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The surface of a mountain is modeled by the equation h(x, y) = 5000 - 0.001x² - 0.004y². A mountain climber is at the point (500, 300, 4390). In what direction should the climber move in order to ascend at the greatest rate?

Answers

Answer 1

Answer:

Answer:

i-2.4j

Step-by-step explanation:

Given that,

The surface of a mountain is modeled by the equation as follows :

$h(x,y)=5000 -0.001x^2-0.004y^2$

A mountain climber is at the point (500, 300, 4390).

We need to find the direction in which he should move in order to ascend at the greatest rate.

To find direction, first finding the gradient of h as follows :

$\nabla h(x,y)=-0.002xi-0.008yj$

Now put x = 500 and y = 300

So,

$\nabla h(x,y)=-0.002(500)i-0.008(300)j\n\n\nabla h(x,y)=i-2.4j$

The direction of the climber is i-2.4j

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please show how you got the answer.

Answers

Answer:

F. 6s > 4s +8

Step-by-step explanation:

From a reference point at the beginning of the track, Ward's car will be located 4s+8 feet down the track after s seconds. That is, it starts 8 feet down the track, and increases its distance by 4 feet every second.

From the same reference point, Heskey's car will be located 6s feet down the track after s seconds. Its distance starts from zero and is increasing at the rate of 6 feet every second.

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Let C be the unit circle in the xy-plane, oriented counterclockwise as seen from above. The divergence of the vector field F~ = (z, x, y) is zero, and as a result the flux through every surface with boundary C should be the same. Confirm that this is the case with the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane

Answers

Upper half of the unit sphere (call it $S_1$ ): parameterize by

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Lower half of the sphere (call it $S_2$ ): all the details remain the same as above, but with $\frac\pi2\le v\le\pi$ . The flux is again $\boxed{0}$ .

Unit disk (call it $D$ ): parameterize the disk by

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with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to be

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Then the flux across $D$ is

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Final answer:

The flux through every surface with boundary C, such as the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane, should be the same and it is zero.

Explanation:

The divergence of the vector field F~ = (z, x, y) is zero. Therefore, the flux through every surface with boundary C, such as the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane, should be the same.

This can be confirmed by considering that the electric flux through a closed surface is zero if there are no sources of electric field inside the enclosed volume. Since there are no charges inside the surfaces mentioned, the flux through each surface is zero.

Therefore, the flux through the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane is the same, and it is zero.

Learn more about Electric Flux here:

brainly.com/question/38239959

#SPJ3

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Answers

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Answers

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Answers

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