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Gwar [14]
3 years ago
9

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.

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Please HELP with these questions!! Legit answers only!
Lelechka [254]

Answer:

answers below

Step-by-step explanation:

hi! you can plug in the x values given into the equation and solve for y to get your table values.

y=-1(0)+2

y=2

y=-1(1)+2

y=1

y=-1(3)+2

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y=-3/2 (0) -1

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7 0
3 years ago
1. tentukan hasil dari 243⅔?
Vesnalui [34]

Penjelasan langkah demi langkah:

1)

= 243^{\frac{2}{3} }\\= (\sqrt[3]{243})^2\\= 7^2\\= 49

2) √32 +3√18-2√50

= √16*2 +3√9*2-2√25*2

= 4√2 + 3(3√2)-2(5√2)

= 4√2 + 9√2-10√2

= 13√2-10√2

= 3√2

3) 1000 ⅔×64⅙

 = (\sqrt[3]{1000}) ^2 \times (2^6)^{1/6}  \\= 10^2 \times 2\\= 100 \times 2\\= 200

4) 3/4+√2

3/4+\sqrt{2} \\= \frac{3+4\sqrt{2} }{4 }

5) 2√3×√18

= 2√3×√9*2

= 2√3×3√2

= (2*3)(√3*√2)

= 6√6

6) 12/3+√3

= 4+√3

7) √1000—2√40

= 10 -2 (√4*10)

= 10-2(2√10)

= 10 - 4√10

8) 2- ¹+3-¹

= \frac{1}{2} + \frac{1}{3}\\ = \frac{3+2}{6}\\ = \frac{5}{6}

9)

\frac{5}{\sqrt{5} }\\ merasionalisasikan\\= \frac{5}{\sqrt{5} }\times \frac{\sqrt{5} }{\sqrt{5} }\\= \frac{5\sqrt{5} }{\sqrt{25} }\\= \frac{5\sqrt{5} }{5}\\ = \frac{\sqrt{5} }{1}

Jika pernyataannya opsional, penyebutnya adalah 1

10) 2√3×√18

= 2√3×√9*2

= 2√3×3√2

= (2*3)(√3*√2)

= 6√6

7 0
3 years ago
Jun used 56 cm of ribbon to go around the edge of a rectangular lid. The lid was 13 cm long. What is the width of the lid?
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Answer:

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Step-by-step explanation:1. Let's review the information given to us to answer the question correctly:

Length of the ribbon used by Jun = 56 cmLength of the rectangular lid = 13 cm

2. What is the width of the lid? The ribbon used by Jun is equivalent to the perimeter of the rectangular lid, therefore:Perimeter = 2 * Length + 2 * WidthReplacing with the values we have:56 = 2 * 13 + 2 * Width56 = 26 + 2Width2Width = 56 - 262Width = 30Width = 30/2Width = 15

5 0
2 years ago
Read 2 more answers
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2 1/4 = 9/4

2 1/4 / 5/8 = 9/4 / 5/8 = 9/4 * 8/5 = 18/5 = 3 3/5

The correct result would be 3 3/5.
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3 years ago
I’ll give you brainiest who ever answer this right
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Answer:

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Step-by-step explanation:

at each x you move up by 1

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