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
choli [55]
3 years ago
8

Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0).

Mathematics
1 answer:
aliya0001 [1]3 years ago
7 0

Answer:

The closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

Step-by-step explanation:

Let B(x, y, z) denote a point on the cone.

Therefore, the distance between the points (6, 2, 0) and B(x, y, z) is;

d = √[(x - 6)² + (y - 2)² + (z - 0)²]

d = √[(x - 6)² + (y - 2)² + z²]

Since we are given that z² = x² + y², we now have;

d = √[(x - 6)² + (y - 2)² + x² + y²]

Taking the square of both sides gives;

d² = [(x - 6)² + (y - 2)² + x² + y²]

x² is an increasing function. Thus, minimizing d is also the same as to minimize f (x, y) = d²

Thus, f' = 0. So;

df/dx = 2(x - 6) + 2x = 0

2x - 12 + 2x = 0

4x = 12

x = 12/4

x = 3

Similarly,

df/dy = 2(y - 2) + 2y = 0

2y - 4 + 2y = 0

4y - 4 = 0

4y = 4

y = 4/4

y = 1

Now,from earlier;

z² = x² + y²

Thus;

z = ±√(3² + 1²)

z = ±√10

Thus, the closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

You might be interested in
HELPPPPPPPPppppppppppppp
alekssr [168]

Answer: 16

Step-by-step explanation:

5 0
3 years ago
The student enrollment of South High School was 1,350 students in 1995 and increased by 15% per year until 2010. Approximately h
vlabodo [156]

Answer: A.

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Evaluate: 32 + (8 − 2) • 4 − 6/3
Ipatiy [6.2K]
The expression to evaluate is 32 + (8 - 2) * 4 - 6/3. In the first step you can solve the parenthesis and the fraction => 32 + (6)*4 - 2. In the second step you mutiply 6*4 => 32 + 24 - 2. Finally, you do the maths: 32 + 24 - 2 = 54. <span>Answer: 54</span>
8 0
3 years ago
How.to find domain and.range of.a.function?
mestny [16]
Depends greatly on the type of function.
Some things to keep in mind:
1.) the value of the denominator of a fraction cannot be zero
2.) the inside of an even root cannot be less than zero
3. The argument of a logarithmic function must be greater than zero
4. Plus many more other rules and such

But a simpler explanation, just find out what values x can be for the given function, and what y can be.
The x values make up the domain, the y, the range

Graphs are helpful
Hope this helps!
8 0
3 years ago
*LAST QUESTION, PLEASE HURRY AND ANSWER* What is the volume of the cone below? (Use 3.14 for pi)
enyata [817]

Answer:

<h2>           The third:  5.32 cubic units</h2>

Step-by-step explanation:

R = 1.52

H = 2.2

π = 3.14

V=\frac13\pi R^2\cdot H\\\\V=\frac13\cdot3.14\cdot(1.52)^2\cdot2.2=5.3200810\overline6\approx5.32

4 0
3 years ago
Other questions:
  • In a geometric sequence, the ____ between consecutive terms is constant.
    12·1 answer
  • The product of the page numbers on two facing pages of a book is 156. Find the page numbers
    11·1 answer
  • Help with this question please
    10·2 answers
  • hi I'm looking for the answers for my work I already did this agistment but failed it and need help getting my grade up
    6·1 answer
  • I need help ASAP PLEASE please...
    11·1 answer
  • (11x+9)+(5x-9) pls solve this for me I have no clue and i need this fast
    9·1 answer
  • ANYone who WANTS TO WATCH OR PLAY SOME VIDEOGAMES JOIN this meeting
    13·1 answer
  • ) (i) Simplify:<br>Permudahkan:-<br>9 + 3t - 4​
    11·1 answer
  • A man jogs from his home to the nearst market 25km away jogs at an average speed 5km 1h. how long does it taken him to reach the
    5·1 answer
  • Helppppppp plissssssssssss
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!