the correct answer is letter D. 3 1/7
:)
Answer: the number of the cookies in the original batch is 120
Step-by-step explanation:
Let x represent the number of cookies that were in the original batch.
She gave one-quarter of the batch to Kevin. This means that the number of cookies given to Kevin is 1/4×x = x/4
She gave one-fifth to Katie. This means that the number of cookies given to Katie is 1/5×x = x/5
She gave one-sixth to Mike.
This means that the number of cookies given to Mike is 1/6×x = x/6
If those three were given a total of 74 cookies, it means that the sum of the cookies given to Kevin, Katie and Mike 74. It is expressed as
x/4 + x/5 + x/6 = 74
Taking 60 as LCM and multiplying through with it, it becomes
15x + 12x + 10x = 4440
37x = 4440
x = 4440/37
x = 120
![\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)
if your wanting to know how far the diver will be down you do 240+25 which is 265
265-80=185 (cause the diver swims up)
185+12+30 =227
227-16 =211
the deep see diver is at 211 meters below the surface
Answer:
The continents were once connected as one landmass?