By the binomial theorem,
![\displaystyle \left(x^2 + \frac px\right)^6 = \sum_{n=0}^6 \binom 6n \left(x^2\right)^n \left(\frac px\right)^{6-n} = \sum_{n=0}^6 p^{6-n} \binom 6n x^{3n-6}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28x%5E2%20%2B%20%5Cfrac%20px%5Cright%29%5E6%20%3D%20%5Csum_%7Bn%3D0%7D%5E6%20%5Cbinom%206n%20%5Cleft%28x%5E2%5Cright%29%5En%20%5Cleft%28%5Cfrac%20px%5Cright%29%5E%7B6-n%7D%20%3D%20%5Csum_%7Bn%3D0%7D%5E6%20p%5E%7B6-n%7D%20%5Cbinom%206n%20x%5E%7B3n-6%7D)
where
![\dbinom kn = \dfrac{k!}{n!(k-n)!}](https://tex.z-dn.net/?f=%5Cdbinom%20kn%20%3D%20%5Cdfrac%7Bk%21%7D%7Bn%21%28k-n%29%21%7D)
is the so-called binomial coefficient.
The term that's independent of x is the constant term, which occurs when
, or
. Given that this constant 240, we have
![p^{6-2} \dbinom62 = 240 \implies p^4 = 16 \implies p = \pm2](https://tex.z-dn.net/?f=p%5E%7B6-2%7D%20%5Cdbinom62%20%3D%20240%20%5Cimplies%20p%5E4%20%3D%2016%20%5Cimplies%20p%20%3D%20%5Cpm2)
but
must be positive, so ![\boxed{p=2}](https://tex.z-dn.net/?f=%5Cboxed%7Bp%3D2%7D)
Answer: Common difference
Step-by-step explanation:
You keep subtracting the lower number from the higher number next to it in the sequence. If you keep getting the dame difference, that is the common difference, and the sequence is arithmetic
If the US could make 14 stereos/hr or 7 cars/hr, this is a ratio of 2 stereos/1 car, or 1 stereo/0.5 cars. Therefore the US opportunity cost of producing 1 stereo is 0.5 car of half a car.
If China (or Japan? given the question in #2) makes 15 stereos/hr or 5 cars/hr, this is a ratio of 3 stereos/1 car, or 1 stereo/0.33 cars.
Answer: d) acute isoceles
Step-by-step explanation:
it has 2 acute angles and it's isoceles because it has 2 sides of equal length
Answer: 241 days a year
Step-by-step explanation: 365*0.66=240.9 and then you round up to 241