A museum part resorted 354,605 visitors last summer what is this number rounded to the nearest thousand

Mathematics

1 answer:

Alla [95]3 years ago

6 0

355,000 is the answer

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If it takes two people six hours to paint a room, how long will it take four people

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12 hours

Step-by-step explanation:

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2 years ago

When a result from a simple is extended to the population

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3 years ago

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Can you define it much more simpler

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3 years ago

We need to optimize f(x, y, z) = x + 2y subject to the constraints g(x, y, z) = x + y + z = 8 and h(x, y, z) = y2 + z2 = 4. To f

Evgesh-ka [11]

The Lagrangian is

$L(x,y,z,\lambda,\mu)=x+2y+\lambda(x+y+z-8)+\mu(y^2+z^2-4)$

with critical points where the partial derivatives vanish:

$L_x=1+\lambda=0\implies\lambda=-1$

$L_y=2+\lambda+2\mu y=0\implies\mu=-\dfrac1{2y}$

$L_z=\lambda+2\mu z=0\implies\mu=\dfrac1{2z}$

$L_\lambda=x+y+z-8=0$

$L_\mu=y^2+z^2-4=0$

The second and third equations tell us $z=-y$ , so that in the last equation we find

$y^2+(-y)^2=2y^2=4\implies y=\pm\sqrt2\implies z=\mp\sqrt2$

and from the fourth equation we get

$x+y+z=x=8$

So we have two critical points, $(8,\sqrt2,-\sqrt2)$ and $(8,-\sqrt2,\sqrt2)$ , which give respective extreme values of $f(8,\sqrt2,-\sqrt2)=8+2\sqrt2$ (maximum) and $f(8,-\sqrt2,\sqrt2)=8-2\sqrt2$ (minimum).