Line / and line m are straight lines what is the measurement of angle y

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

Law Incorporation [45]

Answer:

Step-by-step explanation:

To solve this problem, we will use the following two theorems/definitions:

- Given a vector field F of the form (P(x,y,z),Q(x,y,z),W(x,y,z)) then the divergence of F denoted by $\nabla \cdot F = \frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}}+\frac{\partial W}{\partial z}$

- (Gauss' theorem)Given a closed surface S, the following applies

$\int_{S} F\cdot \vec{n} dS = \int_{V} \nabla \cdot F dV$

where n is the normal vector pointing outward of the surface and V is the volume bounded by the surface S.

Let us, in our case, calculate the divergence of the given field. We have that

$\nabla \cdot F = \frac{\partial}{\partial x}(x)+\frac{\partial}{\partial y}(2y)+ \frac{\partial}{\partial z}(5z) = 1+2+5 = 8$

Hence, by the Gauss theorem we have that

$\int_{S} F\cdot \vec{n} dS = \int_{V} 8 dV = 8\cdot\text{Volume of V}$

So, we must calculate the volume V bounded by the cube S.

We know that the vertices are located on the given points. We must determine the lenght of the side of the cube. To do so, we will take two vertices that are on the some side and whose coordinates differ in only one coordinate. Then, we will calculate the distance between the vertices and that is the lenght of the side.

Take the vertices (1,1,1) and (1,1-1). The distance between them is given by

$\sqrt[]{(1-1)^2+(1-1)^2+(1-(-1)^2} = \sqrt[]{4} = 2$ .

Hence, the volume of V is $2\cdot 2 \cdot 2 = 8$ . Then, the final answer is

$\int_{S} F\cdot \vec{n} dS =8\cdot 8 = 64$

5 0

3 years ago

Graph the piecewise function<br><br> f(x)= {-2x-3 if -1

irakobra [83]

Answer:

The points are (0,-1) (1,-1)

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Lengths of full-term babies in the US are Normally distributed with a mean length of 20.5 inches and a standard deviation of 0.9

mash [69]

Answer:

66.48% of full-term babies are between 19 and 21 inches long at birth

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean length of 20.5 inches and a standard deviation of 0.90 inches.

This means that $\mu = 20.5, \sigma = 0.9$

What percentage of full-term babies are between 19 and 21 inches long at birth?

The proportion is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19. Then

X = 21

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{21 - 20.5}{0.9}$

$Z = 0.56$

$Z = 0.56$ has a p-value of 0.7123

X = 19

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{19 - 20.5}{0.9}$

$Z = -1.67$

$Z = -1.67$ has a p-value of 0.0475

0.7123 - 0.0475 = 0.6648

0.6648*100% = 66.48%

66.48% of full-term babies are between 19 and 21 inches long at birth

5 0

2 years ago

The length of a rectangle is six times it’s width. If the area of the rectangle is 150ft^2, find its perimeter.

sineoko [7]

Answer:

Perimeter = 70ft

Step-by-step explanation:

Area of a rectangle is:

area = (length * width)

150 = a * b

a = 6b

a = length

b = width

then:

150 = 6b*b

150 = 6b²

b² = 150/6

b² = 25

√b² = √25

b = 5ft

a = 6b

a = 6*5

a = 30ft

then:

perimeter of a rectangle is:

p = 2(a+b)

p = 2(30 + 5)

p = 2*35

p = 70ft

7 0

3 years ago

Help me with this Please.

sukhopar [10]

35
the ratio for the two is 5:7 and you want to find _:49. to get from 7 to 49 you multiply the 7 by 7. because you did that to one side you have to do the same to the other and multiply 5 by 7 which gives you 35

6 0

2 years ago