The volume of a box can be found with the function V, where x is the length of the shortest edge of the box: V(x) = x3 + 5x2 – 14x What is the length of the shortest edge of the box if it has a volume of 30 cubic units? +/-

The length of the shortest edge of the box is 3 units

Step-by-step explanation:

Since the volume of the box is given by the function

V(x) = x³ + 5x² – 14x

Where V is the volume and x if the length of the shortest edge of the box.

To determine the length of the shortest edge of the box if it has a volume of 30 cubic units, we will put V(x) = 30 and then find the value of x.

30 = x³ + 5x² – 14x

∴ x³ + 5x² – 14x – 30 = 0

The solution to the cubic equation is shown in the attachments below.

x₁ = 3 , x₂ = – 1.55, and x₃ = – 6.45

Since the length cannot be negative, the length of the shortest edge of the box is 3 units.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204