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3 years ago

Converted 108° to radians, give your answer in terms of

Mathematics

2 answers:

lisabon 2012 [21]3 years ago

8 0

Answer: 1.88496

Step-by-step explanation:

Flura [38]3 years ago

6 0

Answer:

1.88496

Step-by-step explanation:

sorry i did not give step by step explanation its cuz i am outside

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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

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

7 0

3 years ago

What is the probability that 2 randomly selected months have 31 days?

aniked [119]

Answer:

31.8%

Step-by-step explanation:There are 7 months that have 31 days so,

The odds the first selected month has 31 days is 7/12

The next month there are only 6 months left with 31 days of only 11 months to choose from

so the odds for the second are 6/11

To calculate the odds they BOTH have 31 months you multiply the two odds:

(7/12) x (6/11) = 42/132 = .318 so 31.8%

6 0

3 years ago

Read 2 more answers

Two cars leave town at the same time and travel in opposite directions. Speed of car A is 12 km/h more than car B. They are 312k

Zina [86]

Answer:

Speed of car B is 33 km/h and speed of car A is $45\,\,km/h$

Step-by-step explanation:

Let speed of car B be $x$ km/h

Speed of car A is 12 km/h more than car B.

Therefore,

Speed of car A = $(12+x)$ km/h

Distance = Speed × Time

Distance travelled by car A in 4 hours = $4(12+x)$ km = $(48+4x)$ km

Distance travelled by car B in 4 hours = $4x$ km

Also, cars A and B are 312km apart after 4 hours.

$48+4x+4x=312\\48+8x=312\\8x=264\\\\x=\frac{264}{8}\\\\x=33\,\,km/h$

Speed of car B is 33 km/h and speed of car A is $12+x=12+33=45\,\,km/h$

5 0

3 years ago

Marcus sorts his 85 baseballs cards into stacks of 9 each. How many stacks of 9 cards can marcus make

PSYCHO15rus [73]

Answer:

He can only make 9

Step-by-step explanation:

He will have 4 cards left over so it will not be enough to make another stack.

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3 years ago

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I need help anyone??? please??????

olchik [2.2K]

The principal square root of 49 is just 7 because 7 times 7 is 49.
It can not be -7 because a principle square root cannot be negative.

$\sf\ Answer: A)\ 7$

$\sf\ \sqrt{49}=\\\±7\\\\-7\ and\ 7\ are\ both\ square\ roots\ of\ 49\ because\ 7\times7=49\ and\\\\-7\times-7=49.\\\\But\ as\ I\ said\ before,\ principal\ square\ roots\ can\ not\ be\ negative\\\\numbers.\\\\That\ will\ eliminate\ any\ options\ with\ -7.\\\\So\ the\ only\ principal\ square\ root\ that\ we\ have\ is\ {\boxed{7}$

8 0

3 years ago

Read 2 more answers