Brook makes this conjecture: Because the angles are equal, the proportion of area of each sector relative to the area of the given circle is also equal.

Answers

Answer 1

Answer:

The Brooks conjecture is true as the proportion of the area of a sector to the area of a circle is only dependent on the angle.

Step-by-step explanation:

The area of a sector for a radius r and an angle θ is given as

[tex]\Delta Sector=\dfrac{1}{2}r^2\theta[/tex]

Whereas the area of a circle for a radius r is given as

[tex]\Delta Circle=\pi r^2[/tex]

Now the ratio is given as

[tex]\dfrac{\Delta Sector}{\Delta Circle}=\dfrac{\dfrac{1}{2}r^2\theta}{\pi r^2}[/tex]

Here as r is the radius of the circle and it is the same therefore the above ratio is simplified to

[tex]\dfrac{\Delta Sector}{\Delta Circle}=\dfrac{\theta}{2\pi }[/tex]

Here as π is constant the only variable here is θ. Thus according to Brooks conjecture when the angles are equal, the proportion of area of each sector relative to the area of the given circle is also equal is true.


Related Questions

a parallelogram has one side that is 4 centimeters long and one side that is 6 centimeters long. what is the perimeter of the parallelogram? (also i’ll be giving out brainiest to those who provide the correct answer and don’t leave a link)

Answers

Answer:

P = 20 cm

Step-by-step explanation:

The appropriate formula is P = 2W + 2L.

Here that comes to P = 2(6 cm) + 2(4 cm) = 20 cm

Solve using the quadratic equation.
[tex]3x^{2} -6x-24[/tex]
Solution 1: ___
Solution 2: ___

Answers

Answer:

X = 4

X = -2

Step-by-step explanation:

Rate And Like. Salute.

please answer quick I’ll mark you brainliest pls the quarter ends at 12:00

Answers

Answer:

46/100

Step-by-step explanation:

also what grade is this

if p is inversely proportional to the square of q, and p is 9 when q is 5, determine p when q is equal to 3

Answers

Answer: tell me if i am wrong

p = 304

Step-by-step explanation:

Given p is inversely proportional to q² then the equation relating them is

p = [tex]\frac{k}{q^{2} }[/tex] ← k is the constant of proportion

To find k use the condition p = 19 when q is 8, then

19 = [tex]\frac{k}{8^{2} }[/tex] =[tex]\frac{k}{64}[/tex]  ( multiply both sides by 64 )

k = 1216

p = [tex]\frac{1216}{q^{2} }[/tex] ← equation of proportion

When q = 2, then

p =  [tex]\frac{1216}{2^{2} }[/tex]=[tex]\frac{1216}{4}[/tex]=304

Someone please help this is due soon

Answers

Answer:

Step-by-step explanation:

the picture is telling us that the angles Q and R are equal so set them equal

9x-17 = 4x + 28

5x = 45

x = 9

How to solve for P in a compound interest formula?

Answers

Calculation. Formula.

P (1 + r/n)^(nt)

Calculate accrued amount. Principal + Interest. A = P(1 + r)t

Calculate principal amount. Solve for P in terms of A. P = A / (1 + r)t

Calculate principal amount. Solve for P in terms of I. ...

Calculate rate of interest. As a decimal. ...

Calculate rate of interest. As a percent. ...

Calculate time. Solve for t.

The solution for P (Principal amount) in a compound interest Formula is; P = A/(1+ r)^t.

Changing the Subject of a formula

By convention, the formula for calculating the compound interest is;

A = P(1 + r)^t

On this note, it follows that; the principal amount, P can be calculated by dividing both sides of the equation by the expression; (1+ r)^t.

Ultimately, the solution for P is; P = A/(1+ r)^t.

Read more on subject of the formula;

https://brainly.com/question/24924853


Please help me!! I need this answered really quick

Answers

Answer:

Perimeter = 4x + 18

Step-by-step explanation:

{(x + 3) + (x + 3) + [(x + 3) -x]} × 2 = (2x + 6 + 3) × 2 = 4x + 18

[(        width     ) + (  length )] × 2

Help, please! I want to finish this last quarter good or I may get kicked out. Thank you!!

Answers

Yellow is 28.26
Purple is 43.99

Please help asap. No links for a answer or I will report you
8th Grade

Answers

Answer= b
Because all the other choices are quadratic

Answer:

B

Step-by-step explanation:

A linear function is described by a x term to the power of 1 or even 0. A function when x is to the second power is most usually not a linear function.

In answer A, you have x multiplied against -3x. This will cause an x squared term, so this is not a linear function.

In answer B, you have 1/2 multiplied against x, which is a regular x term subtracted by 2x, causing a regular x term, meaning this function is linear. However, in the small possibility it is not, we will keep going.

In answer C, there is an x squared term so this is not linear.

In answer D, the expression has 1/2x times 2x, which will cause an x squared term.

Thus, the answer is B, which is the only equation without an x squared term.

PLEASE SOMEONE HELP ME RN MATH

Answers

Answer:

Sure but what's the math problem?

Answer:

where is the pic??

Please help me asap. No links or I will report you
8th Grade

Answers

Answer:

D. square root of 7 to the power of 3

R. b=6/8

HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP

Answers

Answer:

D

Step-by-step explanation:

Answer:

the answer is d

Step-by-step explanation:

we can use point-slope form to find this answer.

first, make this equation

y-y 1=m(x-x1)

y-4=-6(x-1)

m=-6 because you can use slope intercept form to find the slope (as the name states lol)

then just distribute!!

y-4=-6x+6

add four to both sides

y=-6x+10

whoops, i did a little too much the answer is in bold!!!

good luck!! hope this helped! <3

If triangle ABC is dilated by a scale factor of 2 with a dilation center of A, what will be the coordinates of point B?

Answers

Answer:

0,6

Step-by-step explanation:

I hope this helps lol

3. Mrs. Sinclair is finding the selling price of a pair of $40
skates with a 30% markup. Find her mistakes and correct it.

Answers

Answer:

Selling price : $52

Step-by-step explanation:

First, find 30% out of 40.

x= (40)(30)=1200/ 100= 12

x=12

Add 30% to the original selling price.

So then you add $12 to $40 to get $52.

(((4\sqrt(2) - 2 \sqrt(6)) - (\sqrt(2)- \sqrt(6) )))/(\sqrt(3)-1)

Answers

Uh- is this a question-

Answer:

thx for points

Marco mixed 2 teaspoons of sugar and 1 teaspoon of milk into his coffee. What is the ratio of teaspoons of sugar
to teaspoons of milk?

A. 2 : 1
B. 1 : 2
C. 1 : 3
D 3 : 2

Answers

Answer:

A..................... is answer

The correct answer is: A. 2 : 1

The radius of a circle is 6 miles. What is the circle's area? use 3.14 for ​.

Answers

Answer:

113.04

Step-by-step explanation:

A=Pr^2

6^2=36

36 * 3.14=113.04

Hope it helps.

(ASAPPPPPP)The diameter of a circle is 4 units.
What is the radius of the circle?
units
I

Answers

the answer is 2 because if half of the diameter

∠C and \angle{D}∠D are vertical angles. If the m\angle{C} m∠C=66o, then what is the m\angle{D} m∠D ?

Answers

Answer:

The measure of angle D is of 66º.

Step-by-step explanation:

Vertical Angles:

If two angles are vertical, they have the same measure.

In this question:

Angles C and D are vertical.

Angle C measures 66º.

So the measure of angle D is of 66º.

A 3 digit number is such that twice the hundreds digit is more than the tens digit by 2.The digit is thrice the hundreds digit.When the digits are reversed, the number is increased by 594.Find the number.

Answers

Answer:

The number is -341

Step-by-step explanation:

Let the three digit number be represented as 100a+10b+c

Given

2a -b = 2 ---(1)

a = 3c ----(2)

100a+10b+c - 100c -10b -a = 594

99a -99c = 594 ---(3)

From 2 & 3 , we get -

99*a - (99*3*a) = 594

99*2 a = 594

a = -3

a = 3c, c = -1

2*-3 -b = 2, b = -4

Number is -341

you are building a rectangular deck the area of the deck should be 250 ft2 you want the length of the deck to be 5 feet longer than twice its width what should the dimensions of the deck be​

Answers

Answer:

500 feet brainliest please

Step-by-step explanation:

Geometry help please. What is J? What is G?

Answers

Answer:

j = 32

g = 78

Step-by-step explanation:

because they are similar you can use CPCTC corresponding parts of congruent triangles are congruent to determine f = j and h = g

hurry pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Option 2 is the correct one. A and B
I think it’s option 2



1_4/5 + 2_1/10 pls help

Answers

Answer:

3.9

Step-by-step explanation:

please mark this answer as brainliest

Olivia used colored ribbon for a craft project. She used 1/6 of a yard of green, 1/3of a yard of red, and 1/4 of a yard of yellow. Which ribbon is the longest? *

Answers

Answer: Red ribbon.

Step-by-step explanation:

When it comes to fractions, if all the fractions being compared have the same numerator, the fraction with the smallest denominator is the largest.

In this question, all the fractions have a numerator of 1 so the longest one will be the one with the smallest denominator which is 1/3. The red ribbon is the longest.

Another way is to convert them to percentages:

1/6 * 100% = 16.7%

1/3 * 100% = 33.3%

1/4 * 100% = 25%

Red ribbon is again the largest.

Examine the quadratic equation 9x^2+12x +4= 0.
A: What is the discriminant of the quadratic equation?
B: Based on the discriminant, how many roots does the equation have?
C: State whether the root(s) are real or complex.

Answers

Answer:

See answers and explanations

Step-by-step explanation:

A) Discriminant = b² - 4ac = (12)² - 4(9)(4) = 144 - 144 = 0

B) Since the discriminant is 0, this means the equation only has one root.

C) The root is real in this case since the discriminant is not negative. Otherwise, we would have two imaginary roots if it were (remember that complex roots come in pairs)

Debbie borrows $45, and then pays $5 back each week. She currently owes $20. What will the variable stand for?

Answers

Answer:

The variable would stand for the number of weeks that she has left to pay.

Answer: 12

Step-by-step explanation:

Write 10x² + 3x -2=-1 in the form a(x+h)²+k clearly stating 

the turning point or vertex.

Y intercept 

The roots of the equation ​

Answers

Answer:

Below in bold.

Step-by-step explanation:

10x² + 3x -2 = -1

10x^2 + 3x  - 1 = 0            Taking 10 out from the first 2 terms:-

10(x^2 + 0.3) - 1 = 0           Completing the square:

10[(x + 0.15)^2 - 0.15^2] - 1 = 0

10[(x + 0.15)^2 - 0.0225] - 1 = 0

10(x + 0.15)^2 - 0.225 - 1 = 0

10(x + 0.15)^2 - 1.225 = 0  is vertex form.

The vertex (turning point is at (-0.15, -1.225).

y- intercept is at the point where x = 0,

- that is at y = 10(0.15)^2 - 1.225 = -1

So at (0, -1).

Solving for x:

10(x + 0.15)^2 - 1.225 = 0

(x + 0.15)^2 = 0.1225

x + 0.15 = +/- sqrt 0.1225

x = -0.15 +/- sqrt 0.1225

The roots are  -0.5, 0.2

What is the area of the figure?
A. 48
B. 84
C. 66
D. 72

Answers

Answer:

D

Step-by-step explanation:

5 x 8 = 40

2 x 2 = 4

4 x 7 = 28

40 + 4 + 28 = 72

D.72 hope this helps

A plane travels a distance of 21,000 kn in a time of 3.2 hours what is its average speed rounded to the nearest whole number

Answers

Answer:

6563kmph

Step-by-step explanation:

take 21,000 divided by 3.2 hours to get the speed

21,000/3.2 = 6562.5

It says to round 6562.5 to the nearest whole number so its 6563

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