In the right -angled tringles began the ABC in the ED :8cm ,and DC :10cm then the length of the air

if you can travel 156 miles on 4 gallons of gasoline how many miles can you travel on 6 gallons of gas

Luden [163]

Its 234!!!!!!!!!!!!!! Just checked my work

3 0

3 years ago

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

2 years ago

Help me solve this. Please, it's math.(I suck at math ngl ︺︹︺ )

fredd [130]

Answer:

Vertical angles are congruent, so the

equation 3x-6 = 114 can be used to find x.

The value of x is 40.

Convince Me!

Why can you use an equation when solving for x in

the diagram?

You can use the eqution because they are equal to each other. When they are equal to each other, you can find x by using the equation to simplify and get x alone.

6 0

1 year ago

Type only a number for your answer

UNO [17]

Answer:

x = 80

Step-by-step explanation:

x + 30 = 110 (opposite sides are congruent/equal)

x = 110 - 30 (subtract the 30 from both sides to get X by itself)

x = 80 (simplify)

7 0

2 years ago

a parallelogram has one side that is 4 centimeters long and one side that is 6 centimeters long. what is the perimeter of the pa

Ilia_Sergeevich [38]

Answer:

P = 20 cm

Step-by-step explanation:

The appropriate formula is P = 2W + 2L.

Here that comes to P = 2(6 cm) + 2(4 cm) = 20 cm

6 0

2 years ago