1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lerok [7]
2 years ago
9

Evaluate the surface integraliintegral.gifSF � dSfor the given vector field F and the oriented surface S. In other words, find t

he flux of F across S. For closed surfaces, use the positive (outward) orientation.F(x, y, z) = xy i + yz j + zx kS is the part of the paraboloidz = 2 ? x2 ? y2 that lies above the square 0 ? x ? 1, 0 ? y ? 1,and has upward orientation
Mathematics
1 answer:
ehidna [41]2 years ago
8 0

Looks like the paraboloid has equation

z=2-x^2-y^2

and S is the part of this surface with 0\le x\le1 and 0\le y\le1. Parameterize S by

\vec s(u,v)=u\,\vec\imath+v\,\vec\jmath+(2-u^2-v^2)\,\vec k

with 0\le u\le1 and 0\le v\le1. Take the normal vector to S to be

\vec s_u\times\vec s_v=2u\,\vec\imath+2v\,\vec\jmath+\vec k

Then the flux of \vec F across S is

\displaystyle\iint_S\vec F\cdot\mathrm d\vec S

\displaystyle=\int_0^1\int_0^1(uv\,\vec\imath+v(2-u^2-v^2)\,\vec\jmath+u(2-u^2-v^2)\,\vec k)\cdot(2u\,\vec\imath+2v\,\vec\jmath+\vec k)\,\mathrm du\,\mathrm dv

\displaystyle=\int_0^1\int_0^1(2u^2v+(2v+1)u(2-u^2-v^2))\,\mathrm du\,\mathrm dv=\boxed{\frac{293}{180}}

You might be interested in
The aspect ratio is used when calculating the aerodynamic efficiency of the wing of a plane. For a standard wing area, the
xxMikexx [17]

Answer:

Y=s^2/36 and y=5.7;14.3 ft

Step-by-step explanation:

The question was not typed correctly. Here, a better version:

<em>The aspect ratio is used when calculating the aerodynamic efficiency of the wing of a plane for a standard wing area, the function A(s)=s^2/36 can be used to find the aspect ratio depending on the wingspan in feet. If one glider has an aspect ratio of 5.7, which system of equations and solution can be used to represent the wingspan of the glider? Round solution to the nearest tenth if necessary.  </em>

<em> </em>

<em>Y=s^2/36 and y=5.7;14.3 ft </em>

<em>Y=5.7s^2 and y=36; s=2.5ft </em>

<em>Y=36s^2 and y=0; s=0.4 ft </em>

<em>Y=s^2/36 +5.7 and y=0; s=5.5 ft</em>

In the function A(s)=s^2/36 A(s) represents the aspect ratio and s the wingspan. If one glider has an aspect ratio of 5.7, then A(s) = 5.7. We want to know the wingspan of the glider. Replacing A(s) by Y we get the following system of equation:

Y=s^2/36    

with y = 5.7

5.7 = s^2/36    

5.7*36 =  s^2

√205.2 = s

14.3 ft

7 0
3 years ago
Read 2 more answers
Draw a tree diagram to represent the following scenario. You choose a random letter from the word SANDWICH. How many possible ou
VARVARA [1.3K]

Probability helps us to know the chances of an event occurring. There are 8 different scenarios possible.

<h3>What is Probability?</h3>

Probability helps us to know the chances of an event occurring.

\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}

For the given word SANDWICH, there are 8 different scenarios possible, which can be represented as shown below.

Hence, there are 8 different scenarios possible.

Learn more about Probability:

brainly.com/question/795909

#SPJ1

8 0
1 year ago
1)cot a/2 -tan a/2 = 2 cot a<br>2) cot b/2 + tan b/2= 2 cosec b<br> prove​
VladimirAG [237]
1)

LHS = cot(a/2) - tan(a/2)

= (1 - tan^2(a/2))/tan(a/2)

= (2-sec^2(a/2))/tan(a/2)

= 2cot(a/2) - cosec(a/2)sec(a/2)

= 2(1+cos(a))/sin(a) - 1/(cos(a/2)sin(a/2))

= 2 (1+cos(a))/sin(a) - 2/sin(a)) (product to sums)

= 2[(1+cos(a) -1)/sin(a)]

=2cot a

= RHS

2.

LHS = cot(b/2) + tan(b/2)

= [1 + tan^2(b/2)]/tan(b/2)

= sec^2(b/2)/tan(b/2)

= 1/sin(b/2)cos(b/2)

using product to sums

= 2/sin(b)

= 2cosec(b)

= RHS
8 0
2 years ago
The figure shows a triangle with its three angle bisectors intersecting at Point P.
NeX [460]

Check the picture below.

we know the lines are angle bisectors, so the line makes twin angles, so the line FP is making twin angles, we also know the angle FZP and the angle FYP are right-angles, as well as FP is a common hypotenuse to two right triangles, thus by the HA postulate for right triangles, triangle FPZ and triangle FPY are both congruent, so their sides are also congruents, thus PY = PZ.

7 0
2 years ago
How many Japanese yen are equal to $100?
disa [49]
If you mean american dollars (which you most likely do) then it would be:
100 = 12285.
1000 = 122850.
10.000 = 1228.10
hope i helped
3 0
2 years ago
Read 2 more answers
Other questions:
  • Betty bought a package of meat that weighed 1.75 kilograms and another that weighed 1.54 kilograms how much meat did she buy alt
    6·1 answer
  • Two friends, Andrew and Liz, are playing a game using this spinner. If the spinner lands on region 4, Andrew wins. If it lands o
    5·1 answer
  • Order the following expressions by their values from least to greatest.<br> b-a<br> a -0.5<br> a
    7·2 answers
  • Write an equation in slope intercept form of the line going through the points (6,2) and (8, -4)
    9·1 answer
  • Hannah drove her car 318.4 km in 4 h.<br> At this speed, how far can she expect to travel in 5.5 h?
    11·1 answer
  • What's the domain of this function graph?
    12·1 answer
  • H3LP HELP PLZ...... . . . ..
    10·1 answer
  • ! URGENT EMERGENCY !<br> what is the value of x and y
    10·1 answer
  • (x-8)x(-7x-17) - simplify
    13·1 answer
  • If you roll a number cube, what is the probability that you will roll an even number?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!