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Snowcat [4.5K]
3 years ago
5

Find the directional derivative of f(x, y, z) = xy + yz + zx at p(1, −1, 7) in the direction from p to q(2, 4, 5). duf(1, −1, 7)

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
7 0
f(x,y,z)=xy+yz+zx

\implies\nabla f(x,y,z)=(y+z,x+z,y+x)

\vec{pq}=\mathbf q-\mathbf p=(2-1,4-(-1),5-7)=(1,5,-2)

\|\vec{pq}\|=\sqrt{30}

D_{\vec{pq}}f(1,-1,7)=\nabla f(1,-1,7)\cdot\dfrac{(1,5,-2)}{\sqrt{30}}=\dfrac{(6,8,0)\cdot(1,5,-2)}{\sqrt{30}}=\dfrac{46}{\sqrt{30}}
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3 years ago
An employment agency specializing in temporary construction help pays heavy equipment operators $138 per day and general laborer
prisoha [69]

Answer:

L = 2,

O = 31

Step-by-step explanation:

First using the givens, write out some formulas.

Heavy equipment operators = O

General laborers = L

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Now use substitution, it doesn't matter which one you substitute.

  • O = -L +33
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Distribute and solve for L.

  • -138L + 4554 + 87L = 4044
  • -138L - 87L = 4044 - 4554
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L = 2, meaning number of laborers employed is 2.

Now plug 2 = L into one of the original equations.

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  • O + 2 = 33
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O = 31, meaning number of heavy equip. operators employed is 31.

4 0
3 years ago
What is 1+7/30(4x)=12
ahrayia [7]
165 X= ——— 14 1 + 7/30 (4x) = 20
8 0
3 years ago
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3 years ago
Read 2 more answers
Andrea is buying a car for $21,450 she will finance $16,450 of it with a 5 year loan at 2.9% apr what will her monthly auto paym
Citrus2011 [14]
2.9% apr

5 years to pay

loan= 21450-16450= $5000

apr = .029

.029/12 =.0024

.0024(5000)=12.08

.0024+1=1.0024

1.0024^(5*12)= 1.15

1/1.15= .86

1-.86 = .14

60/ .14= $294.85$

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3 0
3 years ago
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