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1 year ago

1,3,2,6,3,9,4,12... what will be the eleventh number in the pattern?

Mathematics

2 answers:

katrin [286]1 year ago

7 0

Answer:

11th number is 6

Step-by-step explanation:

elixir [45]1 year ago

6 0

Answer: 9

Step-by-step explanation:

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Evaluate c (y + 7 sin(x)) dx + (z2 + 9 cos(y)) dy + x3 dz where c is the curve r(t) = sin(t), cos(t), sin(2t) , 0 ≤ t ≤ 2π. (hin

saw5 [17]

Treat $\mathcal C$ as the boundary of the region $\mathcal S$ , where $\mathcal S$ is the part of the surface $z=2xy$ bounded by $\mathcal C$ . We write

$\displaystyle\int_{\mathcal C}(y+7\sin x)\,\mathrm dx+(z^2+9\cos y)\,\mathrm dy+x^3\,\mathrm dz=\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r$

with $\mathbf f=(y+7\sin x,z^2+9\cos y,x^3)$ .

By Stoke's theorem, the line integral is equivalent to the surface integral over $\mathcal S$ of the curl of $\mathbf f$ . We have

$\nabla\times\mathbf f=(-2z,-3x^2,-1)$

so the line integral is equivalent to

$\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\mathrm d\mathbf S$
$=\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv$

where $\mathbf s(u,v)$ is a vector-valued function that parameterizes $\mathcal S$ . In this case, we can take

$\mathbf s(u,v)=(u\cos v,u\sin v,2u^2\cos v\sin v)=(u\cos v,u\sin v,u^2\sin2v)$

with $0\le u\le1$ and $0\le v\le2\pi$ . Then

$\mathrm d\mathbf S=\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv=(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv$

and the integral becomes

$\displaystyle\iint_{\mathcal S}(-2u^2\sin2v,-3u^2\cos^2v,-1)\cdot(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv$
$=\displaystyle\int_{v=0}^{v=2\pi}\int_{u=0}^{u=1}u-6u^4\sin^3v-4u^4\cos v\sin2v\,\mathrm du\,\mathrm dv=\pi$ <span />

4 0

2 years ago

Solve the following system. x-y=2. 3x+z=11. y-2z=-3

dexar [7]

For the 1st one we need to solve x. x-y=2 step1: x-y+y=2+y answer: x=y+2

5 0

2 years ago

Find the angel x in d diagram above with a well structured solution.<br><br>Thanks

Tom [10]

Step-by-step answer:

Please refer to attached image.

1. Quad PQRS is cyclic (all vertices on the same circle), so opposite angles are supplementary, meaning

that

angles QPS and QRS are supplementary =>

QPS+QRS=180 =>

QRS = 180 - 74 = 106

2. Triangle RSQ is isosceles with RS=RQ =>

angles RSQ and RQS are congruent.

3. Angle RSQ = (180 - 106) /2 = 74 / 2 = 37

4. QP is a diameter => angle QSP is a right-angle.

5. From (3) and (4) above,

angle RSP = 37+90 = 127

6. Since PQRS is cyclic, angles RQP and RSP are supplementary =>

RQP+RSP = 180 =>

x + 127 = 180 =>

x = 180 - 127 = 53 degrees.

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3 years ago

English 10 mugshots week 3

Reil [10]

Thts a nice quote. i dont get wht ur q is

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3 years ago

If you hike 1/2 mile every 1/5 hour how far do you hike in two hours?

Anarel [89]

Answer:

5 miles

Step-by-step explanation:

0.5 x 10

= 5

4 0

2 years ago

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