Ten pieces of candy are in a bag. They all have the same shape; but 2 pieces are butterscotch flavored, 5 pieces are
1 answer:
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The unit disk can be parameterized by the function
where
and 
. The squared distance between any point in this region 
and the point (1, 1) is
The average squared distance is then going to be the ratio of [the sum of all squared distances between every point in the disk and the point (1, 1)] to [the area of the disk], i.e.
![=\dfrac{\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}[r^2-2r(\cos\theta-\sin\theta)+2]r\,\mathrm dr\,\mathrm d\theta}{\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}r\,\mathrm dr\,\mathrm d\theta}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%5Cdisplaystyle%5Cint_%7B%5Ctheta%3D0%7D%5E%7B%5Ctheta%3D2%5Cpi%7D%5Cint_%7Br%3D0%7D%5E%7Br%3D1%7D%5Br%5E2-2r%28%5Ccos%5Ctheta-%5Csin%5Ctheta%29%2B2%5Dr%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%7D%7B%5Cdisplaystyle%5Cint_%7B%5Ctheta%3D0%7D%5E%7B%5Ctheta%3D2%5Cpi%7D%5Cint_%7Br%3D0%7D%5E%7Br%3D1%7Dr%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%7D)
where
The average squared distance is then going to be the ratio of [the sum of all squared distances between every point in the disk and the point (1, 1)] to [the area of the disk], i.e.
Answer:
<em>Gardener will need 4 more plants.</em>
Step-by-step explanation:
Gardener has 780 plants and wants to plant them in an array of n rows and n columns.
The number of plants needed to do that is:
He actually has 780 plants, thus it should occur:
Taking the square root:
n=27.9
Since n needs to be an integer, we round up n to get
n=28
But , 4 more than the actual number of plants, thus:
Gardener will need 4 more plants.
Note: There are other possible results for n. If we set n=29, then and Gardener would need 841-780=61 more plants, but the question asked for the minimum number of plants.