A Ferris wheel is 20 meters in diameter and completes 1 full revolution in 8 minutes.



A round Ferris wheel

A Ferris wheel is 20 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn.



a. Find the amplitude, midline, and period of h(t).



Enter the exact answers.



Amplitude: A= meters

Midline: h= meters

Period: P= minutes



b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t=0. Find a formula for the height function h(t).



Hints:

What is the value of h(0)?
Is this the maximum value of h(t), the minimum value of h(t), or a value between the two?
The function sin(t) has a value between its maximum and minimum at t=0 , so can h(t) be a straight sine function?
The function cos(t) has its maximum at t=0, so can h(t) be a straight cosine function?


c. If the Ferris wheel continues to turn, how high off the ground is a person after 30 minutes?

Answers

Answer 1

Given that the Ferris diameter is 20 meters, with a rate of rotation of 1 turn in 8 minutes, we have;

a. Amplitude: A = 10 meters

Midline: h = 11 meters

Period, P = 8 minutes

b. h(t) = 10•cos((π/4)•t + π) + 11

c. 11 meters

How can the Ferris wheel be evaluated?

The amplitude is the same as the radius of the Ferris wheel,

The radius of the Ferris wheel = 20 ÷ 2 = 10

Therefore;

Amplitude: A = 10 meters

[tex]the \: midline \: = \frac{max \: height \: + min \: height}{2} [/tex]

Therefore;

[tex]midline \: = \frac{10 + 10 + 1 + 1}{2} = 11[/tex]

Midline: h = 11 meters

The period is the time to complete one rotation, therefore;

Period, P = 8 minutes

b. h(t) = A•cos(B•t + C) + h

Where;

B = 2•π/P

When t = 0, h(t) = 1

Which gives;

h(0) = 1 = 10 × cos(B×0 + C) + 11

-10/10 = -1 = cos(C)

C = arcos(-1) = π

Therefore;

h(t) = 10•cos((π/4)•t + π) + 11

h(0) = 1

h(0) is the minimum value of h(t)

h(t) cannot be a straight sine function because of the vertical shift

h(t) cannot be a straight cosine function because at t = 0, is the minimum point

c. After 30 minutes, we have;

h(30) = 10•cos((π/4)×30 + π) + 11 = 11

The height of a person after 30 minutes is 11 meters

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Related Questions

The length of the base of an isosceles triangle is x. The length of a leg is 3x−6. The perimeter of the triangle is 65. Find x.

Answers

Answer:

x = 11

Step-by-step explanation:

Hello!

In an isosceles triangle, the two legs are congruent by the property Base angle Theorem. It is isosceles when both angles on the base are congruent.

So, since the base is x, and the measure of one leg is 3x - 6, we know that the other leg is also 3x - 6 in length.

The equation for perimeter is :  leg + leg + base = Perimeter

We can plug in 65 for the perimeter because it's given

Solve for x:

x + 3x - 6 + 3x - 6 = 657x - 12 = 657x = 77x = 11

The value of x is 11.

the length of a rectagle is twice its width. if the perimeter of the rectangle is 36in, find its length and width

Answers

Answer:

Perimeter=36in

Length of one side=12

Length of the other side=12

Width of one side=6

Width of the other side=6

Step-by-step explanation:

6*2=12, so if the length is 12 half would be six. All of them added up is 36

Answer:

Length = 12inWidth = 6in

Step-by-step explanation:

[tex]perimeter \: of \: a \: rectangle = 2(2x) + 2(x) \\ 36in = 4x + 2x = 6x \\ \frac{36in}{6} = \frac{6x}{6} \\ x = 6in \\ 2x = 2 \times 6in = 12in[/tex]

Mark me brainliest!

camilo uses 32 ounces of filling to make empanadas. he puts 8 empanadas on each of 3 trays. Write a fraction to show how many ounces of filling camilo uses in each empanada. Please reply quickly!

Answers

Answer:

32/4

Step-by-step explanation:

 

please help me I will mark BRAINLIEST ​

Answers

Answer:

See attached diagram

a) Points shown in blue

b) correlation is negative since the y-values decrease as the x-values increase.

c) Line of best fit needs to have the same number of points above as below.


7. The area of the parallelogram is 450 m2. What is
the height?
A. 25 m
B. 36 m
C. 50 m
D. 72m

Answers

The answer is 36 sq. ft. Find the area of the following parallelograms. Example 3. Base = 7 meters, Height = 3.5 meters. First, write

h = height of the parallelogram. a = side of the parallelogram (AD) x = any angle between the sides of the parallelogram (∠DAB or ∠ADC) d1 = diagonal of the parallelogram (p)
...
Area = ½ × d1 × d2 sin (y)

In a parallelogram ABCD, angle a=70, find 2angle d​

Answers

Answer:

D = 110

Step-by-step explanation:

Given,

In a parallelogram ABCD,

∠A =70∘

∠A + ∠B = 180∘.. (supplementary angles)

∠B = 180∘ – 70∘ = 110∘

∠A = ∠C and ∠B = ∠D.. (Opposite angles of parallelogram)

∠A = 70∘, ∠B = 110∘, ∠C = 70∘, ∠D = 110

the answer is gon b 110

100 points! need done asap

An unfair spinner has sections labeled 1 2 or 3 that are all twice as large as each of the sections labeled 4 5 or 6 Develop a probability model to describe all possible outcomes of one spin of the spinner

Answers

Answer:

look at the pic and stay safe!! hope it helps

Olivia borrowed $5,000 for 5 years at 5% simple interest.

Answers

Answer:

The answer is $1250

Step-by-step explanation:

Solution,

Principle (P) = $ 5,000

Time (T) = 5 years

Rate(R) = 5 %

Simple Interest (I) = ?

Now,

We have,

Simple Interest (I) = P×T×R/ 100

= 5,000×5×5/100

= $1250

can someone please help me

Answers

Like the given triangle is an isosceles triangle, the value of ∠ABC is 72°.

Types of Triangles

There are 3 main classifications for triangles refer to its sides.

Equilateral triangle - This triangle presents all sides with the same dimensions and the all angles equal to 60°.Isosceles triangle - This triangle presents two sides with the same dimensions and it has two angles with equal size.Scalene triangle  - This triangle presents all sides with different dimensions and it has all angles no equal size.

The figure shows that the given triangle is an isosceles triangle because it has two equal sides (AB=AC). If it is an isosceles triangle, this triangle presents two sides with the same dimensions (AB=AC). and it has two angles with equal size(∠ACB=∠ABC).

Knowing the sum internal angles of triangle is 180°. You can write:

3x+6x+6x=180

15x=180

x=12

Like ∠ABC=6x, then ∠ABC=6*12=72°.

Read more about the types of triangles here:

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If tomorrow i said, "the day before yesterday was saturday",then what is today?​

Answers

Answer:

Monday

Step-by-step explanation:

If day before yesterday was Saturday, so today is Monday.

Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)

Part B: Solve for k in each type of transformation. (4 points)

Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Answers

A) The transformations can be a vertical translation and an horizontal translation.

B) K = 8 and K' = 16

C) g(x) = f(x + 8)

    g(x) = f(x) + 16.

Which type of transformation could be used?

A ) By looking at the graph, we see that g(x) can be a translation to the left by K units or up by K' units.

B) In the case the translation is to the left, we can see that it the graph is moved 8 units, so K = 8.

In the case that the translation is up, we can see that it is for 16 units, so we have k' = 16.

C) How to write the equations?

An horizontal translation is written as:

g(x) = f(x + K).

Because the translation is to the left, we have that K is positive, then in our case we have:

g(x) = f(x + 8).

For the vertical translation the formula is:

g(x) = f(x) + K'

In our case, we have:

g(x) = f(x) + 16

If you want to learn more about transformations, you can read:

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Answer:The transformations can be a vertical translation and an horizontal translation.B) K = 8 and K' = 16C) g(x) = f(x + 8)    g(x) = f(x) + 16.Which type of transformation could be used?A ) By looking at the graph, we see that g(x) can be a translation to the left by K units or up by K' units.B) In the case the translation is to the left, we can see that it the graph is moved 8 units, so K = 8.In the case that the translation is up, we can see that it is for 16 units, so we have k' = 16.C) How to write the equations?An horizontal translation is written as:g(x) = f(x + K).Because the translation is to the left, we have that K is positive, then in our case we have:g(x) = f(x + 8).For the vertical translation the formula is:g(x) = f(x) + K'In our case, we have:g(x) = f(x) + 16

Step-by-step explanation:

Whats 5-5-5-5-5-5x5757575

Answers

Answer:

-28787890

Step-by-step explanation:

14. You deposit $500 in a savings account that
carns 7% interest compouncted anually.
A.) write a function that represents the balance
after t years
B.) What is the balance after 2 years?

Answers

A) Balance = 500(1.07)^t
B) Balance after 2 years = 500(1.07)^2 = $572.45

Answer:

A)    A(t) = 500e^(0.07)(t)

B)    575.137

Step-by-step explanation:

3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations described below. a. The account pays 3% annual interest compounded monthly. b. The account pays 4% annual interest compounded continuously.​

Answers

Answer:

Part A)

About $3767.34.

Part B)

About $3692.47.

Step-by-step explanation:

Part A)

Recall that compound interest is given by the formula:
[tex]\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}[/tex]

Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

To obtain $4000 after two years, let A = 4000 and t = 2.

Because the account pays 3% interest compounded monthly, r = 0.03 and n = 12.

Substitute and solve for P:

[tex]\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}[/tex]

In concluion, about $3767.34 should be deposited.

Part B)

Recall the formula for continuous compound:

[tex]\displaystyle A = Pe^{rt}[/tex]

Where e is Euler's number.

Hence, let A = 4000, r = 0.04 and t = 2. Substitute and solve for P:

[tex]\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}[/tex]

In conclusion, about $3692.47 should be deposited.

which fraction is larger: 3/10 or 2/7
Plot on a number line

Answers

Answer:

3/10 is bigger

Step-by-step explanation:

covert into a decimal so 0.3 is bigger than 0.2857

What common donminator of 1/3 and 3/4

Answers

Answer:

12

Step-by-step explanation:

The least common denominator (LCD) of 1/3 and 3/4 is 12, because if you multiply the denominators of both fractions, 3 * 4 = 12.

This would change the fractions to-

1/3 * 4/4 = 4/12

3/4 * 3/3 = 9/12

I hope this was helpful! Have a lovely day!! :)

A silo of a barn consists of a cylinder capped by a hemisphere. The
height of a cylinder is 60 feet and its diameter is 30 feet. What is the approximate volume of the entire silo

Answers

The approximate volume of the entire silo which consists of a cylinder capped by a hemisphere is 42,390 cubic feet

Volume of the silo

Volume of a cylinder = πr²h

where,

π = 3.14

Radius, r = diameter / 2

= 30 ft / 2

= 15 ft

Height, h = 60 ft

Volume of a cylinder = πr²h

= 3.14 × 15 × 15 × 60

= 42,390 cubic feet

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#SPJ1

Answer:the largest angle has a measure of ____degrees.

Answers

el angulo mayor tiene una medida de 360° grados


Angle 1=x
Angle 2= 3x
Angle3= x+40
5x+40= 180
180-40=140 140/5=28 =x
Angle 1= 28
Angle2=84
Angle 3=68
Largest =angle2: 84degrees

what is the area of this object? ​

Answers

Answer: no idea

Step-by-step explanation:

BRAINLIEST AND 100 POINTS!

The equation yˆ=−5.131x2+31.821x−3.333 approximates the number of people standing in line to catch a commuter train x hour after 5 a.m.

What is the best estimate for the number of people in line at 7 a.m.?

23

27

32

40

Answers

Answer:

The answer is 40. I'm 100% sure.

Answer:

D.40

Step-by-step explanation:

An arrow is shot vertically upward at a rate of 190 feet per second from ground level. Use the projectile formula
h
=

16
t
2
+
v
0
t
+
h
0
h
=
-
16
t
2
+
v
0
t
+
h
0
to determine when the height of the arrow will be 471 feet.

Answers

The height of the arrow will be 471 feet at 8.35s and 3.53s

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

h represent the height of the arrow after t seconds.

h(t) = -16t² + v₀t + h₀

v₀ is the initial velocity = 190 ft/s, h₀ is the initial height = 0m, hence:

h(t) = -16t² + 190t

At 471 feet:

471 = -16t² + 190t

0 = -16t² + 190t - 471

t = 8.35 or 3.53

The height of the arrow will be 471 feet at 8.35s and 3.53s

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Find the measure of ∠ABC.

Answers

Answer:

170°

Step-by-step explanation:

There is a total of 180° and the angle is 10° less...

So, 180°-10° = 170°

Please 5 stars if correct!!!

I hope this helps!!!

Help? Anything can help I’m in a rush

Answers

Answer: A vertical line from (-5 , 4 ) to (5 , 4)

Step-by-step explanation: The y axis is the vertical  one. Go up 4 and draw a line connecting all the points with 4 in the coordinates.

Hope that helps :)

Answer:

Step-by-step explanation:

go up 4 lines on the y-axis then draw a straight line from left to right on y=4

I don't know if you can see the picture, but I drew a line on the picture you provided...

Please 5 stars if correct!!!

I hope this helps

Leon and Omar went to grab ice cream after track practice. They each chose a container shaped like a cone or a cylinder. The dimensions of each container are shown in the drawing.

Answers

The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.

What is volume?

Volume is the amount of space occupied by a three dimensional shape or object.

Let us assume the cone and cylinder has a radius of 7 cm and height of 10 cm, hence:

Volume of the cone = (1/3) * π * radius² * height = (1/3) * π * 7² * 10 = 513.33 cm³

Volume of the cylinder = π * radius² * height = π * 7² * 10 = 1540 cm³

The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.

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how do i solve (2[tex](\frac{2}{3} r^{2} s^{7} )^{2} * (\frac{1}{6} r^{3}s)[/tex]

Answers

Answer:

5x+1=7

Step-by-step explanation:

solve plssss before i dieee i give points

Answers

Answer:

should be 66% of children and 1650 children in the town

Step-by-step explanation:

Eli planted 14 out of his 20 tomato plants so far in his garden. What percentage of his tomato plants has he planted?

Answers

Answer:

70%

Step-by-step explanation:

First we express this as a fraction:

14/20

Then we express it as a decimal: (by doing 14÷20)

0.7

Now we express it as a percentage by multiplying the decimal by 100:

0.7×100%

70%

Answer:

70%

Step-by-step explanation:

GIven:

Eli planted 14 out of his 20 tomato plants so far in his garden. What percentage of his tomato plants has he planted?

Solve:

14/20 x 100

0.7 x 100

70%

Hence, 70% of his tomato plants he planted.

~Lenvy~

PLEASE HELP ME MATH IS HARD
Use the rectangle shown in the coordinate plane to answer each question.
1. Rotate rectangle KLMN 90º counter-clockwise about the origin. List the ordered pairs for each vertex of K'L'M'N'.
2. What do you notice about the ordered pairs of the original figure and the ordered pairs of the rotation about the origin?

Answers

Answer:

See below ↓

Step-by-step explanation:

1)

On rotating KLMN by 90° counterclockwise,the new coordinates are :K' = (-3, -6)L' = (-5, -4)M' = (-2, -1)N' = (0, -3)

2)

What do we notice here?We notice that on rotating from Quadrant II to Quadrant III, we find that all the x and y values become negative (other than N' which changes intercepts from x to y)

Answer:

Step-by-step explanation:

Rotate counter-clockwise = from right towards left  

Rotate 90° about the origin = We can think that our rectangle is a flag and that we added a pole to it. The pole is rotated counter-clockwise about the origin until we have the 90°. Where is the flag now positioned?

(Draw a line from origin to one of the rectangle's points; draw another line from origin that is ⊥ to the previous one. You rotate that point 90° from right to left and will lend on the new line.)

1. K (-6, 3) L (-4, 5) M (-1, 2) N (-3, 0) → K' (-3,-6) L'(-5, -4) M'(-2, -1) N'(0, -3)

2. We notice that the rule for rotating 90° about the origin is (x, y)→(-y, x)

At Garland School,
3/5 of the 490 students are boys.
At Bowood School, 5/7
of the 945 students are girls.
Which school has the greater number of girls and by how many?
You must show your working.

Answers

490 x 2/5 = 980/5 = 196 girls at Garland


945 x 5/7 = 4725/7 = 675 girls at Bowood


Bowood has more girls:

675-196 = 479 more

oshua wants to buy a flat-screen TV that costs $625. He saves $62.50 each week to buy the TV. In how many weeks will he have enough money to make his purchase?

Answers

Answer:

ten weeks

Step-by-step explanation:

62.50 multiped by 10 moves the decimal over 1 to the right which makes it 625 :)

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