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sammy [17]
3 years ago
6

A square is inscribed In a circle with radius 6

\sqrt{2} " alt=" \sqrt{2} " align="absmiddle" class="latex-formula">
inches. what is the perimeter of the square in inches? help pls​

Mathematics
1 answer:
34kurt3 years ago
6 0

Answer:

48 in

Step-by-step explanation:

The diagonal of the inscribed square equals the diameter of the circle.

1. Calculate the diagonal of the square

d = 2r = 2 × 6√2 in =12√2 in

2. Calculate the side of the square

∆ACB is an isosceles right triangle.

We can use Pythagoras' Theorem to calculate the length of a side s.

\begin{array}{rcl}s^{2} + s^{2} & = & (12\sqrt{2})^{2}\\2s^{2} & = & 144 \times 2\\s^{2} & = & 144\\s & = & \text{12 in}\\\end{array}

3. Calculate the perimeter of the square

P = 4s = 4 × 12 in = 48 in

The perimeter of the square is 48 in.

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Probability of landing in the white not the red. Please helpppppppppppp!
Iteru [2.4K]

Fun, geometry disguised as probability.

That's a pentagon, which we can view as 10 right triangles with legs a and s/2 (half of s) and hypotenuse r.  So area of the pentagon is

P = 10 × (1/2) a (s/2) = 10 (1/2) (3.2) (4.7/2) = 37.6

The area of the circle is πr² so the circle area is

C = π (4²) = 50.265482

The white area is the difference, C-P, and the probability we seek is the fraction of the circle that's white, so (C-P)/C.

p = (C-P)/C =1-P/C = 1-37.6/50.265482 = 0.251971

Answer: 0.25

Higher than I would have guessed from the figure.

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Evaluate the expression if k = 5 and w = 3 *<br> 3k + 2w - 4K
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A farmer wants to fence in a rectangular field that encloses 3600 square feet. One side of the field is along a river and does n
andriy [413]

Answer:

C(x) = \$3.50(\frac{x^2+7200}{x})

Step-by-step explanation:

Data provided in the question:

Area of the field = 3600 square feet

Fencing charges = $3.50 per foot

Let the side along the river be 'x' feet and the other side of the 'B'

now,

Area of rectangle = Bx = 3600 square feet

or

B = \frac{3600}{x} feet

and total length to be fenced = x + 2B

therefore,

Total cost of fencing = Fencing charges × total length to be fenced

or

Total cost of fencing = $3.50 × ( x + 2B )

substituting the value of B from (1)

Total cost of fencing, C(x) = \$3.50(x+2\times\frac{3600}{x})

or

C(x) = \$3.50(\frac{x^2+7200}{x})

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The ratio of men to women in a room is 3:4. Eight women enter the room, no men enter the room and none of the original people in
vampirchik [111]
There are 64 people in the room.

Since the ratio for women increases 1 when 8 women enter the room, for every time there is 1 in the ratio there are 8 people. That means that originally you have to do 3x8 and 4x8. You get 24 and 32 which equals 56. Then when 8 more women enter the room, you get 64.
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2 years ago
Read 2 more answers
Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation 2 h tt = − 16t^2+
tekilochka [14]

Answer:

It will take 5.61 seconds for the coin to reach the stream.

Step-by-step explanation:

The height of the coin, after t seconds, is given by the following equation:

h(t) = -16t^{2} + 72t + 100

How long will it take the coin to reach the stream?

The stream is the ground level.

So the coin reaches the stream when h(t) = 0.

h(t) = -16t^{2} + 72t + 100

-16t^{2} + 72t + 100 = 0

Multiplying by (-1)

16t^{2} - 72t - 100 = 0

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

16t^{2} - 72t - 100 = 0

So

a = 16, b = -72, c = -100

\bigtriangleup = (-72)^{2} - 4*16*(-100) = 11584

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t_{2} = \frac{-(-72) - \sqrt{11584}}{2*16} = -1.11

Time is a positive measure, so we take the positive value.

It will take 5.61 seconds for the coin to reach the stream.

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