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solniwko [45]
3 years ago
8

Could someone do a step-by-step? 2x < x − 4 ≤ 3x + 8

Mathematics
1 answer:
navik [9.2K]3 years ago
4 0

Answer:

−

6

≤

x

<

−

4

Interval Notation:

[

−

6

,

−

4

)

Step-by-step explanation:

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The perimeter of a given parallelogram is 46 inches. If the length of one side is 14 inches , what is the length of a side adjac
Ann [662]

Perimeter = 2*14 + 2x   where x is length of the adjacent side

46 = 28 + 2x

2x =  18

x = 9 inches Answer

4 0
3 years ago
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
HELP ON ALL QUESTIONS!! *repost* NO ONE IS HELPING ME ILL GIVE 56 POINTS
mafiozo [28]

Answer:

2. 8 * 3 - 10 = 14

3. 9 * 2 - 10 = 0

4. 5 - 15 = -10

5. 0.5 * 40 = 20

Part 3.

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William charges $4 per hour to babysit. LaRhonda charges a $10 flat fee, plus an additional $2 per hour to babysit. After how ma
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Answer:

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Read 2 more answers
Graph the solution set for the inequality z-4≤3
OleMash [197]

Answer:

  see below

Step-by-step explanation:

Add 4 to find the solution:

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3 years ago
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