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3 years ago

Determine the equations of the vertical and horizontal asymptotes if any for f(x)=x/x-5

Mathematics

1 answer:

Gelneren [198K]3 years ago

5 0

Answer:

Horizontal Asymptote: x = 0

Vertical Asymptote: x = 5

Step-by-step explanation:

The function is given as $f(x)=\frac{x}{x-5}$

Horizontal asymptotes are found by equating numerator to 0 and solving for x

Vertical asymptotes are found by equating denominator to 0 and solving for x

Horizontal Asymptote:

x = 0

Vertical Asymptote:

x - 5 = 0

x = 5

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2 years ago

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Liula [17]

This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.

Area of a rectangle:

The area of rectangle of length l and width w is given by:

$A = wl$

w(2w + 3) = 9

From this, we get that:

$l = 2w + 3, A = 9$

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:

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

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

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In this question:

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$2w^2 + 3w - 9 = 0$

Thus a quadratic equation with $a = 2, b = 3, c = -9$

Then

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$w_{1} = \frac{-3 + \sqrt{81}}{2*2} = 1.5$

$w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3$

Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.

Another similar problem can be found at brainly.com/question/16995958

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2 years ago

Read 2 more answers

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Svetradugi [14.3K]

Answer:

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Step-by-step explanation:

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2 years ago

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Answer:

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3 years ago