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3 years ago

If 6x + 5y = 10, what is y in terms of x? Please include an explanation!

Mathematics

1 answer:

Mnenie [13.5K]3 years ago

6 0

what you're trying to do is form an equation for y

6x + 5y = 10

5y = -6x + 10 we need y to be singular so divide by numeral before y

y = - 6x/5 + 10/5

y = - 6x/5 + 2

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You plan to purchase a bike costing $795. write an equation that could be used to find the amount m, that you must save per mont

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3 years ago

N=8 x=9<br> What is 2n+(-6)?

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3 years ago

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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

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

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2 years ago

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gizmo_the_mogwai [7]

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3 years ago

1. If the domain of a function f(x) is the set {10, 20, 30}. What does the information tell you about f-1(x)?

ziro4ka [17]

PART A (1 in diagram)

Each mapping diagram represents a function because none of the elements in the inputs maps on to two different elements in the outputs.

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All we can say about

${f}^{ - 1} (x)$

is that, it has a range of {10, 20, 30}.

This is because the domain of a function becomes the range of its inverse function.

2. If the graph of a function f(x) includes the point (3, 0), then the graph of the inverse function ,

${f}^{ - 1} (x)$

will contain the point (0,3).

Reason:The point on the graph of the inverse function is obtained by reflecting the corresponding point on the graph of the function in the line y=x. We just have to swap the coordinates.

In simple terms the domain of the function becomes the range of the inverse function and vice versa.

3. If the first term in an arithmetic sequence is 2.

Then we have a=2.

If the twelfth term is 211, then

$a + 11d = 211...(1)$