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
Un camión traslada 12 vehículos. Algunos son autos y otros son camionetas. Cada auto tiene una masa de 2 toneladas y cada camioneta de 3 toneladas. En total, el camión lleva una carga de 33 toneladas.
Escribe un sistema de ecuaciones que permita calcular cuántos vehículos de cada tipo traslada el camión. Usa a para representar la cantidad de autos y c para representar la cantidad de camionetas que traslada el camión.
Answers
El sistema de ecuaciones queda descrita por las siguientes expresiones:
[tex]a+c = 12[/tex]
[tex]2\cdot a + 3\cdot c = 33[/tex]
Donde [tex]a[/tex] y [tex]c[/tex] son las cantidades de autos y camionetas.
El enunciado es equivalente a un sistema de dos ecuaciones lineales con dos incógnitas. Una ecuación para la cantidad de vehículos trasladados por el camión y otra ecuación para la masa total trasladada:
[tex]a+c = 12[/tex] (1)
[tex]2\cdot a + 3\cdot c = 33[/tex] (2)
Donde:
[tex]a[/tex] - Cantidad de autos.[tex]c[/tex] - Cantidad de camionetas.El sistema de ecuaciones queda descrita por las siguientes expresiones:
[tex]a+c = 12[/tex]
[tex]2\cdot a + 3\cdot c = 33[/tex]
Donde [tex]a[/tex] y [tex]c[/tex] son las cantidades de autos y camionetas.
Invitamos cordialmente a ver este problema sobre sistemas de ecuaciones: https://brainly.com/question/17174746
help meeeee it's some math stuffff
Answers
Side or Angle
3. George is at the craft show selling homemade ice cream. He must pay
$45 for a booth rental and costs him $3.50 to make each Ice cream
cone. He sells each ice cream cone for $5.00.
The inequality 45 + 3.50c < 5c represents the situation in which George
makes a profit
a). Will George make a profit if he sells 29 cones? Explain why or why not.
Answers
Answer:
no 146.5 > 145
Step-by-step explanation:
what is f (x) = (3x^4 +1) ^2
Answers
Answer:
Cancel the common factor. Divide x x by 1 1 . Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=2x3+43 f - 1 ( x ) = 2 x 3 + 4 3 is the inverse of f(x)=3x−42 f ( x ) = 3 x - 4 2
Step-by-step explanation:
Edward deposited $6,000 into a savings account 5 years ago. The simple interest rate is 3%. How much money did Edward earn in interest?
Answers
Answer:
$900
Step-by-step explanation:
3% of 6,000 is 180
so, he earns $180 per annum
5 YEARS LATER
he has been earning $180 every year, so,
180+ 180+ 180+ 180+ 180, or 180*5
$900
Hope this helps!
(3 x^-2 y^3)^3 Please help ASAP
Answers
Answer:
I don't understand what do you mean by (3 x^-2 y^3)^3
by itself?
2 X a =11+11 ayudaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answers
Answer:
2 × a = 11 + 11 ---> 2a = 22 ---> a = 22/2 = 11
Follow me and hope it helps #The spirit of learningExpress in the form n:1
12:2
Answers
Answer:
6:1
Step-by-step explanation:
The ratio 12/2 is equivalent to the ratio 6/1, or 12:2 = 6:1 .
a box is shaped like a cube.the box a length of 1 foot, a width of 1 foot and a height of 1 foot. what is the volume of the box
Answers
Answer:
1 ft^3
Step-by-step explanation:
Answer:
1 ft^3
Step-by-step explanation:
Volume = Length x Width x Height, so 1x1x1. For volume ft would be cubed.
Simplify the expression 8h + (-7.7d) -14 + 5d - 2.4h.
Answers
Answer:
8h - 7.7d - 14 + 5d - 2.4h
5.6h - 2.7d - 14
Answer:
8h+-7.7d-14+5d-2.4h
Combine -7.7d and 5d to get -2.7d.
8h-2.7d-14-2.4h
Combine 8h and -2.4h to get 5.6h.
5.6h-2.7d-14
Step-by-step explanation:
id k
Which of the following sets of lengths could form the sides of a triangle? Choose all that
apply.
А
7, 9, 17
B
7, 2,8
C
3, 1,5
D
6, 3,5
E
12, 12, 13
F
3,11,8
Answers
Answer:
B, D and E
Step-by-step explanation:
The first triangle inequality theorem states:
the lengths of any two sides of a triangle must add up to more than the length of the third side.
So as long as the sum of the two shortest is greater than the longest side a triangle is possible
А
7 + 9 < 17 NO
B
2 + 7 > 8 YES
C
1 + 3 < 5 NO
D
3 + 5 > 6 YES
E
12 + 12 > 13 YES
F
3 + 8 = 11 NO
There are 6 circles and 9 triangles. What is the simplest ratio of circles to total
shapes?
Answers
Answer:
2:5
Step-by-step explanation:
6 circles : 9 triangles.
Solving for ratio of circles and total
6 circles: 15 shapes ( added 6 and 9 )
thus this can reduce to
2:5 <-- by 3 ( 3*2=6) and (3*5=15)
Leave a comment if this doesn't make sense ;)
-6) -6x — 10y = 3
12х + 20 y = 0
Elimination or substitution?
Solve
Answers
Answer:
Elimination and y=4 x=6
Step-by-step explanation:
1. ) Find the mean for each data set. ROUND FINAL ANSWERS TO THE TENTHS PLACE.
Answers
Answer:
710
Step-by-step explanation:
81+74+72+66+67+72+66+66+72+65+71= 701
701 rounded to the nearest tenth is 710
Plzzz help meeee plzzzzzz
Answers
Answer:
a) $560
b) 80%
c) $1134
Step-by-step explanation:
a)The profit is the difference between selling price and cost price:
profit = $1260 -700 = $560
__
b)As a fraction of the cost price, the profit is ...
$560/$700 × 100% = 80% . . . . of the cost price
__
c)A 10% discount from the selling price makes it ...
$1260 × (1 -10%) = 0.90×$1260 = $1134
A student will pay $1134 for a calculator.
Determine whether the lines are parallel, intersect, or coincide y=-7x-+1 y=-7x-3
Answers
Answer:
Parallel
Step-by-step explanation:
what 1.9 divided by 4
Answers
Answer:
0.457
Steps bye step explanation:
Use the diagram to the right for questions 16 - 20.
MNP ~ SRP
Answers
Answer:
16) 16/3
17.) ength of PM = 20/3
18.) 60
19.) 30
20.) true
Step-by-step explanation:
4/6 = x/8
32/6=x
16/3=x
4/6 = x/10
20/3 = x
Someone help me pls!
You can buy 3 apples at Quick Mart for $1.17. You can buy five of the same apples at Shop & Save for $2.40
How much will you save per apple if you buy them at the cheaper store?
Answers
Answer:
You save $0.09 at Quick Mart for price per apple
Step-by-step explanation:
Quick mart = 1.17/3 = $0.39 per apple
Shop & Save = $0.48
$0.39 - $0.48 = $0.09
You save $0.09 per apple at Quick Mart
-Chetan K
URGENT!!!! i'll mark u as brainliest!
Answers
Answer:
a) 180°
b) 360°
c) 180° (Interior angles)
d) 180°
e) (n-2)180
f) Equal
g) Equal
h) Equal
Step-by-step explanation:
Identify two opposite rays.
Answers
Answer:
B and D
Step-by-step explanation:
opposite rays 180° to each other
here B and D are opposite rays
Answer:
B and D
Step-by-step explanation:
Each opposite ray need 180 degree.
I WILL GIVE BRAINLIEST
Answers
Answer:
= -3x +3
Step-by-step explanation:
like terms (7x) -(4x)
or 7x + -4x = -3x
no like terms to condense 3
13 What is the equation of the line that has a slope of -3 and passes through the point (4,6)?
A-3x+y=-14
B -3x+y=-6
C 3x+y=18
D 3x+y=22
Answers
Step-by-step explanation:
the general equation of a line is
y = ax + b
a is the slope of the line.
b is the y-intercept (the point, where the line crosses the y-axis, meaning the y value when x=0).
we get b by using the point coordinates in the equation and solve for b :
6 = -3×4 + b = -12 + b
18 = b
so, the full line equation is
y = -3x + 18
which is answer C : 3x + y = 18
2÷2563783939282727262626266262534434262788900
Answers
Answer:
128189196964136363133131267217131394450
Step-by-step explanation:
hope this is helpful
-7/10 + 7 2/3
show all ur work
Answers
Answer:
-7/10 + 7 2/3 = 209/ 30 = 6 29/ 30 ≅ 6.9666667
Hope This Helps!!!
Answer:
6 29/30 or 209/30
Step-by-step explanation:
-7/10+ 7 2/3
-7/10+23/3
-21/30+ 230/30
209/30
which is 6 29/30
a restaurant bill is $53.15. what is the estimated total cost of the bill with a
15% tip?
not a multi choice you enter a answer !
Answers
Answer: the answer is 7.95 because 15% tip on 53.15 is 7.95
Please help me with this.
Answers
Answer:
D
Step-by-step explanation:
a,c,d are same but b is different.
evaluate -4(5-(36÷4))
Answers
Answer:
16
Step-by-step explanation:
- 4 ( 5 - ( 36 ÷ 4 ) )
= - 4 ( 5 - 9 )
= - 4 ( - 4 )
= - 4 * - 4
= 16
Please help me please pleaee
Answers
Hello,
A.i. the circumference of a circle is nothing else but its perimeter which formula is π × diameter = π × 2 × radius
Let π = 22/7 ≈ 3.142857, the egyptian approximation
Then if C is the circumference of the circle i., C = 22/7 × 21 = (22 × 21) / 7 = (22× 7×3 )/7 = 22 ×3 = 66 cm
ii. Applying the same formula for the second circle gives us C = 22/7 × 8 = 176/7 ≈ 25.14 meters, rounded to the nearest hundredth...
Good luck !
Answer:
a) 66cm. b) 50.28cm. or 50 2/7cm.
Step-by-step explanation:
The circumference of a circle is C=2πr or C=πd.
π=22/7
a) C=πd
Plugin the diameter.
C=22/7 x 21
=66cm.
b) C=2πr
Plugin the radius.
C=2 x 22/7 x 8
=50.28cm. or 50 2/7cm.
Hope this helps :)
о
3. Aspect Ratios (Tires)
If you have changed the tires on your car, the original diameter is 21 inches. to a new diameter of 25.2 inches,
how fast are you actually going if your speedometer is reading 53 mph?
a
44.2 mph
b. 63.6 mph
c. 60.8 mph
d. 53 mph