Answer:
log₉2873 ≈ 3.6242
Step-by-step explanation:
First off all you can estimate by applying a fundamental property of a logarithm
![\vec f(x,y,z)=y\,\vec\imath-4yz\,\vec\jmath+3z^2\,\vec k](https://tex.z-dn.net/?f=%5Cvec%20f%28x%2Cy%2Cz%29%3Dy%5C%2C%5Cvec%5Cimath-4yz%5C%2C%5Cvec%5Cjmath%2B3z%5E2%5C%2C%5Cvec%20k)
![\implies\nabla\cdot\vec f(x,y,z)=0-4z+6z=2z](https://tex.z-dn.net/?f=%5Cimplies%5Cnabla%5Ccdot%5Cvec%20f%28x%2Cy%2Cz%29%3D0-4z%2B6z%3D2z)
By the divergence theorem,
![\displaystyle\iint_{\partial W}\vec f\cdot\mathrm d\vec S=\iiint_W2z\,\mathrm dV](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_%7B%5Cpartial%20W%7D%5Cvec%20f%5Ccdot%5Cmathrm%20d%5Cvec%20S%3D%5Ciiint_W2z%5C%2C%5Cmathrm%20dV)
I'll assume a sphere of radius
centered at the origin, and that
is bounded below by the plane
. Convert to spherical coordinates, taking
![x=\rho\cos\theta\sin\varphi](https://tex.z-dn.net/?f=x%3D%5Crho%5Ccos%5Ctheta%5Csin%5Cvarphi)
![y=\rho\sin\theta\sin\varphi](https://tex.z-dn.net/?f=y%3D%5Crho%5Csin%5Ctheta%5Csin%5Cvarphi)
![z=\rho\cos\varphi](https://tex.z-dn.net/?f=z%3D%5Crho%5Ccos%5Cvarphi)
Then
![\displaystyle\iiint_W2z\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^r2\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\pi r^4](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciiint_W2z%5C%2C%5Cmathrm%20dV%3D%5Cint_0%5E%7B%5Cpi%2F2%7D%5Cint_0%5E%7B2%5Cpi%7D%5Cint_0%5Er2%5Crho%5E3%5Ccos%5Cvarphi%5Csin%5Cvarphi%5C%2C%5Cmathrm%20d%5Crho%5C%2C%5Cmathrm%20d%5Ctheta%5C%2C%5Cmathrm%20d%5Cvarphi%3D%5Cpi%20r%5E4)
Answer:
x = -4/5 or x = 71/8
Step-by-step explanation:
Solve for x:
(5 x + 4) (8 x - 71) = 0
Split into two equations:
5 x + 4 = 0 or 8 x - 71 = 0
Subtract 4 from both sides:
5 x = -4 or 8 x - 71 = 0
Divide both sides by 5:
x = -4/5 or 8 x - 71 = 0
Add 71 to both sides:
x = -4/5 or 8 x = 71
Divide both sides by 8:
Answer: x = -4/5 or x = 71/8
Answer:
trapeziod
Step-by-step explanation:
A trapezoid is a quadrilateral with only one pair of opposite sides parallel. The parallel sides are called bases, and the nonparallel sides are called legs. A segment that joins the midpoints of the legs is called the median of the trapezoid