CRITICAL THINKING Find the area between the three congruent tangent circles. The radius of each circle is 6 inches. Round your answer to the nearest hundredth. Three congruent circles touch each other. The centers are marked as points A, B, and C. Equilateral triangle A B C is formed and the region inside triangle, but not in a circle, is shaded. The area is about a square inches.

Answers

Answer 1

The area of the shaded region which is inside the triangle but not in a circle is 22.43 sq. inches.

A triangle is a geometrical figure with 3 angles, 3 edges, and 3 vertices. It is one of the most basic geometrical figures.

Given that

Vertices A, B, and C of a triangle, ΔABC are centers of three circles touching each other.

As the triangle, ΔABC is an equilateral triangle,

therefore,

∠A = ∠B = ∠C = 60°. (Since the sum of all angles is 180° and the angles of an equilateral triangle are equal.)

To obtain the area of the shady region, it is needed to obtain the areas of the triangle and of the quadrants of each circle.

Area of ΔABC = [tex]\frac{\sqrt{3}}{4} a^2[/tex], where a is the length of the equal sides.

Here, a = 2 × radius of the circles

So, a = 2 × 6 = 12 inches.

Now,

Area of ΔABC = [tex]\frac{\sqrt{3}}{4} 12^2[/tex]

                        [tex]=\frac{\sqrt{3}}{4} \times144\\=\sqrt3 \times 36\\=36\sqrt3\ sq.\ inches\\= 62.35\ sq.\ inches[/tex]

Area of a quadrant of a circle = [tex]\frac{1}{4}\pi r^2[/tex]

The sum of areas of quadrants of three circles = [tex]3\times\frac{1}{4}\pi r^2[/tex]

                                                                              [tex]= 3\times\frac{1}{4}\times3.14\times 6^2\\= 3\times\frac{1}{4}\times3.14\times 36\\= 84.78\ sq.\ inches[/tex]

Area of the shaded region = The sum of areas of quadrants of three circles - Area of ΔABC

Area of the shaded region = 84.78 - 62.35

                                             = 22.43 sq. inches.

Thus the area of the shaded region is 22.43 sq. inches.

Learn more about Triangles here:

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Related Questions

What is the y-intercept

Answers

Answer:

The y-intercept is (0,0) or the origin, it's basically the point that intercepts the line of y.

Answer:

0

Step-by-step explanation:

I think 0...

...

...

...

Hope this helps <3

hehe it hit 0 and it is on y so uhh yeah...

Write in index form
9 x 9 x 4 x 4 x 4 x 9 x 9 x 9

Answers

Answer:

9^5×4^3

Step-by-step explanation:

9 has to multiply itself 5 times and 4 has to multiply itself 3 times

Answer:

[tex]9^{5}[/tex] × 4³

Step-by-step explanation:

9 is multiplied by itself 5 times and 4 is multiplied by itself 3 times.

This is expressed in index form as

[tex]9^{5}[/tex] × 4³

which ordered pair represents a point on the line y=2x+1

Answers

Answer:

(0,1) , (1,3) , (2,5) , (3,7) , (4,9) , (5,11) are examples of  points on the line

y = 2x + 1.

Solve for x HURRY PLEASE

Answers

Answer:

x = 4

Step-by-step explanation:

Intersecting chords theorem:

NQ*QL = KQ*QM

Substitute and solve for x:

2(3x) = 3(8)6x = 24x = 24/6x = 4

Answer:

Given:

KQ:3

NQ:2

MQ:8

QL:3x

According to theorem of intersecting chords

NQ×QL=QM×QK

now=

Substituting value

2×3x=8×3

x=24/6

x=4 is a required answer.

I NEED HELP FAST
PLEASEEEEEEE

Answers

Answer: D

Step-by-step explanation:

Answer:

Step-by-step explanation:

D none of them hope this helps

12x-2y=-10
y=6x+ 5
Is it a solution?
Х
?
(x, y)
Yes
No
(-4, -19)
(0,5)
Bolololo
(-1,8)
Olo
(2, -3)

Answers

Answer:

The first 2 are definitetaletly right

Step-by-step explanation:

First off all you were not that clear.

Just plug them in

A Circle has diameter 18cm. Work out the circumference of the circle.​

Answers

Step-by-step explanation:

diameter=18

radius=18/2=9

circumference=2πr

,2×22/7×956.57cm

stay safe healthy and happy.

Answer:

56.5486677646

Step-by-step explanation:

Circumference is pi Times diameter

Please help me and show working. I have a test very soon.

Answers

Answer:

c = 3

Step-by-step explanation:

Given

[tex]\frac{2}{c-2}[/tex] - [tex]\frac{3}{c+2}[/tex] = [tex]\frac{7}{c^2-4}[/tex] ← factor the difference of squares

[tex]\frac{2}{c-2}[/tex] - [tex]\frac{3}{c+2}[/tex] = [tex]\frac{7}{(c-2)(c+2)}[/tex]

Multiply through by (c - 2)(c + 2) to clear the fractions

2(c + 2) - 3(c - 2) = 7 ← distribute and simplify left side

2c + 4 - 3c + 6 = 7

- c + 10 = 7 ( subtract 10 from both sides )

- c = - 3 ( multiply both sides by - 1 )

c = 3

A number cube is rolled. What is the probability that the result is a number greater than 4. the numbers on the dice are 4,5, and 2. show your work.

Answers

Let A : getting an odd number (i.e. 1,3 or 5), B: getting a number greater than 4 (i.e 5 or 6) . So, the required probability is  P(A∪B)=P(A)+P(B)−P(A∩B)=36+26−16=46=23

Re-write the quadratic function below in Standard Form
y = 3(x - 5)(x - 2)

Answers

Answer:

3x² - 21x + 30

Step-by-step explanation:

y = 3(x - 5)(x - 2) ← expand factors using FOIL

  = 3(x² - 7x + 10) ← distribute parenthesis by 3

y = 3x² - 21x + 30 ← in standard form

What is the median number of TVs in Mrs. Jamison's Class?

Answers

Answer:

its the 4 on the number line under her name

ok i retook it anyways help

Answers

Positive numbers are the cups that are received. While negative numbers are the cups being used for coffe

Graph points (-4,-1) (4, 3). Write the equation of the line that passes through the points in slope-intercept form.

Hurry please! I need it by the next 15 minutes ♡︎☺︎︎.

Answers

Answer: y=1/2x+1
I upload a picture on solving it. Hope this helps!

Can someone help me calculate the ✨surface area✨ for this prism ?
I'm not even sure if I understand the formula "( ​

Answers

Answer:

216 cm^2.

Step-by-step explanation:

Surface area = 2 * area of triangular sides + area of 3 rectangles

= 2 * 1/2 * 6 * 8 + 8*7 + 6 * 7 + 10*7

= 48 + 56 + 42 + 70

= 216.

Answer:

216cm^2

Step-by-step explanation:

The surface area is equal to the sum of areas of the walls.

We've got 2 triangular walls with area 6*8/2, for 6*8 = 48cm^2 total

We've got a wall with 7x10 = 70cm^2

We've got a wall with 6x7 = 42cm^2

And the last wall is 8x7 = 56cm^2

So total surface area is: 48 + 70 + 42 + 56 = 216

algebra 1 help!!!!!!!!!

Answers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of expo functions.

f(x) = -8(2)^x - 12 ,

for f(0) ,here substitute x = 0

so we get as ,

==> f(0) = -8(2)^0 -12

==> f(0) = -8-12

==> f(0) = -20

hence, f(0) = -20

Answer:

Step-by-step explanation:

If it went from f(x) ⟹ f(0), that means that x=0.

So, you would plug in 0 for x in f(x)=-8(2)^x-12.

After plugging in the value of x, x=0, into the equation, you should have

f(0)=8(2)^0-12

Now, we are solving for f(0) (or f(x)).

You would use PEMDAS to solve this:

P-PARENTHESIS

E-EXPONENT

M-MULTIPLICATION

D-DIVISION

A-ADDITION

S-SUBTRACTION

There are no parenthesis

there are exponents,

(2)^0 and that =1

so we have f(0)=8(1)-12

there is multiplication, 8(1) which =8

so now we have f(0)=8-12

there is no division

there is subtraction

8-12, which equals -4

f(0)=-4

Dennis has a credit card with an APR of 13.09% and a billing cycle of 30 days. The following table shows his transactions with that credit card in the month of November.

If the finance charge for November is $4.93, which method of calculating the finance charge does Dennis’s credit card company use?

Answers

Answer:

previous questions have been asked using this same question

Step-by-step explanation:

A.) adjusted balance method

GIVING BRAINIEST IF CORRECT!!!!!
Out of 300 diners, 60 ordered salads. What percent of diners ordered a salad?
A. 2%
B. 20%
C. 5%
D. 15%

Answers

Answer:

20%

Step-by-step explanation:

300 divide by 60. the answer is 20 percent

can someone help me plzz !! i need to know the answer!! its an Algebra 1 question.​

Answers

Answer: C

Step-by-step explanation:

Mistook the last one for different type of math apologies...

I just answered in the comments.

The correct answer is option C.

How are the shapes alike?
1) Each shape has 6 edges.
Each shape has 8 faces.
Each shape has 12 edges.
Each shape has 7 faces.

Answers

Answer:

B

Step-by-step explanation: Count the egdes

HELP DUE IN 15 MINS!

The center of a circle is (3, 2) and a point on the circle is (5, -2). Find the radius and write the equation for the circle.

Answers

Answer:

r = [tex]2\sqrt{5}[/tex]

[tex](x - 3)^{2} + ( y - 2)^{2} = 20[/tex]

Is this a live test question or a homework question?

Step-by-step explanation:

the radius is the distance between (3, 2) and (5, -2)

[tex]r^{2}[/tex] = [tex]{(3 - 5)^{2} + (2 + 2)^{2} }[/tex]

    =  [tex](-2)^{2} + 4^{2}[/tex]

    =  4 + 16 = 20

r = [tex]\sqrt{20 } = 2\sqrt{5}[/tex]

Equation of circle:   [tex](x - 3)^{2} + ( y - 2)^{2} = 20[/tex]

Answer:

Radius: [tex]2\sqrt{5}[/tex]

Equation of circle: [tex](x-3)^2+(y-2)^2=20[/tex]

Step-by-step explanation:

The radius of a circle is equal to the distance between the center of the circle and any point on the circle. Therefore, we have:

[tex]r=\sqrt{(5-3)^2+(2-(-2))^2},\\r=\sqrt{2^2+4^2},\\r=\sqrt{20}=\boxed{2\sqrt{5}}[/tex]

The equation of a circle with radius [tex]r[/tex] and center [tex](h, k)[/tex] is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex].

What we know:

radius of [tex]2\sqrt{5}[/tex] center at [tex](3, 2)[/tex]

Substituting known values, we get:

[tex](x-3)^2+(y-3)^2=(2\sqrt{5})^2,\\\boxed{(x-3)^2+(y-2)^2=20}[/tex]

A cable that is 45 feet long is attached to the top of a vertical pole. The cable is anchored to the ground 36 feet from the base of the pole . How tall is the pole? Round your answer to the nearest hundredth .

Answers

Answer:

27

Step-by-step explanation:

The stem-and-leaf plot below gives the test scores for the 18 students in Mr. Uzun's English class. Use the plot to answer the questions that follow.
Test score

Answers

(A) 4 students

There are 4 values in the 90s

(B) 69

9 was the highest value in the 60s

(C) 53

3 was the lowest value in the lowest set

Help please!!! Quick!

Answers

B is the correct answer i am positive

Answer:

Choice B

Step-by-step explanation:

Choice A equals 20x=20 which is one solution.

Choice B equals 0x=0 which is infinitely many solutions.

Choice C equals 0x=20 which is one solution.

Choice D equals 20x=0 which is one solution.

The first 4 terms of the sequence defined by the rule f(n) = 4n^2 + 4

Answers

Answer:

[tex]f(n) = 4n^2 + 4[/tex]

f(1) = 4 x 1 + 4 = 4 + 4 = 8

f(2) = 4 x 4 + 4 = 16 + 4 = 20

f(3) = 4 x 9 + 4 = 36 + 4 =40

f(4) = 4 x 16 + 4 = 64 + 4 = 68

25 POINTS AND BRAINLIEST WHOEVER ANSWERS At a glass vase store, 88 out of the last 20 vases shipped were chipped.
​ What is the experimental probability that the next vase shipped will be chipped? ANSWER AS PERCENTAGE

Answers

Answer:

20/88=.227

Step-by-step explanation:

The experimental probability of a situation can be found by dividing the total amount of times outcome a happened by the number of times outcome b happened. A good example of this i flipping a coin.

Lea wrote a number riddle. Her clues were: The value of the 9 is ten times the value of the 9 in 329,513. The value of the 2 is one-tenth the value of the 2 in 7,562. The value of the 6 is one-tenth the value of the 6 in 4.68. Which number is an answer to Lea's riddle?

Answers

Answer:

iohrrojberu0fb0u35gbu5bi4i

Step-by-step explanation:

,eknefinfkirnr

What is the slope of the function y = 6x+4

Answers

the slope of the the function is 6

54 is 32% of what number? Round to the nearest hundredth if necessary.

Answers

Answer:

The answer 168.75 without rounding and rounding its also 168.75

EASY MATH PLEASE HELP! NO LINKS! NEED COMPLETE EXPLAINATION WITH ANSWER!!

Answers

Answer: a.) 18 x 8

Step-by-step explanation: if you break down the equation 6^3= 18 and 4^2=8 then take 18x8 simple as that

The product of two rational number is 7. If one of the number
is 12, Find the other national number

Answers

Answer:

7/12 OR 0.58 (2.d.p)

Step-by-step explanation:

Product means that the two rational numbers are being multiplied to get 7.

The question also tells us that one of them is 12. Therefore we can write an equation to express this information where we represent the unknown rational number using the letter 'r':

r x 12 = 7

Rearrange to find r:

r x 12 / 12 = 7 /12

r = 7/12 = 0.5833....

= 0.58 (2.d.p)

Hope this helped!

Answer:

[tex]y = \frac{7}{12}[/tex]

Step-by-step explanation:

x × y = 7

We are given x = 12.

12 × y = 7

Rearrange.

y × 12 = 7

Divide each side by 12.

y × 12 ÷ 12 = 7 ÷ 12

Simplify.

[tex]y = \frac{7}{12}[/tex]

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