If
![\nabla f=(ye^x+\sin y)\,\vec\imath+(e^x+x\cos y)\,\vec\jmath](https://tex.z-dn.net/?f=%5Cnabla%20f%3D%28ye%5Ex%2B%5Csin%20y%29%5C%2C%5Cvec%5Cimath%2B%28e%5Ex%2Bx%5Ccos%20y%29%5C%2C%5Cvec%5Cjmath)
then
![\dfrac{\partial f}{\partial x}=ye^x+\sin y\implies f(x,y)=ye^x+x\sin y+g(y)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%3Dye%5Ex%2B%5Csin%20y%5Cimplies%20f%28x%2Cy%29%3Dye%5Ex%2Bx%5Csin%20y%2Bg%28y%29)
Differentiating with respec to
gives
![\dfrac{\partial f}{\partial y}=e^x+x\cos y=e^x+x\cos y+g'(y)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3De%5Ex%2Bx%5Ccos%20y%3De%5Ex%2Bx%5Ccos%20y%2Bg%27%28y%29)
![\implies g'(y)=0\implies g(y)=C](https://tex.z-dn.net/?f=%5Cimplies%20g%27%28y%29%3D0%5Cimplies%20g%28y%29%3DC)
So
is indeed conservative, and
![f(x,y)=ye^x+x\sin y+C](https://tex.z-dn.net/?f=f%28x%2Cy%29%3Dye%5Ex%2Bx%5Csin%20y%2BC)
Answer:
$180
Step-by-step explanation:
step one 86+4 =90
step two 90×2=180
Based on the quadrilateral given, the values of the missing measures will be:
- VU = 15
- SU = 21.21
- TV = 21.21
- SW = 10.61
<h3>
Solving quadrilateral.</h3>
A quadrilateral simply means a polygon that has four sides, edges and vertices.
Based on the information given, SU = TV and this will be:
= ✓450 = 21.21
SW = 21.21/2 = 10.61
Also, for the second shape, the values will be:
OM = 46; PN = 23, ON = 46; MN = 46.
Learn more about quadrilateral on:
brainly.com/question/224113
Answer:
This is not a function graph as no variables are present.
Is your question "There is enough batter to make 18 cupcakes. How many cupcakes cpuld make if they were 3/4 the original size?" Because that makes more sense and can be answered.