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Sagot :
Answer:
3x+1
Step-by-step explanation:
The easiest way to think about this problem is to understand that volume is area multiplied by height.
So if volume = l*w*h, and area = l*w, then if you divide volume by area you will be left with height.
Assuming the volume equation is 3x^3+7x^2+2x and the area is x^2+2x, this problem can be solved using polynomial long division.
I'll be using 1. , 2. , etc to show steps for this part.
1. Divide 3x^3 by x^2
(3x^3/x^2) = 3x
2. Multiply 3x from step 1 by the area equation
3x(x^2+2x)=3x^3+6x^2
3. Subtract 3x^3+6x^2 from the volume equation
3x^3+7x^2+2x - 3x^3+6x^2 = x^2+2x
NOTE: This is equal to the area equation
4. Divide x^2+2x (from step 3) by x^2 +2x (from area equation)
Please note that this skips steps but is allowed in this case because the result from step 3 was equal to the area equation.
(x^2+2x)/(x^2+2x) = 1
5. Combine the results from step 1. and step 4.
3x+1
This answer is the height of the prism.
You can check this by multiplying 3x+1 by the area equation:
(3x+1)*(x^2+2x) = 3x^3+6x^2+x^2+2x = 3x^3+7x^2+2x = volume
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