Guys Ik it’s cut but you can still understand it. I don’t know how to do this percentage. Help!

Use the Divergence Theorem to evaluate the following integral S F · N dS and find the outward flux of F through the surface of t

Xelga [282]

Answer:

Result;

$\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = 32\pi$

Step-by-step explanation:

Where:

F(x, y, z) = 2(x·i +y·j +z·k) and

S: z = 0, z = 4 -x² - y²

For the solid region between the paraboloid

z = 4 - x² - y²

div F

For S: z = 0, z = 4 -x² - y²

We have the equation of a parabola

To verify the result for F(x, y, z) = 2(x·i +y·j +z·k)

We have for the surface S₁ the outward normal is N₁ = -k and the outward normal for surface S₂ is N₂ given by

$N_2 = \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} }$

Solving we have;

$\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{N}_1 d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \textbf{N}_2 d {S}$

Plugging the values for N₁ and N₂, we have

$= \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{(-k)}d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} } d {S}$

Where:

F(x, y, z) = 2(xi +yj +zk) we have

$= -\int\limits\int\limits_{S1} 2z \ dA + \int\limits\int\limits_{S2} 4x^2+4y^2+2z \ dA$

$= -\int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 2z \ dA + \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2+2z \ dA$

$= \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2 \ dxdy$

$= \int\limits^2_{-2} \frac{(16y^2 +32)\sqrt{-(y^2-4)} }{3} dy$

= 32π.

6 0

4 years ago

the manager of a grocery store has taken a random sample of 100 customers the average length of time it took these 100 customers

lora16 [44]

Answer:

with a .95 probability, the sample mean will provide a margin of error 0.196

Step-by-step explanation:

margin of error (ME) from the mean can be calculated using the formula

ME= $\frac{z*s}{\sqrt{N} }$ where

z is the corresponding statistic in the .95 confidence level (1.96)

s is the population standard deviation (1 min.)

N is the sample size (100)

ME= $\frac{1.96*1}{\sqrt{100} }$ =0.196

95% confidence interval for check-out time would be 3 ±0.196 min

8 0

4 years ago

A stock has produced returns of 14.5 percent, 4.8 percent, 10.2 percent, and 6.1 percent over the past four years respectively.

Anettt [7]

<span>The geometric average return is the the nth root of the product of the stock returns. So we have nâš r1 * r2 * r3. Where n is the number of returns. So we have 4âš(14.5 * 4.8 * 10.2 * 6 1) This gives us 4âš ( 4330.512) The fourth root of 4330.512 is 8.1121 percent.</span>

3 0

4 years ago

Hello! I need some help figuring out what 12 x 6,012 is. Ty!

elixir [45]

Answer:

12 times 6012 u can type in calculator is 72144

5 0

4 years ago

Read 2 more answers

What is the answer to 6/7 simplified

tigry1 [53]

Hi there!

6/7 itself is already simplified in it's smallest form.

6/7 = 6/7.

In a decimal form this is 0.857143.

Hope this helps!