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3 years ago

Suppose that

1 answer:

6 0

If 15 inches of wire costs 45 cents, that means each inch of wire costs 3 cents. So 12 inches of wire will cost 36 cents.

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How many cm3 is in 1 liter? i just wondering...

natali 33 [55]

Hello,

1 liter of water in normal conditions has a volume of 1dm^3=(1dm)^3=(10 cm)^3=10^3 cm^3=1000 cm^3

4 0

3 years ago

Evaluate the surface integral:S

rjkz [21]

Assuming $S$ does not include the plane $z=0$ , we can parameterize the region in spherical coordinates using

$\mathbf r(u,v)=\left\langle3\cos u\sin v,3\sin u\sin v,3\cos v\right\rangle$

where $0\le u\le2\pi$ and $0\le v\le\dfrac\pi/2$ . We then have

$x^2+y^2=9\cos^2u\sin^2v+9\sin^2u\sin^2v=9\sin^2v$
$(x^2+y^2)=9\sin^2v(3\cos v)=27\sin^2v\cos v$

Then the surface integral is equivalent to

$\displaystyle\iint_S(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^2v\cos v\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times \frac{\partial\mathbf r(u,v)}{\partial u}\right\|\,\mathrm dv\,\mathrm du$

We have

$\dfrac{\partial\mathbf r(u,v)}{\partial u}=\langle-3\sin u\sin v,3\cos u\sin v,0\rangle$
$\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle3\cos u\cos v,3\sin u\cos v,-3\sin v\rangle$
$\implies\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle$
$\implies\left\|\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}\|=9\sin v$

So the surface integral is equivalent to

$\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv\,\mathrm du$
$=\displaystyle486\pi\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv$
$=\displaystyle486\pi\int_{w=0}^{w=1}w^3\,\mathrm dw$

where $w=\sin v\implies\mathrm dw=\cos v\,\mathrm dv$ .

$=\dfrac{243}2\pi w^4\bigg|_{w=0}^{w=1}$
$=\dfrac{243}2\pi$

4 0

3 years ago

3(у - 3) - 2(у 4) = 4

Dennis_Churaev [7]

Answer:

y = 5

Step-by-step explanation:

3(у - 3) - 2(у -4) = 4

Distribute

3y -9 -2y +8 =4

Combine like terms

y -1 =4

Add 1 to each side

y-1+1 = 4+1

y = 5

3 0

3 years ago

Read 2 more answers

Make b the subject of the formula P=2a+b

Gelneren [198K]

In order to make b the subject of this equation, we must isolate it on the left side. We can do this by following these steps:

$P = 2a+b$

Subtract b from both sides

$P - b = 2a+b-b$

$P-b=2a$

Subtract P from both sides

$P-b-P=2a-P$

$-b=2a-P$

Now, we have isolated b, but it is negative. We can fix this by multiplying both sides of the equation by -1.

$-(-b)=-(2a-P)$

$b=-2a+P$

Which is your final answer.
$b = -2a+P$ .
Hope that helped! =)

5 0

3 years ago

Read 2 more answers

How do i simplify this (x/x+3)-(3/x+2)-(1/x^2+5x+6)

ludmilkaskok [199]

Answer:

−5x3−4x2−3x−1/x2

Step-by-step explanation:

7 0

2 years ago