3 years ago

What’s is the answer to these two problems?

Mathematics

1 answer:

Len [333]3 years ago

8 0

Answer:

Step-by-step explanation:

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Find the directional derivative of f(x,y,z)=2z2x+y3f(x,y,z)=2z2x+y3 at the point (−1,4,3)(−1,4,3) in the direction of the vector

Feliz [49]

$f(x,y,z)=2z^2x+y^3$

$f$ has gradient

$\nabla f(x,y,z)=2z^2\,\vec\imath+3y^2\,\vec\jmath+4xz\,\vec k$

which at the point (-1, 4, 3) has a value of

$\nabla f(-1,4,3)=18\,\vec\imath+48\,\vec\jmath-12\,\vec k$

I'm not sure what the given direction vector is supposed to be, but my best guess is that it's intended to say $\vec u=15\,\vec\imath+25\,\vec\jmath$ , in which case we have

$\|\vec u\|=\sqrt{15^2+25^2}=5\sqrt{34}$

Then the derivative of $f$ at (-1, 4, 3) in the direction of $\vec u$ is

$D_{\vec u}f(-1,4,3)=\nabla f(-1,4,3)\cdot\dfrac{\vec u}{\|\vec u\|}=\boxed{\dfrac{294}{\sqrt{34}}}$

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3 years ago

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Pavel [41]

Answer:

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3 years ago

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Angles R and S are complementary. If angle R is = 4x - 20 and angle S = 6x - 7, then angle R measures ___ degrees.

Shalnov [3]

Answer:

26.8°

Step-by-step explanation:

4x - 20 + 6x - 7 = 90

10x -27 =90

10x = 90+27

10x= 117

x = 11.7

so, the angle R = 4x-20 =4(11.7)-20

= 46.8-20 = 26.8°

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3 years ago

Is 144 a perfect square?

garri49 [273]

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Yes

Step-by-step explanation:

Because its the square root of 12

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What pair of lines are parallel

MAVERICK [17]

Answer:

D and C

Step-by-step explanation:

any line that is convergent, no divergent lines, and intersecting lines.

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3 years ago