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3 years ago

ABCD is a quadrilateral inscribed in a circle, as shown below:

Mathematics

1 answer:

german3 years ago

3 0

Answer:

A. (x + 16) + (6x − 4) = 180

Step-by-step explanation:

Inscribed quadrilateral has opposite angles supplementary.

So

m∠A + m∠C = 180°

m∠B + m∠D = 180°.

Since

m∠A = x + 16,
m∠B = x,
m∠C = 6x - 4,
m∠D = 2x + 16

we can use either pair of angle measures to work out the value of x and then find the value of each angle.

We can verify the first option is the only correct one.

m∠A + m∠C = 180°
(x + 16) + (6x − 4) = 180

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Simplify: (3 √u^2v)(5 √v^2)=

kirill [66]

Answer: Do you know the values of u and v?

Step-by-step explanation:

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2 years ago

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Consider the vector add = a + b = [13 12 11 10 10] and sub = a - b = [-11 - 6 - 14 8]. Find the vector a and b.

prisoha [69]

Answer:

a = [1 3 5 7 9] and b = [12 9 6 3 1]

Step-by-step explanation:

The addition of two vectors a and b is defined as

a + b = [13 12 11 10 10] .... (1)

The subtraction of two vectors a and b is defined as

a - b = [-11 - 6 - 1 4 8] .... (2)

After adding (1) and (2), we get

(a + b) + (a - b)= [13 12 11 10 10] + [-11 - 6 - 1 4 8]

On simplification we get

2a = [13-11 12-6 11-1 10+4 10+8]

2a = [2 6 10 14 18]

Divide both sides by 2.

a = [1 3 5 7 9]

Substitute the value of vector a in equation (1).

[1 3 5 7 9] + b = [13 12 11 10 10]

Subtract vector a from both sides.

b = [13 12 11 10 10] - [1 3 5 7 9]

On simplification we get

b = [13-1 12-3 11-5 10-7 10-9]

b = [12 9 6 3 1]

Therefore the vectors a and b are defined as a = [1 3 5 7 9] and b = [12 9 6 3 1].

4 0

2 years ago

Compute the loss of head and pressure drop in 200 ft of horizontal 6-in diameter asphalted cast iron pipe carrying water with a

laiz [17]

Answer:

The answer is below

Step-by-step explanation:

12 inches = 1 ft.

6 inches = 6 inches * (1 ft./12 inches) = 0.5 ft.

Therefore the diameter of the cast iron (D) = 6 inches = 0.5 ft.

The area of cast iron (A) = πD²/4 = π(0.5)²/4 = 0.196 ft²

The velocity (V) = 6 ft./s, the acceleration due to gravity (g) = 32.2 ft./s²

ε/D = 0.0004 ft./ 0.5 ft. = 0.0008

Using the moody chart, find the line ε/D = 0.0008 and determine the point of intersection with the vertical line R = 2.7 * 10⁵. Hence we get f = 0.02.

The head loss (h) is:

$h_f=f*\frac{L}{d}* \frac{V^2}{2g}=0.02*\frac{200\ ft}{0.5\ ft} *\frac{(6\ ft/s)^2}{2*32.2\ ft/s^2}=4.5\ ft$

The pressure drop (Δp) is:

Δp = ρg $h_f$ = $(62.4\ lbf/ft^3)(4.5\ ft)= 280\ lbf/ft^2$

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3 years ago

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zvonat [6]

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