S(p)=D(p)
400-4p+0.00002p4=2,800-0.0012p3
Solve for p
P=96.24
I think it should be 31.5
6 builders over 21 days would be equal to 9 builders over X days. Then you would cross multiply
Answer:I don’t know sorry
Step-by-step explanation:
1.one and seventy five thousandths this is word form 2.(1 x 1) + (0/10) + (7/100) + (5/1000) this is expanded form
Convert to polar coordinates with
![x = r \cos(\theta)](https://tex.z-dn.net/?f=x%20%3D%20r%20%5Ccos%28%5Ctheta%29)
![y = r \sin(\theta)](https://tex.z-dn.net/?f=y%20%3D%20r%20%5Csin%28%5Ctheta%29)
so that
, and the Jacobian determinant for this change of variables is
![dx\,dy = r \, dr \, d\theta](https://tex.z-dn.net/?f=dx%5C%2Cdy%20%3D%20r%20%5C%2C%20dr%20%5C%2C%20d%5Ctheta)
D is the disk centered at the origin with radius 2; in polar coordinates, this is the set
![D = \left\{(r, \theta) \mid 0\le\theta\le2\pi \text{ and } 0 \le r \le 2\right\}](https://tex.z-dn.net/?f=D%20%3D%20%5Cleft%5C%7B%28r%2C%20%5Ctheta%29%20%5Cmid%200%5Cle%5Ctheta%5Cle2%5Cpi%20%5Ctext%7B%20and%20%7D%200%20%5Cle%20r%20%5Cle%202%5Cright%5C%7D)
Then the integral is
![\displaystyle \iint_D (x + y + 10) \, dx \, dy = \int_0^{2\pi} \int_0^2 (r \cos(\theta) + r \sin(\theta) + 10) r \, dr \, d\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ciint_D%20%28x%20%2B%20y%20%2B%2010%29%20%5C%2C%20dx%20%5C%2C%20dy%20%3D%20%5Cint_0%5E%7B2%5Cpi%7D%20%5Cint_0%5E2%20%28r%20%5Ccos%28%5Ctheta%29%20%2B%20r%20%5Csin%28%5Ctheta%29%20%2B%2010%29%20r%20%5C%2C%20dr%20%5C%2C%20d%5Ctheta)
![\displaystyle = \int_0^{2\pi} \int_0^2 (r^2 \cos(\theta) + r^2 \sin(\theta) + 10r) \, dr \, d\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%3D%20%5Cint_0%5E%7B2%5Cpi%7D%20%5Cint_0%5E2%20%28r%5E2%20%5Ccos%28%5Ctheta%29%20%2B%20r%5E2%20%5Csin%28%5Ctheta%29%20%2B%2010r%29%20%5C%2C%20dr%20%5C%2C%20d%5Ctheta)
![\displaystyle = \int_0^{2\pi} \left(\frac83 (\cos(\theta) + \sin(\theta)) + 20\right) \, d\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%3D%20%5Cint_0%5E%7B2%5Cpi%7D%20%5Cleft%28%5Cfrac83%20%28%5Ccos%28%5Ctheta%29%20%2B%20%5Csin%28%5Ctheta%29%29%20%2B%2020%5Cright%29%20%5C%2C%20d%5Ctheta)
![\displaystyle = 20 \int_0^{2\pi} d\theta = \boxed{40\pi}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%3D%2020%20%5Cint_0%5E%7B2%5Cpi%7D%20d%5Ctheta%20%3D%20%5Cboxed%7B40%5Cpi%7D)
(since cos and sin are 2π-periodic)