i. Which of the following polynomial function V (x) gives the volume of the pan
Answers
Answer
The volume of a box is represented by the function v(x)=x^3+2x^2-11x-12. If the height of the box is 4.5m, determine the dimensions of the box.
Answer:
V(x) = x3 + 2x2 - 11x - 12
To factor, you want 3 numbers that multiply to give -12 (the constant term) and add to give 2 (coefficient of the x2 term). The answer is 4, -3, and 1: (4)(-3)(1) = -12, 4 + (-3) + 1 = 2. So the volume polynomial factors to:
V(x) = (x+4)(x-3)(x+1)
Now the volume of a rectangular box is:
V = Length*Width*Height = (x+4)(x-3)(x+1)
So let's pick height = (x+1) = 4.5 (you could pick any one of the three factors).
x+1 = 4.5
x = 3.5
Length = (x+4) = 3.5+4 = 7.5
Width = (x-3) = 3.5 - 3 = 0.5
The box's dimensions are 7.5 m by 0.5 m by 4.5 m
Step-by-step explanation:
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