Answers
=====================================================
Explanation:
We'll apply the arc length formula
L = theta*r
Theta is the central angle and r is the radius. This formula only works when the angle is in radian mode. In this case, theta = 4/3 radians.
Arc length AB is part of a circle that has radius r = 8, so,
L = theta*r
L = (4/3)*8
L = 32/3
That represents the length of arc AB. This length is in cm.
-----------------------
Let x be the length of segment BD. This is also the length of AC as well due to rotational symmetry.
Arc CD is part of the larger circle that has radius r = 8+x
L = theta*r
L = (4/3)(8+x)
-----------------------
We found the following lengths so far
arc AB = 32/3segment BD = xarc CD = (4/3)(8+x)segment AC = xThese four pieces form the sides of the blue region. Therefore, they form the perimeter of the blue region. Add up these four sides and set the sum equal to the given perimeter 48. Then solve for x.
(arcAB)+(segmentBD)+(arcCD)+(segment AC) = perimeter of blue region
(32/3) + (x) + (4/3)(8+x) + (x) = 48
32/3 + x + (4/3)*8+(4/3)*x + x = 48
32/3 + 2x + 32/3+(4/3)*x = 48
64/3 + 2x +(4/3)*x = 48
64/3 + 6x/3 +(4/3)*x = 48
64/3 + (10/3)*x = 48
(10/3)*x = 48-64/3
(10/3)*x = 144/3-64/3
(10/3)*x = 80/3
10x = 80
x = 80/10
x = 8
-----------------------
Since x = 8, we know that AC and BD are each 8 cm long.
This means that the larger circle has radius 8+8 = 16 cm
Now we'll apply the sector area formula. You can think of a sector as a pie slice or pizza slice. The formula shown below only works if theta is in radian mode.
Let's find the area of sector AOB. This is the smaller pie slice.
A = area of sector
A = (1/2)*theta*r^2
A = (1/2)*(4/3)*8^2
A = (1/2)*(4/3)*64
A = (1*4*64)/(2*3)
A = (2*64)/3
A = 128/3
Sector AOB is 128/3 square cm. Let's make m = 128/3 so we can use it later.
Now let's find the area of sector COD. We use the same theta value, but the radius is now 16 cm.
A = (1/2)*theta*r^2
A = (1/2)*(4/3)*16^2
A = (2/3)*256
A = 512/3
The area of sector COD is 512/3 square cm. Let n = 512/3.
-----------------------
The last thing to do is subtract the values of m and n to get the area we want.
blue area = (area of sector COD) - (area of sector AOB)
blue area = n - m
blue area = 512/3 - 128/3
blue area = (512-128)/3
blue area = 384/3
blue area = 128 square cm
Related Questions
Calculate the slope (12,5) (17,5)
Answers
Answer:
The slope is zero
Step-by-step explanation:
If the second number is the same (In this case it is) it is Impossible for there to be a slope so.. Slope = 0
Answer:
0
Step-by-step explanations:
y₂-y₁/x₂-x₁
[tex]\frac{5-5}{17-12} =\frac{5}{0} =0[/tex]
What is the true solution to 2 In eln5x = 2 In 15?
O X=0
O X=3
O X=9
O X= 15
Answers
9514 1404 393
Answer:
x = 3
Step-by-step explanation:
Maybe you want the solution ...
[tex]2\ln{(e)}\cdot\ln{(5x)}=2\cdot\ln{(15)}\\\\2\cdot1\cdot\ln{(5x)}=2\cdot\ln{(15)}\\\\5x=15 \qquad\text{divide by 2, take antilog}\\\\x=3 \qquad\text{divide by 5}[/tex]
Divide 8/9 by 1/4" Your answer
Answers
The US consumers in average of 5.15 million metric tons of banana per year. There are 319 million people in the US and there are 1000 kg in one metric ton. Round answer except last one to three significant digits. How many kilogram of bananas are consumed per person per year.
Answers
Answer:
bananas consumed per person per year are 4.42 × [tex]10^{-2}[/tex]
Step-by-step explanation:
given data
consumers in average = 5.15 million metric tons
population = 319 million
solution
we get here bananas are consumed per person per year that is express as
bananas consumed = total banana consumed ÷ ( total population × 365 ) .................1
put here value and we get
bananas consumed = [tex]\frac{5.15 \times 1000}{319 \times 365}[/tex]
so, bananas consumed per person per year are 0.044231 kg = 4.42 × [tex]10^{-2}[/tex]
× _____ ÷ =
ALGEBRAALGEBRAALGEBRAALGEBRAALGEBRA
Answers
Answer:
ALGEBRA indeed
Step-by-step explanation:
lololol
Select the equation of a straight line that is perpendicular to the line y = 3x-2
Answers
y = 3x - 2
is -3.
The slope of the perpendicular line will be m, and m needs to satisfy the equation
3 * m = -1
Hence m = -1/3.
Our perpendicular line is thus
y = (-1/3)x + b
for some constant b.
We are told that the perpendicular line goes through the point (-9,5). If so, then the following must hold:
5 = (-1/3)(-9) + b
= 3 + b
b = 2
Ans: y = (-1/3)x + 2
helppppppppppppp plzzzzzzzzzzzzzzzzz
Answers
Answer:
33.25
Step-by-step explanation:
Answer:
33.25
Step-by-step explanation:
this is probably the answer
You want to put a 3 inch thick layer of topsoil for a new 13 ft by 31 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order
Answers
Answer:
30 cubic yards
Step-by-step explanation:
You will multiply 13 by two because there is two sides of 13ft
13 x 2 = 26
Then do the same thing with 31, so 31 multiply by 2
31 x 2 = 62
After that add 62 and 26
62+26=88
Then divide 88 by 3
88÷3=29.9
after that you will round 29.9 by the nearest 10 which is 30
The list shows 8 of Takisha's math quiz scores.
70, 81, 82, 82, 82, 89, 94, 100
What is the mean absolute deviation of her quiz scores?
Answers
Answer: 85
Step-by-step explanation:
Add all the numbers together than
divide by 8
♡ The Question/Task ♡
-What is the mean absolute deviation of her quiz scores?
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Answer ♡
-The mean absolute deviation of her quiz scores is 7!
I apologize in advance if this is incorrect! ♡
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Explanation/Step-By-Step ♡
-No Explanation/Step-By-Step Provided!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ Tips ♡
-No Tips Provided!
At an electronics store, a smart phone is on sale for 35% off the original price of $679. If you use the store credit card, you can receive an additional 15% off the sale price. What is the final price of the smart phone if you use the store credit card? Round to the nearest cent.
Answers
Answer:
%375.15
Step-by-step explanation:
Hope this helps u out
Answer:
The final price of the smartphone is $375.15
Step-by-step explanation:
Percentages
The original price of a smartphone at an electronics store is $679. The store is on sale for 35% off that price.
Thus the sale price can be calculated by subtracting the discount from the original price.
Discount= 35% of $679 = 35/100 * $679 = $237.65
Sale price=$679 - $237.65 = $441.35
If you use the store credit card, there is an additional discount of 15% off the sale price. The new discount is:
New discount = 15% of $441.35 = $66.20
And the final price is: $441.35 - $66.20 = $375.15
The final price of the smartphone is $375.15
One leg of a right triangle is 12, and the hypotenuse is 20.
The length of the other leg is ___
Answers
Answer:
i believe it is 16.
hope this helped :)
Answer:
The answer is 16.
Step-by-step explanation:
To solve you need to use Pythagorean Theorem. a^2 + b^2 = c^2 .
12^2 + b^2 = 20^2
144 + b^2 = 400
400 - 144 = 256
b^2 = 256
Next we need to take away the power of 2.
√256 = √b^2
√16 x 16 = √b * b
b = 16
Dave Drove 15 Miles For 20 Minutes
Raul Drove 15 Miles For 15 minutes
Sinead Drove 20 Miles For 30 Minutes
Whose Speed Was The Slowest.
Answers
Answer:
Sinead
Step-by-step explanation:
Sinead drove 20 miles for 30 minutes, it means that they were the slowest since wherever they were going they got there last.
hope this helps!!!
Suzie needs to borrow $6,000 from a local bank. What is the monthly payment for a one year, 11.25% loan?
Answers
Given :
Suzie needs to borrow $6,000 from a local bank.
Interest rate, r = 11.25%.
To Find :
The monthly payment of Suzie for one year to pay of the loan.
Solution :
Total amount to return is :
[tex]A = 6000 + \dfrac{6000\times 11.25}{100}\\\\A =\$6675[/tex]
Let, monthly payment is x.
So,
[tex]x =\$ \dfrac{6675}{12}\\\\x = \$556.25[/tex]
Therefore, the monthly payment for loan is $556.25 .
please answer i will mark brainliest!!
Answers
Answer:
16 and 3
Step-by-step explanation:
A prime number has only 2 factors, 1 and itself
2, 5 and 7 meet this criteria and are prime, however
factors of 16 are 1, 2, 4, 8, 16
16 does not meet the criteria and is not prime
--------------------------------------------------------
The factors of 18 are 1, 2, 3, 6, 9, 18
The only one of these factors which is prime is 3
i’ll mark you brainliest
Answers
find a formula for the nth term in this arithmetic sequence. a1=0, a2=0.5, a3=1, a4=1.5
Answers
Answer:
nth term is;
0.5n-0.5
Step-by-step explanation:
As we can see, the first term is 0
The common difference is 0.5-0= 1-0.5 = 1.5-1 = 0.5
Formula for nth term of an arithmetic sequence is;
a + (n-1)d
So we have
0 + (n-1) 0.5
= 0.5n-0.5
5-4c-2-9c
evaluate the expression
Answers
Answer:
-13c + 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
5 - 4c - 2 - 9c
Step 2: Simplify
Combine like terms (c): -13c + 5 - 2Combine like terms (Z): -13c + 3Answer:
-13c + 3
Step-by-step explanation:
if three quarters of the pizza provided 12 pieces to the table how many pieces were in the pizza when it was ful
Answers
Answer:
16
Step-by-step explanation:
 which type of lines is shown below?
Answers
Answer:
Perpendicular
Step-by-step explanation:
Answer:
Perpendicular
Step-by-step explanation:
The lines shown are intersecting meaning they cannot be parallel as parallel lines never intersect. Moreover, the square in the corner means these lines form a right angle. Lines that intersect and form right angles are perpendicular.
Which of the following values for x is true for 4x > 10?
A.x = 34
B.x = 2
C.x = 2.5
D.x = 3
Answers
Answer:
A and D
Step-by-step explanation:
34 * 4 = 136 136 > 10
3 * 4 = 12 12 > 10
Pls help!!! 30 points
Answers
Answer:
2.4x-4.4
Step-by-step explanation:
0.3(4x-8)-0.5(-2.4x+4)
1.2x-2.4+1.2x-2
2.4x-4.4
Answer:
D. 2.4x -4.4
Step-by-step explanation:
0.3(4x-8)-0.5(-2.4x+4)
1.2x-2.4-0.5(-2.4x+4)
1.2x-2.4+1.2x-2
2.4x-4.4
How far up a house will an 18 foot ladder reach if the angle the ladder makes with the ground is 60˚?
(Round to the nearest tenth)
Answers
Answer:
15.588 ft
Step-by-step explanation:
2x + 3y = 16
4x - 3y =-4
Answers
If the Cable Company offers cable for $110 a month but gives a 10%
discount for new customers. Find the cost for the new customers. (SHOW
ALL WORK)
Answers
$110-$11= $99
New costumers would pay $99
Find x - y subtracted from 0.
Answers
Answer:
0-(x-y)
Step-by-step explanation:
Answer:
Step-by-step explanation:
simplify 0-(x-y).
0-(x-y)
=-(x-y)
=-x+y
You have to treat the negative sign in front of (x-y) as a -1 and distribute it to x and -y.
help pleaseeeeeeeeeeeeeeeeeeeee
Answers
Answer:
2/11 will be your answer :)
Step-by-step explanation:
Hope this helps ✨
Answer:
2/11
Step-by-step explanation:
They definitley aren't equal, and 2/11 is closer to 0 than 4/5, so therefore it is less.
(hope this helps!)
i need help someone help pls and thx
Answers
Answer:
Two
Step-by-step explanation:
hope this helps tell me if I'm wrong though
Product of (4x+5)(2x+1)
Answers
Answer:
25 maybe
Step-by-step explanation:
please help, would be greatful :)
Answers
Answer:
16.9
Step-by-step explanation:
Hope u get it correct
a. 4.0
b. 16.0
c. 12.5
d. 11.7
Answers
Answer:
D
Step-by-step explanation:
to find the answer you do the square root of (x2-x1)^2+(y2-y1)^2.
So you just plug it in and get the equation of
the square root of (-4-2)^2+(-8-2)^2 which equals 11.66190379
then you round to the tenths which then comes out to 11.7
Answer:
D. 11.7
Step-by-step explanation:
= √(−4−2)^2 + (−8−2)^2
= √(-6)^2 + (−10)^2
= √36 + 100
= √136
= 11.66 which rounds to 11.7
