Solve 13-m=2(-4+m).

Mathematics

2 answers:

Alekssandra [29.7K]3 years ago

7 0

-4+m=7 next do 13-m=2 m equals 11 it all equals 14

Alborosie3 years ago

4 0

The answer is m = 7.

1. (13−m=2(m−4) Regroup terms
2. Expand (13−m=2m−8)
3. Add m to both sides (13=2m−8+m)
4. Simplify (2m−8+m to 3m−8)
5. add 8 to both sides (13 + 8 = 3m)
6. Simplify 13+8 to 21
7. Divide both sides by 33 (21/3 = m)
8. simplify 21/3 to 7 (7 = m)
9. switch sides ( finally m = 7)

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Lagrange multipliers:

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

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$-y^2z^2=-2xyz^2\implies y=2x$ (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.