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
mihalych1998 [28]
3 years ago
10

Consider the surface f (x comma y comma z )f(x,y,z)equals=negative 2 x squared plus 2 y squared minus 3 z squared plus 3 equals

0−2x2+2y2−3z2+3=0​, which may be regarded as a level surface of the function wequals=f (x comma y comma z )f(x,y,z). The point P(negative 2 comma 2 comma 1 )(−2,2,1) is on the surface. a. Find the​ (three-dimensional) gradient of f and evaluate it at P. b. The heads of all the vectors orthogonal to the gradient with their tails at P form a plane. Find an equation of that plane.
Mathematics
1 answer:
trapecia [35]3 years ago
3 0

Answer:

a) (8,8,-6)

b) 4x+4y+3z = -3

Step-by-step explanation:

a)

The surface is given by the equation  

f(x,y,z) = 0 where

f(x,y,z)=-2x^2+2y^2-3z^2+3

The gradient of this function is the vector

(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})=(-4x,4y,-6z)

If we evaluate it in the point P = (-2,2,1) we obtain the point

(8,8,-6)

b)

The vectors with their tails at P are of the form  

(-2,2,1)-(x,y,z) = (-2-x, 2-y, 1-z)

as they must be orthogonal to the gradient, they must be orthogonal to the vector (8,8,6) so their inner product is 0

(-2-x,2-y,1-z)\cdot(8,8,6)=0\Rightarrow -16-8x+16-8y+6-6z=0\Rightarrow 4x+4y+3z=-3

and the equation of the desired plane is

4x+4y+3z = -3

You might be interested in
Change the equation from standard form to slope-intercept form -5x-2y=-3
horrorfan [7]

Answer:Your Mom

<h2>Step-by-step explanation:Cause she is fat No but it srsly is 123</h2>
5 0
3 years ago
Order of Operations with and without variables
lyudmila [28]
I think the answer is -4
6 0
3 years ago
18 is ( blank ) % of 30
meriva
Make an equation.

'is' is an equal sign

The blank can be 'x'

'of' = multiplication

18 = x * 30

Multiply:

18 = 30x

Divide 30 to both sides:

x = 0.6

Multiply by 100:

0.6 * 100 = 60%
4 0
3 years ago
Read 2 more answers
The formula for the perimeter of a rectangle is . What is the length of the unknown side of the rectangle below, if the perimete
Troyanec [42]

Answer:

Step-by-step explanation:

P=2l+2w

28=2l+2w

2l=2w-28

l = (2w-28)/2

l =2(w-14)/2

l = w-14

7 0
3 years ago
Susan’s stylist has done a great job of coloring her hair. She wants to leave a 20 percent tip. If the bill was $150, how much s
irina [24]
0.20(150) = 30....her 20% tip would be 30 bucks
6 0
3 years ago
Read 2 more answers
Other questions:
  • Romeo is using a common algorithm to find the product of 8,125 × 9. Drag the correct numbers to the problem to show the partial
    9·2 answers
  • Using the least number of coins how many quarters, dimes, nickels, and pennies to make $1.74
    15·1 answer
  • 2/3 [ (15 - 6) -8 (8 + 1]
    6·1 answer
  • Each car on a comuter train can seat 114 pessengers. If the train has 7 cars,how many pessengers can the train Seat
    10·2 answers
  • PLZ HELP NEED ANSWER ASAP TIA
    7·2 answers
  • rob says all numbers have an even number of factors marcia says some numbers have an odd number who is correct
    15·2 answers
  • The area of a rectangular wall of a barn is 192 sq. Ft. It's length is 8 ft. Longer than twice it's width. Find the length and w
    11·1 answer
  • Solve the problem and then click on the correct graph.<br><br> y = |x|
    6·1 answer
  • Find the median number for 10,5,7,9,18,15,17,14,16,17,15,19,5
    9·2 answers
  • Solve the system of equations by adding them together term by term to eliminate one variable:
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!