Answer:
x=4
Step-by-step explanation:
3x-6=6
3x=12
x=4
(3*4)-6
12-6
=6
Answer:
108
Step-by-step explanation:
Since angle AFB and angle BFC are next to each other and form a straight line, we can subtract 72 from 180 to get the missing angle measurement. (all straight lines add up to 180)
180-72=108
So 108 would be your answer
![\vec F(x,y,z)=x^3\,\vec\imath+x^2y\,\vec\jmath+x^2e^y\,\vec k](https://tex.z-dn.net/?f=%5Cvec%20F%28x%2Cy%2Cz%29%3Dx%5E3%5C%2C%5Cvec%5Cimath%2Bx%5E2y%5C%2C%5Cvec%5Cjmath%2Bx%5E2e%5Ey%5C%2C%5Cvec%20k)
has divergence
![\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(x^3)}{\partial x}+\dfrac{\partial(x^2y)}{\partial y}+\dfrac{\partial(x^2e^y)}{\partial z}=4x^2](https://tex.z-dn.net/?f=%5Cnabla%5Ccdot%5Cvec%20F%28x%2Cy%2Cz%29%3D%5Cdfrac%7B%5Cpartial%28x%5E3%29%7D%7B%5Cpartial%20x%7D%2B%5Cdfrac%7B%5Cpartial%28x%5E2y%29%7D%7B%5Cpartial%20y%7D%2B%5Cdfrac%7B%5Cpartial%28x%5E2e%5Ey%29%7D%7B%5Cpartial%20z%7D%3D4x%5E2)
so that by the divergence theorem, the flux of
through
is the integral of
over the interior of
(call it
):
![\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=4\iiint_Rx^2\,\mathrm dV](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_S%5Cvec%20F%5Ccdot%5Cmathrm%20d%5Cvec%20S%3D4%5Ciiint_Rx%5E2%5C%2C%5Cmathrm%20dV)
is a tetrahedron in the first quadrant defined by the set
![R:=\left\{(x,y,z)\mid0\le x\le5,0\le y\le3,0\le z\le3-y\right\}](https://tex.z-dn.net/?f=R%3A%3D%5Cleft%5C%7B%28x%2Cy%2Cz%29%5Cmid0%5Cle%20x%5Cle5%2C0%5Cle%20y%5Cle3%2C0%5Cle%20z%5Cle3-y%5Cright%5C%7D)
(and this is by no means the only way to define
)
Then the integral over
is
![\displaystyle4\int_0^5\int_0^3\int_0^{3-y}x^2\,\mathrm dz\,\mathrm dy\,\mathrm dx=\boxed{750}](https://tex.z-dn.net/?f=%5Cdisplaystyle4%5Cint_0%5E5%5Cint_0%5E3%5Cint_0%5E%7B3-y%7Dx%5E2%5C%2C%5Cmathrm%20dz%5C%2C%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx%3D%5Cboxed%7B750%7D)
It is a hot summer day, and Jade is trying to save money to buy a new shoe. She has 32 dollars, and she plans to sell smoothies at her neighborhood for four dollars a cup. At the end of the day, she is left with a total of 164 dollars in her wallet. How many smoothies did Jade sell?