Answer: it goes down (decreases) steadily
Step-by-step explanation:
Notice that
(1 - <em>x</em>)⁵ (1 + 1/<em>x</em>)⁵ = ((1 - <em>x</em>) (1 + 1/<em>x</em>))⁵ = (1 - <em>x</em> + 1/<em>x</em> - 1)⁵ = (1/<em>x</em> - <em>x</em>)⁵
Recall the binomial theorem:
![\displaystyle(a+b)^n = \sum_{k=0}^n\binom nk a^{n-k}b^k](https://tex.z-dn.net/?f=%5Cdisplaystyle%28a%2Bb%29%5En%20%3D%20%5Csum_%7Bk%3D0%7D%5En%5Cbinom%20nk%20a%5E%7Bn-k%7Db%5Ek)
Let <em>a</em> = 1/<em>x</em>, <em>b</em> = -<em>x</em>, and <em>n</em> = 5. Then
![\displaystyle\left(\frac1x-x\right)^5 = \sum_{k=0}^5\binom5k\left(\frac1x\right)^{5-k}(-x)^k = \sum_{k=0}^5 (-1)^k\binom5k x^{2k-5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cleft%28%5Cfrac1x-x%5Cright%29%5E5%20%3D%20%5Csum_%7Bk%3D0%7D%5E5%5Cbinom5k%5Cleft%28%5Cfrac1x%5Cright%29%5E%7B5-k%7D%28-x%29%5Ek%20%3D%20%5Csum_%7Bk%3D0%7D%5E5%20%28-1%29%5Ek%5Cbinom5k%20x%5E%7B2k-5%7D)
We get an <em>x</em> ³ term for
2<em>k</em> - 5 = 3 ==> 2<em>k</em> = 8 ==> <em>k</em> = 4
so that the coefficient would be
![(-1)^4\dbinom54 = \boxed{5}](https://tex.z-dn.net/?f=%28-1%29%5E4%5Cdbinom54%20%3D%20%5Cboxed%7B5%7D)
Given the proportion 7/5=x/3, you can cross-multiply to find the value of x.
21=5x.
Divide both sides by 5.
x=4.2.
Hope this helps!
Answer: 13+16x
Step-by-step explanation:
Okay so I just learned how to do that haha, so if the answer is wrongdoing I'm a sorry.
I added the 8 and five, then multiplyed the 4 and the 4 then added the x on the end.