Answer:
Before raise: 65 chocolates/hour*60=3900 chocolates
Raise=65 * (15%=15/100=.15) .15=9.75 more chocolates per hour
With raise 74.75 chocolates/hour*60=4485 chocolates
4485-3900=585 more chocolates per 60 hour week
Step-by-step explanation:
Answer:
b.) distance north or south of the equator
Step-by-step explanation:
Lines of latitude are horizontal lines parallel with the equator.
The equator is the central line of latitude, and latitude is measured north or south of the equator.
Answer: b.) distance north or south of the equator
For
to be conservative, we need to have
![\dfrac{\partial f}{\partial x}=\cos z](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%3D%5Ccos%20z)
![\dfrac{\partial f}{\partial y}=10y](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D10y)
![\dfrac{\partial f}{\partial z}=-x\sin z](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20z%7D%3D-x%5Csin%20z)
Integrate the first PDE with respect to
:
![\displaystyle\int\frac{\partial f}{\partial x}\,\mathrm dx+\int\cos z\,\mathrm dx\implies f(x,y,z)=x\cos z+g(y,z)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%5C%2C%5Cmathrm%20dx%2B%5Cint%5Ccos%20z%5C%2C%5Cmathrm%20dx%5Cimplies%20f%28x%2Cy%2Cz%29%3Dx%5Ccos%20z%2Bg%28y%2Cz%29)
Differentiate with respect to
:
![\dfrac{\partial f}{\partial y}=10y=\dfrac{\partial g}{\partial y}\implies g(y,z)=5y^2+h(z)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D10y%3D%5Cdfrac%7B%5Cpartial%20g%7D%7B%5Cpartial%20y%7D%5Cimplies%20g%28y%2Cz%29%3D5y%5E2%2Bh%28z%29)
Now differentiate
with respect to
:
![\dfrac{\partial f}{\partial z}=-x\sin z=-x\sin z+\dfrac{\mathrm dh}{\mathrm dz}\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20z%7D%3D-x%5Csin%20z%3D-x%5Csin%20z%2B%5Cdfrac%7B%5Cmathrm%20dh%7D%7B%5Cmathrm%20dz%7D%5Cimplies%5Cdfrac%7B%5Cmathrm%20dh%7D%7B%5Cmathrm%20dz%7D%3D0%5Cimplies%20h%28z%29%3DC)
So we have
![f(x,y,z)=x\cos z+5y^2+C](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3Dx%5Ccos%20z%2B5y%5E2%2BC)
so
is indeed conservative.
Answer:
its cut off Step-by-step explanation:
its cut off dude
6 < c < 20,
Of course if you knew the triangle was a right triangle you could use the Pythagorean theorem to directly get the size of the third side.