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dmitriy555 [2]
3 years ago
10

What is the sum of the rational expressions below? x+3/x-2 + 3x-8/x-2

Mathematics
1 answer:
Mamont248 [21]3 years ago
6 0

Answer:      \bold{\dfrac{4x-5}{x-2}}

<u>Step-by-step explanation:</u>

Since the expressions have the same denominator, we simply need to add the numerators.

\dfrac{x+3}{x-2}+\dfrac{3x-8}{x-2}\quad =\quad \dfrac{x+3+3x-8}{x-2}\quad = \quad \large\boxed{\dfrac{4x-5}{x-2}}

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Answer:

A)

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B)

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Step-by-step explanation:

Under the assumption the earth is a perfect circle, then in one complete rotation about its axis ( 24 hours) the Earth will cover 360 degrees or 2π radians.

A)

In every 24 hours the earth rotates through 360 degrees ( a complete rotation). We are required to determine the length of time it will take the Earth to rotate through 225 degrees. Let x be the duration it takes the earth to rotate through 225 degrees, then the following proportions hold;

(24/360) = (x/225)

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B)

In 24 hours the earth rotates through an angle of 2π radians (a complete rotation) . We are required to determine the length of time it will take the Earth to rotate through 9π radians. Let x be the duration it takes the earth to rotate through 9π radians, then the following proportions hold;

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C)

If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;

circumference = 2*π*R = π*D

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(24891.43miles)/(24 hours) = 1037.14 miles/hr

The distance covered by the point in 2 hours will thus be;

1037.14 * 2 = 2074.29 miles

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