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2 years ago

Which of the following functions has the function rule y = x +4?

Mathematics

1 answer:

Alexus [3.1K]2 years ago

7 0

Replace x with the given values and solve for y.

The answer is:

f(-3,1),(0,4), (2, 6))

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Simplify the expression:z2-z(z+3)+3z

n200080 [17]

$z^2-z(z+3)+3z=z^2-z\cdot z-z\cdot3+3z=z^2-z^2-3z+3z=0$

8 0

3 years ago

How to solve this problem and the answer.

weqwewe [10]

I’m not sure sorry cau

8 0

2 years ago

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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

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

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2 years ago

Why is 0.03 less than 7.85?

IRINA_888 [86]

I think 0.3 is less 7.85 because there is a 1 on the end that was is a 3 and if you round it would be 0

7 0

2 years ago

Shelia went snowboarding. She spent $118 for the pass and snowboard rental. The snowboard rental cost $25. What percent of the t

padilas [110]

I believe the answer is about 78.81% because you subtract 25 from 118. Then that would be 93. 118 is equal to the 100% and 118 divide by 1.18 equals 100. Divide 93 from 1.18 gives you the answer

5 0

3 years ago

Read 2 more answers