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Westkost [7]
1 year ago
15

Here is a diagram of a black circle inside a white square and a diagram of a small grey square inside a white square.

Mathematics
1 answer:
nika2105 [10]1 year ago
6 0

The ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2

<h3>How to determine the ratio of the areas?</h3>

The side length AB is given as:

AB = 8x

The area of the white square is calculated as

White = (AB)²

This gives

White = (8x)²

Evaluate

White = 64x²

The side length AB represents the diameter of the black circle.

So, the radius is:

r =AB/2

This gives

r = 8x/2 = 4x

The area is then calculated as:

Circle = πr²

This gives

Circle = π(4x)²

Evaluate

Circle = 16πx²

Next, calculate AW and AZ using:

AZ = AW = AB/2

Evaluate

AZ = AW = 8x/2 = 4x

Calculate WZ using the following Pythagoras theorem

WZ² = AW² + AZ²

This gives

WZ² = (4x)² + (4x)²

Evaluate

WZ² = 2(4x)²

Take the square root of both sides

WZ = 4x√2

The area of the gray square is:

Gray = WZ²

This gives

Gray = 2(4x)²

Evaluate

Gray = 32x²

At this point, the areas are:

  • White = 64x²
  • Circle = 16πx²
  • Gray = 32x²

The ratio is then represented as:

Ratio = Circle : White : Gray

This gives

Ratio = 16πx² : 64x² : 32x²

Divide through by 16x²

Ratio = π : 4 : 2

Hence, the ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2

Read more about areas at:

brainly.com/question/24487155

#SPJ1

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The center of a circle is at (2, −5) and its radius is 12.
stiv31 [10]

Answer:

The equation of the circle is (x - 2)² + (y + 5)² = 144 ⇒ A

Step-by-step explanation:

The form of the equation of the circle is (x - h)² + (y - k)² = r², where

  • r is the radius of the circle
  • h, k are the coordinates of the center of the circle

Let us solve the question

∵ The center of the circle is at (2, -5)

→ From the rule above

∴ h = 2 and k = -5

∵ The radius of the circle is 12

∴ r = 12

→ Substitute the values of r, h, and k in the form of the equation above

∵ (x - 2)² + (y - -5)² = (12)²

∴ (x - 2)² + (y + 5)² = 144

∴ The equation of the circle is (x - 2)² + (y + 5)² = 144

7 0
3 years ago
Vertices A and B of triangle ABC are on one bank of a river, and vertex C is on the opposite bank. The distance between A and B
AURORKA [14]
A suitable solver will tell you instantly that the measure of b is 179.18 ft.

_____
If you want to do it yourself (meaning also with the aid of a calculator), you can use the Law of Sines. The given side is side "c", so you need the measure of angle C. That will be
  180° -33° -63° = 84°
Then side "b" can be found from
  b/sin(B) = c/sin(C)
  b = c*sin(B)/sin(C)
  b = (200 ft)*sin(63°)/sin(84°) ≈ 179.183 ft

7 0
3 years ago
Read 2 more answers
If a concrete column is 6 inches by 6 inches square and 8 ft. long, calculate its weight in Newtons, given a specific weight of
tangare [24]
<h2>Weight of column is 555.83 N</h2>

Step-by-step explanation:

Size of column = 6 inch x 6 inch x 8 ft

Size of column = 0.5 ft x 0.5 ft x 8 ft

Volume of column = 0.5 x 0.5 x 8 = 2 ft³

Specific weight of concrete = 62.4 lb/ft³

Mass = Volume x Specific weight

Mass = 2 x 62.4

Mass = 124.8 lb = 124.8 x 0.454 = 56.66 kg

Weight = 56.66 x 9.81 = 555.83 N

Weight of column is 555.83 N

7 0
3 years ago
T = 320.00 + 0.40b
Gemiola [76]

Answer:

c) The total price for the service  when Terrance's price was equivalent to Sylvester's price  is $600.

Step-by-step explanation:

   Here,   t = 320.00 + 0.40 b

and  t = The total prices charged by Terrance for packing and moving b boxes.

s = 250.00 +0.50 b

and  s = The total prices charged by Sylvester  for packing and moving b boxes.

Now, to find the number of boxes, when both the prices are equal.

⇒320.00 + 0.40 b  = 250.00 +0.50 b

or, 320 - 250 = 0.50 b - 0.40 b

or, 0.10 b =  70

or, b= 70/0.10 = 700

Hence, for packing and moving b = 700 boxes, both companies charge the same amount.

Now, the price charged = 320 + 0.4 (b)

                                         = 320 + 0.4(70) = 320 + 280

                                         = 600

or,  the total price for the service  when Terrance's price was equivalent to Sylvester's price  is $600.

3 0
3 years ago
HELP ASAP 40 POINTS
AleksandrR [38]

Given:

The sequence is -8, -12, -16.

To find:

The nth and 52th term  of the given sequence.

Solution:

We have,

-8, -12, -16

It is an AP because the difference between consecutive terms are equal. Here, first term is -8 and the common difference is

r=a_2-a_1

r=-12-(-8)

r=-12+8

r=-4

The nth term of an AP is

a_n=a+(n-1)d

Where, a is first term and d is common difference.

Putting a=-8 and d=-4, we get

a_n=-8+(n-1)(-4)

a_n=-8-4n+4

a_n=-4-4n

Putting n=52, we get

a_{52}=-4-4(52)

a_{52}=-4-208

a_{52}=-212

Therefore, the equation for the nth term of the given sequence is a_n=-4-4n and the 52nd term of the sequence is -212.

3 0
3 years ago
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