What is the side length of a cube with a volume of 166 yd^3

Mathematics

1 answer:

Inga [223]3 years ago

6 0

Answer: 5.5 yd

Step-by-step explanation:

To find the side length of the cube, the volume is a clue. We know that all sides of a square are equal, and the volume of a cube is length×width×height. Since the length, width and height are all the same, we know it is V=x³. Since we know the volume, we can plug in and solve for x.

166=x³

In order to get x alone, we have to cube root both sides.

x≈5.5 yd

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Determine the equations of the vertical and horizontal asymptotes if any for h(x)=(x+1)^2/x^2-1

shepuryov [24]

ANSWER

Vertical asymptote:

x=1

Horizontal asymptote:

y=1

EXPLANATION

The given rational function is

$h(x) = \frac{ {(x + 1)}^{2} }{ {x}^{2} - 1 }$

$h(x) = \frac{ {(x + 1)}^{2} }{ ({x} - 1)(x + 1)}$

$h(x) = \frac{ (x + 1)(x + 1) }{ ({x} - 1)(x + 1)}$

$h(x) = \frac{ x + 1}{ {x} - 1}$

The vertical asymptote occurs at

${x} - 1 = 0$

$x = 1$

The vertical asymptotes is x=1

The degree of the numerator is the same as the degree of the denominator.

The horizontal asymptote of such rational function is found by expressing the coefficient of the leading term in the numerator over that of the denominator.

$y = \frac{1}{1}$