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Helen [10]
2 years ago
10

simplify the rational expression. state any restrictions on the variable. ((n^(4)-11n^(2)+30))/(n^(2)-7n^(2)+10)

Mathematics
1 answer:
sergeinik [125]2 years ago
4 0
Hi, (n2 -6 ) (n2 - 5) - 2 (3n2 - 5)
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Thereisalinethatincludesthepoint(10, 5)andhasaslopeof1 . What isitsequationin slope -intercept form?
Eva8 [605]

Answer:

Step-by-step explanation:

m=1, (10,5)

y=mx+b

5=1(10)+b

5=10+b

b=-5

y=x-5

3 0
3 years ago
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
Masja [62]

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

Since V = 2x − 5x²y + 3yz²

dV/dx = d(2x − 5x²y + 3yz²)/dx

= d2x/dx - d5x²y/dx + d3yz²/dx

= 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

= 0 - 0 + 6z

=  6z

<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]

So, the electric field at (-2, 2, 0) is

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

#SPJ12

3 0
1 year ago
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4 0
2 years ago
Evaluate the expression 10 + 2p - 3r, when p=3 and r=-2
dmitriy555 [2]

Answer:

<em>The expression is equal to 22</em>

Step-by-step explanation:

<u>Expression Evaluation</u>

We are given the expression

10 + 2p - 3r

And it's required to evaluate it when p=3 and r=2. This means we have to replace the letter for the value assigned to them, as follows:

10 + 2*3 - 3*(-2) = 10 + 6 - (-6)

= 10 + 6 + 6

= 22

The expression is equal to 22

7 0
2 years ago
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