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iragen [17]
2 years ago
6

Pamela hired a contractor to paint 75% of

Mathematics
1 answer:
Afina-wow [57]2 years ago
8 0

Answer:

Solution is in photo

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Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.
irina1246 [14]
Lagrange multipliers:

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

L_x=y^2z^2+\lambda=0
L_y=2xyz^2+\lambda=0
L_z=2xy^2z+\lambda=0
L_\lambda=x+y+z-5=0

\lambda=-y^2z^2=-2xyz^2=-2xy^2z

-y^2z^2=-2xyz^2\implies y=2x (if y,z\neq0)

-y^2z^2=-2xy^2z\implies z=2x (if y,z\neq0)

-2xyz^2=-2xy^2z\implies z=y (if x,y,z\neq0)

In the first octant, we assume x,y,z>0, so we can ignore the caveats above. Now,

x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of f(1,2,2)=16.

We also need to check the boundary of the region, i.e. the intersection of x+y+z=5 with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force f(x,y,z)=0, so the point we found is the only extremum.
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ohaa [14]

Answer:

1)An angle bisector is basically the division of an angle into two equal parts, so you should just draw a line in the middle after you found the angles using the compass

2) parallel lines is a pair of lines that never intersect, and are always the same distance apart. you should use the compass to draw a 90-degree angle at the end of the line XY, and use the straightedge to draw a line that is parallel to the line XY.

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Please help with these problems!!!
nataly862011 [7]

Answer:

12345678901234567890

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3 years ago
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