Answer:
3. 1/2 4. 13/20
Step-by-step explanation:
Those are the only one I know, sorry :/
is conservative if we can find a scalar function
such that
. This would require
![\dfrac{\partial f}{\partial x}=5y^2z^3](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%3D5y%5E2z%5E3)
![\dfrac{\partial f}{\partial y}=10xyz^3](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D10xyz%5E3)
![\dfrac{\partial f}{\partial z}=15xy^2z^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20z%7D%3D15xy%5E2z%5E2)
Integrate both sides of the first PDE with respect to
:
(*)
Differentiate both sides of (*) with respect to
:
![\dfrac{\partial f}{\partial y}=10xyz^3=10xyz^3+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D10xyz%5E3%3D10xyz%5E3%2B%5Cdfrac%7B%5Cpartial%20g%7D%7B%5Cpartial%20y%7D%5Cimplies%5Cdfrac%7B%5Cpartial%20g%7D%7B%5Cpartial%20y%7D%3D0%5Cimplies%20g%28y%2Cz%29%3Dh%28z%29)
Differentiate both sides of (*) with respect to
:
![\dfrac{\partial f}{\partial z}=15xy^2z^2=15xy^2z^2+\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%3D15xy%5E2z%5E2%3D15xy%5E2z%5E2%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)=5xy^2z^3+C](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3D5xy%5E2z%5E3%2BC)
and so
is indeed conservative.
Answer:
<ACB is supplementary to the < ECD by the definition of supplementary angles. Therefore the first part of your answer is <ACB = <ECD
We know that similar triangles have the same corresponding angle measurements for their angles and therefore one of the triangles is just a scaled up or down version of the original. Triangle EDC is a scaled down version of ABC. Therefore, the corresponding sides of triangle ECD have the same ratio to the corresponding sides of ABC. For example line segment EC and BC are corresponding line segment and lets find the ratio: 14/21 = 2/3
THe ratio of EC to BC is 2/3 and the ratio of CD to AC is also 2/3 (18 / 27=2/3)
Therefore, CE / BC is equal to DC / AC
Your full answer is
<ACB = <ECD, CE / BC = DC / AC
So triangle ABC ~ triangle CDE
Step-by-step explanation:
Answer:
q^8/p^7
Step-by-step explanation:
.............
For this question you have to find how many heartbeats are in 1 minute.
So if you divide 210 by 3 you get 70
So, my answer here would be. 70 heartbeats per minute