Q.72 - Intermediate Algebra

Question

The polynomial $C\left(x\right) = 6x^2 + 90x$ gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side $x$ feet and height $4$ feet. Find the cost of producing a box with $x = 6$ feet.

Step-by-Step Solution

Answer

The cost of producing a box with $x=6$ is$756$.

Step 1. Given Information

The polynomial $C\left(x\right) = 6x^2 + 90x$ gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side $x$ feet and height $4$ feet.

We find the cost of producing a box with $x = 6$ feet.

Step 2. The given polynomial function is C ( x )   =   6 x 2   +   90 x

The function is $C\left(x\right) = 6x^2 + 90x$

putting $x=6$

$$\begin{gathered} C\left(6\right) = 6{\left(6\right)}^2 + 90\times 6 \\ C\left(6\right) = 6\times 36 + 90\times 6 \\ C\left(6\right) =216+540 \\ C\left(6\right) =756 \end{gathered}$$