we know that
The volume of the box is equal to
V=area of the base*height
solve for the height
height=Volume/(area of the base)
[tex]V=2x^{3}+3x^{2}- 11x- 6\ ft^{3} \\ Area\ of\ the\ base=x^{2}+x-6\ ft^{2}[/tex]
using a graph tool-----> find the roots
see the attached figures
so
[tex]2x^{3}+3x^{2}- 11x- 6=2*(x+3)*(x+0.5)*(x-2)[/tex]
[tex]x^{2}+x-6=(x+3)*(x-2)[/tex]
substitute
height=Volume/(area of the base)
[tex]height= \frac{2*(x+3)*(x+0.5)*(x-2)}{(x+3)*(x-2)} = 2*(x+0.5)[/tex]
[tex]height=2x+1[/tex]
therefore
the answer is
[tex]height=2x+1[/tex]
Answer:
Height of the box = 2x+1
Step-by-step explanation:
Leslie is making a cardboard box that has a
volume of cubic feet. [tex]2x^3 + 3x^2 − 11x − 6[/tex]
the base has an area of [tex]x^2 + x − 6[/tex] square feet.
Volume of a box = Base area * height of the box
we are given with volume and base area
Replace it in the formula. LEts factor the given expression
[tex]2x^3 + 3x^2 - 11x - 6 [/tex]
[tex]\left(x-2\right)\left(2x+1\right)\left(x+3\right)[/tex]
Now we factor[tex]x^2 +x -6 = (x+3))x-2)[/tex]
Volume of a box = Base area * height of the box
[tex]\left(x-2\right)\left(2x+1\right)\left(x+3\right)= (x+3)(x-2) * height[/tex]
Divide both sides by (x+3)(x-2)
Height of the box = 2x+1
