answer:
(3×2) + (3×4)
Step-by-step explanation:
One box's area is 3×2 and the other box's area is 3×4, so when you add them, you get the total area.
1. The diameter of each tire on a model car is 10.668 mm. The actual diameter of a car's tire is 5.29 X 102 mm. About how many times larger is the actual diameter of a car tire than the diameter of the tire on the model car? A 5 times B 50 times +90 100 times D 500 times
Answers
The number of times the actual diameter is larger than the model is 50 times.
A tire has the shape of a circle. The diameter is line that goes through the center of a circle and divides the circle into two.
In order to determine how many times larger the actual diameter is greater than the model, the actual diameter would be divided by the diameter of the model.
5.29 x 10² ÷ 10.668
529 ÷ 10.668
= 49.6
= 50 times
Please find attached an image of a circle. To learn more, please check: https://brainly.com/question/13590859
answer this
help me with this question.
Answers
Answer:
i cant read the handwriting
Step-by-step explanation:
Can someone help me. All i need o know is what is the value after 10 years i done the equation part by myself
NO BOTS OR ILL REPORT YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
ILL GIVE BRAINLY TO CORRECT ANSWER
100 points
Answers
Answer:
$4811
Step-by-step explanation:
Initial price = 35,000
18% decrease anually = 18/100 = -0.18
after 10 years
substitute these values in the formula shown in below figure
A = 35000 * ( 1 + -0.18/1 ) ^10
= 35000 * 0.82^10
= 4,810.681
= $4811
Can someone reflect (7,6) across the x axis then reflect across the y axis
Answers
Answer:
(7, -6)
(-7, -6).............
..
Answer: -7,-6
Step-by-step explanation:
So if we look at a graph 7,6 is on the right upper quadrant since its completely positiv, once we relfect the x axis then it becomes 7,-6 then once we reflect across the why axis it finally becomes -7,-6
Two trains are traveling at a constant rate. Find the rate of each train. Which train is traveling at a faster rate?
Answers
Answer:
Train A
Step-by-step explanation:
Look at the table.
Train A : 75 - 50/ 3 - 2 = 25 mi/n
Train B : 40 - 0/ 2 - 0 = 20 mi/n
25 > 20
So it's train A.
{ RATE }
A regular polygon has 45 sides.
Find the size of each of its exterior angles.
100 POINTS
Answers
Answer:
8
Step-by-step explanation:
360/45 = 8
We know
Sum of exterior angles of any polygon is 360°Let every angle be x
[tex]\\ \sf\longmapsto 45x=360[/tex]
[tex]\\ \sf\longmapsto x=360/45[/tex]
[tex]\\ \sf\longmapsto x=8°[/tex]
What is the range
of 98, 99, 100,
90, 98, 100?
Answers
Answer:
10
Step-by-step explanation:
Increasing order:-
90,98,98,99,100,100Range = Highest term - Lowest term
Range = 100 - 90
Range = 10
Hence,
Range of the given term is 10
Answer:
10Step-by-step explanation:
The data set in ascending order:
90, 98, 98, 99, 100It has min = 90, max = 100
The range is the difference between min and max:
100 - 90 = 10a. 17 + 6 10=17,6 b. 45 + 6 100 5 c. 3 + + 10 2 100 7 8 d. 6 + + 9 + 10 100 1 000 6 e. 11 + + 10 8 1 000 f. 84 + 1 3 + 100 10
Need help me
Answers
Step-by-step explanation:
a. 17 + 6/10 = (17 x 10) / (1 x 10) + 6/10 = 170/10 + 6/10 = 176/10 = 17,6
b. 45 + 6/100 = (45 x 100) / (1 x 100) + 6/100 = 4 500/100 + 6/100 = 4 506/100 = 45,06
c. 3 + 5/10 + 2/100
= (3 x 100) / (1 x 100) + (5 x 10) / (10 x 10) + 2/100
= 300/100 + 50/100 + 2/100
= 352/100 = 3,52
d. 6 + 7/10 + 8/100 + 9/1 000
= (6 x 1 000) / (1 x 1 000) + (7 x 100) / (10 x 100) + (8 x 10) / (100 x 10) + 9/1 000
= 6 000/1 000 + 700/1 000 + 80/1 000 + 9/1 000
= 6 789/1 000 = 6,789
e. 11 + 6/10 + 8/1 000
= (11 x 1 000) / (1 x 1 000) + (6 x 100) / (10 x 100) + 8/1 000
= 11 000/1 000 + 600/1 000 + 8/1 000
= 11 608/1 000 = 11,608
f. 84 + 1/100 + 3/10
= (84 x 100) / (1 x 100) + 1/100 + (3 x 10) / (10 x 10)
= 8 400/100 + 1/100 + 30/100
= 8 431/100 = 84,31.
Hope this helps!!
AB, BC and CD are three sides of a regular octagon.
Find the size of angle BAC.
Give reasons for your answer.
Answers
Answer:
22.5°
Step-by-step explanation:
The exterior angle at B is 360°/8 = 45°. The congruent interior angles of the triangle at A and C total this amount. The angle BAC is 45°/2 = 22.5°.
What is the range of f(x)?
Answers
Answer:
{ f(x)| -∞ < f(x) ≤ 4 }
Step-by-step explanation:
The range of a function is the interval of every y-value represented on the function. Since the highest this function goes on the y-axis is to y=4, we know that the upper limit of the range is 4, which is inclusive because the function actually reaches this value. The function also appears to go down indefinitely on the right side, so the lower limit is -∞, which is non-inclusive because we will never reach that value.
The range is -∞ < f(x) ≤ 4
What is the measure of angle x?
Answers
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today!
We can solve this problem in two steps, one being comprehension and another being solving. I'll start off with comprehension.
Comprehension
We can start to solve this problem by looking at it.
We can see that there is a right angle, therefore the angles that are in it are Complementary (Add up to 90).
That means that 30+3x=90.
We can now begin solving.
Solving
We can start solving by setting up an equation.
[tex]30+3x=90[/tex]
We can do this because we know due to the law of complementary angles that 30 and 3x MUST equal to 90.
[tex]3x=60\\x=20[/tex]
We can do basic algebra, we can find out that x is equal to 20 degrees. Let's now check our answer.
[tex]30+3(20)=90?\\30+60=90?\\90=90[/tex]
Therefore the answer is x=20 degrees
Cheers!
Benny loves eating fruits. Benny paid $4.30 for apples, and $7.02 for peaches with
a $20 bill. How much change did Benny receive?
Answers
Help needed, this is timed :’)
Answers
Answer:
Step-by-step explanation:
last answer
David descarga un video de 72 megabytes en 8 minutos ¿cuantos megabytes descargara en 13 minutos ?
Answers
Answer:
117 megabytes
Step-by-step explanation:
Por regla de tres:
72 mb son a 8 mins
D mb son a 13 minutos
D = 13*72/8
D = 117 mb
PLEASE HELP ME ASAP TYSM
Answers
The sale price is 85% of the regular price.
-If regular price is 100% and there is a 15% discount, The sale price will be 85% of reg. price.
100-15=85
Answers:
- Sale price: $25.50
-85%of 100%
-Discount: 15%
-$4.50
You can check by the following:
30-25.5=4.5
30-4.5=25.5
4.5+25.5=30
25.5+4.5=30
100-15=85
100-85=15
85+15=100
15+85=100
(Brainliest?) ^^
Which numbers are irrational
Answers
Answer:
A & B
Step-by-step explanation:
A rational number is a number that can be written as a fraction or a terminating or repeating decimal. An irrational number is one that cannot be written as a fraction, or one that goes on forever without terminating or repeating in any way. Let's check all of our options and find the ones that are irrational.
Our first option (A) looks irrational! The "..." shows us that it goes on forever, and it doesn't look like it repeats. So this option is irrational.
Our next option is B, the square root of 24. What is the square root of 24? Well, if we look it up on a calculator, we get 4.89897948557..., and it looks like this one doesn't terminate or repeat either. So option B is also irrational.
Option C is the square root of 121. The square root of 121 is 11, which can be written as a fraction (11/1) and is a terminating decimal. So it's rational.
Our last option is D, and it is written already as a fraction, so we know for sure that it's rational. If we divide it out, we get 0.44444... with the 4 going on forever. It's a repeating decimal, and repeating decimals are rational.
So our final answers for which are irrational are A & B.
7. Two numbers are at a ratio of 5: 9. Find the larger number if the smaller number is 35.
Answers
Answer:
63
Step-by-step explanation:
HELP ME PLEASE
whats 9+10?
Answers
Answer:
21
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
PLEASE HELP NEED TO GET THIS RIGHT WILL GIVE BRAINLIEST
Answers
Answer:
27 / 4x^6y^8.
Step-by-step explanation:
= 4 * 3^3 x^6 y^12 / 16 x^12 y^20
= 4*27 / 16 x^6y^8
= 4*27/ x^6y^8
= 27 / 4x^6y^8
Between what two whole numbers is 5/6 located on the number line? help please!
Answers
Answer:
Hello there!
5/6 is located between 0 and 1.
Step-by-step explanation:
5/6 is less than 1, because 1 = 6/6 in this scenario.
At the same time, it's greater than 0!
5/6 is located between 0 and 1 on the number line!
On a coordinate graph the following points of a rectangle are given. A(0,2) B (0,-2) C (3,-2) 4 Where do the coordinates of Dneed to be to form the rectangle? 0 (3,2) O (2, 3) 0 (1,3) 0 (3,1)
Answers
Answer:
(3, 2)
Step-by-step explanation:
Please mark me brainliest if this helped! :P
The measures of angles x and y in the above figure is:
Answers
Step-by-step explanation:
sum of 2 angles on a straight line = 180°
therefore,
y + 120 = 180
y = 180 - 120 = 60
y = 60°
now apply angle sum property of triangle
now,
50 + x + y = 180
50 + x + 60 = 180
110 + x = 180
x = 180 - 110
x = 70
therefore, x = 70 & y = 60
hope this answer helps you dear! take care
Answer:
x = 70°
y = 60°
Step-by-step explanation:
hope it helps u
plzz plzz pLZZ MARK AS BRAINLIEST
an electrician has 4.1 meters of wire.How many strips of 7 tenths can be cut?and how much wire will be left over?
Answers
0.5 meters per strip
0.6 meters left over
Will give brainliest no files plz
Answers
Answer:
x=3 and y= 4 / 3 (Fraction)
Step-by-step explanation:
Substitute x for 6y-5.
2(6y−5)−3y=2
Add 6y and 3y, and multiply 5 by 2/Simplify the equation.
9y−10=2
Add 10 to both sides, and then divide each side by 9.
9y−10+10=2+10
9y / 9 = 12 / 9
y = 4/3.
Repeat the process but replace y with 4/3!
Answer:
x=3
y= 4/3
Step-by-step explanation:
2(6y-5)-3y=2
y= 4/3
x=6x 4/3-5
x=3
what is (x-2) (3x-4)=
a.3x² - 6x-8
b.3x² - 2x - 8
c.3x² + 10x + 8
d.3x² - 10x + 8
Answers
Answer:
D. 3x^2-10x+8
Step-by-step explanation:
[tex] \: \: \: \: \: [/tex]
D. 3x²- 10x + 8hope it helps
refer to the attachment
[tex] \: \: \: \: \: [/tex]
Answer this middle school math equation for 30 points lol
Answers
Answer:
n
Step-by-step explanation:
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
Multiply both sides by -5:
[tex]-\frac{1}{5} (x-4)=-2[/tex]:
[tex]-\frac{1}{5} (x-4)*-5=-2*-5[/tex]
[tex]1(x-4)=10[/tex]
[tex]x-4=10[/tex]
Add 4 to both sides:
[tex]x-4+4=10+4[/tex]
[tex]x=14[/tex]