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GarryVolchara [31]

3 years ago

9

For breakfast, Tyrell can choose from scrambled eggs or an omelette, bacon or sausage and orange juice or milk. How many differe

nt outcomes are possible

1 answer:

Sav [38]3 years ago

8 0

Answer:

Step-by-step explanation:

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Use stoke's theorem to evaluate∬m(∇×f)⋅ds where m is the hemisphere x^2+y^2+z^2=9, x≥0, with the normal in the direction of the

ludmilkaskok [199]

By Stokes' theorem,

$\displaystyle\int_{\partial\mathcal M}\mathbf f\cdot\mathrm d\mathbf r=\iint_{\mathcal M}\nabla\times\mathbf f\cdot\mathrm d\mathbf S$

where $\mathcal C$ is the circular boundary of the hemisphere $\mathcal M$ in the $y$ - $z$ plane. We can parameterize the boundary via the "standard" choice of polar coordinates, setting

$\mathbf r(t)=\langle 0,3\cos t,3\sin t\rangle$

where $0\le t\le2\pi$ . Then the line integral is

$\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=\int_{t=0}^{t=2\pi}\mathbf f(x(t),y(t),z(t))\cdot\dfrac{\mathrm d}{\mathrm dt}\langle x(t),y(t),z(t)\rangle\,\mathrm dt$
$=\displaystyle\int_0^{2\pi}\langle0,0,3\cos t\rangle\cdot\langle0,-3\sin t,3\cos t\rangle\,\mathrm dt=9\int_0^{2\pi}\cos^2t\,\mathrm dt=9\pi$

We can check this result by evaluating the equivalent surface integral. We have

$\nabla\times\mathbf f=\langle1,0,0\rangle$

and we can parameterize $\mathcal M$ by

$\mathbf s(u,v)=\langle3\cos v,3\cos u\sin v,3\sin u\sin v\rangle$

so that

$\mathrm d\mathbf S=(\mathbf s_v\times\mathbf s_u)\,\mathrm du\,\mathrm dv=\langle9\cos v\sin v,9\cos u\sin^2v,9\sin u\sin^2v\rangle\,\mathrm du\,\mathrm dv$

where $0\le v\le\dfrac\pi2$ and $0\le u\le2\pi$ . Then,

$\displaystyle\iint_{\mathcal M}\nabla\times\mathbf f\cdot\mathrm d\mathbf S=\int_{v=0}^{v=\pi/2}\int_{u=0}^{u=2\pi}9\cos v\sin v\,\mathrm du\,\mathrm dv=9\pi$

as expected.

7 0

3 years ago

Equivalent expression for 7a+21

Mila [183]

Answer:

Step-by-step explanation:

If you factor the expression 7a+21 you can get:

7 × (a+3)

6 0

3 years ago

write an equation in standard form for the line that has an undefined slope and passes through (-6,4)

Verdich [7]

Undefined slope is rise/0
run is equal to 0
that means it doesn't go left or right
means it is vertcal
means it is x=somethig

(x,y)
(-6,4)
x=-6 is the equation

oh, forgot about standard form

standard form is
ax+by=c

so

x+0y=-6 would be the equation in standard form

6 0

3 years ago

PLEASE HELP ME!!!!!!!!<br>does anyone know how to do this I am clueless please help

vredina [299]

Maybe this will help! (:
https://youtu.be/1wPJfzStBqE

6 0

3 years ago

Is y/7 = 2/x direct variation?

jenyasd209 [6]

Answer:

It is not direct variation

Step-by-step explanation:

y/7 = 2/x

y = 7×2/x

y = 14/x

And

y = k/x

k = 14 which is the constant of proportionality

: y ∞ 1/x

This is inverse variation

3 0

3 years ago