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3 years ago

Is 100 mm less or greater than 1 dm

Mathematics

1 answer:

kipiarov [429]3 years ago

6 0

$1m=10dm=100cm=1,000mm\\\\1dm=10cm=100mm\\\\\boxed{100mm=1dm}$

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Evaluate the surface integral. s x2 + y2 + z2 ds s is the part of the cylinder x2 + y2 = 4 that lies between the planes z = 0 an

Leya [2.2K]

Parameterize the lateral face $T_1$ of the cylinder by

$\mathbf r_1(u,v)=(x(u,v),y(u,v),z(u,v))=(2\cos u,2\sin u,v$

where $0\le u\le2\pi$ and $0\le v\le3$ , and parameterize the disks $T_2,T_3$ as

$\mathbf r_2(r,\theta)=(x(r,\theta),y(r,\theta),z(r,\theta))=(r\cos\theta,r\sin\theta,0)$
$\mathbf r_3(r,\theta)=(r\cos\theta,r\sin\theta,3)$

where $0\le r\le2$ and $0\le\theta\le2\pi$ .

The integral along the surface of the cylinder (with outward/positive orientation) is then

$\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\left\{\iint_{T_1}+\iint_{T_2}+\iint_{T_3}\right\}(x^2+y^2+z^2)\,\mathrm dS$
$=\displaystyle\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}((2\cos u)^2+(2\sin u)^2+v^2)\left\|{{\mathbf r}_1}_u\times{{\mathbf r}_2}_v\right\|\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+0^2)\left\|{{\mathbf r}_2}_r\times{{\mathbf r}_2}_\theta\right\|\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+3^2)\left\|{{\mathbf r}_3}_r\times{{\mathbf r}_3}_\theta\right\|\,\mathrm d\theta\,\mathrm dr$
$=\displaystyle2\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r^3\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r(r^2+9)\,\mathrm d\theta\,\mathrm dr$
$=\displaystyle4\pi\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv+2\pi\int_{r=0}^{r=2}r^3\,\mathrm dr+2\pi\int_{r=0}^{r=2}r(r^2+9)\,\mathrm dr$
$=136\pi$

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3 years ago

If an angle is obtuse what type of angle is its supplement

Butoxors [25]

The supplement of an obtuse angle is an acute because the angle number for an obtuse angle is any number greater than 90 degrees. So an acute angle is less than 90 degrees. The "supplement" definition is "any number less than 180 degrees."

Hope this helps,

kwrob

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2 years ago

What Is The Rate Of Change In This Function?

Marrrta [24]

Answer:The answer would be 35 miles per day.

Step-by-step explanation:

We know the x axis is in days and the y axis is the distance in miles. There are only three answers left. We can also cross out 50 miles per day since the rate of change is less then 50. The answer is 35 miles per day because if the rate of change were to be 25 in 4 days the distance would be 100 miles, while is you look at where the point is at it is closer to 150.

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3 years ago

I need help with question 20

luda_lava [24]

20 because 10+10=20 and 20+20=40 and 20+40=60

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2 years ago

Read 2 more answers

How would you solve this question?

motikmotik

Answer:

Step-by-step explanation:

techincally, I don't know if I am right, but there is more than one answer. The boundries/restrictions of what length DF could be are 2.477 < x < 8.477

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2 years ago