Rectangular pyramid has a base area of x^2+3x-10/2x square centimeters and a height of x^2-3x/x^2-5x+6 centimeters. Wright a rational expression to describe the volume of the rectangular pyramid

(1/3)(base area)(height)

(1/3) [(x-2)(x+5)/2x] [x(x-3)/ {(x-3)(x-2)} ]

(1/3) [(x+5)/2 ] = (1/6)(x+5)

Well wrought!

Why did the pyramid go on a diet? It wanted to reduce its base area!

Now, to answer your question, we can calculate the volume of the rectangular pyramid by multiplying the base area by the height and dividing the result by 3. So, the rational expression to describe the volume would be:

V = (1/3) * [(x^2 + 3x - 10) / (2x)] * [(x^2 - 3x) / (x^2 - 5x + 6)]

Just remember, when it comes to pyramids, it's all about keeping things in proportion.

The volume of a rectangular pyramid is given by the formula V = (1/3) * base area * height.

Let's substitute the given values into the formula:

V = (1/3) * [(x^2 + 3x - 10) / (2x)] * [(x^2 - 3x) / (x^2 - 5x + 6)]

To simplify this expression, we can multiply the two fractions together:

V = (1/3) * [(x^2 + 3x - 10) * (x^2 - 3x) / (2x) * (x^2 - 5x + 6)]

Now, let's simplify the numerator and denominator separately:

For the numerator:
(x^2 + 3x - 10) * (x^2 - 3x) = x^4 - 3x^3 + 3x^3 - 9x^2 - 10x^2 + 30x = x^4 - 16x^2 + 30x

For the denominator:
(2x) * (x^2 - 5x + 6) = 2x^3 - 10x^2 + 12x

Now, substitute these simplified expressions back into the original formula:

V = (1/3) * [(x^4 - 16x^2 + 30x) / (2x^3 - 10x^2 + 12x)]

Therefore, the rational expression to describe the volume of the rectangular pyramid is:
V = (x^4 - 16x^2 + 30x) / (3 * (2x^3 - 10x^2 + 12x))

To find the volume of a rectangular pyramid, we use the formula:

Volume = (1/3) * base area * height

Given that the base area is (x^2+3x-10)/(2x) square centimeters and the height is (x^2-3x)/(x^2-5x+6) centimeters, we can substitute these values into the formula to get the rational expression for the volume of the rectangular pyramid.

Volume = (1/3) * [(x^2+3x-10)/(2x)] * [(x^2-3x)/(x^2-5x+6)]

Simplifying this expression, we get:

Volume = [(x^2+3x-10) * (x^2-3x)] / [6x * (x^2-5x+6)]

Therefore, the rational expression to describe the volume of the rectangular pyramid is:

Volume = [(x^2+3x-10) * (x^2-3x)] / [6x * (x^2-5x+6)]