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
Margarita [4]
3 years ago
13

Find a parametric representation for the surface. The part of the sphere x2 + y2 + z2 = 144 that lies between the planes z = â’6

and z = 6. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of θ and/or Ď•.) (where â’6 < z < 6)

Mathematics
1 answer:
ryzh [129]3 years ago
8 0

We can use the standard set of parametric equations in spherical coordinates:

\begin{cases}x(u,v)=12\cos u\sin v\\y(u,v)=12\sin u\sin v\\z(u,v)=12\cos v\end{cases}

with 0\le u\le2\pi. Then the part of the sphere that lies between the planes z=-6 and z=6 is determined by the domain of v. To find that, we can sketch a picture of the situtation (attached below).

The right triangle in the image has its hypotenuse coinciding with the radius of the sphere so its length is 12, and the vertical leg has length 6 because it coincides with the plane z=6. The angle between them is the upper limit of v. At any point along the intersection of the sphere with the plane z=6, we want to have

\cos v=\dfrac6{12}=\dfrac12\implies v=\dfrac\pi3

and so by symmetry, we need to set -\dfrac\pi3\le v\le\dfrac\pi3

You might be interested in
266 divided by 27 as a fraction.
notsponge [240]
<span> the answer is 9 23/27

</span>
8 0
3 years ago
Read 2 more answers
Nestor works at a garden center where he posts plants. It takes him 2 1/2 hours to pot 15 plants. How many plants can Nestor pot
guapka [62]

Answer:

Nestor can pot 6 plants in 1 hour.

Step-by-step explanation:

first lets convert 2 1/2 hours in mixed fraction form for better calculation

2 1/2 hours = (2*2 + 1)/2 = 5/2 hours

no of plants pot in  5/2 hours = 15

to find no. of plants pot in 1 hours lets

divide both side by 5/2

no of plants pot in  5/2/(5/2)  hours = 15/(5/2) = 15*2/5 = 6

no. of plants pot in 1 hour = 6

Thus, Nestor can pot 6 plants in 1 hour.

6 0
3 years ago
HELPP <br> Complete the ratio table.<br> 5 1<br> 30 6<br> 60 _<br> 75 _<br> 80 _
goldfiish [28.3K]

Answer:

12 27 32 it could be wrong though

5 0
2 years ago
Which of the following equations is of a parabola with a vertex at (0, -5)
Harlamova29_29 [7]

The x, which is zero in this case will always be the number that goes on the inside of the equation, so far you have y=(x+0)^2 or y=x^2.

The y, which is negative will go on the end of the equation. So you get y=x^2-5

The equation is y=x^2-5 or C if it is multiple choice

4 0
3 years ago
Read 2 more answers
10 divided by 12 yeah
padilas [110]

Answer:

10 divided by 12 equals 0.833333333

8 0
3 years ago
Other questions:
  • The sum of 5 consecutive integers is 265. What is the fifth number in this sequence?
    11·1 answer
  • On a scale drawing of a dock for a marina, 1 inch equals 15 feet. the dock is 200 feet long. what is the length of the dock on t
    10·1 answer
  • The skateboard that Jose wants costs $90. Jose has a coupon for 1 5 off the retail price. If Jose saves $18 a week, how long wil
    14·1 answer
  • Chapter
    13·1 answer
  • Four friends are racing. Lisa finishes four hours ahead of Tony, with Pete finishing eight hours ahead of Max. Max needed six mo
    7·1 answer
  • Thirty-six members of the middle school choir, which represents 30%, participated in the regional contents. How many total stude
    12·1 answer
  • a pencil cells at 18 Ghana cedis in an eraser class at 12 Ghana cedis how much will you pay if you buy three pencils and for era
    12·1 answer
  • Alguien que me ayude con esto​
    6·1 answer
  • A company's profit tripled from 2015-2016. If they earned $140,000 all together how much did they earn in each year?
    15·1 answer
  • Whats the sum of -32 and 4?<br><br><br> A.-27<br> B.-3<br> C.3<br> D.27
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!