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
Ira Lisetskai [31]
3 years ago
5

If a parametric surface given by r1(u,v)=f(u,v)i+g(u,v)j+h(u,v)k and −2≤u≤2,−3≤v≤3, has surface area equal to 4, what is the sur

face area of the parametric surface given by r2(u,v)=4r1(u,v) with −2≤u≤2,−3≤v≤3?
Mathematics
1 answer:
katovenus [111]3 years ago
3 0
The area of the first surface is given to be

\displaystyle\iint_{\mathcal S_1}\left\|\frac{\partial\mathbf r_1}{\partial u}\times\frac{\partial\mathbf r_1}{\partial v}\right\|\,\mathrm du\,\mathrm dv=4

Recall that for any scalar k and vectors \mathbf a,\mathbf b\in\mathbb R^3,

(k\mathbf a)\times\mathbf b=\mathbf a\times(k\mathbf b)=k(\mathbf a\times\mathbf b)

which means

\left\|\dfrac{\partial\mathbf r_2}{\partial u}\times\dfrac{\partial\mathbf r_2}{\partial v}\right\|=\left\|4\dfrac{\partial\mathbf r_1}{\partial u}\times\dfrac{4\partial\mathbf r_1}{\partial v}\right\|
=16\left\|\dfrac{\partial\mathbf r_1}{\partial u}\times\dfrac{\partial\mathbf r_1}{\partial v}\right\|

So it follows that the area of the \mathcal S_2 is 16 times that of \mathcal S_1.
You might be interested in
The height of 6 pictures placed end to end on a bulletin board is 57 centimeters.
Elden [556K]
Ummm I think b orrr A good luck!
7 0
2 years ago
What is the property used in 25+0=25
xz_007 [3.2K]

math teacher said its associative

5 0
3 years ago
Read 2 more answers
Syria has the 5 apps on her phone wich is 3 less than twice the amount the Khary has. How many apps does Khary have?
jek_recluse [69]
She has 7 apps on her phone
3 0
3 years ago
Which of the following forms of I.D. is not an acceptable form of I.D. for opening a savings account?
larisa86 [58]
Answer:  [A]:  "library card".
____________________________________
Explanation:   One would need a valid, government-issued photo ID card (i.e. that has not expires).

Although SOME library cards include one's picture, library cards do not constitute "valid ID's" because they are not "government-issued" and would, theoretically, be easy to be made fraudulently (e.g. not have security-issued seals and features). 

Even "school ID's"; or "college ID cards"; even if "current" (e.g. currently enrolled" with a photo ID) would not be considered "official" and would only be considered "secondary ID".
_____________________________________________
6 0
3 years ago
Read 2 more answers
A piece of paper is chosen from a bag that contains 10 pieces of paper numbered 1 through 10. Find the probability that the pape
motikmotik

Answer:

1/5

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • A student government organization is selling Christmas trees as a fundraiser. On Friday, they sold 5 noble fir trees and 3 dougl
    12·1 answer
  • 113.6 grams is equal to how many ounces ?
    7·1 answer
  • Which is the graph of f(x)= √x
    15·1 answer
  • The position of an object at time t is given by s(t) = 3 - 4t. Find the instantaneous velocity at t = 8 by finding the derivativ
    10·2 answers
  • Decimal form of 92/125
    14·2 answers
  • Expand the following 2(x+3)
    6·2 answers
  • D
    10·1 answer
  • Find the exact value of cos A in simplest radical form
    7·1 answer
  • What is the range of possible sizes for x?
    11·1 answer
  • How do you factorise 2k + 10ak
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!