Respuesta :
Answer:[tex]C=2x^2+\frac{8400}{x}[/tex]
Step-by-step explanation:
Given
Volume of box [tex]V=350\ m^3[/tex]
Suppose base square has a length [tex]x\ m[/tex]
and vertical walls has length of [tex]y\ m[/tex]
volume [tex]V=x^2y[/tex]
[tex]y=\frac{350}{x^2}[/tex]
Cost of bottom material [tex]=\$ 2[/tex] per square meter
Cost of side material [tex]=\$ 6[/tex] per square meter
Total cost
[tex]C=x^2 \times 2+4xy\times 6[/tex]
[tex]C=2x^2+4x\times \frac{350}{x^2}\times 6[/tex]
[tex]C=2x^2+\frac{8400}{x}[/tex]
The expression that represents the cost of constructing the box in term of x, the side length of the base is [tex]C = 2x^2 + 8400\div x[/tex].
Calculation of the expression:
Since
An open top box with a square base is to have a volume of 350 cubic meters. The material for the bottom of the box costs $2 per square meter and the material for the sides costs $6 per square meter.
So, here we can say that
[tex]C = x^2 \times 2 + 4xy \times 6\\\\C = 2x^2 + 4x \times 350\div x^2 \times 6\\\\C = 2x^2 + 8400\div x[/tex]
Hence, The expression that represents the cost of constructing the box in term of x, the side length of the base is [tex]C = 2x^2 + 8400\div x[/tex].
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