The Ferris Wheel has a diameter of 30 meters, the center is 19 meters off the ground and it makes 2 revolutions per min.
Draw this Ferris Wheel, labeling the radius, height, and center. Supposing the minimum height of the Ferris Wheel occurs when t=0, write the sinusoidal function for the height as a function of time. Last graph on a coordinate plane, label the key points.
Answers
The sinusoidal function for the height as a function of time will be h= -15 cos (πt/15)+19 meter
As the Ferris wheel starts with the rider from the bottom position (which is the minimum point in the cycle), we can represent the position of the rider with a negative cosine function.
The general form of the cosine function representing the displacement of the rider is:
f(t) = a cos(bt+c) + d, where:
amplitude = |a| which is the distance that travels above and below the midpoint
period = 2 π/|b| which is the time period i.e. time required to complete one cycle
-c/b is the phase shift.
d = vertical displacement of the function
Given the diameter of the wheel is 30 m, then r = 30/2 = 15 m.
So the distance that travels above and below the midpoint is the radius for which a=15. As we have the negative cosine function, a = -15.
The time period is 0.5min. As it is given the frequency is 2 revolutions per min for which b= 2(2π) rad/min.= 4π/60 rad/sec.= π/15 rad/sec.
The rider starts from the bottom position, so there will be no phase shift, so c=0
Given that the center of the wheel is 19 m above the ground, so d=19m
Therefore the equation will be
height of rider as function of time(t) = h = -15 cos (πt/15)+19 meter
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Related Questions
What is the solution for the system of x - y = -1 and 2x - 5y = -5 ?
Show your work.
Answers
Step-by-step explanation:
please mark me as brainlest
x - y = -1 multiply by 5
we get 5x -5y = -5
subtract the equations:
5x - 5y = -5
-
2x - 5y = -5
5x - 5y -(2x - 5y ) = - 5 - - 5
5x - 5y - 2x + 5y =0
3x = 0
x = 0
2(0) - 5y = -5
- 5y = -5
y = 1
2 3/5t + 5 1/4t + 4t
Answers
Answer:
11 17/20t
Step-by-step explanation:
add the whole numbers first then add the numbers in fraction then there you get your answer.
Given line AC is tangent to circle O.
If m(arc BY)= 44, enter the m∠YAC.
(The figure is not drawn to scale.)
Answers
The measure of <YAC from the figure is. 68 degrees
Circle theoremThe given figure is made up of line and angles.
Since the line AC is tangential to the circle, hence <BAC = 90 degrees and;
<BAY + <YAC = 90degrees
Determine the measure of <BAY
<BAY = 1/2(arcBY)
<BAY = 1/2(44)
<BAY = 22degrees
From the expression above;
<YAC = 90 - 22
<YAC = 68 degrees
Hence the measure of <YAC from the figure is. 68 degrees
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What is the expression for f(x) when we rewrite 36^x•6^(x-2) as 6^f(x)?
Answer: 3x-2
Answers
Using the given information, the expression for f(x) is 3x - 2
Writing an expressionFrom the question, we are to determine the the value of f(x)
The given expression is
36^x•6^(x-2)
That is
[tex]36^{x} \times 6^{x-2}[/tex]
This can be expressed as
[tex]6^{2x} \times 6^{x-2}[/tex]
Applying one of the laws of indices, we get
[tex]6^{2x+x-2}[/tex]
= [tex]6^{3x-2}[/tex]
Since the expression was rewritten as
[tex]6^{f(x)}[/tex]
By comparison,
f(x) = 3x - 2
Hence, the expression for f(x) is 3x - 2
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a fence is 2m high by 33m long, if a gallon of paint is enough to paint 2.5m^2, how many gallons will be used to paint the entire fence?
Answers
The number of gallons of paint needed to paint the entire fence is 26.4 gallons.
Area of rectangleLength = 33 mWidth = 2 mArea = length × width
= 33 m × 2 m
= 66 square meter.
A gallon of paint = 2.5 m²Number of gallons of paint needed = 66 square meter / 2.5 m²
= 26.4 gallons
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Figure B is a scaled copy of figure A.
What is the scale factor from figure A to figure B
Answers
Answer:
1/3
Step-by-step explanation:
We multiply 33(Figure A side) by 1 /3 to get 11(Figure B side).
Which of the following angles are congruent?
Answers
Answer:
C
Step-by-step explanation:
if you rotate either of the triangles by 180 degrees, compare the angles and you will see that the answer is C
The circle below is centered at the origin and has a radius of 7. What is its
equation?
A ²+2²=7
B. x²-y²=7
C. x²-²2²=49A
D. x² + y² = 49
Answers
Answer:
x² + y² = 49
Step-by-step explanation:
The equation for a circle is: x² + y² = r²
here, we know our circle's radius (r) to be 7
So, the equation for our circle is: {replace "r" with value}
x² + y² = 7²
which can be simplified to:
x² + y² = 49
hope this helps!! have a lovely day :)
Consider the systems of equations below. determine the number of real solutions for each system of equations. system a has real solutions. system b has real solutions. system c has real solutions.
Answers
System A has 2 real solutions, System B has 0 real solutions and System C has 1 real solution.
Given a system of equations for A is x²+y²=17 and y=-(1÷2)x, a system of equations for B is y=x²-7x10 and y=-6x+5 and a system of equations for C is y=-2x²+9 and 8x-y=-17.
For system A,
The two systems of equations are
x²+y²=17 ......(1)
y=-1÷2x ......(2)
Substitute the value of equation (2) into equation (1) as
x²+(-x÷2)²=17
x²+(x²÷4)=17
Simplify the above equation by taking L.C.M. as
(4x²+x²)÷4=17
5x²=68
x²=68÷5
x=±3.688
Find the value of y by substituting the value of x in equation (2).
When x=3.688 then y is
y=-(1÷2)×3.688
y=-1.844
And When x=-3.688 then y is
y=-(1÷2)×(-3.688)
y=1.844
Thus, the points where the equations of system A intersect each other is (3.688,-1.844) and (-3.688,1.844)
So, the system of equations of A has 2 real solutions.
For system B,
The two systems of equations are
y=x²-7x+10 ......(3)
y=-6x+5 ......(4)
Substitute the value of equation (4) into equation (3) as
-6x+5=x²-7x+10
x²-7x+10+6x-5=0
x²-x+5=0
Simplify the above quadratic equation using the discriminant rule,
x=(-b±√(b²-4ac))÷(2a)
Here, a=1, b=-1 and c=5
Substitute the values in the discriminant rule as
x=(1±√(1-4\times 5\times 1))÷2
x=(1±√(-19))÷2
x=(1±√(19)i)÷2
Here, the value of x goes into the complex.
So, the system of equations of B has 0 real solutions.
For system C,
The two systems of equations are
y=-2x²+9 ......(5)
8x-y=-17 ......(6)
Substitute the value of equation (6) into equation (5) as
8x-(-2x²+9)=-17
8x+2x²-9+17=0
2x²+8x+8=0
Simplify the above quadratic equation using factorization method as
2x²+4x+4x+8=0
2x(x+2)+4(x+2)=0
(2x+4)(x+2)=0
x=-2,-2
Find the value of y by substituting the value of x in equation (5).
When x=-2 then y is
y=-2(-2)²+9
y=-8+9
y=1
Thus, the point where the equations of system C intersect each other is (-2,1)
So, the system of equations of C has 1 real solutions.
Hence, the system of equations for A is x²+y²=17 and y=-(1÷2)x having 2 real solution, a system of equations for B is y=x²-7x10 and y=-6x+5 having 0 real solution and a system of equations for C is y=-2x²+9 and 8x-y=-17 having 1 real solution.
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help please
Find the sum or type
"impossible"
[3 -8] + [4 -5 -6]
Answers
Base area = 18 ft²
Volume=
11 ft
7
Answers
Answer:
nhddhdbndbd
Step-by-step explanation:
jh h benrheoek
[tex]\sf\large\green{\underbrace{\red{Befikra*}}}:[/tex].
The first term of an arithmetic sequence is 1 and the sum of the first four terms is 100. Find the first four terms
Answers
First term f = 1
If first four terms are f, f + d, f + 2d, f + 3d
f + f + d + f + 2d + f + 3d = 100
4f + 6d = 100 (divided by 2 , both sides )
2f + 3d = 50
2 + 3d = 50
3d = 50 – 2
3d = 48
d = 48/3
d = 16
The arithmetic sequence is 1, 17, 33, 49, ………….
Answer:
[tex]\sf\large\blue{\underbrace{\red{itz \: jass*}}}:[/tex]
Step-by-step explanation:
[tex]\sf\large\green{\underbrace{\red{hlo \: \: sat \: shri \: akal \: ji \: \: \: *}}}:[/tex]
Select the correct answer.
The speed of a ship is given by , where d is the distance the ship travels in 3 hours. If the ship travels 48 miles in 3 hours, what is the speed of the ship?
A.
12 miles per hour
B.
16 miles per hour
C.
45 miles per hour
D.
51 miles per hour
Answers
Determine whether each set of ordered pairs shown below is from a geometric sequence or from an arithmetic sequence.
{(-3, 7.5) , (-2, 10) , (-1, 12.5)}
Write the equation of the graph for the set of ordered pairs.
{(1, 150) , (2, 112.5) , (3, 84.375)}
Write the equation of the graph for the set of ordered pairs.
Answers
Using sequences concepts, it is found that:
The set of ordered pairs {(-3, 7.5) , (-2, 10) , (-1, 12.5)} is an arithmetic sequence with equation a(n) = 15 + 2.5d.The set of ordered pairs {(1, 150) , (2, 112.5) , (3, 84.375)} is a geometric sequence with [tex]a_n = 150(0.75)^{n-1}[/tex].What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a(n) = a(0) + nd[/tex]
The sequence {(-3, 7.5) , (-2, 10) , (-1, 12.5)} continues with points (0, 15), (1, 17.5), and so on, hence the first term and the common ratio are given, respectively, by:
a(0) = 15, d = 2.5.
Hence the equation is:
a(n) = 15 + 2.5n.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
For the sequence {(1, 150) , (2, 112.5) , (3, 84.375)}, the first term and the common ratio are given, respectively, by:
[tex]a_1 = 150, q = \frac{112.5}{150} = \frac{84.375}{112.5} = 0.75[/tex]
Hence the equation is given by:
[tex]a_n = 150(0.75)^{n-1}[/tex]
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What is the approximate horizontal distance between Amelia and Brendon? Explain your reasoning
Answers
Answer:
60 ft
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{CD}{AD}[/tex] = [tex]\frac{30}{AD}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
AD = 60 ft
Solve the equation for x.
√x-5 = x-11
Answers
Answer:
√x-5 = x-11 = 9.
Step-by-step explanation:
Isolate the radical, then raise each side of the equation to the power of its index.
x = 9 Solve the equation for x.9
If g = 8, what is the value of the expression 2+3?
OA.
B.
815
(11)
OC. 7
OD. 19
Answers
The value of the expression, g/2 + 3 when x = 8 is: 7.
How to Evaluate an Expression?Given the expression, g/2+3, to find it's value when g = 8, plug in the value of g into the expression and solve.
g/2 + 3
8/2 + 3
Divide
4 + 3
= 7
The value of the expression is: 7.
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Let g be the piecewise defined function shown.
g(x)=
x + 4, −5 ≤ x ≤ −1
2 − x, −1 < x ≤ 5
Evaluate g at different values in its domain.
g(−4) =
g(−2) =
g(0) =
g(3) =
g(4) =
Answers
Answer:
g(4)= -2
g(-2)= 2
g(0)= 2
g(3)= -1
g(-4)= 0
Step-by-step explanation: See attachment, and don’t forget to check just in case ;)
Answer:
g(−4) = 0
g(−2) = 2
g(0) = 2
g(3) = -1
g(4) = -2
Step-by-step explanation:
Please Thank!
Sienna is solving the quadratic equation by completing the square.
3x2 + 9x – 4 = 0
3x2 + 9x = 4
A(x2 + 3x) = 4
Answers
Answer:
See below
Step-by-step explanation:
3 (x^2 + 3x) = 4
3 ( x + 3/2)^2 = 4 + 27/4
Can some help me with this, it’s urgent pls? It’s geometry
Answers
7. the diameter is segment WY
8. radius is 1/2 of the diameter so 1/2(15) = 7.5 meters
9. diameter is 2 times the radius so 2(4) = 8 cm
10. segment XW, segment XZ, segment XY
11. arc YW, arc WZ, arc ZY
Select the correct answer.
Which value of x makes this equation true?
-12x2(x + 9) = 5(x + 4)
O A.
OB.
O C.
O D.
Answers
Answer:
B. -2
Step-by-step explanation:
-12x -2(x+9) = 5(x+4)
*ALWAYS REMEMBER YOUR BODMAS*
-12x -2x - 18 = 5x + 20
*group the like terms*
-14x - 5x = 20 + 18
-19x = 38
x = -2
The value of x that makes the equation true is: x = -2.
B. -2.
Here, we have to find the value of x that makes the equation true, we need to solve for x.
Let's solve the equation step by step:
-12x - 2(x + 9) = 5(x + 4)
Distribute the -2 and 5 on the right side of the equation:
-12x - 2x - 18 = 5x + 20
Combine like terms on both sides:
-14x - 18 = 5x + 20
Move the variable terms (5x) to one side of the equation and the constant terms to the other side.
Let's subtract 5x from both sides:
-14x - 5x - 18 = 5x - 5x + 20
-19x - 18 = 20
Move the constant term (-18) to the other side of the equation.
Let's add 18 to both sides:
-19x - 18 + 18 = 20 + 18
-19x = 38
Finally, divide both sides by -19 to isolate x:
x = 38 / -19
x = -2
So, the value of x that makes the equation true is: x = -2.
B. -2.
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Which expression is equivalent to (3^2) ^-2
Answers
[tex](3^{2} )[/tex]^-2=(9)^-2=1/9^2=1/81
hope it helps!
40. Se desea distribuir las bancas dentro de un salón de clases cada 1.5 m como
se muestra en la imagen, ¿de qué forma se puede saber el área requerida para
conservar la separación de las bancas?
1.5m
Answers
La forma adecuada para saber el área requerida para conservar la separación de las sillas es multiplicar (7.5) (4.5) opción B.
¿Cómo calcular el área requerida para mantener la separación?Para identificar la operación necesaria para calcular el área requerida para ubicar las sillas con su respectiva separación de 1.5 metros es:
7.5 × 4.5 = 33.75Esta expresión nos va a permitir calcular el área necesaria debido a que la separación entre sillas es 1.5 metros y tenemos 6 sillas a lo largo y 4 sillas a lo ancho, es decir:
1.5 × 5 = 7.5 distancia a lo largo1.5 × 3 = 4.5 distancia a lo anchoNota: Esta pregunta está incompleta porque falta la imagen y las opciones. Aquí está la información faltante:
Opciones:
A. Multiplicar (6)(4)
B. Multiplicar (7.5)(4.5)
C. Multiplicar (9)(6)
D. Multiplicar (9.5)(4.5)
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The expression 55 + 14m - 2n + 3p has _________ terms.
1. 3
2. 4
3. 2
4. 5
Answers
If anyone could help me, it would be greatly appreciated!
Answers
Answer: [tex]x=65^{\circ}, y=65^{\circ}, z=65^{\circ}[/tex]
Step-by-step explanation:
All radii of a circle are congruent, so by the base angles theorem
z = y = (180-50)/2 = 65.Also, angles x and y are inscribed in the same arc, and they are thus congruent, meaning x = 65.
Which angles are vertical angles select two options
Answers
The pair of the vertically opposite angles are ∠ABC = ∠DBE and ∠CBD = ∠ABE Then the correct options are B and E.
The complete question is attached below.
What is Vertically opposite angle?When two lines intersect, then their opposite angles are equal.
The diagram is given below.
∠ABC = ∠DBE
∠CBD = ∠ABE
Then the correct options are B and E.
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If side c measures 32.3 units long, how long is side a?
Answers
Answer:
16.15
Step-by-step explanation:
sin(30) = a / c
a = c * sin(30)
a = 32.3 * 0.5
a = 16.15
What is the scale factor of this dilation?
Answers:
A. 1/2
B.3/5
C.1 2/3
D.2
Answers
Answer:
3/5
Step-by-step explanation:
scale factor of ab to A'B'
AB:A'B'
5 : 3
in fraction the scale
factor is 3
—
5
heance a reduction.
hope it helps thank me later
#galadohannadivine29
#carry on learning
please help me i need help quick
Answers
Answer:
x = -2
y = -6
Step-by-step explanation:
Equating the equations :
x - 4 = 4x + 23x = -6x = -2y = -2 - 4y = -6Equate both
x-4=4x+2-4-2=4x-x-6=3xx=-2And
y=-2-4=-6Graph attached
Select the correct answer.
The speed of a ship is given by , where d is the distance the ship travels in 3 hours. If the ship travels 48 miles in 3 hours, what is the speed of the ship?
A.
12 miles per hour
B.
16 miles per hour
C.
45 miles per hour
D.
51 miles per hour
Answers
Hope this helps
