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KATRIN_1 [288]
3 years ago
7

Select the equations whose graphs are parallel to the graph of the equation y=23x+5.

Mathematics
1 answer:
iren [92.7K]3 years ago
6 0

Answer:

2x-3y=9    and    4x-6y=30

Step-by-step explanation:

hello :  

note y=(2/3)x+5  no y=23x+5

2/3 is the slope....... all lines parallel to this line has same slope.

1)   2x-3y=9   means : 3y = 2x-9   divide by 3 : y=(2/3)x-3..same slope.

2)  4x-6y=30  means : 6y= 4x-30 divide by 6 : y=(4/6)x -30/6

but 4/6 = 2/3 so : y=(2/3)x-5..same slope.

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Lagrangian:

L(x,y,z,\lambda)=x^2+(y-2)^2+(z-5)^2+\lambda(x-2y+3z-6)

where the function we want to minimize is actually \sqrt{x^2+(y-2)^2+(z-5)^2}, but it's easy to see that \sqrt{f(\mathbf x)} and f(\mathbf x) have critical points at the same vector \mathbf x.

Derivatives of the Lagrangian set equal to zero:

L_x=2x+\lambda=0\implies x=-\dfrac\lambda2
L_y=2(y-2)-2\lambda=0\implies y=2+\lambda
L_z=2(z-5)+3\lambda=0\implies z=5-\dfrac{3\lambda}2
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Substituting the first three equations into the fourth gives

-\dfrac\lambda2-2(2+\lambda)+3\left(5-\dfrac{3\lambda}2\right)=6
11-7\lambda=6\implies \lambda=\dfrac57

Solving for x,y,z, we get a single critical point at \left(-\dfrac5{14},\dfrac{19}7,\dfrac{55}{14}\right), which in turn gives the least distance between the plane and (0, 2, 5) of \dfrac5{\sqrt{14}}.
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Answera:The answer is 0.3333333333 repeated

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d

=

−

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Decimal Form:

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