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qwelly [4]
3 years ago
8

Please help me solve this problem

Mathematics
1 answer:
olga2289 [7]3 years ago
7 0
1,025. Multiply 55 by 15, then add the $200 fee. I hope this helps :)
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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.
4 0
3 years ago
Is 4 a solution of2=8
JulsSmile [24]

Answer:

Two doesn’t equal 8. Theoretically, eight is the solution...

Step-by-step explanation:

5 0
3 years ago
Points giveaway<br><br>2+3=?​
Nata [24]

Answer:

5

Step-by-step explanation:

  • 2+3
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Hence it is correct.. thanks for points.

5 0
2 years ago
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anastassius [24]

Answer:

plz mark brainliest

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3 years ago
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If gas costs $3.19 per gallon, how many whole
sergiy2304 [10]

Answer:

13 gallons

Step-by-step explanation:

42 / 3.19 = 13.166144200626959,

which can be rounded down to 13 whole gallons.

5 0
3 years ago
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