The formula for the volume of a rectangular prism is V = lwh. A rectangular prism has a length of 2y

3 and
width of 5y. The volume of the prism is 20y
10 + 70y
4
. What is the height of the prism? Show your work.

Confusing but screw down a little steve have already given a hint to that question

A

(3x - 1) + (2x^2 + 5)

To find the height of the prism, we can rearrange the formula for volume:

V = lwh

Since we are given the length (2y^3) and width (5y), we can substitute these values into the formula:

20y^10 + 70y^4 = (2y^3)(5y)(h)

Simplifying the equation:

20y^10 + 70y^4 = 10y^4 * 2y^3 * h

Dividing both sides by 10y^4:

2y^6 + 7 = 2y^3 * h

Now, divide both sides by 2y^3 to solve for h:

h = (2y^6 + 7) / (2y^3)

This simplifies to:

h = y^(6-3) + 7/(2y^3)

h = y^3 + 7/(2y^3)

Therefore, the height of the prism is y^3 + 7/(2y^3).

To find the height of the rectangular prism, we need to rearrange the formula for volume and substitute the given values.

The formula for the volume of a rectangular prism is V = lwh.

In this case, we are given:
Length (l) = 2y^3
Width (w) = 5y
Volume (V) = 20y^10 + 70y^4

We can rearrange the formula to solve for height (h):

V = lwh
Divide both sides by lw:
h = V / (lw)

Substituting the given values:
h = (20y^10 + 70y^4) / (2y^3 * 5y)

To simplify this expression, we can divide the coefficients and subtract the exponents of the variables:

h = (20y^10 + 70y^4) / (10y^4)

Now, simplify the expression further by dividing each term in the numerator by the denominator:

h = 2y^6 + 7

Therefore, the height of the prism is 2y^6 + 7.