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2 years ago

Identify the number of terms in the expression. Type the answer in the space provided.

Mathematics

1 answer:

nadya68 [22]2 years ago

3 0

Answer:

Step-by-step explanation:

Terms are separated from one another by + and/or - signs. In this case neither appears, so the given expression constitutes a single term.

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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

Fun fact

pav-90 [236]

Answer: wow

I'd want nothing more than to swim in a pool of saliva.

8 0

2 years ago

Lou Harris is guaranteed a minimum $275 weekly salary plus 5.25% of his total sales. What were his total sales for a week in whi

Aleks [24]

His total sales were 402.68 dollars. 700 minus 275 minus 22.31

7 0

3 years ago

Reflect A (1,3) over the y-axis

gulaghasi [49]

Answer:

Up 1 and over 3

Step-by-step explanation:

4 0

3 years ago

Examine the linear table to find the slope, y-intercept, and write the equation for this linear relationship . NEED HELP PLEASE

gizmo_the_mogwai [7]

Answer:

$y = \frac{4}{3} x + 17$

Step-by-step explanation:

The table shows a set of x and y values, thus showing a set of points we can use to find the equation.

1) First, find the slope by using two points and substituting their x and y values into the slope formula, $\frac{y_2-y_1}{x_2-x_1}$ . I chose (-3, 13) and (0,17), but any two points from the table will work. Use them for the formula like so:

$\frac{(17)-(13)}{(0)-(-3)} \\= \frac{17-13}{0+3} \\= \frac{4}{3}$

Thus, the slope is $\frac{4}{3}$ .

2) Next, identify the y-intercept. The y-intercept is where the line hits the y-axis. All points on the y-axis have a x value of 0. Thus, (0,17) must be the y-intercept of the line.

3) Finally, write an equation in slope-intercept form, or $y = mx + b$ format. Substitute the $m$ and $b$ for real values.

The $m$ represents the slope of the equation, so substitute it for $\frac{4}{3}$ . The $b$ represents the y-value of the y-intercept, so substitute it for 17. This will give the following answer and equation:

$y = \frac{4}{3} x + 17$

7 0

2 years ago