Mathematics College

In a circle with a radius of 36 3/5 cm, an arc is intercepted by a central angle of 2π7 radians.



What is the arc length?

Use 3.14 for π and round your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.


cm

Answers

Answer 1

Answer:

The arc length is [tex]32.84\ cm[/tex]    

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=36\frac{3}{5}\ cm=\frac{36*5+3}{5}=\frac{183}{5}\ cm[/tex]

substitute

[tex]C=2(3.14)(\frac{183}{5})=229.848\ cm[/tex]

Remember that

[tex]2\pi[/tex] radians subtends the complete circle of length [tex]229.848\ cm[/tex]

so

by proportion

Find the arc length by a central angle of [tex]2\pi/7[/tex] radians

[tex]\frac{229.848}{2\pi}=\frac{x}{2\pi/7}\\ \\x=229.848*(2\pi/7)/(2\pi)\\ \\x=`32.84\ cm[/tex]

Answer 2

The arc length is approximately 32.81 cm.

Step 1

To find the arc length intercepted by a central angle, we can use the formula:

[tex]\[ \text{Arc Length} = \text{radius} \times \text{central angle} \][/tex]

Given:

- Radius [tex](\( r \)[/tex]) = 36 3/5 cm

- Central angle [tex](\( \theta \)) = \( \frac{2\pi}{7} \)[/tex] radians

First, let's convert the radius to a decimal:

[tex]\[ \text{Radius} = 36 \frac{3}{5} \text{ cm} = 36.6 \text{ cm} \][/tex]

Step 2

Now, we can use the formula to find the arc length:

[tex]\[ \text{Arc Length} = 36.6 \times \frac{2\pi}{7} \]\[ \text{Arc Length} = 36.6 \times \frac{2 \times 3.14}{7} \]\[ \text{Arc Length} = 36.6 \times \frac{6.28}{7} \]\[ \text{Arc Length} = 36.6 \times 0.897 \]\[ \text{Arc Length} \approx 32.808 \][/tex]

Rounded to the nearest hundredth, the arc length is approximately 32.81 cm.

Related Questions

Find the midpoint of side EF. Figure EFGH is shown. E is at negative 2, 3. F is at 1, 6. G is at 4, 3. H is at 1, 0. (−1, 4) (−0.75, 4.25) (−0.5, 4.5) (−0.25, 4.75)

Answers

The midpoint can be found using the midpoint formula.

[x1+x2/2 , y1+y2/2]
[-2+1/2 , 3+6/2]
[-1/2 , 9/2]
[-0.5 , 4.5]

The midpoint is [0.5 , 4.5]
Answer:

Hence, the mid-point of side EF is located at:

                    (-0.5,4.5)

Step-by-step explanation:

We know that the coordinates of a mid-point C(e,f) of a line segment AB with vertices A(a,b) and B(c,d) is given by:

[tex]e=\dfrac{a+c}{2},\ f=\dfrac{b+d}{2}[/tex]

Here we have to find the mid-point of side EF.

E(-2,3) i.e. (a,b)=(2,3)

and F(1,6) i.e. (c,d)=(1,6)

Hence, the coordinate of midpoint of EF is:

  [tex]e=\dfrac{-2+1}{2}\ ,\ f=\dfrac{3+6}{2}\\\\\\e=\dfrac{-1}{2}\ ,\ f=\dfrac{9}{2}\\\\\\e=-0.5\ ,\ f=4.5[/tex]

                Hence, the mid-point of side EF is:

                          (-0.5,4.5)

A student who was ineligible for financial aid needed to borrow 775,000 for tuition,books,and living expenses. Some money was borrowed at 8%, some at 9%, and some at 10%. How much was borrowed at each interest rate if the annual interest owed was 67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%.
8%:
9%:
10%:

Answers

$75,000 was borrowed at 10%; $300,000 was borrowed at 8%; and $400,000 was borrowed at 9%.

Since we are only looking at one year, and we assume the interest is compounded no more than annually, we can use the formula for simple interest:

I = prt

Let p be the amount borrowed at 10%.  Then 4p, or 4 times the amount borrowed at 10%, is borrowed at 8% interest.  The remaining amount, (775000-4p-p) or (775000-5p) is borrowed at 9%.  The amount of interest for each portion of the loan is given by:

I=p(0.1)(1)
I=4p(0.08)(1)
I=(775000-5p)(0.09)(1)

Adding these together for the total amount of interest, $67,500, we have:

67500=p(0.1)(1)+4p(0.08)(1)+(775000-5p)(0.09)(1)

Simplifying the right hand side we have:
67500=0.1p+0.32p+69750-0.45p

Combining like terms gives us:
67500= -0.03p+69750

Subtract 69750 from both sides:
67500-69750= -0.03p+69750-69750
-2250= -0.03p

Divide both sides by -0.03:
-2250/-0.03 = -0.03p/-0.03

75000 = p

So $75000 is the amount borrowed at 10%; 4(75000)=$300,000 borrowed at 8%; and 775000-75000-30000= $400,000 borrowed at 9%.

Pepper Jackie has 12 picks. 1 out of every 4 picks is orange . The rest are green. How many picks are orange?

Answers

3 are orange 9 are green


at halloween 3/10 of the candy robin receivd was chocolate. what percent of candy was chocolate,


PLEASE HELP ME!!!!!!!

Answers

if 3/10 was chocolate 
3/10=0.3
0.3 *100=30% was chocolate 

one bag of toy animals weigh12 ounces. what is the total weight, in ounces, of the bags of toy animals in one crate

Answers

Assuming I understand what you're saying, if there are 2 boxes in a crate and 18 bags in a box, the answer would be 12 * 36 = 432

What is BP? Enter your answer as a decimal in the box

Answers

check the picture below.

Nancy has nine books and she has read 8 total books Sally has two times more books the Nancy how many books does Sally have

Answers

Sally has eight-teen books.

Sally has 18 books, as she has two times more books than Nancy, who has 9 books. The equation used is Sally's books = 2 × Nancy's books. Therefore, 2 × 9 = 18.

To determine how many books Sally has, we need to understand that she has two times more books than Nancy. Nancy has a total of 9 books.

The equation we use here is:

Sally's books = 2 × Nancy's books

Given Nancy's books = 9:

Sally's books = 2 × 9 = 18

Therefore, Sally has 18 books.

Using synthetic division, find (x4 − 2) ÷ (x + 1).

Answers

Answer:

Step-by-step explanation:

We have given:

x^4-2/x+1

Put x+1 = 0

x= 0-1

x= -1

-1 | 1   0   0   0   -2

  |      -1   1   -1     1

_______________

    1    -1   1  -1    -1

Thus it makes the expression:

x^3-x^2+x-1 - 1/x+1

You can further confirm this expression by solving the expression:

(x4 − 2) ÷ (x + 1).

x^4 - 1 -1/x+1

x^4-1/x+1 - 1/x+1

(x^2-1) (x^2+1)/x+1 - 1/x+1

(x-1)(x+1) (x^2+1)/x+1  - 1/x+1

x+1 n the numerator will be cancelled out by x+1 in the denominator.

(x-1) (x^2+1) - 1/x+1

Multiply (x^2+1) by x-1

x(x^2+1) -1(x^2+1)  - 1/x+1

x^3+x-x^2-1 - 1/x+1

x^3-x^2+x-1 - 1/x+1 ....

Experts/ace/geniuses helpp

Answers

square root 144 =  12 so this is the rational number

In a circle with a radius of 6 m, an arc is intercepted by a central angle of 7π4 radians. What is the arc length? Use 3.14 for π . Enter your answer as a decimal in the box.

Answers

[tex]\bf \textit{arc's length}\\\\ s=r\theta \quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=6\\ \theta =\frac{7\pi }{4} \end{cases}\implies s=6\cdot \cfrac{7\pi }{4}\implies s=\cfrac{21\pi }{2}[/tex]

Answer:

[tex]Arc length=32.97m[/tex]        

Step-by-step explanation:

It is given that In a circle with a radius of 6 m, an arc is intercepted by a central angle of [tex]\frac{7\pi}{4}[/tex] radians.

Then, the arclength of the circle is given as:

[tex]Arc length=radius{\times}central angle[/tex]

⇒[tex]Arc length=6{\times}\frac{7\pi}{4}[/tex]

⇒[tex]Arc length=\frac{21\pi}{2}[/tex]

⇒[tex]Arc length=10.5{\times}3.14[/tex]

⇒[tex]Arc length=32.97m[/tex]

Thus, the arc length of the given circle is 32.97m.

The perimeter of parallelogram ABCD is equal to 10 cm. Find the length of diagonal
BD if you know that the perimeter of triangle ABD is 8 cm.

how do you solve it??? thanks

Answers

the perimeter of ABCD is 10, therefore, AB+AD=half of 10=5
the perimeter of ABD is 8, therefore, BD=ABD-(AB+AD)=8-5=3
3cm is the answer. 

What is the name of the line of reflection for the pair of figures?

Answers

Hi there!

The name for the line of reflection of the two figures is called the "line of symmetry". It's the line that marks a point where you can fold a figure evenly.

Hope this helps!

Hope this helps!

The sum of two numbers is 67. The smaller number is 21 less than the larger number. What are the numbers?

Answers

Let the bigger number be x.

bigger number = x
smaller number = x - 21

The sum of the two numbers is 67.
x + x - 21 = 67
2x - 21 = 67
2x = 67 + 21
2x = 88
x = 44

x = 44
x - 21 = 44 - 21 = 23

The larger number is 44 and the smaller one is 23

The equations are x + y = 67 and x = y + 21. Then the two numbers are 44 and 23.

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The sum of the two numbers is 67. The smaller number is 21 less than the larger number.

Let the two numbers be 'x' and 'y' and x > y. Then the equations are given as,

x + y = 67       ...1

x = y + 21       ...2

From equations 1 and 2, then we have

y + 21 + y = 67

2y = 46

y = 23

Then the value of 'x' is given as,

x = 23 + 21

x = 44

The equations are x + y = 67 and x = y + 21. Then the two numbers are 44 and 23.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

How do you find the perimeter of a tennis court with an area of 7,200?

Answers

most likely divide it by 4

Trey graphs the equations y = –x2 + 2x + 3 and y = x2 – 2x + 3 to solve the equation –x2 + 2x + 3 = x2 – 2x + 3. His graph is shown below.

mc011-1.jpg

What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?

Answers

all you have to do is go on desmos calculator and type those two equations in the two point where the graph meets are the solutions to this problems (0,3) and (2,3)

The solution of the equation [tex]-x^2+2x+3=x^2-2x+3[/tex] are the x-coordinates of common points on the graphs of the function [tex]y=-x^2+2x+3[/tex] and [tex]y=x^2-2x+3.[/tex]

As you can see from the attached diagram these graphs intersect at points (0,3) and (2,3), then the solutions of the previous equation are x=0 and x=2.

Answer: x=0, x=2.

the sum of two integers is 9 and the sum of their squares is 53. Find the integers.

Answers

x + y = 9 Subtract x from both sides.
y = 9 - x

x^2 + y^2 = 53
x^2 + (9 - x)^2 = 53 Remove the brackets.
x^2 + 81 - 18x + x^2 = 53 Collect the like terms on the left.
2x^2 - 18x + 81 = 53 Subtract 53 from both sides.
2x^2 - 18x + 81 - 53 = 0
2x^2 - 18x + 28 = 0 This factors, but you can see it much easier if you pull out 2 as a common factor.
2(x^2 - 9x + 14) = 0
2(x - 2)(x - 7) =0 You could divide by 2 on both sides. But you can also leave it.
x - 2 = 0
x =  2
x - 7 = 0
x = 7
If x = 2 then y = 7
If x = 7 then y = 2

A set of scores ranges from a high of x = 96 to a low of x = 11. if these scores were placed in a grouped frequency distribution table, what is the best value for the interval width?

Answers

There is no hard and fast rule to select the class width. It largely depends on our application.However, one thing that should be kept in mind is that the number of classes should neither to be too low nor too high. So keeping this thing in mind, the class width is select.

The range of the data is = Maximum- Minimum = 96 - 11 = 85
10 classes will be most suited for this data.

The class width for each data can be calculated as:
 
Class Width = Range / Number of Classes  = 85/10 = 8.5
Class width is always rounded to nearest next integer. So the class width will be 9 in this case.
 
So, the best value of class width or interval width for the given data will be 9.

The best value for the interval width is 17

The highest and the lowest data elements are given as:

x = 96

x = 11

Start by calculating the range

Range = High - Low

So, we have:

Range = 96 - 11

Range = 85

The interval width depends on the number of classes.

Assume that the number of classes is 5,

Then the width is calculated as:

Width = Range / Class

So, we have:

Width = 85/5

Width = 17

Hence, the number of interval width is 17

Read more about interval width at:

https://brainly.com/question/16631975

The prices of six different types of cell phones, in dollars are 49, 189, 79, 250,125,85. how many data points are closer ti the center than the mean absolute deviation?

Answers

The mean of these prices is 129.50, and the mean of the absolute deviation is 60. Four (4) data points are between 69.50 and 189.50.

Solve for x. x − 4 1/6 = 9 1/3 A) −131 2 B) −51 6 C) 131 2 D) 51 6

Answers

I believe the answer is B
The answer would be: B -51 6

if 10/4 = 14/x what is x?

Answers

Is there answer choices? Because if you do 10/4=2.5 and if you do 14/2.5 you get 5.6
Answer: 5.6

Explanation:

1) set the proportion:

 10        14
----- =   -----
  4           x

2) clear the unknown, x

10x = 14(4)

=> 10x = 56

=> x = 56 / 10

=> x = 5.6

mark's soup recipe makes 6 servings and uses 4 carrots and 2 potatoes. Drag carrots and potatoes into the box to show how many Mark needs for 15 servings.

Answers

Answer:

10 carrots and 5 potatoes

Step-by-step explanation:

If 6 servings uses 4 carrots and 2 potatoes we can determine how many carrots and potatoes must be used per serving.

Lets look at the carrots:

[tex]=4/6=0.67[/tex]

Therefore for 15 servings:

[tex]=0.67×15=10.05≈10[/tex]

Lets look at potatoes:

[tex]=2/6=0.33[/tex]

Therefore for 15 servings:

[tex]=0.33×15=4.95≈[/tex]

Bob traveled 90 miles which was 250/3 % of his trip. How many miles did he still have to travel?

Answers

250/3 more than 100% So Bob traveled much more than he expected.

Answer:

18

Step-by-step explanation:

[tex]90[/tex] ÷ [tex]\frac{250}{3} = 1.08[/tex]

This is 1% of the trip

[tex]1.08[/tex] · [tex]100 = 108[/tex]

This is the amount of the whole trip

[tex]108 - 90 = 18[/tex]

So the answer is he has to 18 more miles to travel.

which ratio is porportional to 18/21? A.2/3 B. 30/35 C. 36/48 D.1/3

Answers

You can solve this problem by applying the proccedure below:
 
 You have:
 
 a) 18/21=2/3
 18x3/21x2
 36≠42 (2/3 is not proportinal to 18/21).
 
 b)18/21=30/35
 18x35/21x30
 630=630  (30/35 is proportional to 18/21)
 
 c)18/21=36/48
 18x48/21x36
 864≠756  (36/48 is not proportinal to 18/21)
 
 d)18/21=1/3
 18x3/21x1
 54≠21  ( 1/3 is not proportinal to 18/21)
 
 Therefore, you can conclude that the correct option is: B.30/35

Verify the identity. Show your work. (1 + tan^2u)(1 - sin^2u) = 1

Answers

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\ 1+tan^2(\theta)=sec^2(\theta)\\\\ -------------------------------\\\\\ [1+tan^2(u)][1-sin^2(u)]=1 \\\\\\\ [sec^2(u)][cos^2(u)]\implies \cfrac{1}{cos^2(u)}\cdot cos^2(u)\implies \cfrac{cos^2(u)}{cos^2(u)}\implies 1[/tex]

What is an atom? GIVING BRAINLIEST 30 POINTS PLEASE HELP

Question 1 options:

an indivisible particle


one of the three particles that make up all matter


an element without an electrical charge


the basic particle that makes up matter

Question 2 (1 point) Question 2 Unsaved
What is a neutron?

Question 2 options:

a subatomic particle with no electric charge, found in the electron cloud


a subatomic particle with no electric charge, found in the nucleus of an atom


a subatomic particle with no electric charge, found in the neutron cloud


a subatomic particle with either a positive or negative electric charge, found in the nucleus of an atom

Question 3 (1 point) Question 3 Unsaved
What is a proton?

Question 3 options:

a subatomic particle with a -1 negative electric charge, found in the proton cloud


a subatomic particle with a +1 positive electric charge, found in the nucleus of an atom


a subatomic particle with a -1 negative electric charge, found in the nucleus of an atom


a subatomic particle with a +1 positive electric charge, found in the proton cloud

Question 4 (1 point) Question 4 Unsaved
What is an electron?

Question 4 options:

a subatomic particle with a +1 positive electric charge, found in the electron cloud


a subatomic particle with a -1 negative electric charge, found in the nucleus of the atom


a subatomic particle with a +1 positive electric charge, found anywhere in an atom


a subatomic particle with a -1 negative electric charge, found in the electron cloud

Question 5 (1 point) Question 5 Unsaved
What is an electron cloud?

Question 5 options:

the area surrounded by the nucleus of an atom, where electrons and neutrons can be found


the area that surrounds the nucleus of an atom, where electrons can be found


the area that surrounds the nucleus of an atom, where electrons and neutrons can be found


the area surrounded by the nucleus of an atom, where electrons can be found

Question 6 (1 point) Question 6 Unsaved
What is an ion?

Question 6 options:

an atom with either more or fewer electrons than protons, giving the atom either a positive or negative charge


an atom with either more or fewer neutrons than protons, giving the atom a different atomic mass


an atom with either more or fewer electrons than protons, giving the atom a significantly different atomic mass


an atom with either more or fewer neutrons than protons, giving the atom either a positive or negative charge

Question 7 (1 point) Question 7 Unsaved
What are isotopes?

Question 7 options:

atoms of the same element that have different atomic masses because they have different numbers of protons


atoms of the same element that have different atomic masses because they have different number of electrons


atoms of the same element that have different electric charges because they have different numbers of neutrons


atoms of the same element that have different atomic masses because they have different numbers of neutrons

Question 8 (1 point) Question 8 Unsaved
Which statement is FALSE?

Question 8 options:

An ion can be either positively or negatively charged


Isotopes are caused by different numbers of neutrons in the electron cloud

Question 9 (1 point) Question 9 Unsaved
Look at the timeline below. What is missing from the timeline?



Question 9 options:

1913 CE: Bohr proposed that electrons can change their orbit with a change of energy. He calls the orbits valence shells.

Question 10 (1 point) Question 10 Unsaved
What is the overall charge of an atom’s nucleus?

Question 10 options:

positive


neutral


negative


It depends on how many protons are in the nucleus.


It depends on how many neutrons are in the nucleus.

Question 11 (1 point) Question 11 Unsaved
Where is most of the mass in an atom?

Question 11 options:

electrons


nucleus


electron cloud


protons


neutrons

Answers

1. Option 4
2. Option 2
3. Option 2
4. Option 4 (not completely sure)
5. Option 2
6. Option 1 (not completely sure)
7. Option 4
8. Isotopes are caused by different numbers of neutrons in the electron cloud
9.  Not sure of the question
10. Positive charge
11. nucleus

Answer:

1. Option 4

2. Option 2

3. Option 2

4. Option 4 (not completely sure)

5. Option 2

6. Option 1 (not completely sure)

7. Option 4

8. Isotopes are caused by different numbers of neutrons in the electron cloud

9.  Not sure of the question

10. Positive charge

11. nucleus

Step-by-step explanation:

Give the guy above me brainliest.

A triangle has side lengths of 14 cm, 48 cm, and 55 cm.

Answers

It is a scalene triangle.

The diagonals of a rhombus are 12 in. and 16 in. long. The length of a side of the rhombus is 10 in. What is the height of the rhombus? Explain how you found your answer.

Answers

If d₁ and d₂ are the lengths of the diagonals, the area is given by
.. A = (1/2)*d₁*d₂
.. A = (1/2)*(12 in)*(16 in)
.. A = 96 in²

If b is the base and h is the height, the area is given by
.. A = b*h
We know the values of A and b, so
.. 96 in² = (10 in)*h
.. (96 in²)/(10 in) = h = 9.6 in

The height is 9.6 in.

What are the solutions to the equation √ ̅5x + 1 = x + 1?

Answers

0 

0 is your solution

√5(0) + 1 = (0) + 1

0 + 1 = 0 + 1 (True)

No other number works, because it will not equal


hope this helps

Zakir loans Panji $20,000 for one year at 8% simple interest. Three months later, Zakir sells the note to Ben at a simple discount rate of 7 3/4%. How much does Ben pay for the note?

Answers

The maturity value of the note is
.. mv = P*(1 +rt) = 20,000*(1 +.08*1) = 21,600

The note is sold to Ben at the discounted price of
.. 21,600*(1 -rt)
.. = 21600*(1 -.0775*0.75) . . . . . 9 months is 0.75 years
.. = 20,344.50

Ben pays $20,344.50 for the note, which has a maturity value of $21,600.

find the area of an equilateral triangle (regular 3-gon) with the given measurement 9-inch A=sq. in.

Answers

assuming is a 9 inch side.

[tex]\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}\qquad \begin{cases} s=length~of\\ \qquad a~side\\ -------\\ s=9 \end{cases}\implies A=\cfrac{9^2\sqrt{3}}{4}\implies A=\cfrac{81\sqrt{3}}{4}[/tex]
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