Which of the following best describes the graphs below?

G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =

Svetach [21]

Presumably you should be doing this using calculus methods, namely computing the surface integral along $\mathbf r(u,v)$ .

But since $\mathbf r(u,v)$ describes a sphere, we can simply recall that the surface area of a sphere of radius $a$ is $4\pi a^2$ .

In calculus terms, we would first find an expression for the surface element, which is given by

$\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k$
$\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j$
$\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k$
$\implies\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|=a^2\sin u$

So the area of the surface is

$\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u$
$=-2\pi a^2(\cos\pi-\cos 0)$
$=-2\pi a^2(-1-1)$
$=4\pi a^2$

as expected.

6 0

3 years ago

URGENT will give brilliant mark For the reaction 2Na + Cl2 ------ 2NaCl, how many grams of sodium chloride can be produced from

SVETLANKA909090 [29]

Answer:

825 g

Step-by-step explanation:

Here's my work:

500g Cl2 l 1mol Cl2 l 2 mol NaCl l 58.5 g NaCl

l 71 g Cl2 l 1 mol Cl2 l 1 mol NaCl

= 823.94 - the rounding can be a little off

The first thing you have to do is convert the 500 g of Cl2 into moles. So you get the mass of Cl which is 35.5, but Cl is diatomic by itself so you multiply 35.5 x 2 and get 71. now on the third column you are comparing the mol ratios of the equation. The equation is 2Na + Cl2 ---> 2NaCl, so you see that there is no coefficient in front of Cl2 so that means there is 1 mol, and then you see that in the product there is a coefficient of 2 in front of NaCl so that means there is 2 moles. Then finally you have to convert the moles backs into grams where you just add the masses of Na and Cl . You multiply across the top and then divide that number by the bottom row.

6 0

3 years ago

Two stands at a craft fair sell cone-shaped candles. They are made by pouring wax into a mold. Booth A sells a candle with a rad

frez [133]

In order to compare the amount of wax, you have to calculate the volume of both candles.

Candle of booth A = πr² h/3
A = π * 4² * 6/3
A = π * 16 * 2
A = 32π

Now, Candle of Booth B = π * 5² * 5/3
B = π * 25 * 5/3
B = 41.6π

In short, Booth B sells the candle with more wax.

Hope this helps!

6 0

3 years ago

Are G and F mutually exclusive events? Explain. G and F are mutually exclusive because if you are not a finalist, then you canno

Alika [10]

Answer: G and F are mutually exclusive because they cannot occur together

Step-by-step explanation:

According to the definition of mutually exclusive events,

The events which can not occur together and probability of them occurring together is 0 are known as mutually exclusive events.

The first statement gives an implication that if one happens then other happens meaning they could both still happen so it is not true.

The second statement contradict the question about being mutually exclusive events.

The third statement also is a implication that if one event occurs then other does or does not occur.

The last statement is correct one that conforms with the question and obeys the definition of mutually exclusive events.

8 0

3 years ago

postnew [5]

12-3=9 they switch up and it still equals the same thing

5 0

3 years ago

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