the volume of a rectangular solid is given by expressions given below.in each case find the dimentions of the solid.
a)15x^2-51x+18.
b)x^3+13x^2+32x+20.
c)x^2-5x/2-3/2.
d)x^4+x^3-x-1
plz everyone help me out.till 2 o'clock...plz plz plz
See your other post:
http://www.jiskha.com/display.cgi?id=1338372207
To find the dimensions of a rectangular solid given the volume expression, we need to factorize the expression and match it to the formula for the volume of a rectangular solid.
a) Volume: 15x^2 - 51x + 18
First, let's try to factorize the given expression:
15x^2 - 51x + 18
We can factor it as: (3x - 2)(5x - 9)
The volume formula for a rectangular solid is V = lwh, where l is the length, w is the width, and h is the height.
Comparing the factored expression to the volume formula, we can see that:
l = 3x - 2
w = 5x - 9
h = 1 (since no value is given, we assume it as 1)
Therefore, the dimensions of the rectangular solid are:
Length = 3x - 2
Width = 5x - 9
Height = 1
b) Volume: x^3 + 13x^2 + 32x + 20
Let's factorize the given expression:
x^3 + 13x^2 + 32x + 20
We can factor it as: (x + 1)(x + 5)(x + 4)
Comparing the factored expression to the volume formula:
l = x + 1
w = x + 5
h = x + 4
Therefore, the dimensions of the rectangular solid are:
Length = x + 1
Width = x + 5
Height = x + 4
c) Volume: x^2 - 5x/2 - 3/2
Again, let's factorize the given expression:
x^2 - 5x/2 - 3/2
We can factor it as: (x - 3/2)(x + 1)
Comparing the factored expression to the volume formula:
l = x - 3/2
w = x + 1
h = 1
Therefore, the dimensions of the rectangular solid are:
Length = x - 3/2
Width = x + 1
Height = 1
d) Volume: x^4 + x^3 - x - 1
Let's factorize the given expression:
x^4 + x^3 - x - 1
Unfortunately, this expression cannot be easily factorized by simple methods. So, the dimensions of the rectangular solid cannot be determined directly from the given expression.