Select “Rational” or “Irrational” to classify each number.

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

The length of a rectangle is 3cm more than twice the width. The perimeter of the rectangle is 42 cm. Find the dimensions of the

bogdanovich [222]

The width is 6cm
And the length is two times + 3 of the width
6 X 2 + 3 = 15
Add all 4 sides for the perimeter 6+6+15+15=42
The the dimensions are a rectangle that is 6cm wide and 15cm tall

5 0

3 years ago

To answer that question

Mars2501 [29]

First, we get ax^2+bx+c. Next, we know that the line of symmetry is -b/2a. Since we know that there is a maximum value, the parabola is facing downwards, so a is negative. For random numbers, we can say that a = -0.5 and b=-10 (b needs to be negative for -b/2a to equal -10), getting -0.5x^2-10x+c. Plugging -10 in for x (since -10 is the middle it is the max), we get -50+100=50. Since the maximum needs to be 5, not 50, we subtract 45 from the answer to get it and therefore make c = -45, getting -0.5x^2-10x-45

5 0

3 years ago

Which term best describes the shape of this distribution?

borishaifa [10]

The shape of the distribution described the Left skewed.

<h3>What is left- skewed histogram?</h3>

A left skewed histogram is a histogram that attains a peak (which is the mode) towards the right side of the graph and has a “tail” towards the left side.

A histogram in which most of the data falls to the left of the graph's peak is known as a left-skewed histogram.

A left-skewed histogram is a type of histogram that is not symmetrical and in which the peak of the graph lies to the right of the middle value or the median.

Hence, considering the above definition the given histogram data falls on right side.

So, it is left skewed graph.

Learn more about left- skewed graph here:

brainly.com/question/1518646

#SPJ1

4 0

2 years ago

><br> 40 cm out of 3.5m .

vovikov84 [41]

Answer:

Your answer is 11.42

Step-by-step explanation:

hope it helps

3 0

3 years ago