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Alik [6]
3 years ago
13

line L passes through point (2, -5) and is perpendicular to the line with equation y=7. determine the equation of line L

Mathematics
1 answer:
Andrew [12]3 years ago
7 0

Answer:

The equation of the line L is x=2

Step-by-step explanation:

we know that

The line y=7

Is a horizontal line (parallel line to the x-axis)

The slope of a horizontal line is equal to zero

A line L perpendicular to the given line must be a vertical line (parallel to the y-axis)

The slope of the line L is undefined

The line L passes through the point (2,-5)

therefore

The equation of the line L will be equal to the x-coordinate of the given point

x=2

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2*127=234

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Step-by-step explanation:


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3 years ago
Use the method of lagrange multipliers to find
Yanka [14]

Answer:

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g(x, y) = x*y - 196 = 0

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L(x, y, λ) = f(x, y) +  λ*g(x, y)

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λ*y + 1 = 0

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Now we can replace this in the second equation and get;

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Now let's isolate x.

x = y

Now we can replace this in the last equation, and we will get:

(x*x - 196) = 0

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x = √196 = 14

then the minimum will be:

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b) Now we have:

f(x) = x*y

g(x) = x + y - 196

Let's do the same as before:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y, λ) = x*y +  λ*(x + y - 196)

Now let's do the derivations:

dL/dx = y + λ

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dL/dλ = x + y - 196

Now we have the system of equations:

y + λ = 0

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x + y - 196 = 0

To solve it, we can isolate lambda in the first equation to get:

λ = -y

Now we can replace this in the second equation:

x - y = 0

Now we can isolate x:

x = y

now we can replace that in the last equation

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The maximum will be:

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kodGreya [7K]

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Step-by-step explanation:

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