Consider The Giant Wheel at Cedar Point again. The Giant Wheel is a circle with diameter 128 feet which sits on an 8 foot tall platform making its overall height 136 feet.
It completes two revolutions in 2 minutes and 7 seconds. Assuming that the riders are at the edge of the circle, find a sinusoid which describes the height of the passengers above the ground t seconds after they pass the point on the wheel closest to the ground.
Answers
Answer:
h(t) = 72 + 64·sin(2π(t -31.75)/127)
Step-by-step explanation:
The generic form will be ...
h(t) = a +b·sin(c(t -d))
The value of 'a' is the midline of the height function, halfway between the minimum (8) and the maximum (136).
a = (8 +136)/2 = 144/2 = 72
The value of 'b' is the amplitude of the height function, half the difference between the minimum and the maximum.
b = (136 -8)/2 = 128/2 = 64
The value of 'c' is the frequency of the motion in radians per second. It will be ...
c = 2π/(period in seconds) = 2π/127
The value of 'd' is the number of seconds from the minimum (8 ft) until the wheel first reaches the midline. It will be 1/4 of the revolution time:
d = 127/4 = 31.75
Then our finished sinusoidal function is ...
h(t) = 72 + 64·sin(2π(t -31.75)/127)
_____
Additional comment
If we were to use the cosine function instead, the equation could be simpler:
h(t) = 72 -64·cos(2πt/127)
The cosine already starts at its maximum value, so height will be at a minimum if we use the negative of the cosine function.
Related Questions
Area of a circle
You might need:
Calculator
What is the area of the following circle?
Either enter an exact answer in terms of or use 3.14 for it and enter your answer as a decimal.
T = 1
units
Answers
Answer:
If the radius is 1, then the answer is pi.
Radius=r=1
Area
πr²π(1)²1ππ3.14 units²Find X for brainiest
Answers
Answer:
136°
Step-by-step explanation:
Look at the attached paper for the steps.
Answer:
136°
Step-by-step explanation:
In quadrilateral ABCD,
[tex]m\angle A = 180\degree - 107\degree = 73\degree[/tex](Angles in linear pair)
[tex]m\angle B = 61\degree [/tex](Vertical Angles)
[tex]m\angle C= 90\degree [/tex](Given)
[tex]m\angle A +m\angle B+m\angle C+m\angle D= 360\degree[/tex](Interior angle sum postulate of a quadrilateral)
[tex]73\degree +61\degree+90\degree+x= 360\degree[/tex]
[tex]224\degree+x= 360\degree[/tex]
[tex]x= 360\degree-224\degree[/tex]
[tex]x= 136\degree[/tex]
Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 16 cm.
(1) How many equilateral triangles are there? _____
(2) What is the measure of each of the three angles in the equilateral triangle? _____
(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____
(4) What is the vocabulary word for the segment a? _____
(5) What is the length of the short side of one of the 30-60-90 triangles? _____
(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____
(8) What is the height of one of the the equilateral triangles? _____
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____
Answers
Answer:
(1) How many equilateral triangles are there? ___6__
(2) What is the measure of each of the three angles in the equilateral triangle? __60°_
(3) If we cut an equilateral triangle down the middle (green line), what special right triangle do you create? _30-60-90_
(4) What is the vocabulary word for the green line? _Perpendicular bisector_
(5) What is the length of the short side of one 30-60-90 triangle? __4_cm_
(6) What is the length of the hypotenuse of one 30-60-90 triangle? __8 cm
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg. _4√3_cm
(8) What is the height of the equilateral triangle? _4√3_cm
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. ½(8)(4√3) = 16√3 cm²
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _8(16√3) = 128√3 cm²_
Step-by-step explanation:
In geometry, a hexagon can be defined as a polygon with six sides. The two-dimensional shape has 6 sides, 6 vertices and 6 angles
What is Hexagone?In geometry, a hexagon can be defined as a polygon with six sides. The two-dimensional shape has 6 sides, 6 vertices and 6 angles
The answers of all the fill in the blanks are given below:
(1) How many equilateral triangles are there ___6__
(2) What is the measure of each of the three angles in the equilateral triangle __60°_
(3) If we cut an equilateral triangle down the middle (green line), what special right triangle do you create? _30-60-90_
(4) What is the vocabulary word for the green line? _Perpendicular bisector_
(5) What is the length of the short side of one 30-60-90 triangle? __4_cm_
(6) What is the length of the hypotenuse of one 30-60-90 triangle? __8 cm
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg. _4√3_cm
(8) What is the height of the equilateral triangle? _4√3_cm
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. ½(8)(4√3) = 16√3 cm²
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _8(16√3) = 128√3 cm²
To know more about Hexagone follow
https://brainly.com/question/1615720
A color printer prints 5 pages in 9 minutes.
How many minutes does it take per page?
PLS HELPPPPPP
Answers
Answer: 1.8
Step-by-step explanation: Divide 9/5
For all horizontal lines the range is
Answers
When you have a function where y equals a constant, your graph is a truly horizontal line,
In that case, the range is just that one and only value. No other possible values can come out of that function! Many other functions have limited ranges.
Evaluate the expression for the given variable values.
3∣m+2n∣2−(mn)2 if m=3 and n=−5
Answers
Please take a look at the picture
Answers
Answer:
C
Step-by-step explanation:
it is none of the above, because
x - (-x) = x + x = 2x
and that is not -x
0 - (-x) = 0 + x = x
and that is not -x
2/3 times what equals 3/2
Answers
[tex]\dfrac 23 \cdot x = \dfrac 32 \\\\\implies 2x = \dfrac 92\\\\\implies x =\dfrac 94[/tex]
What is the slope of the function?
O-6
O 4
O 4
O 6
Answers
Answer:
12/2 = 6
Step-by-step explanation:
2 ways to do it, graph it, or do the slop finding formula y2-y1/x2-x1
answer:
Step-by-step explanation:
I hope she is correct answer
1cm +4cm+2cm+1.5cm+2.5cm
find its perimeter
Answers
Answer:
11 cm
Step-by-step explanation:
add whole numbers
1 + 4 + 2 = 7
add decimal numbers
1.5 + 2.5 = 4
add the answers
7 + 4 = 11
have a splendid day <3
Answer:
11cm
Step-by-step explanation:
To find perimeter, you simply just add each of the side lengths.
To make this easier to read, lest group some of the terms
1cm + 4cm = 5cm
2cm + 1.5cm = 3.5cm
5cm + 3.5cm = 8.5cm
8.5cm + 2.5cm = 11cm
The five terms are bolded to make sure that we added each term in the sum.
Hi. can you help me?
Answers
Answer:
Sure
Step-by-step explanation:
First you need to ____
Next you need to ____
Last, put nothing
That's what you did, so I helped you out.
Is dis good
i- I think you forgot to put the picture.
What is the answer to 14÷22 ?
Answers
Answer:
0.63636363636363636
Step-by-step explanation:
14/22
Answer:
7/11 or 0.6363636363... and so on in that pattern.
Step-by-step explanation:
Well 14/22 is an irrational decimal which is 0.6363636363... and it goes on forever, so to put it in simple terms you can write it as a fraction as 7/11. (Sorry for being vague).
I hope this answer helped you if it is wrong please let me know. Thank you!
One thousand dollars is deposited into an ordinary annuity after each 6 month period for 2 years. The account pays 4 percent interest compounded semiannually.what is the future value of the account in 2 years ??
Answers
Answer:
$4121.61
Step-by-step explanation:
Use the formula for the balance of an ordinary annuity.
A = P((1 +r/n)^(nt) -1)/(r/n)
A = $1000((1 +.04/2)^(2·2) -1)/(.04/2) ≈ $4121.61
The future value of the account is $4121.61.
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.23.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 98% confidence level with an error of at most 0.03? Round your answer up to the next integer.
Answers
Using the z-distribution, it is found that a sample size of 1066 is required.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of .
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
From the previous study, the estimate is of 0.23, hence [tex]\pi = 0.23[/tex].
98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so [tex]z = 2.327[/tex].
The sample size is n for which M = 0.03, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 2.327\sqrt{\frac{0.23(0.77)}{n}}[/tex]
[tex]0.03\sqrt{n} = 2.327\sqrt{0.23(0.77)}[/tex]
[tex]\sqrt{n} = \left(\frac{2.327\sqrt{0.23(0.77)}}{0.03}\right)[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.327\sqrt{0.23(0.77)}}{0.03}\right)^2[/tex]
[tex]n = 1065.5[/tex]
Rounding up, a sample size of 1066 is required.
A similar problem is given at https://brainly.com/question/12517818
Dwayne read 3/8 of a chapter of his history book in 1/5 of an hour. At this rate, how many chapters of his history book can he read in 1 hour?
Answers
Answer:
1 7/8 (1, 2)
Step-by-step explanation:
60/5=12 so dwayne reads 3/8 chapter per 12 minutes
12/3=4 so dwayne reads 1/8 chapter per 4 minutes
4x8=32 dwayne reads a chapter per 32 minutes.
2x32=64 and got 4 minute extra which is the time for dwayne to read 1/8 chapter
So Dwayne can read 1 7/8 chapter in 1 hour, if rounding off then 2 chapters, if only an entire chapter counts then 1
what is the inverse of f(x) = x2 − 36
Answers
help help help help!
Answers
Answer:
Is a give number 4 5 is a reflexive property
(03.09)
What is the equation of the quadratic graph with a focus of (3, -1) and a directrix of y
= 1? (1 point)
two - od
1
f(x) = -4 (x - 3)2 + 1
O 1
f(x) = -4 (x - 3)2
O
.
1
f(x) = 4 (x - 3)2 + 1
0
1
f(x) = 4 (x - 3)
Answers
35 if the answer is correct
Answers
Answer:
A.
Step-by-step explanation:
The attached graph has a y-intercept of -1 and a slope of 2, as the equation says it must.
__
The equation is in slope-intercept form, where the coefficient of x is the slope of the line. That is, the ratio of "rise" to "run" is 2: the line rises 2 grid squares for each grid square it runs to the right.
Harper was out at a restaurant for dinner when the bill came. She wanted to leave a tip of 16%. What number should she multiply the cost of the meal by to find the total plus tip in one step?
Answers
Answer:
Harper would take the Total Bill after tax and mutiply it by 0.16.
The formula for this would be
Total Bill = x
Tip = 16% -> 16/100 = 0.16
So
0.16x
What are some of the consequences the employee face
Answers
Answer:
rude customers and complaints
Answer:
Ignorant managers.
Step-by-step explanation:
Ignore them
Find somewhere else to move.
Janelys buys milk and apples at the store.
• She pays a total of $41.22.
• She pays a total of $3.22 for the milk.
• She buys 8 bags of apples that each cost the same amount.
.
Write and solve an equation which can be used to determine x, how much each bag
of apples costs.
Answers
Answer:
Each bag costs $4.75
Step-by-step explanation:
41.22 = 3.22 + 8x
38 = 8x
4.75 = x
A package contains 12 ounces of cereal .If you use 1 portion of this cereal which is 1 1/3 how much would be left in the cereal box?
Answers
To answer this question, you would need to divide the total amount of cereal in the box by the serving size.
This would be 12 2/3 divided by 1 1/3.
We can write each mixed number as an improper fraction first before we divide:12 2/3 = 38/3 and 1 1/3 = 4/3
Now divide 38/3 by 4/3. Recall that dividing by a fraction is accomplished by multiplying by the reciprocal of the divisor: 38/3 * 3/4 = 114/12 = 38/4 OR 19/2
Also, 19/2 is equivalent to 9 and 1/2. There would be 9 and 1/2 servings in the box of cereal.
Hope this helps
help me out guys !!!?
Answers
Answer:
4
Step-by-step explanation:
yeah-ya............. right?
Answer:
16
Step-by-step explanation:
because :-
f(x) =[x+6] x=-10
=[-10+6]
=10+6
16
What fraction of the rectangle is shaded? PLS PLS PLS help ASAP! Ty
Answers
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Calculate the total area of the rectangle:
21 x 12 = 252
Half of the rectangle is unshaded so:
252 ÷ 2 = 126
For clarification, side A is the top, side B is the left hand side and side C is the bottom.
Now, find the area of the unshaded side of the other triangle. As the length of side C is 21 and the shape is a rectangle, side A is also 21. We need to calculate the amount is unshaded on this side so:
21 - 14 = 7
(7 x 12) ÷ 2 = unshaded
84 ÷ 2 = 42
So now we know the total of the shape that is shaded, we can now subtract this from the total area of the shape:
252 - 126- 42 = 84
Which in fraction form is:
[tex]\frac{84}{252}[/tex]
This can be simplified down by dividing both the numerator and the denominator by 3:
[tex]\frac{84 \div 3}{252 \div 3}[/tex]
=[tex]\frac{1}{3}[/tex]
Hope this helps!
Write an equation for the sentence.
Four times a number less 10 is equal to 16 ?
Answers
Answer:
four times a number less 10 is equall to 16 ia not
Patrick is paid
$12 for 3 hours of work
How many hours does she work is she gets payed $1
Answers
Answer:
Step-by-step explanation:
Answer:
0.25 Hours or 15 minutes
Step-by-step explanation:
Please give me brainliest
Numeros comprendidos entre 20
Answers
One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, and nineteen/Uno, dos, tres, cuatro, cinco, seis, siete, ocho, nueve, diez, once, doce, trece, catorce, quince, dieciséis, diecisiete, dieciocho y diecinueve
Select the property of equality used to arrive at the conclusion.
If x = 2, then x + 8 = 10Select the property of equality used to arrive at the conclusion. If x = 2, then x + 8 = 10
1. the subtraction property of equality
2. the addition property of equality
3. the multiplication property of equality
4. the division property of equality
Answers
Answer:
addition property of equality
Step-by-step explanation:
This is because the addition property of equality means
if [tex]a=b[/tex] then [tex]a+c=b+c[/tex]
So if, [tex]x=2[/tex] then [tex]x+8=2+8[/tex]
Please look at picture for question.
Answers
Answer:
2/5m - 1/5
Step-by-step explanation: