the arc measure of a sector in a given circle is doubled. will the area of the sector also be doubled? explain your reason

Answers

Answer 1

Answer:

Yes. See explanation below.

Step-by-step explanation:

The central angle and the degree arc measure of a sector of a circle are  equal. Doubling the arc measure, doubles the central angle measure and vice versa.

Area of the the original sector:

[tex] A_{sector} = \dfrac{n}{360^\circ}\pi r^2 [/tex]

where n = measure of the central angle of the sector

Since the central angle and the arc measure of the sector are equal, changing the arc measure has the same effect as changing the central angle measure.

Let's double the central angle to 2n which is the same as doubling the arc measure.

Area of the sector with a doubled central angle or a doubled arc measure:

[tex] A_{sector} = \dfrac{2n}{360^\circ}\pi r^2 [/tex]

Now we divide the area of the doubled sector by the area of the original sector.

[tex]\dfrac{\frac{2n}{360^\circ}\pi r^2}{\frac{n}{360^\circ}\pi r^2} =[/tex]

Simplify:

[tex]= \dfrac{2n}{n} \times \dfrac{360^\circ \pi r^2}{360^\circ \pi r^2}[/tex]

[tex] = \dfrac{2n}{n} [/tex]

[tex] = 2 [/tex]

The ratio of the areas is 2, so the area of the sector is indeed doubled.

Answer: Yes.


Related Questions

the function \:h=-0.01x^2+0.9x models the height in feet, h, of a soccer ball as it travels a horizontal distance in feet, x. What is the maximin height of the soccer ball and how long does it take for the ball to reach this height

Answers

Answer:

Nice!

Step-by-step explanation:

Which would be the next step? Does anyone know? Please, help.

Answers

Answer:

∠DAB = ∠DBA

Then AD=DB from above statement

PLEASE HELP IM BEGGING YOU ITS EASY IM JUST SLOW

Answers

Answer:

6

Step-by-step explanation:

Formula for area A=0.5(bh)

12=0.5(4h)

12=2h

6=h

Answer:

6

Step-by-step explanation:

Area of triangle equation:

A=[tex]\frac{1}{2}[/tex] base * height

For this triangle...

12=[tex]\frac{1}{2}[/tex] (4) (x)

we need to figure out what x is to find the height.

To get x alone in this equation we can first divide both sides by 4

12/4=[tex]\frac{1}{2}[/tex] (x) ---> 3= [tex]\frac{1}{2}[/tex] (x) Then multiply by the reciprocal of 1/2 which is 2/1

x=6

someone helpp!!!!!!!

Answers

Answer:

the rate of change is 3

Step-by-step explanation:

if im wrong im sorry but if im right give me brainliest

Find the missing side lengths.

Need help please.

This is the 6th time I post.

Answers

Answer:

x = 9.238 y = 4.619

Step-by-step explanation:

I kind of forgot how to do sohcahtoa but we do cosine for one of them. I used a calculator but the lengths seems reasonable so I'm sure they should be right.

Jacob runs 5 miles in 1 1/2 hours . Robert runs 3 miles in 45 minutes or 3/4 hour. Who runs faster

Answers

Answer:

Robert

Step-by-step explanation:

If Robert runs 3 miles in 45 minutes, by the end of 90minutes, Robert would have covered 6miles, while Jacob covered 5miles in 90 minutes, therefore, Robert ran faster than Jacob.

the scatterplot shows the number of hours that 12 people spent learning to type on a keyboard and each persons average typing speed. Based on the scatterplot, what is the best prediction of a persons average typing speed in words per min. if the person has spent 70 hours learning to type?

Answers

Answer:

85 wpm

Step-by-step explanation:

From the scatter plot, we can see the following;

At 20 hours, average typing speed = 34 wpm

At 30 hours, the average typing speed = 40 wpm

At 40 hours, the average typing speed = 51 wpm

At 50 hours, the average typing speed = 65 wpm

Average differences = ((40 - 34) + (51 - 40) + (65 - 51))/3 = 10.3

Approximating to a whole number = 10

Now, we can approximate that at 60 hours, average typing speed = 65 + 10 = 75 wpm

At 70 hours, the average typing speed = 75 + 10 = 85 wpm

Answer:

85 wpm

Step-by-step explanation:

I took this test!

Which expression is equivalent to 2 (3x – 4)?
ОА) 3х - 4
O B) 5x - 6
Ос) 6x - 4
OD) 6x – 8

Answers

The answer is d




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Tad and his buddies drove to the orange bowl to see their favorite football team win the national championship because of heavy traffic they only avsraged 50 mph however on the return trip they averaged 75 mph if the total round trip took 12 hours how long did it take tad and his buddies to drive to the orange bowl

Answers

Answer:

7.2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Distance "D" = rate × time

or d = r × t.

Tad and his buddies drove to the orange bowl(while going) -50mph

Tad and his buddies while returning from a trip -75mph

Total round trip = 12 hours

Distance while going = 50 x t

Distance while returning = 75 (12 - t)

50t = 75(12 -t)

50t = 900 -75t

50t + 75t = 900

125t = 900

t = 900/125

t= 7.2

The total number of hours it takes Tad and his buddies to drive to the orange bowl is 7.2 hours.


no link just put the answerrrrr

Answers

Answer:

4in

Step-by-step explanation:

Max gets a weekly allowance of $17. He spends $3 each week on snacks. He splits the rest of his allowance into equal amounts for his college fund and spending money. How much money does Max keep for spending money each week? $

Answers

Answer:

$7

Step-by-step explanation:

The amount max keeps for spending = 1/2(total allowance - amount he spends on snacks)

total allowance = $17

amount he spends on snacks = $3

Amount he would have for  his college fund and spending money. = $17 - $3 = $14

Since he splits the amount equally between his college fund and spending money, the amount he would have for spending can be determined by dividing 14 by 2

$14/2 = $7

Over a 5-year period, a company reported annual profits of $8 million, $3 million, $2 million, and $9 million. In the fifth year, it reported a loss of $7 million. What was the mean annual profit?


Answers

Given

Annual profits of four years $8 million, $3 million, $2 million, and $9 million.

In the fifth year, it reported a loss of $7 million.

To find:

The mean annual profit.

Solution:

Formula for mean is:

[tex]\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]

Annual profits are $8 million, $3 million, $2 million, $9 million and -$7 million. Here negative sign represent loss.

So, the mean annual profit is:

[tex]\text{Mean}=\dfrac{8+3+2+9+(-7)}{5}[/tex]

[tex]\text{Mean}=\dfrac{22-7}{5}[/tex]

[tex]\text{Mean}=\dfrac{15}{5}[/tex]

[tex]\text{Mean}=3[/tex]

Therefore, the  mean annual profit is $3 million.

What are the angles in degreees

Answers

Answer: A is 70 B is 45 and C is 50

Step-by-step explanation:

3. if u get this right i’ll give u brainliest

Answers

Answer:

(-3,2)

Step-by-step explanation:

3/4 of eight is six so go to two and then find the x, as x wasn't on the numbers it is not a multiple of two, so three was the closest number

may be wrong

Alan and Beth share $1190 in the ratio Alan : Beth = 5:2.
Work out how much Alan receives.
options:
$850
$1666
$34
$119​

Answers

The share of money Alan receives is $850. Therefore, option C is correct answer.

Given that, the total amount is $1190 and the ratio Alan: Beth = 5:2.

We need to find the how much money Alan gets.

What is the ratio?

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other.

Now, 5+2=7

Money Alan receives=5/7×1190

=$850

The share of money Alan receives is $850. Therefore, option C is correct answer.

To learn more about ratios visit:

https://brainly.com/question/1504221.

#SPJ2

NO FILES PLEASE! THANKS!

Answers

Answer:

C, A and D

Step-by-step explanation:

(z^6/z)^2 QUICK ILL GIVE BRANLIEST

Answers

Answer,  z10

Step-by-step explanation:

Someone please help me.

Answers

Felipe's age is ≥ 5

Step-by-step explanation:

Difference of F's age and 4: f - 4

Twice: 2 (f -4) ≥ 2

2f - 8 ≥ 2

2f ≥ 10

f ≥ 5

Answer:

Step-by-step explanation:

how many meters are their in centimeter​

Answers

Answer:

You mean how many centimerters are in a meter?

In that case 100.

Step-by-step explanation:

What is the area of a parallelogram that has a base of 4 ½ inc. and a height of 2 ¼ in. ?

Answers

Answer:

4.5

Step-by-step explanation:

4.5 is the answer Bc I dived

Determine the number of centimeters in 2 inches.

Answers

Answer:

5

Step-by-step explanation:

Answer:

5 centimeters

Step-by-step explanation:

You have to look at where it says 2 inches, and follow the line up to where the red stops and see how many centimeters it crosses

Find the slope of the line

Answers

Answer:

m = 3/4

Step-by-step explanation:

slope of a line equation:

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

m = (3-0)/(2-(-2))

m = 3/4

help plzzzzzzzzzzzzz

Answers

Answer:

Building new bike paths.

Step-by-step explanation:

The reason I choose this answer was because the other ones would all use more gas when bike paths would limit the amount of driving and add to the amount of biking done.

PLSS HELP IMMEDIATELY!!! i’ll give brainiest if u don’t leave a link!

Answers

Answer: Evaluate the findings to compare to his hypothesis

Step-by-step explanation: Since the biologist already has the findings and has a hypothesis, he now has to compare both of them together.

the answer is D. ........

Compare each set of rational numbers.

Answers

hey.. don’t click on that link or any links on here !!! but i jus wanna say you didn’t attach an image of your question :).

Which theorem can you use to show that the quadrilateral on the tile floor is a parallelogram?

Answers

Answer:

Parallelogram Theorem #1 Converse

Step-by-step explanation: : If each of the diagonals of a quadrilateral divide the quadrilateral into two congruent triangles, then the quadrilateral is a parallelogram. Parallelogram Theorem #2 Converse: If the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Parallelogram opposite sides converse. Therefore, option A is the correct answer.

What is parallelogram?

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Let the diagonals AC and BC intersect at O.

Consider, triangle BOC and triangle AOD

OA=OC (Shown in the figure)

∠AOD=∠BOC (Vertically opposite angles are equal)

BO=DO (Shown in the figure)

By SAS congruence theorem

triangle BOC and triangle AOD are congruent

So, by CPCT AD=BC

Similarly,

From, triangle AOB and triangle DOC

AB=DC

Therefore, option A is the correct answer.

Learn more about the parallelogram here:

https://brainly.com/question/19187448.

#SPJ6

I'll give brainliest please help​

Answers

Answer:

∠R = 38°

Step-by-step explanation:

∠R = 1/2(arc PE - arc SQ)

∠R = 1/2(140 - 64) = 1/2(76) = 38°

5. Andrea ate half as many crackers as Darnell. Darnell ate 3 more crackers than Ziyah. If Ziyah ate 21 crackers, how many did Andrea eat?

A. 24 crackers
B. 18 crackers
C. 10 crackers
D. 63 crackers
E 7 crackers
F. 12 crackers

Answers

12, if Darnell ate 3 more crackers then Ziyah, that’ll be 21+3 which is 24 and half of 24 is 12

Graph a line that has a slope of 5/2 and includes the point (-2, -7)

Answers

First make an equation
Y = 5/2x + b
Plug in the points
-7 = 5/2(-2) + b
-7 = -5 + b, b = -2
Equation: y = 5/2x - 2

Find two points and draw a line
(0, -2) and (-2, -7)
Draw a line between the points

K divided by 5 = 12.4

Answers

Answer:

k=62

Step-by-step explanation:

K divided by 5 = 12.4

Multiply both sides by 5

5k/5=12.4×5

Simplify;

k=62

Hope this helped!!

Answer:

k = 62

Step-by-step explanation:

To solve we need to get k on one side alone.

To do this we can multiply buth sides by 5

[tex]\frac{k}{5} =12.4[/tex] --->  =12.4*5

This gives us x=62

You can check this by putting 62 in for k and solving the problem.

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