Answer:
answer is 2x / 8.
a number = x
quotient = division of 8
times = multiplication
hope this helps, i also hated my algebraic expressions unit haha
Use a graphing calculator Site.or Go by graphing calculator.
Answer:
10 milligrams
Step-by-step explanation:
You can parameterize the curve
![C](https://tex.z-dn.net/?f=C)
and compute the integral along each component curve, or you can use the fact that
![f(x,y)=(\sin x,\cos y)](https://tex.z-dn.net/?f=f%28x%2Cy%29%3D%28%5Csin%20x%2C%5Ccos%20y%29)
is the continuous gradient of a function
![F(x,y)](https://tex.z-dn.net/?f=F%28x%2Cy%29)
and observe that the line integral is path independent.
In other words, there is a function
![F(x,y)](https://tex.z-dn.net/?f=F%28x%2Cy%29)
such that
![\nabla F(x,y)=f(x,y)](https://tex.z-dn.net/?f=%5Cnabla%20F%28x%2Cy%29%3Df%28x%2Cy%29)
, so the integral along any curve
![C](https://tex.z-dn.net/?f=C)
from the points
![\mathbf a](https://tex.z-dn.net/?f=%5Cmathbf%20a)
to
![\mathbf b](https://tex.z-dn.net/?f=%5Cmathbf%20b)
is simply
![\displaystyle\int_Cf(x,y)\,\mathrm dS=\int_C(P(x,y)\,\mathrm dx+Q(x,y)\,\mathrm dy)=F(\mathbf b)-F(\mathbf a)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_Cf%28x%2Cy%29%5C%2C%5Cmathrm%20dS%3D%5Cint_C%28P%28x%2Cy%29%5C%2C%5Cmathrm%20dx%2BQ%28x%2Cy%29%5C%2C%5Cmathrm%20dy%29%3DF%28%5Cmathbf%20b%29-F%28%5Cmathbf%20a%29)
You have
![\nabla F(x,y)=(\sin x,\cos y)](https://tex.z-dn.net/?f=%5Cnabla%20F%28x%2Cy%29%3D%28%5Csin%20x%2C%5Ccos%20y%29)
, and so
![\dfrac{\partial F(x,y)}{\partial x}=\sin x\implies F(x,y)=-\cos x+g(y)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20F%28x%2Cy%29%7D%7B%5Cpartial%20x%7D%3D%5Csin%20x%5Cimplies%20F%28x%2Cy%29%3D-%5Ccos%20x%2Bg%28y%29)
while
![\dfrac{\partial F(x,y)}{\partial y}=\cos y=g'(y)\implies g(y)=\sin y+K](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20F%28x%2Cy%29%7D%7B%5Cpartial%20y%7D%3D%5Ccos%20y%3Dg%27%28y%29%5Cimplies%20g%28y%29%3D%5Csin%20y%2BK)
where
![K](https://tex.z-dn.net/?f=K)
is an arbitrary constant. So we've found that
![F(x,y)=\sin y-\cos x+K](https://tex.z-dn.net/?f=F%28x%2Cy%29%3D%5Csin%20y-%5Ccos%20x%2BK)
which means the line integral has a value of
Answer:
-2
Step-by-step explanation:
Lets factor
(x+2)(x+2)=0
x=-2