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.
try using ^ for powers. That is
y^3 means y cubed.
The formatting has messed things up to where they are incomprehensible.
To find the height of the rectangular prism, we need to rearrange the formula V = lwh to solve for h.
Given:
V = 20y^10 + 70y^4
l = 2y^3
w = 5y
Substituting the given values into the volume formula:
20y^10 + 70y^4 = (2y^3)(5y)(h)
Simplifying the expression on the left side:
20y^10 + 70y^4 = 10y^4 * 2y^3 * h
20y^10 + 70y^4 = 20y^7 * h
Now, we can solve for h by dividing both sides of the equation by 20y^7:
(20y^10 + 70y^4) / (20y^7) = h
Simplifying the equation further:
(2y^3 + 7) / y^3 = h
Therefore, the height of the rectangular prism is (2y^3 + 7) / y^3.
To find the height of the rectangular prism, we can rearrange the formula for volume:
V = lwh
Since we know the length (2y^3) and the width (5y), and the volume (20y^10 + 70y^4), we can substitute those values into the equation:
20y^10 + 70y^4 = (2y^3)(5y)(h)
Simplifying further:
20y^10 + 70y^4 = 10y^4 * 2y^3 * h
Now, divide both sides by 10y^4 * 2y^3 to isolate 'h':
(20y^10 + 70y^4) / (10y^4 * 2y^3) = h
Simplifying the expression on the left side:
(2y^3 + 7) / (2) = h
Therefore, the height of the prism is (2y^3 + 7)/2.