Answer:
How many plates are on the table as it results in only one value with no variability
Step-by-step explanation:
Answer:
![x^6+3x^3+3+\dfrac{1}{x^3}](https://tex.z-dn.net/?f=x%5E6%2B3x%5E3%2B3%2B%5Cdfrac%7B1%7D%7Bx%5E3%7D)
Step-by-step explanation:
We can use the pascal triangle to find the coefficients of the expasion of the cube. It holds that
![(x^2 + \dfrac{1}{x})^3=(x^2)^3+3(x^2)^2\dfrac{1}{x}+3x^2(\dfrac{1}{x})^2+(\dfrac{1}{x})^3\\\\=x^6+3x^4\dfrac{1}{x}+3x^2\dfrac{1}{x^2}+\dfrac{1}{x^3}\\\\=x^6+3x^3+3+\dfrac{1}{x^3}](https://tex.z-dn.net/?f=%28x%5E2%20%2B%20%5Cdfrac%7B1%7D%7Bx%7D%29%5E3%3D%28x%5E2%29%5E3%2B3%28x%5E2%29%5E2%5Cdfrac%7B1%7D%7Bx%7D%2B3x%5E2%28%5Cdfrac%7B1%7D%7Bx%7D%29%5E2%2B%28%5Cdfrac%7B1%7D%7Bx%7D%29%5E3%5C%5C%5C%5C%3Dx%5E6%2B3x%5E4%5Cdfrac%7B1%7D%7Bx%7D%2B3x%5E2%5Cdfrac%7B1%7D%7Bx%5E2%7D%2B%5Cdfrac%7B1%7D%7Bx%5E3%7D%5C%5C%5C%5C%3Dx%5E6%2B3x%5E3%2B3%2B%5Cdfrac%7B1%7D%7Bx%5E3%7D)
9514 1404 393
Answer:
DE = 86
EF = 84
Step-by-step explanation:
We assume that point E lies on segment DF, so that ...
DE + EF = DF
(3x +20) +(2x +40) = 170
5x = 110 . . . . . . . . . . . . . . . collect terms, subtract 60
x = 22 . . . . . . . . . . . . divide by 5
DE = 3×22 +20 = 66 +20 = 86
EF = 2×22 +40 = 44 +40 = 84