Molly had a balance of $72 In her savings account before depositing $25. What is her new balance?

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

a circular native american dwlelling has a diameter of 24 feet. how much are inside the home? use 3.14 for { } (pi)

Marizza181 [45]

Answer :

$A = 452.16 \: {ft}^{2}$

step-by-step explanation:

From the question,

the diameter:

$d = 24 \: ft$

The radius :

$r = \frac{diameter}{2}= \frac{24}{2}=12 \: ft$

$\pi = 3.14$

Area of a circle is given as

$A = \pi {r}^{2}$

By substitution,

$A = 3.14( {12}^{2} )$

$\implies \: A = 3.14 \times 144$

$\implies \: A = 452.16 \: {ft}^{2}$

Hence the area of the home is

$A = 452.16 \: {ft}^{2}$

8 0

3 years ago

2072 divided by 37! Pleaseeeeeeeeee

icang [17]

Answer:

56 is the answer to your question

6 0

3 years ago

Read 2 more answers

Serious inquiries only please and double check ur work please before posting

Darya [45]

To calculate mean: Just add up all the numbers, then divide by how many numbers there are.345 + 673 + 728 +775 + 822 +827 +839 + 951 = 5960/8 = 745
633 + 673 + 728 +775 + 822 +827 +839 + 951 = 6248/8 = 781781- 745 = 35 It increases by 35To find the Median, place the numbers in value order and find the middle. BUT, with an even amount of numbers things are slightly different. In that case we find the middle pair of numbers, and then find the value that is half way between them. This is easily done by adding them together and dividing by two. 345 673 728 775 822 827 839 951 The median = 822-775 /2
The median =23.5After the change633 673 728 775 822 827 839 951 The median = 822-775 /2
The median =23.5The median stays the same.

3 0

3 years ago

mackenzie made 33 out of 50 throws. what is the experimental probability that mackenzie will not make the next free throw she at

siniylev [52]

answer:

1.94117647058

Step-by-step explanation:

33/50 her free throw % is 66% at the moment based on how many she missed you'd do 33 / by 17 you get 1.94117647058

5 0

3 years ago