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2 years ago

What is the expanded form of the expression 3 sigma i^3 i=0

Mathematics

2 answers:

Naddik [55]2 years ago

5 0

Answer:

\bf \sum\limits_{i=0}^{3}~i^3\qquad \implies\qquad \stackrel{i=0}{0^3}~~+~~\stackrel{i=1}{1^3}~~+~~\stackrel{i=2}{2^3}~~+~~\stackrel{i=3}{3^3}

Step-by-step explanation:

Savatey [412]2 years ago

3 0

$\bf \sum\limits_{i=0}^{3}~i^3\qquad \implies\qquad \stackrel{i=0}{0^3}~~+~~\stackrel{i=1}{1^3}~~+~~\stackrel{i=2}{2^3}~~+~~\stackrel{i=3}{3^3}$

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How do you solve 4x+1/3=x-5/2

Lemur [1.5K]

4x+1/3=x-5/2
4x-x=-5/2-1/3
3x=-17/6
1/3(3x)=1/3(-17/6)
X=-17/18

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2 years ago

The slope of a line is -1/2 what is the slope of a line that is parallel to it?

Lynna [10]

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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

2 years ago

A bicycle has a listed price of $848.99 before tax. If the sales tax rate is 8.75%, find the total cost of the bicycle with sale

Aliun [14]

Answer:

$848.99×8.75/100

=$74.29

$848.99+$74.29

=$923.3

3 0

2 years ago

Solve the system of equations –2 + y = 14 and -5x – 7y=10 by combining the

pochemuha

Answer:

Step-by-step explanation:

-2+y=14

-5x-7y=10

y=14+2

y=16

-5x-7(16)=10

-5x-112=10

+112 +112

-5x=122

x=-24.4

5 0

2 years ago