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3 years ago

Is .111111111... a rational number? Yes or No?

Mathematics

2 answers:

Mashcka [7]3 years ago

8 0

Answer:

The answer is no this number is not rational.

Step-by-step explanation:

Because, To show that the rational numbers are dense:

It cannot be expressed as a fraction with integer values in the numerator and denominator. When an irrational number is expressed in decimal form, it goes on forever without repeating.

NeX [460]3 years ago

5 0

Answer:

Yes, yes it is

Step-by-step explanation:

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What is the domain of the graphed function?

elena-s [515]

Answer:

Step-by-step explanation:

The domain is all the possible values of x. The graph starts at x=-2 and continues to positive infinity, so x ≥ -2.

Answer B.

7 0

3 years ago

Nikki drew a rectangle with a perimeter of 18 units on a coordinate grid. Two of the vertices were (4, –3) and (–1, –3). What co

Talja [164]

Answer:

There are two possible solutions for the other two vertices of the rectangle:

(i) (4, 1), (-1, 1), (ii) (4, -7), (-1, -7)

Step-by-step explanation:

Geometrically speaking, the perimeter of a rectangle ( $p$ ) is:

$p = 2\cdot b + 2\cdot h$ (1)

Where:

$b$ - Base of the rectangle.

$h$ - Height of the rectangle.

Let suppose that the base of the rectangle is the line segment between (4, -3) and (-1, -3). The length of the base is calculated by Pythagorean Theorem:

$b = \sqrt{[(-1)-4]^{2}+[(-3)-(-3)]^{2}}$

$b = 5$

If we know that $p = 18$ and $b = 5$ , then the height of the rectangle is:

$2\cdot h = p-2\cdot b$

$h = \frac{p-2\cdot b}{2}$

$h = \frac{p}{2}-b$

$h = 4$

There are two possible solutions for the other two vertices of the rectangle:

(i) (4, 1), (-1, 1), (ii) (4, -7), (-1, -7)

8 0

3 years ago

Solve the following equation with the initial conditions. x¨ + 4 ˙x + 53x = 15 , x(0) = 8, x˙ = −19

Katen [24]

$x''+4x'+53x=15$

has characteristic equation

$r^2+4r+53=0$

with roots at $r=-2\pm7i$ . Then the characteristic solution is

$x_c=C_1e^{(-2+7i)t}+C_2e^{(-2-7i)t}=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)$

For the particular solution, consider the ansatz $x_p=a_0$ , whose first and second derivatives vanish. Substitute $x_p$ and its derivatives into the equation: