How we can apply Quadratic Functions in this situation ?
Given a rectangular water tank with Volume = Length x Breadth x Height
= #x*2*(k-x)#
Given k is a constant and the maximum volume of the water tank is #50m^3# . Find the value of #k# .
Given a rectangular water tank with Volume = Length x Breadth x Height
=
Given k is a constant and the maximum volume of the water tank is
1 Answer
Explanation:
Given:
Multiply the factors, put them in standard form, and mark as equation [1]:
This is standard form
where
Because "a" is negative, we know that the maximum will occur at the vertex. The x coordinate of the vertex is:
Substitute the values for "a" and "b":
We know that
Substitute the known values into equation [1]:
Multiply terms:
Combine like terms:
Substitute into equation [1]:
Here is a graph of of equation [2]:
graph{-2x^2+20x [-14.01, 22.02, 39.21, 57.23]}
Please observe that 50 is the maximum.