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 1

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.

Consider The Giant Wheel At Cedar Point Again. The Giant Wheel Is A Circle With Diameter 128 Feet Which

Related Questions

Identify the sampling technique used. Every 17th person in line to buy tickets to a concert is asked his or her age.

Answers

Answer:

systematic sampling

Step-by-step explanation:

This is when you start at a person (using a number that is randomly generated) and go up in intervals to select a sample.

Hope this helps!

n a very large population that has a proportion of a particular disease p, a researcher conducting a study on this disease, is taking samples sequentially until she receives three cases consecutively. Find the mean and the variance of the number of samples she needs to take.

Answers

Answer:

sorry don't speak Spanish

ITS 100 POINTS!!!! AND DO IT IN A STEP BY STEP EXPLAINATION.

A proportional relationship between the number of pounds of cabbage (x) and the price in dollars (y) is graphed, and the ordered pair (5, 2) is on the graphed line.

Part A: What is the price of 1 pound of cabbage? Show your work. (8 points)
Part B: What does the ordered pair (10, 4) on the graph represent? Explain in words. (2 points)

Answers

Answer:

part a: If  x  represents the number of pounds of cabbage and  y  represents the price in dollars, then  (5, 2)  means that  5  pounds of cabbage costs  $2.00.  If that is true, then  1  pound of cabbage will cost  $0.40. (divide both values by 5)

The ordered pair  (10, 4)  means that  10  pounds of cabbage cost  $4.00.

explanation: sorry its late but hope it helps

What is the answer to the equation 56/3+7=

Answers

Hey there!

56/3 + 7

= 56/3 + 7/1

= 56/3 + 21/3

= 56 + 21/ 3 + 0

= 56 + 21/3

= 77/3

≈ 25 2/3

≈ 25.666667

Therefore, your answer is: [77/3] which is approximately [25.666667]

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

HELP ME OUT PLEASE!!!

Which equation matches the function described in the table?

A) y = 4x

B) y = x + 1

C) y = x + 5

D) y = 4x - 1​

Answers

Answer:

D) y= 4x - 1

Step-by-step explanation:

We are basically trying to see which of the equations provided are true on both sides of the equal sign when you plug in the x and y values.

Let's start!

Choice A:

  plug in 0 for x and -1 for y

-1 = 4(0)

And you are left with...

-1 = 0

This equation is false! Therefore it does not match the function in the table

Choice B:

   plug in the values again

-1 = 0 + 1

-1 = 1

False!

Choice C:

-1 = 0 + 5

-1 = 5

False!

Lastly...Choice D:

-1 = 4(0) -1

Multiply 4 and 0 which is 0, so you are left with...

-1 = -1

This equation is true!!

So your answer is D

Hope this helps :D

Rico opens an ice cream shop. The function f ff models the shop's net worth (in thousands of dollars) as a function of time (in months) after Rico opens it. Plot the point on the graph of f ff that corresponds to the shop's net worth when Rico opens it.

Answers

Answer: -5

Step-by-step explanation:

Based on the graph given, the point that on the graph that corresponds with the shop's net worth when Rico opened it is -5.

What was the shop worth when it was opened?

The point that the shop was opened is represented by the value of the y axis when it was first crossed.

Looking at the graph, the line first intercepted the y axis at -5 which means that this was the shop's net worth when it was opened by Rico.

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What is the solution of this system of equations?
x + 3y = 7
3x +2y = 0
A. (3,2)
B. (-2,3)
C. (2, -3)
D. (-3,2)
E. (-2,-3)

Answers

Answer:

B. (-2,3)

Explanation:

First, we'll turn both lines to slope-intercept form:

x + 3y = 7

Subtract x on both sides to get 3y = -x + 7, then divide 3 on both sides to get y = -1/3x + 7/3.

3x + 2y = 0

Subtract 3x on both sides to get 2y = -3x, then divide 2 on both sides to get y = -3/2x.

Now you can graph (I did it for you above⤴⤴⤴).

Hope this helps you :)

pls pls pls help!!!!
Determine the simple interest earned when $6, 100 is invested at a rate of 5% for 4 years.
$1,220
$305
$610
$1,525

Answers

Answer: I think A 1,220 (I'm not sure)

Step-by-step explanation:

the aswer is A.1,220 si think si correct.

What are the zeros of the function shown in the graph

Answers

Answer:

(-4, 0), (0, 0) and (2, 0)

Step-by-step explanation:

Zero's of the function are the points of intersection of the graph with the x-axis.

From the picture we see zeros:

(-4, 0), (0, 0) and (2, 0)
The zeros of the function are the x intercepts on graph .Let's see the x intercepts

(-4,0)(0,0)(2,0)

Zeros are

[tex]\\ \sf\longmapsto (-4,0)U(0,0)U(2,0)[/tex]

What is the value of -2(x+5)​

Answers

Answer:

-2x-10

Step-by-step explanation:

You have to use the distributive property to solve this problem. You multiply the things inside the parenthesis by -2. -2x+-2x5 = -2x+(-10) = -2x-10

y - 2x=4
3x -5y =15 ddddddddddd

Answers

Answer:

Hope this is right and helps :)

Step-by-step explanation:

-2 5/12 - (-10 8/9)

Answers

[tex]-2 \dfrac 5{12} - \left( - 10 \dfrac 89 \right)\\\\\\=- \left(2 + \dfrac 5{12} \right) + \left(10 + \dfrac 89 \right) \\\\\\=8 + \dfrac 89 - \dfrac 5{12}\\\\\\=8+ \dfrac{32}{36} - \dfrac{15}{36}\\\\\\= 8 + \dfrac{17}{36}\\\\\\= 8 \dfrac{17}{36}[/tex]

Issac wanted to make a homemade bubble solution to play with his friends. A bubble recipe he found requires 4 cups of warm water for every 1/2 cup of soap. If he had 2/3 cup of soap how many cups of warm water will he need

A- 1/12
B- 1 1/3
C- 5/13
D- 8

Answers

Answer: 8/3

You first do 4x2 than you would have to divide by 3. 4x2*3

The number of cups of warm water need for 2/3 cup of soap to make solution is [tex]5\frac{1}{3}[/tex]. Therefore, option C is the correct answer.

What are proportions?

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, a bubble recipe he found requires 4 cups of warm water for every 1/2 cup of soap.

Let the number of cups of warm water need for 2/3 cup of soap be x.

Now, the proportion is

4:1/2 :: x:2/3

1/2 x=4×2/3

x/2=8/3

x=16/3

x= [tex]5\frac{1}{3}[/tex]

Therefore, option C is the correct answer.

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which two expressions are equivalent to 7(t + 5)?


A). 7 • 5 • t

B). 7 • 5 + t

C). 7 • 5 + 7 • t

D). (5 + t) • 7

E). 5(t + 7)



Answers

Answer:

7.5+7.t

and

(5+t).7

are equivalent to 7(t+5)

Option D and E are equivalent to 7(t + 5) That is :

(5 + t) • 7 and 5(t + 7)

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

The given equation is :

7(t + 5)

7(t+5) multiply 7 with inside the parenthesis

7(t+5) = 7t + 7x5

this result is equivalent to option D and E which will give the same result.

Therefore, Option D and E are equivalent to 7(t + 5).

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Find the value of the expression 4a + 7 when a= 1/2.
plssss help quiiick

Answers

Answer:

The answer is 9

Step-by-step explanation:

1/2 of 4 is 2, so you plug that in

2+7=9

what percent equals 44 =33

Answers

Answer:

33/44 = 0.75

0.75*44 = 33

Answer:

44% of 75 = 33

Step-by-step explanation:

In a school there are 200 boys and 800 girls. Find the percentage of girls in that school.

Answers

Answer:

80% girls.

Step-by-step explanation:

20% boy.

80%+20%= 100%

Find the critical points, relative extrema, and saddle points of the function. (If an answer does not exist, enter DNE.) f(x, y) = 25 − (x − 5)2 − y2

Answers

Take the first partial derivatives of f(x, y):

∂f/∂x = -2 (x - 5) = 10 - 2x

∂f/∂y = -2y

The critical points occur where both derivatives are zero:

10 - 2x = 0   ===>   x = 5

-2y = 0   ===>   y = 0

So there is only critical point at (5, 0), which takes on a value of f(5, 0) = 25.

Compute the Hessian matrix for f :

[tex]H(x, y) = \begin{bmatrix}\frac{\partial^2f}{\partial x^2} & \frac{\partial^2f}{\partial x\partial y} \\ \frac{\partial^2f}{\partial y\partial x} & \frac{\partial^2f}{\partial y^2}\end{bmatrix} = \begin{bmatrix}-2&0\\0&-2\end{bmatrix}[/tex]

Since det(H(x, y)) = 4 > 0 for all x, y, the critical point (5, 0) is a relative minimum.

f has no saddle points.

1
21314 JEG B 10
3
Which is the best estimate of -14
of-14; (-20)
ם
10
-42
-28
OOOO
28
42

Answers

Step-by-step explanation:

OOOO

BYE

When I visit my brother it is a 532 mile round trip. If I visit my brother once a month how many miles would I travel in a year round the miles to the nearest thousands to estimate the answer

Answers

Answer:

6384 is the exact answer.

6000 is the answer rounded to the nearest thousand

Step-by-step explanation:

Answer:

6000

Step-by-step explanation:

532 X 12 = 6384 rounded would be 6000 miles a yr

Please lots of points I wasn’t at school when this was taught

Answers

Answer:

4x+2=4x+4, no solution

Step-by-step explanation:

first, i'm assuming the flower bed is a square so that all 4 sides are x+1. next, to find the perimeter you have to add up the side lengths of each shape.

vegetables: x + x+1 + x + x+1 = 4x+2 so the perimeter of the vegetables must be 4x+2

flowers: x+1 + x+1 + x+1 + x+1 = 4x+4

since the two must be equal, we have 4x+2=4x+4, this is the equation Trent can use

next, to solve the equation, subtract 4x from both sides to get 2=4. this obviously isn't true so there is no solution

{6x+5y=4
{6x-7y=-20
solve by elimination

Answers

Answer:

x = -1, y = 2

Step-by-step explanation:

6x + 5y = 4

6x - 7y = -20

We already have a similar leading coefficient (6 for X), so we just subtract equation 1 from equation 2 to get:

12y = 24

Now solve normally:

y = 2

Then substitute into the first equation (or second, it doesn't matter)

6x + 10 = 4

6x = -6

x = -1

A stockbroker estimates that at the end of the year, there is a 40% chance a stock will be worth $50,
a 35% chance it will be worth $60 and a 25% chance it will be worth $70. What expected value
does this broker assign to this stock's end-of-the-year price?

Answers

The expected value  that  this broker assign to this stock's end-of-the-year price is $58.50.

Using this formula

Expected value=Stock worth at $50+ Stock worth at $60+ Stock worth at $70

Where:

Stock worth at $50=40% chance

Stock worth at $60=35% chance

Stock worth at $70=25% chance

Let plug in the formula

Expected value=(40%×$50)+($35%×$60)+($25%×$70)

Expected value=$20+$21+$17.5

Expected value=$58.50

Inconclusion the expected value  that  this broker assign to this stock's end-of-the-year price is $58.50.

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Question
Find the area of the parallelogram.



Area =
units²

Answers

Answer:

9 units²

Step-by-step explanation:

Parallelogram area = base × height

Base = 3 units

Height = 3 units

Area = 3 × 3

Area = 9

The area of the parallelogram is 9 units².

Here, we have,

We know that,

Parallelogram area = base × height

here, from the given figure we get,

Base = 3 units

Height = 3 units

so, we get,

Parallelogram area = base × height

Area = 3 × 3

Area = 9

Hence, The area of the parallelogram is 9 units².

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(x + 1)(x - 1)
I dont understand this could any1 help me

Answers

Answer:

x^2-1

Step-by-step explanation:

you must use the distributive property

first you do x•x=x^2,

then you do x•1 and x•-1 to get x and -x and those cancel out,

the you do 1•-1=-1, then you put it together to get x^2-1

Step-by-step explanation:

It's a factored form of the quadratic equation

[tex] {x}^{2} - 1[/tex]

in the form of [tex] {ax}^{2} + bx + c[/tex]

in which a = 1, b = 0, c = 1.

7.) Solve the system of equations
below.
-2x + 3y = 9 2/3x + 2y = 0

Answers

Answer:

So lets isolate y

we have

-2x+3y=9

2/3x +2y=0

Im gonna do the first equation

so -2x + 3y = 9

Add 2x on both sides

3y= 9+ 2x

Now divide by 3 to isolate y

y= 3+ 2/3x

Now we can subsitute y into any eqaution (I’m gonna do the second one) to solve.

2/3x+ 2(3+ 2/3x)= 0

Solve:

2/3x+ 6 + 4/3x = 0

6/3x +6= 0

2x+6=0

2x= -4

x= -2

Now we can subsitute this for any equation.

so I’m gonna do the first equation

-2(-2)+3y=9

4+3y=9

3y= 5

y= 5/3

y= 1 2/3

Final answer:

x=-2

y= 1 2/3

What is m + 5n where m = 1 and n = 5?

CHOOSE THE RIGHT ANSWER:
A. 26
B. 52
C. 25
D. 62

HELP! (T^T)​

Answers

Answer:

A. 26

Step-by-step explanation:

substitute the number in for the variables (letters).

[tex]m + 5n \\ \\ 1 + 5(5) \\ 1 + 25 \\ 26[/tex]

If one real number is equal to a second real number, and the second real number is equal to a third real number, then the first real number must equal the third:
If a = b and b = c, then a = c

Answers

Answer: In particular, let’s focus our attention on the behavior of each graph at and around . 2 and x= -1 for x < 2. There are open circles at both endpoints (2, 1) and (-2, 1). The third is h (x) = 1 / (x-2)^2, in which the function curves asymptotically towards y=0 and x=2 in quadrants one and two."

Step-by-step explanation: I think this is the problem ur on

The given relation → If a = b and b = c, then a = c is called transitive law and it holds true for all real numbers.

What is an equation and an expression?

An equation is a statement that the depicts the values of two mathematical expressions as equal using an (=) sign. Example -

2x = 5

An expression is written using individual terms (either constant or variable) separated by mathematical operations. Example -

3x + 5y + 3

We have -

If a = b and b = c, then a = c.

The given relation holds true for all real numbers. This law is called transitive law. So, if A=5 for example, then B and C must both also be 5 by the transitive property

Therefore, the given relation → If a = b and b = c, then a = c is called transitive law and it holds true for all real numbers.

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Help please im struggling fighting demons rn

Answers

It’s up then to the left

What is 23=5-2/3m ??????

Answers

Answer:

Step-by-step explanation:

if it's

23 = 5 - (2/3)m

18 = (-2/3)m

m = 18(-3/2)

m = -27

if it's

23 = 5 - 2/(3m)

18 = -2/(3m)

18(3m) = -2

54m = - 2

m = -2/54

m = - 1/27

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