Find the LCM of 6 and 8. A) 12 B) 18 C) 24 D) 36

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

Solve for n. 4n + 19 + 13n = -13 + 15n

STALIN [3.7K]

ANSWER: n = -16

4n + 13n = 17n

19 + 13 = 32

15 - 17 = -2

n = -16

3 0

3 years ago

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How much higher is Checkpoint 5 than Checkpoint 2?

Akimi4 [234]

You have to find the difference in height between both checkpoints. To do this just calculate 196 - 52. Checkpoint 5 is 144 (meters?) higher than Checkpoint 2.

5 0

3 years ago

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A two-dimensional figure with four sides has 2 pairs of opposite parallel sides, 4 congruent sides, and 4 right angles.

kap26 [50]

Parallelogram rectangle square rhombus

8 0

3 years ago

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Given the function w (x) = 9x + 8, evaluate w (5) . Explain all steps.

masya89 [10]

Hi there!