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3 years ago

WILL MARK BRAINLIEST PLZ HELP!!

Mathematics

1 answer:

nignag [31]3 years ago

8 0

Answer:

y=mx+b

-6=5x-4

Step-by-step explanation:

-6=5x-4

than add 4 to both sides

-2=5x

than divide

x= -0.4

graph a vertical line slightly off from the half point between -1 and 0

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What's the flux of the vector field F(x,y,z) = (e^-y) i - (y) j + (x sinz) k across σ with outward orientation where σ is the po

emmasim [6.3K]

$\displaystyle\iint_\sigma\mathbf F\cdot\mathrm dS$
$\displaystyle\iint_\sigma\mathbf F\cdot\mathbf n\,\mathrm dS$
$\displaystyle\iint_\sigma\mathbf F\cdot\left(\frac{\mathbf r_u\times\mathbf r_v}{\|\mathbf r_u\times\mathbf r_v\|}\right)\|\mathbf r_u\times\mathbf r_v\|\,\mathrm dA$
$\displaystyle\iint_\sigma\mathbf F\cdot(\mathbf r_u\times\mathbf r_v)\,\mathrm dA$

Since you want to find flux in the outward direction, you need to make sure that the normal vector points that way. You have

$\mathbf r_u=\dfrac\partial{\partial u}[2\cos v\,\mathbf i+\sin v\,\mathbf j+u\,\mathbf k]=\mathbf k$
$\mathbf r_v=\dfrac\partial{\partial v}[2\cos v\,\mathbf i+\sin v\,\mathbf j+u\,\mathbf k]=-2\sin v\,\mathbf i+\cos v\,\mathbf j$

The cross product is

$\mathbf r_u\times\mathbf r_v=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\0&0&1\\-2\sin v&\cos v&0\end{vmatrix}=-\cos v\,\mathbf i-2\sin v\,\mathbf j$

So, the flux is given by

$\displaystyle\iint_\sigma(e^{-\sin v}\,\mathbf i-\sin v\,\mathbf j+2\cos v\sin u\,\mathbf k)\cdot(\cos v\,\mathbf i+2\sin v\,\mathbf j)\,\mathrm dA$
$\displaystyle\int_0^5\int_0^{2\pi}(-e^{-\sin v}\cos v+2\sin^2v)\,\mathrm dv\,\mathrm du$
$\displaystyle-5\int_0^{2\pi}e^{-\sin v}\cos v\,\mathrm dv+10\int_0^{2\pi}\sin^2v\,\mathrm dv$
$\displaystyle5\int_0^0e^t\,\mathrm dt+5\int_0^{2\pi}(1-\cos2v)\,\mathrm dv$

where $t=-\sin v$ in the first integral, and the half-angle identity is used in the second. The first integral vanishes, leaving you with

$\displaystyle5\int_0^{2\pi}(1-\cos2v)\,\mathrm dv=5\left(v-\dfrac12\sin2v\right)\bigg|_{v=0}^{v=2\pi}=10\pi$

5 0

3 years ago

Please help!( number 10, part A only)

Papessa [141]

Doubling the width would use less cardboard.
Justification:
Doubling the height will use 9in more cardboard
Doubling the width will only use 2 more inches of cardboard

8 0

3 years ago

Read 2 more answers

Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the p

Sphinxa [80]

The possible base and height of a second triangle are 12 and 7, respectively

<h3>How to determine the possible base and height of a second triangle?</h3>

An inverse variation is represented as:

Base * Height = k

Where k is the constant of variation.

In this case, k is the area

So, we have:

Base * Height = Area

For the first triangle, we have:

14 * 6 = Area

Evaluate

Area = 84

Substitute Area = 84 in Base * Height = Area

Base * Height = 84

Express 84 as the product of two numbers

Base * Height = 12 * 7

By comparison;

Base =12 and Height = 7

Hence, the possible base and height of a second triangle are 12 and 7, respectively