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
crimeas [40]
3 years ago
14

g The tangent plane to z=f(x,y) at the point (1,2) is z=5x+2y−10. (a) Find fx(1,2) and fy(1,2). fx(1,2)= Number fy(1,2)= Number

(b) What is f(1,2)? f(1,2)= Number (c) Approximate f(1.1,1.9). f(1.1,1.9)= Number

Mathematics
1 answer:
murzikaleks [220]3 years ago
6 0

Answer:

The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.

Approximation at points (1.1,1.9) is 0.7

Step-by-step explanation:

Given:

Tangent plane to  a surface z=5x+2y-10 as the function at point (1,2)

To find :

f(x,y) at (1,2)

partial derivatives of function w.r.t. (x and y) and value of that function at given points.

Solution:(refer the attachment also)

Now we know that

the equation of tangent plane at given points to the surface is given by,

f(x1,y1,z1) and z=f(x,y)

z-z1=Fx(x1,y1)*(x-x1)+Fy(x1,y1)*(y-y1)

here Fx(x1,y1) and Fy(x1,y1) are the partial derivatives of x and y.

now

taking partial derivative w.r.t. x we get

Fx(x1`,y1)=\frac{d}{dx} (5x+2y-10)

=5.

Then w.r.t y we get

Fy(x1,y1)=

\frac{d}{dy}(5x+2y-10)

=2.

The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.

Using the Linearization or linear approximation we get

L(x,y)=f(x1,y1)+Fx(x,y)*(x-x1)+Fy(x,y)(y-y1)

=-1+5(x-1)+2(y-2)

=5x+2y-10

Approximation at F(1.1,1.9)

=5(1.1)+2(1.9)-10

=5.5+3.8-10

=0.7

Approximation at points (1.1,1.9) is 0.7

You might be interested in
-(3/(2y+12))+2=-(8/(y+6)
musickatia [10]

Answer:

Step-by-step explanation:

3 0
3 years ago
Which of the capital letters G, I, J, L, or Q has at least one line of symmetry?
gladu [14]
I is the right one because it is a half and they both look the same
3 0
2 years ago
If the life of a brake lining costing $3.20 is 40,000 miles what is its cost per 1,000 miles
Sunny_sXe [5.5K]

Answer:

.08

Step-by-step explanation:

COMMENT IF YOU NEED WORK

6 0
3 years ago
A homeless shelter received donations of 18 mittens and 12 winter hats. What is the greatest number of identical winter clothing
Daniel [21]

216........................


8 0
3 years ago
BRAINLIESTTT ASAP! PLEASE HELP ME :)
sergiy2304 [10]

Answer:

\displaystyle Maximum: 11

Step-by-step explanation:

Convert this Quadratic Equation to Vertex Form by completing the square, \displaystyle y = a[x - h]^2 + k:

\displaystyle -5x^2 -10x + 6 \\ \\ -5x^2 - 10x + 25 + k \\ -5[x^2 + 2x - 5] + k \\ -5[x^2 + 2x + 1] + k → -5[x^2 + 2x + 1] + 11 → f(x) = -5[x + 1]^2 + 11 \\ \\ Vertex: [-1, 11]; 11 = Maximum

So as you can see, each time we broke the equation down, we used the formula \displaystyle [\frac{b}{2}]^2 to complete the square.

** In the Vertex Formula, −h gives the OPPOSITE terms of what they really are, so do not forget it.

I am joyous to assist you anytime.

4 0
3 years ago
Other questions:
  • 7 girls and 5 boys in the seventh grade and 3 girls and 9 boys in the eighth grade. teacher randomly selects a seventh grader an
    8·1 answer
  • how do i find the volume of a triangular prism that has a 10m width a 4m base and a 8m hight don't worry about the T
    6·1 answer
  • Which of the binomials below is a factor of this trinomial 3x^2+18x+24
    11·2 answers
  • How to get length of hypotenuse with 30-60-90 right triangle?
    6·1 answer
  • Write the equation of a line that is horizontal and contains the point (-4, 1)
    7·1 answer
  • when xena says a number yoli tripples the number. make a table that shows three pairs of numbers xena and yoli might say.
    11·1 answer
  • Trevor’s total employment compensation is $33,500. If Trevor has no job expenses and his gross pay is $28,600, then his total em
    12·2 answers
  • Sound travels at a rate of 344 meters in 1 second. How many meters does it travel in 1 minute?
    9·2 answers
  • If y = 17.5 when x = 12, find y when x = 6.
    7·2 answers
  • This person mows half of her backyard in one house. Ways power can be increased
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!