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3 years ago

The distance from A to B is 10 and the distance from A to B’ is 2. what is the scale factor?

Mathematics

1 answer:

liberstina [14]3 years ago

3 0

Answer:

The scale factor is 5

Step-by-step explanation:

AB = 10

AB' =2

The ratio will give us the sale factor

AB/AB' = 10/2 = 5

The scale factor is 5

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What is the units digit of 2 to the 50th power

11111nata11111 [884]

Notice that

$2^1=2$
$2^2=4$
$2^3=8$
$2^4=16$
$2^5=32$

so that for each power of 2, there is a pattern of period 4. This means that for integers $k\ge0$ , each of $2^{4k}$ , $2^{4k+1}$ , $2^{4k+2}$ , and $2^{4k+3}$ have the same units digit.

We can write $50=4(12)+2$ , and since $3=4(0)+2$ , it follows that $2^{50}$ and $2^3$ share the same units digits. So the units digit of $2^{54}$ is 8.

6 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

Jackson has 2,000 baseball cards in his collection. Gabe has 110 as many baseball cards in his collection as Jackson. How many b

juin [17]

Answer:

220,000

Step-by-step explanation:

all you do is multiply 2000 by 110

5 0

2 years ago

Which expression has a value of 1/36?

Schach [20]

(1/36) = 0.0277777777778

(1/108)^3 = 7.9383224102<span> x 10^-7 </span>
(1/9)^4 = 0.000152415790276
(1/6)^2 = 0.0277777777778
(1/2)^5 = <span>0.03125

The only one that matches with the value of 1/36 is (1/6)^2. Therefore, your answer is C. (1/6)^2
</span>

6 0

3 years ago

Read 2 more answers

On Tuesday the temperature is 1 ºC. By Wednesday it has dropped to –2 ºC. The temperature drops by twice as much from Wednesday

Finger [1]

Answer: $-8^{\circ}C$