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3 years ago

What is the midpoint of the line segment with endpoints (-5.5 -6.1) and (-0.5 9.1)?

Mathematics

1 answer:

Volgvan3 years ago

4 0

Answer:

(-3, 1.5)

Step-by-step explanation:

(-0.5 - 5.5/2, 9.1 - 6.1/2) = (-3, 1.5)

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|-9c|=8 and solve for c

melisa1 [442]

C = negative 8/9 or 8/9

5 0

3 years ago

200 years ago, as it became more and more evident that the

svp [43]

Answer:

The American population was 20% of the British population.

Step-by-step explanation:

Let us call $A$ the american population, $B$ the British population before the migration, and $x$ the population that migrated from America to Britannia.

Now, the population $x$ that migrated was 20% of the american population:

$(1).\: \: x = 0.2A$ ,

and the same population $x$ increase the British population by 4%:

$x+B = 1.04B \\\\ (2). \:\:x = 0.04B.$

Combining equation (1) and (2) we get:

$0.2A = 0.04B$

$A = \dfrac{0.04B}{0.2}$

$\boxed{A = 0.2B}$

Thus, the American population was 20% of the British population.

5 0

3 years ago

Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li

Sophie [7]

Consider the closed region $V$ bounded simultaneously by the paraboloid and plane, jointly denoted $S$ . By the divergence theorem,

$\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV$

And since we have

$\nabla\cdot\mathbf f(x,y,z)=1$

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

$\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV$
$=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=2}^{z=3-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=1}r(3-r^2-2)\,\mathrm dr$
$=\dfrac\pi2$

Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by $D$ , we have

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS$

Parameterize $D$ by

$\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k$
$\implies\mathbf s_u\times\mathbf s_v=u\,\mathbf k$

which would give a unit normal vector of $\mathbf k$ . However, the divergence theorem requires that the closed surface $S$ be oriented with outward-pointing normal vectors, which means we should instead use $\mathbf s_v\times\mathbf s_u=-u\,\mathbf k$ .

Now,

$\displaystyle\iint_D\mathbf f\cdot\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(-u\,\mathbf k)\,\mathrm dv\,\mathrm du$
$=\displaystyle-4\pi\int_{u=0}^{u=1}u\,\mathrm du$
$=-2\pi$

So, the flux over the paraboloid alone is

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2$

6 0

3 years ago

2 in a math contest, the contestants were given the following piecewise graph. For

marishachu [46]

Answer:

What do think the answer is cause I don't know

3 0

3 years ago

What is the first 5 multiples of the following numbers 10,15,20,24

timofeeve [1]

10 20 30 40 50
15 30 45 55 70
20 40 60 80 100
24 48 72 96 120

6 0

2 years ago