Q.71 - 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 6 feet. Find the cost of producing a box with x = 4 feet.

Step-by-Step Solution

Answer

The cost of producing a box with $x=4$ feet is $456$.

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 $6$ feet.

We find the cost of producing a box with $x = 4$ 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 $x=4$

$$\begin{gathered} C\left(4\right) = 6{\left(4\right)}^2 + 90\times 4 \\ C\left(4\right) = 6\times 16 + 90\times 4 \\ C\left(4\right) = 96 + 360 \\ C\left(4\right) =456 \end{gathered}$$