Answers
See below for the proof that the areas of the lune and the isosceles triangle are equal
How to prove the areas?The area of the isosceles triangle is:
[tex]A_1 = \frac 12r^2\sin(\theta)[/tex]
Where r represents the radius.
From the figure, we have:
[tex]\theta = 90[/tex]
So, the equation becomes
[tex]A_1 = \frac 12r^2\sin(90)[/tex]
Evaluate
[tex]A_1 = \frac 12r^2[/tex]
Next, we calculate the length (L) of the chord as follows:
[tex]\sin(45) = \frac{\frac 12L}{r}[/tex]
Multiply both sides by r
[tex]r\sin(45) = \frac 12L[/tex]
Multiply by 2
[tex]L = 2r\sin(45)[/tex]
This gives
[tex]L = 2r\times \frac{\sqrt 2}{2}[/tex]
[tex]L = r\sqrt 2[/tex]
The area of the semicircle is then calculated as:
[tex]A_2 = \frac 12 \pi (\frac{L}{2})^2[/tex]
This gives
[tex]A_2 = \frac 12 \pi (\frac{r\sqrt 2}{2})^2[/tex]
Evaluate the square
[tex]A_2 = \frac 12 \pi (\frac{2r^2}{4})[/tex]
Divide
[tex]A_2 = \frac{\pi r^2}{4}[/tex]
Next, calculate the area of the chord using
[tex]A_3 = \frac 12r^2(\theta - \sin(\theta))[/tex]
Recall that:
[tex]\theta = 90[/tex]
Convert to radians
[tex]\theta = \frac{\pi}{2}[/tex]
So, we have:
[tex]A_3 = \frac 12r^2(\frac{\pi}{2} - \sin(\frac{\pi}{2}))[/tex]
This gives
[tex]A_3 = \frac 12r^2(\frac{\pi}{2} - 1)[/tex]
The area of the lune is then calculated as:
[tex]A = A_2 - A_3[/tex]
This gives
[tex]A = \frac{\pi r^2}{4} - \frac 12r^2(\frac{\pi}{2} - 1)[/tex]
Expand
[tex]A = \frac{\pi r^2}{4} - \frac{\pi r^2}{4} + \frac 12r^2[/tex]
Evaluate the difference
[tex]A = \frac 12r^2[/tex]
Recall that the area of the isosceles triangle is
[tex]A_1 = \frac 12r^2[/tex]
By comparison, we have:
[tex]A = A_1 = \frac 12r^2[/tex]
This means that the areas of the lune and the isosceles triangle are equal
Read more about areas at:
https://brainly.com/question/27683633
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Related Questions
Chen rode his skateboard 3 1/4 miles in 1/3 of an hour. What was his average speed in miles per hour
Answers
Answer:
9.75 mph
Step-by-step explanation:
3 1/4 ÷ 1/3 = 9 3/4
How many solutions does the system have?
20x−5y=5
4x−y=1
Answers
Answer:
Infinite solutions.
Step-by-step explanation:
Just plug your equation into desmos graphing calculator and it will graph it for you. If it is infinite the two lines will lay on top of one another. If there is only one solution it will be where the two lines intersect. If there are no solutions the two lines will be parallel.
CAN YALL HELP PLSSSSSSSS!!! 8TH GRADE MATH!!!
Answers
where the picture???????????????
help, look at picture
Answers
Answer:
y= 5/3 which is 1 2/3
Step-by-step explanation:
trust me
y=5/3
.......................
Find the standard deviation of the data set below. Round to the nearest tenth,
6, 5, 2, 5,8
Answers
Answer:
The standard deviation = 1.9
Step-by-step explanation:
standard deviation, ρ = sqrt ( [tex]\frac{sum(x_{i} - u)^{2} }{N}[/tex])
Where u is the mean of the data, [tex]x_{i}[/tex] each given value, and N is the number of data given.
Mean, u = [tex]\frac{6+5+2+5+8}{5}[/tex]
= 5.2
So that;
[tex](6-5.2)^{2}[/tex] = [tex](0.8)^{2}[/tex] = 0.64
[tex](5-5.2)^{2}[/tex] = [tex](-0.2)^{2}[/tex] = 0.04
[tex](2-5.2)^{2}[/tex] = [tex](-3.2)^{2}[/tex] = 10.24
[tex](5-5.2)^{2}[/tex] = [tex](-0.2)^{2}[/tex] = 0.04
[tex](8-5.2)^{2}[/tex] = [tex](2.8)^{2}[/tex] = 7.84
Sum = 18.8
So that;
[tex]\sqrt{\frac{18.8}{5} }[/tex] = [tex]\sqrt{3.76}[/tex]
= 1.9391
= 1.9
The standard deviation of the given data is 1.9
Your cousin has $90 to spend on video games and movies. The equation 30x+15y=90 represents this situation, where x is the number of video games purchased and y is the number of movies purchased. Graph the equation.
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The intercepts can be found by setting one variable to zero and solving for the other.
y-intercept: 30·0 +15y = 90 ⇒ y = 90/15 = 6, point (0, 6)
x-intercept: 30x +15·0 = 90 ⇒ x = 90/30 = 3, point (3, 0)
The graph is easily made by plotting the intercepts and drawing a line through them.
__
I like to let a graphing calculator do the graphing.
HELP THIS IS DUE TODAY
I'm stuck on this.
Answers
Step-by-step explanation:
couldn't find the answer but try to get photo math on your phone it would surely help
Answer:
x = 0, y = -4
x = 1, y = -1
x = 2, y = 2
x = 3, y = 5
Step-by-step explanation:
just plug in the x value to get the y smh
if u get it wrong its not on me
In 2030, the Census Bureau estimates that 19 of the 50 states will have a Spanish-speaking majority. What percent of the states will have a Spanish-speaking majority?
Answers
19/50 times 2/2 is 38/100 or 38%
You are analyzing your bills in MERALCO for the consecutive months. Using your bill
at home express the amount per kwh (A) as a function of kilowatt per hour (k) consumed
for the last two consecutive months. Then create austerity plan for the next month.
(austerity measures taken to reduce spending)
Austerity
Plan
Bill for the last two consecutive months:
Create a rational inequality showing the relationship between the bill
in the last consecutive months:
List down the austerity measures to be undertaken to reduce the
electricity consumption:
Answers
Answer:
Php1000
Php2000
₱1000< ₱2000
*reduce using of appliances that's not important
*water conservation
*turning off electric equipment that is not often used like electric fan or light
Step-by-step explanation:
PLEASE HELP ME ON THIS PROBLEM
Answers
Answer:
DB!
Step-by-step explanation:
a) [tex](x+50)^{2} = x^{2} +100x+2500[/tex]
b) Plug the value in! [tex](15+50)^{2} = 65^{2} = 4225[/tex]
Hope I helped! Check out my profile for more answers!
Solve for x please help!!
Answers
14x-15=41
14x=56
x=4
Answer:
x = 4
Step-by-step explanation:
(14x - 15)° + 139° = 180°
14x - 15 + 139 = 180
14x + 124 = 180
14x = 56
x = 4
is 10\3 a improper fraction? Explain
Answers
Answer: Yes
Step-by-step explanation:
An improper fraction is any fraction that has a numerator that is greater than the denominator
A fish is swimming at a constant rate toward the ocean floor. The equation
y = -7x - 3 can be used to represent this situation, where y is the depth of the fish in meters below sea level and x is the number of seconds the fish has been swimming.
Which statement best describes the depth of the fish, given this equation?
Answers
Answer: Y = 21
Step-by-step explanation:
3) Asanji's school is selling tickets to the annual dance competition. On the first day of ticket sales the
school sold 1 senior citizen ticket and 2 child tickets for a total of $32. The school took in $208 on the
second day by selling 12 senior citizen tickets and 8 child tickets.
This situation is modeled by the system below where x-a senior ticket and ya child ticket
x + 2y = 32
12x + 8y = 208
Find the price of a senior citizenticket and the price of a child ticket.
A) senior citizen ticket: $12, child ticket: $4
B) senior citizen ticket: $6, child ticket: $16
C) senior citizen ticket 10$, child ticket 11$
D) senior citizen ticket: $9, child ticket: $6
Answers
Answer:
C) senior citizen ticket 10$, child ticket 11$
Step-by-step explanation:
Simplify: |72 - 9 • 7| - 8|16 - 2|
Answers
Answer:
answer is -103
The first triangle is dilated to form the second triangle.
Select True or False for each statement.
Statement True False
The scale factor is 0.25.
True – The scale factor is 0.25.
False – The scale factor is 0.25.
The scale factor is 4.
True – The scale factor is 4.
False – The scale factor is 4.
A right triangle with a hypotenuse of 4.4. An arrow points to a smaller right triangle with a hypotenuse of 1.1
Answers
Answer:
Both true
Lelelelellele
The solution to 6x = 48 is x = ___.
A. 5
B. 6
C. 7
D. 8
Answers
Multiply something to 6 that makes 48! So 6•8 would be 48!
what are all the equivalent ratios for 48:32
Answers
Step-by-step explanation:
There are infinitely many ratios for 48:32, so I'll just list a few:
24:16
6:4
3:2
9:6
480:320
240:160
60:40
30:20
90:60
PLSSSSSSS HELP ME CORRECT ANSWER
Answers
Answer:
8 units
Step-by-step explanation:
The formula for the area of a parallelogram is base * height = area. You have that the height = 5 and the area = 40, so that means base * 5 = 40.
If base * 5 = 40, you know that base = 8. You can also solve this like an equation:
b * 5 = 40
divide both sides by 5
b = 40/5 = 8 units
Answer: 8 units
uwu ur mom i hate flagotgs fr THAT IS A JOKE NO I DONT PLWAASE IMSS EORRY
Write an equation in y intercept form for the line with slope 3/5 and y intercept: -2. Then graph the line.
Please help asap!!
Answers
Answer:
y=3/5x-2
Step-by-step explanation:
A baseball is thrown straight up in the air with an initial velocity of 2 m/s. Draw a picture that shows the path of the ball as it goes up and comes down. Label the initial velocity, the velocity at max. height, and the acceleration of the ball.
Answers
Answer:
e
Step-by-step explanation:
I don't understand this. Please help!!
Answers
Answer:
-2 5/8
Step-by-step explanation:
(3/8)/(1/-7) = (3/8)(-7/1) = -21/8=-2 5/8
Help ME PLEASE!!!!!!!!!!!
Answers
If half of the pizza was cut into thirds, and you ate 1 of the 3 slices left, you would have eaten 1/6 of the leftovers.
Try 1/6.
Explain, as clearly as you can, why 4/5 of 25 is 20.
Answers
⅘×25=20
of means times.
T Identity
Identify the terms,
and
Coeffectants
0.3+0.6ab+0.5b
Answers
Given:
The expression is
[tex]0.3+0.6ab+0.5b[/tex]
To find:
The terms and the coefficients.
Solution:
In an expression, the variables, constants and product of variable and constant separated by positive sign "+" are called terms.
We have,
[tex]0.3+0.6ab+0.5b[/tex]
Here, the terms are 0.3, 0.6ab and 0.5b. The coefficients of variables are 0.6 and 0.5 respectively and 0.3 is a constant.
Fill blank boxes with the right answer.
Mrs. Favre sees that the Chicken Joint is having a sale. A small bucket of chicken usually cost $12.00 but today they are giving 30% off the small bucket.
How much will Mrs. Favre save on one small bucket of chicken? $______
What is the discount cost of one small bucket of chicken? $________
What is the discount cost of 5 small buckets? $______
Answers
Answer:
1. $3.60
2. $8.40
3. $42
Step-by-step explanation:
Hope this helps.
At an apple orchard, customers use a standard-size box when picking apples. The table shows the total weight of the box of apples and the weight of the apples alone.
Question: Which statement is true?
The equation a= 7.5t models the relationship.
If the total weight of the box is 15 lb, then the weight of the apples is 13.5 lb.
If the total weight of the box is 20 lb, then the weight of the apples is 21.5 lb.
To find any value of a, subtract 2.5 from the corresponding value of t
Table:
Total weight of box (lb), t: 7.5
10
12.5
Weight of apples (lb) a: 6
8.5
11
Answers
Answer:
here's the right answer- someone on a different website said the same weird thing as the person before me smh
Step-by-step explanation:
If the total weight of the box is 15 lb, then the weight of the apples is 13.5 lb.
Option (2) is correct.
What is an equation?Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws.
As per the given data:
The table shows the total weight of the box and the weight of the apples.
From the table:
Total weight of the box - weight of apples = weight of box
7.5 - 6 = 1.5 lb
10 - 8.5 = 1.5 lb
12.5 - 11 = 1.5 lb
If the total weight of the box is 15 lb and the weight of the apples is 13.5 lb
15 - 13.5 = 1.5 lb {weight of box}
Which satisfies the data in the table.
Hence, If the total weight of the box is 15 lb, then the weight of the apples is 13.5 lb.
To learn more about equation, click:
brainly.com/question/10413253
#SPJ2
(The given question is incomplete, the complete question is given below)
What is this answer
Answers
Answer:
t = ≥ 0.1
Step-by-step explanation:
Hope that helps!
What is the least common multiple of 8 and 12?
24
48
96
Answers
Answer:
The least common multiple of 8 and 12 is 24
Explanation:
Find and list the multiples each number until the first common multiple is found.
This is the lowest common multiple .
Multiples of 8
8, 16, 24, 32,40
Multiples of 12
12,24, 36,48
Therefore,
LCM of 8 and 12 is 24
Answer: The answer is 24
Step-by-step explanation: One easy way to find least common multiples is to take the large number and multiply it by increasing numbers (1,2,3,etc.) until a number is found that is also divisible by the smaller number.
In this case, we can multiple 12 by increasing numbers until we find a number that is also divisible by 8.
12
⋅
1
=
12
This is not divisible by 8.
12
⋅
2
=
24
This is divisible by 8.
8
⋅
3
=
24
Therefore, the least common multiple is 24.
what is this polygon called and is it a regular polygon or irregular polygon
Answers
Answer:
hexagon because it have 6 sides
Step-by-step explanation:
it is irregular because it sides are not equal
THIS POLYGON IS IRREGULAR BECAUSE THIS IS HEXAGON AND IT IS IRREGULAR
an hexagon is a six sided irregular polygon
What is polygon?
a simple closed curve which does not interest itself made up if only line system is called a polygon
REGULAR POLYGON- polygon whose all side are of equal length and all angles are of equal measure
are called regular polygon
EX - SQUARE
IRREGULAR POLYGON- polygon which are not regular are called a regular polygon quadrilateral and Isosceles triangle is an example