Radical 16 * redical 12

Nastasia [14]

The answer is -1 4/5

7 0

3 years ago

Use the Divergence Theorem to compute the net outward flux of the field F=<-2x,y,-2z> across the surface S, where S is the

lutik1710 [3]

Answer:

The net outward flux across the boundary of the tetrahedron is: -4

Step-by-step explanation:

Given vector field F = ( -2x, y, - 2 z )

$div F = \nabla F = ( i \dfrac{\partial }{\partial x }+ j \dfrac{\partial}{\partial y} + k \dfrac{\partial}{\partial z}) \langle -2x, y, -2z \rangle$

$div F = \nabla F = ( \dfrac{\partial }{\partial x }(-2x)+ \dfrac{\partial}{\partial y}(y) + \dfrac{\partial}{\partial z}(-2z))$

= -2 + 1 -2

= -3

According to divergence theorem;

Flux = $\int \int \int div \ \ (F) \ dv$

x+y+z = 2; $1^{st}$ Octant

x from 0 to 2

y from 0 to 2 -x

z from 0 to 2-x-y

$= \int\limits^2_0 \int\limits^{2-x}_0 \int\limits^{2-x-y}_0 -3dzdydx$

$=-3 \int\limits^2_0 \int\limits^{2-x}_0 (2-x-y)dy dx$

$= -3 \int\limits^2_0[(2-x)y - \dfrac{y^2}{2}]^{2-x}__0 \ \ dx$

$= -3 \int\limits^2_0(2-x)^2 - \dfrac{(2-x)^2}{2} dx$

$= -3 \int\limits^2_0\dfrac{(2-x)^2}{2} dx = - \dfrac{3}{2} \int\limits^2_0(4-4x+x^2) dx$

$=- \dfrac{3}{2}(4x-x^2 + \dfrac{x^3}{3})^2_0$

$=- \dfrac{3}{2}(8-8+\dfrac{8}{3})$

$=- \dfrac{3}{2}(\dfrac{8}{3})$

= -4

Thus; The net outward flux across the boundary of the tetrahedron is: -4

3 0

4 years ago

Two young sumo wrestlers decided to go on a special diet to gain weight rapidly. They each gained weight at a constant rate.

Sholpan [36]

Answer:

The first wrestler weighed more at the beginning of the diet.
The second wrestler gains weight more quickly.

Step-by-step explanation:

For the first wrestler, we can see that from month $3$ to $4.5$ , the wrestler's weight gets to be from $95$ kilograms to $101.75$ kilograms. This means that the diet made the wrestler gain $\red{6.75}$ kilograms of weight every $\red{1.5}$ month. We can also see that it's consistent with from month $4.5$ to $6$ .

For the second wrestler, we can see on the graph that the diet makes the wrestler gain weight in linear fashion. This means that their weight gain is consistent. Let's find how much the wrestler is gaining weight for every $1.5$ months. At the moment when the wrestler started to diet, their weight is $\red{75}$ kilograms. At month $1.5$ , we can see that the wrestler's weight is $82.5$ . Now we can see that the wrestler gains $\blue{7.5}$ kilograms of weight every $\blue{1.5}$ months.

The first wrestler gains $\red{6.75}$ kilograms of weight every $\red{1.5}$ month while the second wrestler gains $\blue{7.5}$ kilograms of weight every $1.5$ months. The second wrestler gains weight more quickly.

The second wrestler weighed $\blue{75}$ at the beginning of the diet. We are not provided of weight of the first wrestler when they started dieting but we do know that they gain $\red{6.75}$ kilograms of weight every $1.5$ months. The first wrestler must weigh twice of $\red{6.75}$ kilograms of $95$ kilograms because month $3$ is twice $1.5$ months.

$\red{90 -6.75 \cdot 2} \\ \red{90 -13.5} \\ \red{76.5}$

The first wrestler weighed more at the beginning of the diet.

7 0

3 years ago

These tables represents a quadratic function with a vertex at (0,3) what is the average rate of change for the interval from x=8

goblinko [34]

There are a few ways to do it; the easiest is just to follow the pattern of taking away two from the average.

The next lines of the table are

6 to 7 -13

7 to 8 -15

8 to 9 -17

Answer: C. -17

Let's find the equation and do it that way.

We have a vertex at (0,3) so we can fill out the vertex form a bit. In general for vertex (p,q) it's

y = a(x-p)^2+q

We have

f(x) = ax^2 + 3

f(1) = 2

a+3 =2

a = -1

So we found our equation,

y = -x^2 + 3

Let's check it at x=5, y=-5^2+3=-25+3=-22, good

We want the rate of change from 8 to 9, which is

$r = \dfrac{f(9)-f(8)}{9-8}=f(9)-f(8)=-9^2 - -8^2 = -17$

Answer: -17 again, that checks

6 0

4 years ago

PLS HELP ASAP! FIND THE VOLUME OF THE GIVEN FIGURE. Thank you

Lana71 [14]

Answer:

120

Step-by-step explanation:

all you have to do is multiply the length, width, and height.

5x8=40

40x3=120

8 0

3 years ago

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