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2 years ago

Find the surface area of the rectangular prism. 15 cm 3 cm 5 cm

Mathematics

1 answer:

garik1379 [7]2 years ago

5 0

Answer:

Step-by-step explanation:

Formula

SA = 2*L*w + 2*L*h + 2*h*w

Givens

L = 15

w = 5

h = 3

Solution

SA = 2*15*5 + 2*15*3 + 2*5*3

SA = 150 + 90 + 30

SA = 270 cm^2

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a circular railroad-crossing sigh has a radius of 15 inches. which measurement is closest to the area of the sigh in square inch

S_A_V [24]

Answer:

Step-by-step explanation:

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2 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

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

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2 years ago

In August 200920092009, Usain Bolt ran 100100100 meters in 9.589.589, point, 58 seconds (\text{sec})(sec)left parenthesis, start

Sveta_85 [38]

Answer:

<u>Usain Bolt's average speed in yards per second was 11.4</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

World record of Usain Bolt = 9.589 seconds

Distance of the world record = 100 meters

1 yard = 0.9144 meters ⇒ 100 meters = 109.36 yards

2. What was Usain Bolt's average speed in yards per second?

Let's recall that the formula of speed is:

Speed = Distance/Time

Replacing with the values we know:

Usain Bolt's Speed = 109.36/9.589

<u>Usain Bolt's Speed = 11.4 yards per second (Rounding to one decimal place)</u>

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2 years ago

Please help I cannot-

Dmitry [639]

Answer:

1922 m cubed

Step-by-step explanation:

Not gonna do that, I did the work and checked it. Should be right

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2 years ago

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34kurt

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3 years ago