All categories

3 years ago

Find the linear approximation of the function f(x, y, z) =

Mathematics

1 answer:

ser-zykov [4K]3 years ago

3 0

Answer:

See below in bold.

Step-by-step explanation:

f(x, y, z) = x^2 + y^2 + z^2 at (6, 6, 7)

Taking partial derivatives

f'x = 2x + y^2 + z^2 --> f'x(6,6,7) = 12+36+49= 97

f'y = x^2 + 2y + z^2---> f'y(6,6,7) = 36 + 12 + 49 = 97

f'z = x^2 + y^2 + 2z ----> f'z(6,6,7) = 36 + 36 + 14 = 86.

f(6,6,7) = 36 + 36 + 49 = 121

So our linear approximation is:

L(x,y,z) = 121 + 97(x - 6) + 97(y - 6) + 86(z - 7)

Substituting the given values

f(6.012, 5.972,6.982)

= L(6.012, 5.972, 6.982) ≈ 121 + 97(6.012 - 6) + 97(5.972 - 6) + 86(6.982 - 7)

= 117.9.

You might be interested in

<img src="https://tex.z-dn.net/?f=2%20%7Bx%7D%5E%7B2%7D%20%20-%205x%20%3D%207" id="TexFormula1" title="2 {x}^{2} - 5x = 7" alt=

FinnZ [79.3K]

Answer:

x = -7/2 or x =1

Step-by-step explanation:

2xx - 5x - 7 = 0

2x(x - 1) + 7(x - 1) = 0

(2x +7) (x -1) = 0

x = -7/2 or x =1

4 0

3 years ago

Sadie sold 45 cupcakes, which were packed in 9 boxes. How many cupcakes were in each box? 4 5 8 9

Korvikt [17]

45 divided by 9 = 5
5 cupcakes per box

3 0

3 years ago

Read 2 more answers

If your good in math please help me

Feliz [49]

Answer:

350.82

Step-by-step explanation:

To find the surface area, you must add up all of the areas of each shape of the prism in order to get the sum surface area.

The rectangle's area ( $lw$ ):

$7.21*14=100.94$

The triangle's area ( $\frac{1}{2}bh$ ):

$\frac{1}{2} (6)(8)$

$\frac{1}{2} (48)=24$

Now add up all the sides. (3 Rectangles, 2 Triangles.)

$100.94 + 100.94 + 100.94 + 24 + 24$

$=350.82$

The total surface area is 350.82 cm squared.

6 0

3 years ago

How do I Find the slope and Y intercept of each equation:

Nesterboy [21]

$1.\\ \\ the \ slope \ intercept \ form \ is : \\ \\ y= mx +b \\ \\y=2x+1 \\ \\ the \ slope \ (the multiplier \ of \ x \ represented \ by \ m ) \ is \ 2 \\ \\ and \ the \ y-intercept \ (the constantrepresented \ by \ b \ ) \ is \ 1$

$2.\\ \\ y= \frac{1}{3}x-3 \\ \\ the \ slope \ m = \frac{1}{3} \ \ and \ y = -3$

$3.\\ \\ y= -2x + 1\\ \\ the \ slope \ m = -2 \ \ and \ y = 1$

$4.\\ \\-2x +5y=10\\ \\5y=2x +10 \ \ /:5\\ \\y = \frac{2}{5}x +2\\ \\ the \ slope \ m =\frac{ 2}{5} \ \ and \ y = 2$

$5.\\ \\ 4x-2y-5=0\\ \\-2y =-4x +5 \ \ /:(-2)\\ \\y=2x-\frac{5}{2} \\ \\ the \ slope \ m = 2 \ \ and \ y = -\frac{5}{ 2}$

$6.\\ \\ y=-4x-3 \\ \\ the \ slope \ m =-4 \ \ and \ y = -3$

$7.\\ \\3x-5y=20\\ \\-5y=-3x +20 \ \ / :(-5) \\ \\ y= \frac{3}{5}x - 4\\ \\ the \ slope \ m = \frac{3}{5} \ \ and \ y = -4$

6 0

3 years ago

How much Active Mix should she add in order to have a trail mix containing 30% dried fruit? lbs

gregori [183]

You have to give all of the details.

6 0

3 years ago

Read 2 more answers