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The dimensions in inches of a shipping box can be expressed as width x, length x + 1, and height x - 4. The volume is 84 ft^3. Find the dimensions of the box in feet.

1, 1, 4
2, 2, 21
2, 6, 7
3, 4, 7

Please help? If somebody can help put this into an equation for me, I can do the rest. Thanks

Respuesta :

AllisonF
84ft^3= (x-1)•x-4(x)

Maybe, then you would need to solve get the solution of x and plug it in for the demensions, hope this helps! (Not exactly positive that is my is correct but believe it is at least close!)
calculista

Answer:

The dimensions of the box are

[tex]2,6,7[/tex]

Step-by-step explanation:

we know that

The volume of a box in the shape of a cube is equal to

[tex]V=W*L*H[/tex]

where

W is the width of the box

L is the length of the box

H is the height of the box

In this problem we have

[tex]V=84\ ft^{3}[/tex]

[tex]W=x\ ft[/tex]

[tex]L=x+1\ ft[/tex]

[tex]H=x-4\ ft[/tex]

Substitute the values in the formula of volume

[tex]84=x*(x+1)*(x-4)[/tex]

[tex]84=(x^{2}+x)*(x-4)\\84=x^{3} -4x^{2}+x^{2}-4x\\84=x^{3}-3x^{2}-4x\\x^{3}-3x^{2}-4x-84=0[/tex]

Using a graphing tool

Solve the cubic function

see the attached figure

The value of x is equal to

[tex]x=6\ ft[/tex]

the dimensions of the box are

[tex]W=x\ ft=6\ ft[/tex]

[tex]L=x+1\ ft=6+1=7\ ft[/tex]

[tex]H=x-4\ ft=6-4=2\ ft[/tex]


Ver imagen calculista

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