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yaroslaw [1]
3 years ago
13

Garne Problem med

Mathematics
1 answer:
Citrus2011 [14]3 years ago
8 0

Total distance the rover need to travel ​is D = 1miles .

<u>Step-by-step explanation:</u>

We have , Garne Problem med   . A rover needs to travel mile to reach its destination  traveled mile. a rover needs to travel 5/8 mile to reach its destination it has already travel 3/8 miles . We need to find that  how much farther does the rover need to travel ​ , Let's do it step by step:

First , rover has already traveled 3/8 miles , Let total distance to be traveled by rover is D :

⇒ D = \frac{3}{8} + d , where d is distance left to cover .

Now, rover need to travel 5/8 miles more to reach destination :

⇒ D = \frac{3}{8} + d , where d is distance left to cover  , So d = \frac{5}{8}

⇒ D = \frac{3}{8} + d

⇒ D = \frac{3}{8} + \frac{5}{8}

⇒ D = \frac{3+5}{8}

⇒ D = \frac{8}{8}

⇒ D = 1miles

∴ Total distance the rover need to travel ​is D = 1miles .

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In a certain region of space, the potential is given by v=2x−5x2y 3yz2. How much is the magnitude of the electric field at point
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The magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

<h3>How to calculate the electric field?</h3>

Since in a certain region of space, the potential is given by v = 2x − 5x²y 3yz²,

The electric field, E = -grad(V) where grad(V) = (dV/dx)i + (dV/dy)j + (dV/dz)k

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= 2 - 10xy + 0

= 2 - 10xy

dV/dy = d(2x − 5x²y + 3yz²)/dy

= d2x/dy - d5x²y/dy + d3yz²/dy

= 0 - 5x² + 3z²

=  - 5x² + 3z²

dV/dz = d(2x − 5x²y + 3yz²)/dz

= d2x/dz - d5x²y/dz + d3yz²/dz

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<h3>The electric field</h3>

So, E = -grad(V)

= -[(dV/dx)i + (dV/dy)j + (dV/dz)k]

= -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

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E = -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

E = -[(2 - 10(-2)(2))i + (- 5(2)² + 3(0)²)j + (6(0))k]

E = -[(2 + 40)i + (- 5(4) + 0)j + (0)k]

E = -[42i + (-20 + 0)j + (0)k]

E = -[42i - 20j + 0k]

E = -42i + 20j - 0k

<h3>The magnitude of the electric field</h3>

So, the magnitude of E at (-2, 2, 0) is

|E| = √[(-42)² + 20² + 0²]

=  √[1764 + 400 + 0]

= √2164

= 46.52 V/m

So, the magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

Learn more about electric field here:

brainly.com/question/25751825

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