Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the planex + 9y + 4z = 27.

81/4

Step-by-step explanation:

From the given information; we are to use Lagrange multipliers to find the volume of the largest rectangular box

The coordinate planes and the vertex given in the plane is x + 9y + 4z = 27.

By applying Lagrange multipliers, we have;

where;

From;

   --------- equation (1)

From;

 --------- equation (2)

From;

--------- equation (3)

Comparing and solving equation (1),(2) and (3);

divide through by

x = 9 y = 4z

3x = 27

x = 27/3

x = 9

From x = 9y

9 = 9 y

y = 9/9

y = 1

From

x = 4z

9 = 4 z

z = 9/4

Thus; the Volume of the largest rectangular box = 9 × 1  × 9/4

= 81/4

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer

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