Answer:
The think that the answer is question 1 is B and the answer to question 2 is also B.
Step-by-step explanation:
Answer:
Required solution (a)
(b) 40.
Step-by-step explanation:
Given,
![F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k](https://tex.z-dn.net/?f=F%28x%2Cy%2Cz%29%3Dyz%20%5Cuvec%20i%20%2Bxz%5Cuvec%20j%2B%28xy%2B6z%29%5Cuvex%20k)
(a) Let,
![F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k=f_x \uvec{i} +f_y \uvex{j}+f_z\uvec{k}](https://tex.z-dn.net/?f=F%28x%2Cy%2Cz%29%3Dyz%20%5Cuvec%20i%20%2Bxz%5Cuvec%20j%2B%28xy%2B6z%29%5Cuvex%20k%3Df_x%20%5Cuvec%7Bi%7D%20%2Bf_y%20%5Cuvex%7Bj%7D%2Bf_z%5Cuvec%7Bk%7D)
Then,
![f_x=yz,f_y=xz,f_z=xy+6z](https://tex.z-dn.net/?f=f_x%3Dyz%2Cf_y%3Dxz%2Cf_z%3Dxy%2B6z)
Integrating
we get,
![f(x,y,z)=xyz+g(y,z)](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3Dxyz%2Bg%28y%2Cz%29)
Differentiate this with respect to y we get,
compairinfg with
of the given function we get,
![g'(y,z)=0\implies g(y,z)=0+h(z)\implies g(y,z)=h(z)](https://tex.z-dn.net/?f=g%27%28y%2Cz%29%3D0%5Cimplies%20g%28y%2Cz%29%3D0%2Bh%28z%29%5Cimplies%20g%28y%2Cz%29%3Dh%28z%29)
Then,
![f(x,y,z)=xyz+h(z)](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3Dxyz%2Bh%28z%29)
Again differentiate with respect to z we get,
![f_z=xy+h'(z)=xy+6z](https://tex.z-dn.net/?f=f_z%3Dxy%2Bh%27%28z%29%3Dxy%2B6z)
on compairing we get,
(By integrating h'(z)) where C is integration constant. Hence,
![f(x,y,z)=xyz+3z^2+C](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3Dxyz%2B3z%5E2%2BC)
(b) Next, to find the itegration,
![\int_C \vec{F}.dr=\int_C \nabla f. d\vec{r}=f(5,4,2)-f(2,0,-2)=(52+C)-(12+C)=40](https://tex.z-dn.net/?f=%5Cint_C%20%5Cvec%7BF%7D.dr%3D%5Cint_C%20%5Cnabla%20f.%20d%5Cvec%7Br%7D%3Df%285%2C4%2C2%29-f%282%2C0%2C-2%29%3D%2852%2BC%29-%2812%2BC%29%3D40)
Answer:
12x7 4 times add it up u got the anwser
That's we can solve by using a combination algorithm:
Answer:
32%
Step-by-step explanation:
The slope of the road is measured as
slope =
= ![\frac{16}{50}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B50%7D)
To express as a percentage multiply the fraction y 100% , that is
slope =
× 100% = 16 × 2 = 32%