A circle has a sector with area (3/2) pi and central angle of 60°.
What is the area of the circle?
Either enter an exact answer in terms of it or use 3.14 for it and enter your answer as a decimal.

A Circle Has A Sector With Area (3/2) Pi And Central Angle Of 60.What Is The Area Of The Circle?Either

Answers

Answer 1

Answer:

[tex]9\pi[/tex], which is approximately [tex]28.26[/tex].

Step-by-step explanation:

Consider two sectors in the same circle. The area of the two sectors is proportional to their central angles. In other words, if the central angle is [tex]\theta_1[/tex] for the first sector in this circle, and [tex]\theta_2[/tex] for the second, then:

[tex]\displaystyle \frac{\text{Area of Sector 1}}{\text{Area of Sector 2}} = \frac{\theta_1}{\theta_2}[/tex].

In this question, think about the whole circle as a sector. The central angle of this "sector" would be [tex]360^\circ[/tex] (a full circle.) Compare the area of this circle to that of the [tex]60^\circ[/tex]-sector in this circle:

[tex]\displaystyle \frac{\text{Area of Circle}}{\text{Area of $60^\circ$-Sector}} = \frac{360^\circ}{60^\circ} = 6[/tex].

In other words, the area of this circle is six times that of the [tex]60^\circ[/tex]-sector in it.

The area of that [tex]60^\circ[/tex]-sector is [tex]\displaystyle \frac{3}{2}\pi[/tex]. Therefore, the area of this full circle will be [tex]\displaystyle 6 \times \frac{3}{2}\pi = 9\pi \approx 28.26[/tex].


Related Questions

halp me do this pleeeeeasssseee​

Answers

Answer:

Step-by-step explanation:

The question isn't clear...

Samuel has a bell box that contains
4 door bells, 3 office bells, and 7 big
bells. Without looking, Samuel
Chooses a bell from the box, what is the
relative frequency probability the
when he selects a doorbell?



Answers

Answer:

4 out of 14

Step-by-step explanation:

there is only 4 door bells and 14 bells in total

3. If the legs of an isosceles right triangle are 10 inches long, approximate the length of
the hypotenuse to the nearest whole number​

Answers

Answer:

Using the Pythagorean theorem for isosceles right triangle, the length of  the hypotenuse is sqrt( 2 x 10^2) = ~14.1 in

Hope this helps!

:)

Help!!! Please????????

Answers

Answer:

idk

Step-by-step explanation:

i dont know

I think it’s asking to find the roots (zeros). Is so, then:

1.) There are two solutions, X = 1 plus or minus root 145/ 6.

2.) There are 2 solutions with components imaginary. X = 3/2 + i/2 and 3/2 - i/2

3.) There’s 2 solutions X = ( -7 plus or minus root 93)/2

4.) There is one solution X = -4

I hope that helps.

The length of a rectangle is 5 m less than twice the width, and the area of the rectangle is 52m ^ 2 . Find the dimensions of the rectangle.

Answers

The dimension of the rectangle is 8m by 6.5m respectively

Area of a rectangle

The formula for calculating the area of a rectangle is expressed as;

A =lw

If the length of a rectangle is 5 m less than twice the width, then;

l = 2w - 5

Substitute

A = w(2w-5)

52 = 2w² - 5w

2w² - 5w = 52

2w² - 5w - 52 = 0

(2w−13)(w+4)=0

Step 2: Set factors equal to 0.

2w−13=0 or w+4=0

w =13/2 or 6.5m

Determine the length

l = 2w - 5

l = 2(6.5) - 5

l = 13 - 5

l =8m

Hence the dimension of the rectangle is 8m by 6.5m respectively

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Currency on hand = 2,000 Swiss francs Currency desired = Dutch guilders (Holland) How many guilders based on Wednesday rate? (Hint: Convert 2,000 Swiss francs to United States dollars. Then convert United States dollars into guilders.)

Answers

Answer:

4175.40384   Dutch guilders

Step-by-step explanation:

The main objective here is to convert the currency at hand (2,000 swiss francs) to Dutch guilders. In order to achieve that ; we need first require to convert the currency at hand into United states dollars

So ; if 1 swiss francs  =  1.0328 united states dollars  (as at Wednesday)

Then 2000 swiss francs  will be = 2000  ×  1.0328 united states dollars  = 2065.6 united states dollars

SO; if  1 united states dollars = 2.0214 Dutch guilders ( as at Wednesday)

Then 2065.6 united states dollars will be = 2065.6 × 2.0214

= 4175.40384   Dutch guilders

Answer:

closest would be 3,500

Step-by-step explanation:

3. The measure of each inscribed
angle is equal to( )times the
measure of the intercepted arc.
a. 1/2
b. 1
c. 2

Answers

Answer: A. 1/2

Step-by-step explanation:

In ΔNOP, the measure of ∠P=90°, NP = 12, PO = 35, and ON = 37. What ratio represents the cosine of ∠O?

Answers

Answer:

35/37

Step-by-step explanation:

In this question, we are to calculate the ratio that represents the cosine of angle O

Firstly, please check attachment for diagram of the triangle.

Mathematically, the trigonometric term Cos means the ratio of the length of the adjacent to that of the hypotenuse

The hypotenuse is the longest length which is 37 which represents the length ON

The side adjacent to angle O is the side OP which is 35

Thus, the ratio representing the cosine of angle O is 35/37

Answer:

8/15

Step-by-step explanation:

this is another answer, if you get these numbers

An oil storage tank is a cylinder with a height of 50 feet and a diameter of 20 feet what is the volume of the tank

Answers

Answer:

15707.96

Step-by-step explanation:

Answer:

5000pi ft^3 (exactly) or 15,708 ft^3 (approximately)

Step-by-step explanation:

V = (pi)r^2h

r = radius = diameter/2

r = 20 ft/2 = 10 ft

V = (pi)(10 ft)^2(50 ft)

V = 5000(pi) ft^3

V = 5000(3.14159) ft^3 = 15,708 ft^3

Answer: 5000pi ft^3 (exactly) or 15,708 ft^3 (approximately)

Language arts test is worth 100 points there is a total of 26 question There are spelling words question that I wasn't points each in vocabulary words question worth five points each how much of each type of question are there

Answers

Answer: There are 10 two points and 16 five points questions.

Step-by-step explanation:

This is the detailed question:

A language arts test is worth 100 points. There are a total of 26 questions. There are spelling word questions that are worth 2 points each and vocabulary word questions worth 5 points each. How many of each type of question is there?

Let y = the number of 2 points questions

Let z = the number of 5 points questions

y + z = 26 ......... i

2y + 5z = 100 ........ ii

Multiply equation i by 2

Multiply equation ii by 1

2y + 2z = 52 ......... iii

2y + 5z = 100 ....... iv

Subtract iv from iii

-3z = -48

z = 48/3

z = 16

Since y + z = 26

y = 26 - 16

y = 10

y = 10 two points questions

z = 16 five points questions

There are 10 two points and 16 five points questions.

Solve for x in the following figure.

Answers

Answer:

x=80°

Step-by-step explanation:

supplementary angles equal 180°

∠J=80

80+x+20=180

100+x=180

x=80

What is
15,379 times 51





Answers

Answer:

784329

Step-by-step explanation:

the answer is : 784329

A sphere with a radius of 11 in

Answers

Answer:

-The volume of a sphere:

[tex]V \approx 5575.279[/tex] [tex]in ^3[/tex]

     or

[tex]V \approx 5575.28[/tex] [tex]in^3[/tex] (Rounded to the nearest hundredth if needed)

Step-by-step explanation:

-Use the formula for the volume of a sphere and use the radius [tex]11[/tex] [tex]in[/tex] for that formula:

[tex]V = \frac{4}{3} \pi r^3[/tex]

[tex]V = \frac{4}{3} \pi 11^3[/tex]

-Then, you solve the formula:

[tex]V = \frac{4}{3} \pi 11^3[/tex]

[tex]V = \frac{4}{3} \times \pi \times 11^3[/tex]

[tex]V = \frac{4}{3} \times \pi \times 1331[/tex]

[tex]V = \frac{4}{3} \pi \times 1331[/tex]

[tex]V = \frac{5324}{3} \pi \approx 5575.279[/tex]

-Round up to the nearest hundredth (if needed):

[tex]V \approx 5575.28[/tex]

rectangle with length 11 1/2 in. and width 8 in The area of this rectangle is____________
in2.

Answers

Answer:

Step-by-step explanation:

look, area = length x width

so that means that the area of this rectangle is

= 11 1/2 * 8

= 23/2 * 8

= 23 * 4 (simplified)

= 92 in^2

Answer:

[tex]92in.^{2}[/tex]

Step-by-step explanation:

Area of a rectangle= L×W

If length= 11[tex]\frac{1}{2}[/tex]in. and width= 8in.,

∴ Area = 11[tex]\frac{1}{2}[/tex]in. × 8in.

           = [tex]\frac{23}{2}[/tex] × [tex]\frac{8}{1}[/tex] [tex]in.^{2}[/tex]

           = (23 × 4) [tex]in.^{2}[/tex]

           = 92[tex]in.^{2}[/tex]

Hope this helps!!!

 

How would you find the area of this?

Answers

the formula for it is bh , multiply 14 by 24 and the answer is 336

Use the Rate-Factor Model for multiplication. The rate is 320 feet per hour, 320 feethour . The hiking team descended the mountain from 1 pm to 5 pm. The net change is a __________________ of _________________feet.





increase, 320 feet


decrease, 320 feet


increase, 1,280 feet


decrease, 1,280 feet

Answers

Answer:

The net change is a decrease of 1,280 feet

Step-by-step explanation:

From the question, we understand that the hiking team has a work rate of 320 feet / hour

Now that are descending between the hours 1pm and 5pm, this means that they descended for a total of 4 hours.

Now the total number of feet they have descended will be the number of hours * work rate = 4 hours * 320 feet/hour = 1,280 feet

Thus, the net change is decrease of 1,280 feet

Which number has the least value?

Answers

Answer:

Your annswer is b

Step-by-step explanation: because it is least than all of the others

The number that has the least value is given as -13.142.

What are arithmetic operations?

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The number given in the options are |-10.869|, -14⁶/₇, 9.21 and |-10.25|.

Write all the numbers in one equivalent form as below,

⇒ |-10.869| = 10.869

⇒ -14⁶/₇ = -14 + 6/7 = -13.142

⇒ 9.21

⇒ |-10.25| = 10.25

It is clear from the equivalent form that the least value is -13.142.

Hence, the the least value number is obtained as -13.142.

To know more about arithmetic operation click on,

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helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

The answer is C

Step-by-step explanation:

Answer: The answer is C.

hope you do good on quiz! :D

A spinner has 5 equal sections numbered 1 to 5. What is the probability of the spinner stopping on a number that is a multiple of 2 or is less than 3?
help!!!!!!!!!plz.....

Answers

Answer: 1/5, .2, and or 20%

Step-by-step explanation:

The only multiple of 2 that is less than 3 and greater than 1 is 2, so there is a 1/5, .2 and or 20% chance of this happening

To hi a ball over a tree, a golfer hits the ball with a path that is modeled by h = -16t^2 + 80t where h is the height in meters and t is the time in seconds. Determine the hight of the ball after 1 second, the time it takes the ball to reach its maximum height, the maximum height of the ball, and the time it takes for the ball to return to the ground.

Answers

Answer:

After one second, the height is 64 meters high

Step-by-step explanation:

The rest.... Let's wait to find out... Haha tried to find the answer for 10 minutes straight but it's kinda hard since it might equal decimals

Which is the best estimate for the liquid volume of a small carton of milk?

Answers

Answer:

Step-by-step explanation:

The height of a trapezoid is 4 in. And its area is 48 in 2. One base of a trapezoid is 6 inches longer than the other base. What are the lengths of the bases? Complete the explanation of how you found your answer.

Answers

Answer:

a=9

b=15

Step-by-step explanation:

Well the area formula of a trapezoid is: [tex]\frac{a+b}{2} *h[/tex]

[tex]\frac{a+b}{2} *4=48[/tex]

Divide both sides by 4

[tex]\frac{a+b}{2} =12[/tex]

Multiply both sides by 2

a+b=24

Now since one of the sides (b) is 6 inches longer than a, we get;

a+a+6=24

Subtract 6 from both sides

2a=18

Divide both sides by 2

a=9

b=9+6=15

A cylindrical bucket and spherical storage container are shown. The bucket has a radius of 6 inches and a height of 15 inches, and the storage container has a diameter of 24 inches. Nicholas says he can fill the entire storage container with seef by filling the bucket four times and pouring the contents into the container. Is Nicholas correct? Explain why or why not.

Answers

Answer:

since the ratio of both volumes is approximately 4, then we can say Nicholas is correct

Step-by-step explanation:

Firstly, what we need to do is to calculate the volume of both.

For the cylindrical bucket, the volume can be calculated as

pi * r^2 * h

where r is 6 inches and h is 15 inches

The volume is thus

pi * 6^2 * 15 = 540pi inches*3

For the spherical storage, the volume can be calculated using the formula

V = 4/3 * pi * r^3

with r = d/2 = 24/2 = 12 inches

The volume is thus;

V = 4/3 * pi * 12^3 = 2,304 pi inches^3

Now, to confirm the validity of Nicholas’ claims, we shall divide the volume of the spherical storage by the volume of the cylindrical container.

Mathematically that would be 2,304pi/540 pi = 4.267 which is approximately 4 times

Phoebe built the sandbox below for her younger sister.
2 feet
4 feet
5 feet
What is the volume of the sandbox?

Answers

I think its 40ft i hope it helps

Answer: 40 feet

Step-by-step explanation:  Volume = length * width * height

then substitute Volume = 2 * 4 * 5

multiply Volume = 8 * 5

multiply again Volume = 40

hope this helps mark me brainliest if it did have a great day

7h=-(2h-18)7h=−(2h−18) Solve for h

Answers

Answer:

h=2

Step-by-step explanation:

7h=−(2h−18)

Distribute the minus sign

7h = -2h +18

Add 2h to each side

7h +2h = -2h+2h +18

9h = 18

Divide each side by 9

9h/9 =18/9

h =2

Answer:

h = 2

I got it right on Kahn Academy

Help meeee!!! Whats x

Answers

Answer:

74°

Step-by-step explanation:

The angle on a line = 180°

therefore:.

x + 106° = 180°

x = 180° - 106°

x = 74°

Answer: 74 degrees.

Step-by-step explanation:

Angles on the same side of a line add to 180.

The angle measure of 106 and the angle measure of x lie on the same side of the line WZ, so you can add them both to get 180:

106 + x = 180

x = 74

What is the axis of symmetry for the function f(x)=7-4x+x2?
X=-3
x = -2
x = 2
x= 3

Answers

Answer:

x = 2

Step-by-step explanation:

C on edg 2020

The axis of symmetry of f(x) = 7-4x + x^2 is x = 2

How to determine the axis of symmetry?

We have:

f(x) = 7-4x + x^2

Differentiate the function

f'(x) = -4 + 2x

Set the function to 0

-4 + 2x = 0

Add 4 to both sides

2x = 4

Divide by 2

x = 2

Hence, the axis of symmetry of f(x) = 7-4x + x^2 is x = 2

Read more about axis of symmetry at:

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Which graph represents Y=2/5x+2

Answers

the graph should look like this

Answer:

Your graph will have a y intercept of (0,2) and from that point move up 2 and to the right 5 to the point (5,4) then draw a line connecting and extending beyond these two points.

Step-by-step explanation:

y = mx + b

m = slope which is rise over run

b = y intercept

y = 2/5x + 2

m = 2/5

b = 2

This means that your graph will have a y intercept of (0,2) and from that point move up 2 and to the right 5 to the point (5,4) then draw a line connecting and extending beyond these two points.

What is the probability of the complement of rolling a number less than 5 by using a six-sided die? StartFraction 1 over 6 EndFraction One-third Two-fifths Two-thirds

Answers

Answer:

1/3 = 0.3333 = 33.33%

Step-by-step explanation:

In the six-sided die we have 6 possible values, from 1 to 6.

To roll a number less than 5, the options are: 1, 2, 3 or 4.

We have 4 options, so the probability is P = 4/6 = 2/3

To find the complement of this probability, we just need to calculate 1 minus the probability, so we have that:

complement = 1 - P = 1 - (2/3) = 1/3 = 0.3333 = 33.33%

(We could also find the probability of rolling 5 or 6, which is the complement of rolling less than 5)

Answer:

1/3

Step-by-step explanation:

I took the test

hey can anyone pls help me out in dis pls i will mark u as brainliest!!!!! and i will give 30 points

Answers

Answer:

graph b because its a parabola

Step-by-step explanation:

Answer:

Graph B does not belong

Step-by-step explanation:

All the other graphs are linear inequalities, whereas graph B is a quadratic inequality. You can also tell by how they look. The straight lines are linear, and the symmetric curve (parabola) is a quadratic

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