Example 4: Converting Rational Numbers to Decin

The radius of circle A is three feet less than twice the diameter of circle B. If the sun mmm of the diameters of both circles i

yanalaym [24]

Answer:

Area of Circle A = 1133.54

Circumference of Circle A= 119.32

Step-by-step explanation:

Given: Sum of both circle diameters= 49 feet.

Circle A radius= Three feet less than twice the diameter of circle B.

Lets assume diameter of Circle B is "x"

∴ Circle A radius (r)= $(2x-3)$

We know, the diameter of circle is $2r$

Diameter of Circle A is $2\times (2x-3)$

Next as given sum of both circle diameter is 49 feet.

∴ $2(2x-3)+x= 49\ feet$

distributing 2 with 2x and -3

⇒ $4x-6+x= 49$

⇒ $5x-6= 49$

Adding both side by 6

⇒ $5x=55$

Cross multiplying both side.

⇒ $x=\frac{55}{5} = 11$

∴ Diameter of circle B is 11 feet.

Next, subtituting the value of x to get the value of radius for Circle A.

Radius of circle A= $(2x-3)$

⇒ Radius of circle A= $(2\times 11-3)= 22-3$

∴ Radius of circle A= 19 feet.

Area of circle= $\pi r^{2}$

Taking π= 3.14

Area of circle A= $3.14\times 19^{2} = 3.14\times 361$

∴ Area of circle A= 1133.54

Circumference of circle= 2πr

Circumference of Circle A= $2\times 3.14\times 19= 119.32$

∴ Circumference of Circle A= 119.32

3 0

3 years ago

Read 2 more answers

What is the absolute value of the complex number -4-√2

Zepler [3.9K]

|a+bi| = √(a² + b²)

-4-√2 i -> take a = -4 and b = -√2

|-4-√2 i| = √[ (-4)² + (-√2)² ]
 = √[ 16 + 2 ]
 = √[ 18 ] = √[ 9 * 2 ]
 = 3√2
the absolute value is 3√2

6 0

3 years ago

12x + 4 divided by 4 plus 20x + 5 divided by 5

Rasek [7]

12x + 4 ➗ 4 + 20x + 5 ➗ 5

1. PEMDAS (order of operations) solve the division problems

(4 divided by 4 & 5 divided by 5)
12x + 1 + 20x + 1

2. Swap around the order of operations as commutative property states that you can swap the order of an addition problem and get the same answer.

12x + 20x + 1 + 1

3. Add like terms

32x + 2

This is the most simplified answer you could get as you can not add 32x and 2 as they are not like terms.

6 0

2 years ago

What’s the quadrant

Vadim26 [7]

Hey there!!

Always remember this :

90-degree counterclockwise: (x, y) → (-y, x)

180-degree counterclockwise: (x, y) → (-x, -y)

270-degree counterclockwise: (x, y) → (y, -x)

1st quadrant : ( x , y )

second quadrant : ( -x , y )

Third quadrant : ( - x , - y )

Fourth quadrant : ( x , -y )

Now, the triangle abc lies in the 1st quadrant. So, all the vertexes will have positive values.

Let's take the vertex a as ( 1 , 2 )

Vertex b as ( 4 , 7 )

Vertex c as ( 5 , 9 )

If we rotate these values in 90 degress angle, these would become ( -y , x )

Vertex a : ( 1 , 2 ) ; After rotating : ( -2 , 1 )

Vertex b : ( 4 , 7 ) ; After rotating : ( -7 , 4 )

Vertex c : ( 5 , 9 ) ; After rotating : ( -9 , 5 )

Hope my answer helps!

3 0

3 years ago

Determine and state the coordinates of the center and length of the radius of a circle whose equation is

padilas [110]

First, rewrite the equation in standard form.
The center-radius form of the circle equation is in the format:
(x – h)^2 + (y – k)^2 = r^2
with the center being at the point (h, k) and the radius being "r".

(x-3)^2 + (y+4)^2 = 81

From here, you can determine the center and radius. The center is at (3,-4) and the radius is 9.

4 0

3 years ago