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Alexandra [31]
3 years ago
5

Instructions

Mathematics
1 answer:
VladimirAG [237]3 years ago
5 0
Where is the picture?
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Evaluate the surface integral. s (x + y + z) ds, s is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 +
Stolb23 [73]
S is given to be parameterized by

\mathbf r(u,v)=\langle x(u,v),y(u,v),z(u,v)\rangle=\langle u+v,u-v,1+2u+v\rangle

with 0\le u\le3 and 0\le v\le2. We have

\mathbf r_u=\langle1,1,2\rangle
\mathbf r_v=\langle1,-1,1\rangle
\mathbf r_u\times\mathbf r_v=\langle3,1,-2\rangle
\left\|\mathbf r_u\times\mathbf r_v\right\|=\sqrt{14}

The surface integral is then

\displaystyle\iint_S(x+y+z)\,\mathrm dS=\iint_S(x(u,v)+y(u,v)+z(u,v))\left\|\mathbf r_u\times\mathbf r_v\right\|\,\mathrm du\,\mathrm dv
=\displaystyle\sqrt{14}\int_{u=0}^{u=3}\int_{v=0}^{v=2}((u+v)+(u-v)+(1+2u+v))\,\mathrm dv\,\mathrm du
=\displaystyle\sqrt{14}\int_{u=0}^{u=3}\int_{v=0}^{v=2}(4u+v+1)\,\mathrm dv\,\mathrm du
=\displaystyle\sqrt{14}\left(8\int_{u=0}^{u=3}u\,\mathrm du+3\int_{v=0}^{v=2}v\,\mathrm dv+6\right)
=\displaystyle\sqrt{14}\left(8\int_{u=0}^{u=3}u\,\mathrm du+3\int_{v=0}^{v=2}v\,\mathrm dv+6\right)
=48\sqrt{14}
4 0
3 years ago
Use undetermined coefficients to find the particular solution to 7t + 5=y''+y'-4y У, (t) - Preview Get help: Video Points possib
lions [1.4K]

Suppose y_p=a_0+a_1t is a solution to the ODE. Then {y_p}'=a_1 and {y_p}''=0, and substituting these into the ODE gives

a_1-4(a_0+a_1t)=7t+5\implies\begin{cases}-4a_1=7\\-4a_0+a_1=5\end{cases}\implies a_0=-\dfrac{27}{16},a_1=-\dfrac74

Then the particular solution to the ODE is

y_p=-\dfrac{27}{16}-\dfrac74t

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3 years ago
How does Bolsa describe Billy Joe? smart funny crazy
Ne4ueva [31]

Answer:

The ansswer is the last one. (Crazy)

Step-by-step explanation:

3 0
2 years ago
The value of x is .... ?
alexira [117]

Answer: 96

Step-by-step explanation:

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3 years ago
1 pts
lubasha [3.4K]

Answer: I believe the answer to your question is 4

Step-by-step explanation:

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