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IgorLugansk [536]
4 years ago
8

Find the directional derivative of the function at the given point in the direction of vector v. g(x, y, z) = (x + 2y + 3z)3/2,

(5, 4, 4), v = 4j − k dug(5, 4, 4) =
Mathematics
1 answer:
dedylja [7]4 years ago
8 0
g(x,y,z)=(x+2y+3z)^{3/2}

\implies\nabla g(x,y,z)=\dfrac32\left((x+2y+3z)^{1/2},2(x+2y+3z)^{1/2},3(x+2y+3z)^{1/2}\right)

In the direction of \mathbf v=4\,\mathbf j-\mathbf k=(0,4,-1), with norm \sqrt{17}, we have the directional derivative

D_{\mathbf v}g(5,4,4)=\nabla g(5,4,4)\cdot\dfrac{(0,4,-1)}{\sqrt{17}}=\dfrac1{\sqrt{17}}\left(\dfrac{15}2,15,\dfrac{45}2\right)\cdot(0,4,-1)=\dfrac{75}{2\sqrt{17}}
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3 years ago
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torisob [31]

The value for n is \frac{\sqrt{10} }{5}

<h3>solving for n</h3>

<u>given data</u>

10n^{2} - 12 = -8

making n the subject of the formula

10n^{2}  = -8 + 12

10n^{2}  = 4

divide through by 10

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finding the square root of both sides

n = square root ( 4 / 10 )

n = \sqrt{\frac{4}{10}

n = 0.632 or \frac{\sqrt{10} }{5}

Read more the subject of formula here: brainly.com/question/21140562

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2. Abbey rode her bike for 3 3/8 hours in 2 days.

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First make the mixed fraction, improper fractions.

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