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
netineya [11]
3 years ago
11

Calculate the area of the surface S. S is the portion of the cone (x^2/4)+(y^2/4)=(z^2/9) that lies between z=4 and z=5

Mathematics
1 answer:
Ganezh [65]3 years ago
6 0

Parameterize S by

\vec r(u,v)=\dfrac23u\cos v\,\vec\imath+\dfrac23u\sin v\,\vec\jmath+u\,\vec k

with 4\le u\le5 and 0\le v\le2\pi. Take the normal vector to S to be

\vec r_u\times\vec r_v=-\dfrac23u\cos v\,\vec\imath-\dfrac23u\sin v\,\vec\jmath+\dfrac49u\,\vec k

(orientation doesn't matter here)

Then the area of S is

\displaystyle\iint_S\mathrm dA=\iint_S\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv

=\displaystyle\frac{2\sqrt{13}}9\int_0^{2\pi}\int_4^5u\,\mathrm du\,\mathrm dv

=\displaystyle\frac{4\sqrt{13}\,\pi}9\int_4^5u\,\mathrm du=\boxed{2\sqrt{13}\,\pi}

You might be interested in
Can anyone help me plz
mario62 [17]

Answer:

4

Step-by-step explanation:

The answer is four because 10% of the whole tray (40) is 4

Equation:  

.1 * 40 = 4

4 0
3 years ago
Which of the following statements about trapezoids is true?? (Help asap) !!!!!!
vampirchik [111]
It is suppose to be letter d

5 0
3 years ago
Solve for k pls ! <br> extra letters for the question: whfjndnfnfn
makvit [3.9K]

Answer:

k=5

Step-by-step explanation:

hope this was helpful!! c:

8 0
3 years ago
How far can a car travel on 1 gallon of gasoline?
Yuliya22 [10]

Answer:

25 miles

Step-by-step explanation:

50/2=25

8 0
3 years ago
Read 2 more answers
X·|2x+5|+2x·|x-3|=35
VARVARA [1.3K]
You have the answer into the images.

8 0
3 years ago
Other questions:
  • 4(g - 1 )=24<br>what is the answer
    6·2 answers
  • Classify the real number. (Choose all that apply). –9 A.) Rational B.) Whole C.) Irrational D.) Natural E.) Integer
    5·1 answer
  • A number minus 9 is twelve
    10·2 answers
  • What is 7285 divided by 4
    13·1 answer
  • Vicente has a prism- like water tank whose base area is 1.2 square meters. He bought 6 goldfish at the store and the store owner
    5·1 answer
  • In your notebook, set up the following subtraction in a vertical format and select the correct answer. Take -4 + 3a2 from 7a - a
    8·2 answers
  • What is -5/6 ÷ 9 /10 ?
    8·1 answer
  • Write an expression showing a ÷ b without the use of the division symbol.
    6·2 answers
  • Jaden makes 63% of the free throws he shoots. About how many shots do you predict he will have to take to make 15 free throws?
    9·2 answers
  • In a necklace, there are 2 white beads for every 7 purple beads. There is a total of 8 white beads. How many purple beads are in
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!