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Vika [28.1K]
3 years ago
8

Find the sum of the first 20 terms of the arithmetic series 0.5 + 1.1

Mathematics
2 answers:
exis [7]3 years ago
8 0

Answer:

0.5+1.1+1.7+2.3+2.9+3.5+4.1+4.7+5.3+5.9+6.5+7.1+7.7+8.3+8.9+9.5+10.1+10.7+11.3+11.9

Step-by-step explanation:

tell me if this isn't 20 terms

trapecia [35]3 years ago
7 0

Answer:

S_{20} = 124

Step-by-step explanation:

The sum to n terms of an arithmetic series is

S_{n} = \frac{n}{2} [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 0.5 and d = a₂ - a₁ = 1.1 - 0.5 = 0.6 , then

S_{20} = \frac{20}{2} [ (2 × 0.5) + (19 × 0.6) ]

     = 10 (1 + 11.4 )

     = 10 × 12.4

     = 124

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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

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

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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

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7 0
3 years ago
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valentina_108 [34]

The <u>different</u> selections of<u> one</u> meat and <u>one</u> vegetable are possible are 18 selections.

Since the Hickory Stick has a selection of 3 meats and 6 vegetables, the number of ways we can select <u>one </u>meat out of 3 is ³C₁ = 3.

Also, the number of ways we can select <u>one </u>vegetable out of 6 is ⁶C₁ = 6.

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= 18 selections

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Learn more about combination here:

brainly.com/question/19341024

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Step-by-step explanation:

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It's definitely A, gotta be.
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