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
Sunshine Rental Car charges a one-time fee of $30.15 per mile the yellow car agency charges a one-time fee of $20.25 per mile th
11111nata11111 [884]

Answer:

105 miles

Step-by-step explanation:

I used a calculator because it was multi choice until they matched up

5 0
3 years ago
What 2 numbers multiplied comes to 149
wel

Answer:

12.20655562 or 12.2

Step-by-step explanation:

Just square  149 \sqrt{149\\}

That gives you 12.20655562

Round it to 12.2

4 0
3 years ago
Help me to solve problem pless​
sergejj [24]

Answer:

a:

5 x -3 +6

= 5 x 6 + -3

= 30 + -3

= 27

8 0
2 years ago
Read 2 more answers
X-y=3<br> Work out the value for 2x-2y
masha68 [24]

Answer:

6

Step-by-step explanation:

2x-2y = 2(x-y) = 2(3) = 6

8 0
3 years ago
Read 2 more answers
Help me Please ...
wariber [46]
8. 268.632

there is one

4 0
3 years ago
Other questions:
  • Randall is cutting a submarine sandwich into smaller pieces he has 4 ft of Saturday he wants to divide into 1/3 foot sandwiches
    7·1 answer
  • What is the value of x? 36 Degrees, Tangent lines, Acellus, Geometry
    7·1 answer
  • If 25×60 is 1700 W is 1700÷6.8
    5·1 answer
  • Which relationship between x and y in the equation shows a proportional relationship?
    6·2 answers
  • Simplify each of the following expressions and then put each simplified expression in order from greatest to least. −6+(−2) 2−6−
    10·1 answer
  • What is 6/10 as hundredths in fraction form
    5·1 answer
  • A clay block is 12 cm long 6cm wide and 2cm high and the density is 1.25cm3 what is the mass
    9·1 answer
  • Find the value of this expression if x = 7 and y= -2<br> xy^2/9
    9·2 answers
  • A college basketball player makes 70% of his free throws. At the end of a game, his team is losing by two points. He is fouled a
    11·2 answers
  • - Which of the following expressions has a coefficient of 10 and a constant of 5?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!