The volume of a rectangular prism is represented by the function x3 + 9x2 + 6x − 16. The length of the box is x + 2, while the h
eight is x + 8. Find the expression representing the width of the box.
1 answer:
Answer:
width = (x-1)
Step-by-step explanation:
The volume of the prisms is defined in the problem as
Volume = x^3 + 9x^2 + 6x − 16
Volume = width*height* length
And we know that,
length = (x+2)
height = (x+8)
We can find the roots of the equation, which happen to be
x = -8
x = -2
x = 1
(See image below)
This means that the volume can be represented as
Volume = x^3 + 9x^2 + 6x − 16 = (x+8)(x+2)*(x-1)
Therefore,
The width = (x-1)
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Explanation:
Method 1
We can use the pythagorean theorem to find x.
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Method 2
Use the sine ratio to find x. You'll need a reference sheet or the unit circle, or simply memorize that sin(60) = sqrt(3)/2
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Method 3
Similar to the previous method, but we'll use tangent this time.
Use a reference sheet, unit circle, or memorize that tan(60) = sqrt(3)
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Method 4
This is a 30-60-90 triangle. In other words, the angles are 30 degrees, 60 degrees, and 90 degrees.
Because of this special type of triangle, we know that the long leg is exactly sqrt(3) times that of the short leg.
The short leg is always opposite the smallest angle (30 degrees).