2. According to Archimedes, the area of any circle is equal to the area of a right triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Verify this formula for yourself using the formula for the circumference of a circle.

Answers

Answer 1

Formula  [tex]\text { area }=1 / 2 \times \text { base } \times \text { height }=1 / 2 \times 2 \pi r \times r=\pi r^{2}[/tex]  for the circumference of a circle.

How did Archimedes find the circumference of a circle?

Archimedes stated in his Proposition that the area of a circle is equal to the area of a triangle with a base equal to the circumference and a height equal to the radius: (1/2)(r · 2πr) = πr2. Archimedes arrived at his approximation of the circumference of the circle by increasing the number of sides of the hexagon. Archimedes claimed that the area of any circle is equal to the area of a right triangle, where the radius of the circle is represented by one side and the circumference by the other.

Archimedes demonstrated using a similar method that the area of a circle of diameter D is equal to the area of a right-angled triangle with one side equal to the radius and the other to the circumference of the circle on the right angle.

Formula for the circumference of a circle:

A circle's area is equal to pi times the radius squared (A = r2). Discover how to apply this formula to determine a circle's area given its diameter.

The circumference is diameter x pi, or 2 x radius x pi.

[tex]\text { area }=1 / 2 \times \text { base } \times \text { height }=1 / 2 \times 2 \pi r \times r=\pi r^{2}[/tex].

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2. According To Archimedes, The Area Of Any Circle Is Equal To The Area Of A Right Triangle In Which

Related Questions

Alana completed a problem where she had to find the sum of the polynomials (3x^2+8x-4) and (-8x^3-3x+4) Her answer is 0. Describe and correct her mistake. When graphed, how many times does the sum change directions?

Answers

Answer:

la pregunta está en blanco, ¿podría repetirla?

Step-by-step explanation:

Solve for θ. Please help me!!

Answers

We're given the hypotenuse and the opposite side so that means that we're gonna be using the inverse of sine to find the angle.

[tex] {sin}^{ - 1} = \frac{opp}{hyp} = \frac{6}{12} [/tex]

[tex] = 30 \: degrees[/tex]

Having trouble solving this:

Answers

Answer:

It's the third option.

Step-by-step explanation:

Because if [tex]\frac{7}{10}[/tex] was converted into a decimal it would be 0.7 plus 666, it would be 666.7

Answer:

it's the 3rd one

PLEASE HELP ME WITH THIS I WILL MARK BRAINLIEST

Answers

Answer:

a=60

Step-by-step explanation:

all you do is add 90+135+75 which is 300

then subtract 300 from 360, which is 60

360-(90+135+75)=60

What is the variable for For the equation 2n - 3 = 7

Answers

Answer: n= 5

Step-by-step explanation:

Need help ASAP please!!
Don’t know how to give brainliest sorry-

Answers

Answer:

32°

Step-by-step explanation:

All triangles must have a sum of 180°. Given the angle 58° and since this is a right triangle, we have 2 out of the 3 angles to work with.

90 + 58 + x = 180

x = 32

What is the cross product of 1/4 = 5/20?

Answers

THhe cross product is found by multiplying the numerator (top number) of one fraction by the denominator (bottom number) of the other fraction.

1/4 = 5/20

1 x 20 = 20

4 x 5 = 20

The cross product is 20

Answer:

20

Step-by-step explanation:

1 x 20 = 20

4 x 5 = 20

Hope that helps!

Which have the following has a slope of 3 and y - intercept of 4

Answers

Answer:

The first table, and the graph.

Step-by-step explanation:

Suppose f(x) = x^3 + 1. Find the graph of
f(2x).

Answers

Step-by-step explanation:

I am sorry. I just typed the equation into my calculator app. Refer to the attached image above to make a deduction.

Answer:

Mga madlang pipol. The answer is graph 2

Find the length of the hypotenuse of the triangle. 4.5 m 6 m The length of the hypotenuse is meters.​

Answers

Answer:

c = 7.5 meters.​

Step-by-step explanation:

hello :

use phtagore - rule :

c² = 6²+4.5²

c² = 36 + 20.25

c² =56.25

c  = √56.25

c = 7.5 meters.​

HELP!!!
A triangle has sides of 6m and 9m . Which is
a possible length, in meters, of the third side?
A-2m
B-3m
C-5m
D-17m

Answers

Answer:

C-5m

Step-by-step explanation:

Answer:

answer is ( b )

Find the arc length of the semicircle with a radius of 5

Answers

7.85 is the approximate answer. (If pi is 3.14)

Steps are on paper.

Find the area of the inner and the outer circles, shown in the figure below. Use 3.14 for pi.


Answers

The radius of the outer circle is 17 so you put that in the formula to find the area of a circle and solve to get 153.86 squared meters as the final answer. The radius of the inner circle is 7 because it shows that the upper part of the circle is 10 and the whole thing is 17, so you do 17-10 to get 7 as the radius. Then put it in the formula and get the final answer as 907.46 squared meters.

8 + 3n ≥ 38
can yall solve plzzz

Answers

This has multiple solutions but it could b 10 and under

Write an exponential function for a graph that passes through the points (2,16) and (3,32).

Answers

Answer:

[tex]y = 4(2^{x} )[/tex]

Step-by-step explanation:

The general form for an exponential function is [tex]y = kb^{x}[/tex]

When x = 2,  y = 16    So, [tex]16 = kb^{2}[/tex]    

and when x = 3,  y = 32    So, [tex]32 = kb^{3}[/tex]

Divide  [tex]\frac{32}{16} = \frac{kb^{3} }{kb^{2} }[/tex]

2 = b

Now, [tex]16 = k2^{2}[/tex]

16 = 4k

k = 4

Therefore, the exponential function is [tex]y = 4(2^{x} )[/tex]

Solve this system of linear equations. Separate
the x- and y-values with a comma.
9x = 1 - 4y
-7x = -7 + 4y

Answers

Answer:

y = 7 and x =3

Step-by-step explanation:

use elimination method

so we gonna eliminate y first

9x = 1 - 4y

-7x = -7 + 4y

7| 9x = 1 - 4y

9| -7x = -7 + 4y

63x = 7 - 28y

-63x = -63 + 36y

add eqtn 1 to eqtn2

you will get

0 = -56 + 8y

56 = -56 + 56 + 8y

56 = 8y

56÷8 = 8y÷ 8

7 = y

also eliminate x as we have done wth y

4| 9x = 1 - 4y

4| -7x = -7 + 4y

36x = 4 - 16y

-28x = -28 + 16y

add the two equations

u will get

8x = -24 + 0

8x = -24

8x÷8 = 24÷ 8

x = 3


2. Carrie listened to the latest country album 3 times in a row in 2.75 hours. Write an equation to find the length of the album.

a. 3t=2.75
b. 2.75(3)=t
c. 2.75t=3
d. 2.75(3)(t)

HELP ME PLEASE

Answers

The answer is A.
3 is the number of times she listens and “t” is the length of the album.

What is the slope of the line that passes through the points (-2,-1) and (2,-3) answer in simplest form

Answers

Answer:

Step-by-step explanation:

(-3 + 1)/(2 + 2)= -2/4= -1/2 is the slope

A large block of ice is melting and losing 5 grams of mass every minute. After 11 minutes, the ice has lost 70 grams. Assume the relationship is linear.

Answers

The linear equation of line is given by y = 6.5x - 1.5 where the slope of the equation m = 6.5 , y = amount of ice lost and x = time elapsed

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the amount of ice lost = y

Let the time elapsed be = x

A large block of ice is melting and losing 5 grams of mass every minute

So , the first point be A = A ( 1 , 5 )

After 11 minutes, the ice has lost 70 grams

So , the second point is B = B ( 11 , 70 )

Now , the slope of the line is given by the formula ,

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 70 - 5 ) / ( 11 - 1 )

Slope m = 65/10

Slope m = 6.5

Now , the equation of line is given by ,

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 5 = 6.5 ( x - 1 )

y - 5 = 6.5x - 6.5

Adding 5 on both sides of the equation , we get

y = 6.5x - 1.5

Therefore , the value of A is y = 6.5x - 1.5

Substitute the value of x = 11 minutes , we get

y = 6.5 ( 11 ) - 1.5

y = 71.5 - 1.5

y = 70 grams

Hence , The linear equation of line is given by y = 6.5x - 1.5 where the slope m = 6.5

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1. Use the distributive property to factor out the greatest common factor (GCF) and rewrite the
expression 36 minus 96.
a. 2(18-48)
B.6(6-16)
c 12 (3-8)
D. 12(6-2)

Answers

The answer would be c. 12(3-8)

What are all t possible names for these?? Help plz

Answers

Answer:

13.....square

14....parallelogram

15....rhombus

16....trapezium

17...kite

18....rectangle

Answer:

#13 is a square, #14 is a rectangle, #15 is a rhombus, #16 is a trapezoid, #17 is a qaudrilateral, and #18 is a rectangle also.

Hope this helps :)

Chose whether the fraction and percent are equivalent

Yes. No.
A.
40/1,000 and 40%
B.
6/5 and 120%
C.
50/33 and 117%
D.
1/8 and 12.5%

Answers

Step-by-step explanation:

A No because it's 4%

B Yes

C No

D Yes

A lamp post with a height of 12 ft casts a shadow of 6 ft. A fire hydrant near it casts a shadow that is 1.5 ft long. How tall is the fire hydrant?

Answers

Answer:

3ft

Step-by-step explanation:

We are given that

Height of lamp, h=12ft

Height of shadow, l=6ft

Height of shadow of hydrant, l'=1.5ft

Let height of hydrant=h'

We have to find the height of fire hydrant.

All right triangles are similar

When two triangles are similar then, the ratio of their corresponding sides are equal.

Using the property

[tex]\frac{h}{h'}=\frac{l}{l'}[/tex]

[tex]\frac{12}{h'}=\frac{6}{1.5}[/tex]

[tex]h'=\frac{12\times 1.5}{6}[/tex]

[tex]h'=3[/tex]ft

Hence, the height of fire hydrant=3 ft


What is the measure of Zx?
Angles are not necessarily drawn to scale.

Answers

Answer:

the answer is 78*

Step-by-step explanation:

31 and 47 is 78...

i hope this helps

if do then thank me

i want to know if i am right

good luck

please help! not sure how to do this

Answers

Answer:

y=−3x+4

Step-by-step explanation:

Step 1: Flip the equation.

−6x+8=2y

Step 2: Add -8 to both sides.

−6x+8+−8=2y+−8

−6x=2y−8

Step 3: Divide both sides by -6.

−6x −/6 = 2y−8 /−6

cuánto mide el ángulo ABF​

Answers

Answer:

no tengo suficiente information para responder

Step-by-step explanation:

Jimmy's school is selling tickets to the annual dance
competition. On the first day of ticket sales
the school sold 6 adult tickets and 4 child tickets for a
total of $88. The school took in $186 on
the second day by selling 12 adult tickets and 9 child
tickets. Find the price of an adult ticket and
the price of a child ticket.

Answers

a= adult ticket c=child ticket
1. 6a+4c=88
12a+9c=186
2. so you need to multiply the top number by -2 so you can cancel out the 12a
-2(6a+4c=88)=. -12a-8c=-176
3. then you add them all together
12a+9c=186
-12a-8c=-176
——————————-
c=10
4. now you have to find ‘a’
6a+4(10)=88
6a+40=88
-40. -40
6a=48
divide both sides by 6
a=8
And your final answer should be (8,10)
hoped this helped:)



Can anyone help me with this question...please i really need your help....

(Express the variable in the brackets as the subject of formula​)

Answers

9514 1404 393

Answer:

  p = q/(2 -3q)

Step-by-step explanation:

  [tex]\dfrac{2p}{3p+1}=q \qquad\text{given}\\\\2p=q(3p+1) \qquad\text{multiply by the denominator}\\\\ 2p=3pq+q \qquad\text{eliminate parentheses}\\\\ 2p -3pq = q \qquad\text{subtract $3pq$}\\\\ p(2-3q)=q \qquad\text{factor out $p$}\\\\ \boxed{p=\dfrac{q}{2-3q}} \qquad\text{divide by the coefficient of p}[/tex]

In El Salvador the temperature is 87 degrees Fahrenheit at 7AM. By noon the temperature has risen 6 degrees. What is the temperature?

Answers

Answer:

93 Because remember when they said that the Temperature degrees was any 7 right so what they mids I think was to add 6 more to that number If I'm wrong just tell me a probly a 100% got this wrong but alias I try

i'm really confused on this, anything will help

Answers

Answer:

I think its 1200 not sure though

Answer:

1,200

Step-by-step explanation:

first you would divide 480 copies by 4 minutes to see how many copies per minute (120) Then you would take 120 copies per minute and multiply it by the 10 and you would get 1200 copies per 10 minutes! lmk if that helps:)

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