A circle of radius 1 is inside a circle of radius 5. The smaller circle is rotated clockwise
on the larger circle without slipping until it arrives back at its starting point P. How
many revolutions (turns) will the small circle make? Be careful. The answer is not 5.

Answers

Answer 1

9514 1404 393

Answer:

Step-by-step explanation:

Consider the arcs PQ and P'Q. When turns are made without slipping, these have the same measure. The length of arc PQ is ...

PQ = CP·θ

The length of arc P'Q is ...

P'Q = O₂Q·(∠PO₂Q)

Segment O₂A is parallel to CP, so angle AO₂Q is θ. Then ∠PO₂Q = θ+α, where α is the angle by which P' has rotated counterclockwise from A.

We are given that ...

CP = 5, O₂Q = 1

Using the above relations, we can write ...

5θ = 1(θ+α)

α = 4θ

That is, for every full turn θ = 2π, the smaller circle makes turns totalling 4(2π) = 8π, or 4 full turns.

The small circle makes 4 revolutions to arrive at its starting point.

Related Questions

The line that goes through the points (0,-4) and (1,2) is......

Answers

Answer: The equation for the line is “y = 6x - 4”

Step-by-step explanation: To find this answer we will put it in slope-intercept form which is y = mx +b. To first find m which is the slope you subtract the the second y by the first y over the second x by the first x. It looks like this y2 - y1/ x2 - x1. After we find the slope which is 6, to find the y-intercept which is b we just plug a point we used to find the slope into the equation we have. It looks like this y = 6x + b —> 2 = 6(1) + b... I used (1,2). Then you solve for b by multiplying 1 by 6 and then subtracting 6 to both sides to get b by itself. So it goes from 2 = 6(1) + b into -4 = b. Then you just put -4 into b and you get the answer y = 6x - 4.

Have a nice day!

A sound wave is given by the
following equation:
y = 6 sin(324pi t)
where t = time in seconds
How many cycles will occur
between t= 3 and t = 5.5 seconds?

Answers

Answer:

405 cycles

Step-by-step explanation:

We have the equation:

y = 6*sin(324*π*t)

For the properties of the sin function, we know that the period is 2π.

So between:

Sin(x) and Sin(x + 2*pi)

we have a cycle.

between:

Sin(x) and Sin(x + 6*pi)

we have 3 cycles.

and so on.

Now we want to find how many cycles will occur between t = 3 s, and t = 5.5 seconds

Between these times, the difference in the argument of the sin function is:

324*π*5.5 - 324*π*3 = 324*π*(5.5 - 3) = 324*π*2.5

Now, the number of cycles that we will have between these times is equal to the number of times that "2*π" is in 324*π*2.5

That number is just the quotient between 324*π*2.5 and 2*π

N = (324*π*2.5)/(2*π) = (324*2.5)/(2) = 405

There are 405 cycles between 3 seconds and 5.5 seconds.

An angle has a reference angle of 40° in the third quadrant what is a positive measure of the angle and a negative measure of this angle

Answers

Answer:

2, probably

Step-by-step explanation:

Please helplpppppp!!

Answers

Answer:

Step-by-step explanation:

"x" represents the hours.

so 8 is the fee for the hours, rather than insurance.

6 is the insurance fee.

if the cost per hours is doubled, it'll now be 16.

the answer is "6 + 16x" (D)

The Answer is going to be D

Which statements about the system are true? Select two options.
y=x-4
3y - x= -7
The system has one solution.
The system consists of parallel lines.
Both lines have the same slope.
Both lines have the same y-intercept.
The equations represent the same line.
Save and Exit
Next
Submit
Mark this and return

Answers

Answer:

system has 1 solution at (2.5, -1.5)

Step-by-step explanation:

y = x - 4 this equation has a slope of 1 and a y-intercept of -4

3y - x = -7 this equation has a slope of 1/3 and a y-intercept of -7/3

What is the probability of picking a 5 and then picking a 4?

Answers

Was Lincoln’s election the whole reason that the South seceded (left) or was it simply the last event to happen before the South left?

which ones out of the three are no solution?

1. 10 + 6x = 15 + 9x – 3x

2. 11 + 3x – 7 = 6x + 5 – 3x

3. 11 + 3x – 7 = 6x + 5 – 3x

Answers

Answer: I'm going to say 3

Step-by-step explanation:

Solve graphically: 2x - y = 7 and x - 2y = 5.

Answers

Answer:

(3, - 1)

Step-by-step explanation:

We want to solve the system of equations:

2*x - y = 7

x - 2*y = 5

graphically.

To do it, we need to graph both lines, it will be easier if we rewrite both lines in a more general way, like in the slope-intercept form:

y = -7 + 2*x

y = -(5/2) + x/2

Now, a solution of the system is a point (x, y) such that the point is a solution to both equations, then, when we graph the lines, as that point belongs to both equations, we should see that both lines pass through that point.

Then to find the solution of the system, we just need to graph the lines and find the point where the lines intersect.

Below, you can see a graph of the lines, and is easy to see that the lines do intersect at the point (3, - 1)

I’ll mark as brainliest.

Answers

Answer:

12 feet

Step-by-step explanation:

48 divided by 4 is 12 and 48 is the total area

Answer:

12 sq. ft.

Step-by-step explanation:

To find the area of a square (or rectangle) you multiply the length by the width.

To find the length of one side, when you have the area and one side, you divide the area by the side you have.

48 divided by 4 equals 12.

Hope this helps :)

Jacob bought some supplies for his lemonade stand. He purchased lemons for $4.85, sugar for $3.16, containers for $18. Taxes were included in all the prices. How much money did Jacob spend on all his purchases?

Answers

Answer:

26.01

Step-by-step explanation:

The population of Country A is about 1,047,000 and the population of Country B is about 1,080,000,000. Approximately how many times greater is the population of Country B than the population of the Country A?

1.)10
2.)100
3.)1000
4.)10,000

are the choices

Answers

Answer:

1000

Step-by-step explanation:

1,080,000,000/1,047,000

solve for 5 + 6f > 8f -7
linear inequalities

Answers

Answer:

5+6f>8f-7

5+7>8f-6f

12>2f

6>f

f<6

Step-by-step explanation:

A moving company charges $22.50 per hour plus a flat rate of $180 to help a person move from one house to another.
Joel would like to spend less than $315 to move.
How much time should Joel's move take to make sure the total cost is below $315?

Answers

It should take six hours for him to stay below $315 after you add the flat rate of $180. Goodluck :)

The first person that answered is correct just let you know!

which number line shows the solution to fx-5 > 3?
9 10 11
12
13
14 15
9 10 11
12 13
14 15
+++
-6 -5 -4
-3
-2
-1
-6
-5
-4
-3
-2 -1
Dorie

Answers

Answer:

Step-by-step explanation:

send the -5 to where the +3 is then you can now add the value together.

What is a formula for the nth term of the given sequence? 300, 180, 108...

Answers

Answer:

Step-by-step explanation:

The common ratio of the terms is 0.6 (180/300=6/10;108/180=6/10). This is a geometric sequence .

nth term=500(0.6)^n-1

Find the square roots of the following numbers. Give the steps correctly.

\sqrt {19.9 }

Please give me the answer .

Answers

Answer:

(44-(6x-1+9x.-5))=0

We add all the numbers together, and all the variables

(44-(6x+9x.-6))=0

We calculate terms in parentheses: +(44-(6x+9x.-6)), so:

44-(6x+9x.-6)

determiningTheFunctionDomain

-(6x+9x.-6)+44

We get rid of parentheses

-6x-9x.+6+44

We add all the numbers together, and all the variables

-6x-9x.+50

Back to the equation:

+(-6x-9x.+50)

We get rid of parentheses

-6x-9x.+50=0

We move all terms containing x to the left, all other terms to the right

-6x-9x.=-50

Big brutus pizza had two deals on pizza the first was $6 for a cheese pizza plus $3 for each topping the second deal was $20 per cheese pizza and 1 dollar per topping wat is the x and y

Answers

Answer:

[tex]x = 7[/tex] --- toppings

[tex]y = 27[/tex] ---- amount

Step-by-step explanation:

Given

[tex]y \to\ amount[/tex]

[tex]x \to\ topping[/tex]

The first deal is:

[tex]y = 6 + 3x[/tex]

The second is:

[tex]y = 20 + x[/tex]

Required

The value of x and y [for which both deals are equal]

We have:

[tex]y = 6 + 3x[/tex]

[tex]y = 20 + x[/tex]

Equate both

[tex]y=y[/tex]

So, we have:

[tex]6 + 3x = 20 + x[/tex]

Collect like terms

[tex]3x - x = 20 - 6[/tex]

[tex]2x =14[/tex]

Divide by 2

[tex]x = 7[/tex]

A circle of radius 1 is inside a circle of radius 5. The smaller circle is rotated clockwise on the larger circle without slipping until it arrives back at its starting point P. How many revolutions (turns) will the small circle make? Be careful. The answer is not 5.

Answers

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A circle of radius 1 is inside a circle of radius 5. The smaller circle is rotated clockwise
on the larger circle without slipping until it arrives back at its starting point P. How
many revolutions (turns) will the small circle make? Be careful. The answer is not 5.