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
alina1380 [7]
3 years ago
6

Evaluate the surface integral. s x ds, s is the triangular region with vertices (1, 0, 0), (0, −2, 0), and (0, 0, 12).

Mathematics
1 answer:
aniked [119]3 years ago
7 0
Parameterize the surface by

\mathbf r(s,t)=(1-s)(0,0,12)+s\bigg((1-t)(1,0,0)+t(0,-2,0)\bigg)
\implies\mathbf r(s,t)=(x(s,t),y(s,t),z(s,t))=(s-st,-2st,12-12s)

where (s,t)\in(0,1)\times(0,1). We have

\|\mathbf r_s\times\mathbf r_t\|=\|(1-t,-2t,-12)\times(-s,-2s,0)\|=2\sqrt{181}s

The surface integral is then

\displaystyle\iint_Sx\,\mathrm dS=2\sqrt{181}\int_{s=0}^{s=1}\int_{t=0}^{t=1}s(s-st)\,\mathrm dt\,\mathrm ds
=\displaystyle2\sqrt{181}\left(\int_{s=0}^{s=1}s^2\,\mathrm ds\right)\left(\int_{t=0}^{t=1}(1-t)\,\mathrm dt\right)
=\dfrac{\sqrt{181}}3
You might be interested in
a square garden has an area of 225 square feet. how much fencing will a gardener need to buy in order to place fencing around th
IgorC [24]
The gardener will need to buy 60 feet of fencing. Because the square root of 225 if 15, and 15 times 4 is 60. So, 60 is the perimeter of the garden.
6 0
3 years ago
How many degrees in 2/3 of a circle
sergejj [24]

Answer:

A full circle is 360 degrees so 2/3 is 120

Step-by-step explanation:

3 0
3 years ago
Find all intercepts of y=x^2-2x-3
morpeh [17]
There is a math graping app called desmos it can help you graph the equation and give you the intercepts
3 0
3 years ago
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as ed
Travka [436]
Suppose x books are produced by both methods.
Total cost for method 1 = 60346 + 10.5x
Total cost for method 2 = 18682 + 21x

Cost of method 1 = Cost of method 2
60346 + 10.5x = 18682 + 21x
60346 - 18682 = 21x - 10.5x
41664 = 10.5x
x = 41664/10.5
x = 3968

For 3968 books produced the cost by both methods will be the same.
5 0
3 years ago
Read 2 more answers
A brand new car is $22,000 and its value depreciates 7% each year. How many years will it take for your car to be $10,000? Round
Elan Coil [88]

.200 because 22,000 % by 7 is 1540 which you divide by 10,000

4 0
3 years ago
Other questions:
  • Solve for x. (x - 4)(x - 4) = 0
    13·2 answers
  • IM GIVING BRAINLIEST AND 100 POINTS NO JOKE. PLEASE HELP
    5·2 answers
  • Is 1.68 greater than 1.680
    8·1 answer
  • What are the values of the7's in 17,372
    7·1 answer
  • Mark Shaughnessy purchased a $4,250 bond at 91.50 that pays 7% interest. What was the cost of the bond?
    6·1 answer
  • Use the distributive property to rewrite each algebraic expression: Do not solve, just rewrite.
    14·1 answer
  • Y=1/2x+1 and 2y-x=2 the system shown has how many solutions
    8·1 answer
  • Help with this immediately​
    12·1 answer
  • Joanne signed up for 24 dancing lessons she took 3/4 of the by April and 1/5 of them by May .What part of dancing lesson did she
    7·1 answer
  • What's the slope of the line passing through the points -1, 8 - 7, 3​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!