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3 years ago

Three vertices of parallelogram ABCD

Mathematics

1 answer:

hammer [34]3 years ago

6 0

Answer:

(0, -8)

Step-by-step explanation:

The distance must be equal from C to A and points B to D.

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What's 1.27 repeating as a fraction

svet-max [94.6K]

As a improper fraction, its 127/100

5 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

3 years ago

A ball falls from a window. Its height, as a function of time, is modeled by y=-4.9x2 + 12. Which statement best describes the f

ankoles [38]

Answer:The function is nonlinear

Step-by-step explanation:

Took the test made a 100

5 0

2 years ago

Read 2 more answers

Need help ASAP please

inysia [295]

Answer:

m=1

Step-by-step explanation:

y2-y1/x2-x1

3 0

3 years ago

What are the correct intermediate steps of the following data set when it is being sorted with the bubble sort? 15, 20, 10, 18

love history [14]

Answer:

A. 15,10,20,18 -- 15,10,18,20 -- 10,15,18,20

Step-by-step explanation:

Bubble sorting can be defined as a technique or methodology whereby numbers that are not in their proper order are sorted into proper order that is from smallest to highest( increasing to decreasing order).

The method of bubble sorting involves the shuffling or swapping of adjacent numbers until the numbers are well sorted or arranged.

In the above question, we were given, a set of numbers:

15, 20, 10, 18

Step 1

20 is adjacent to 10

20 > 10

hence we swap

= 15,10,20,18

Step 2

From, 15,10, 20,18

20 is adjacent to 18

20 > 18

hence we swap

= 15,10,18,20

Step 3

From step 2, which gave us 15,10,18,20

15 us adjacent to 10

15 > 10

We swap

= 10,15,18,20

Hence,

15, 20, 10, 18 -- 15,10,20,18 -- 15,10,18,20 -- 10,15,18,20

Therefore, Option A is the correct option.

4 0

3 years ago