Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Step-by-step explanation:

Let the rectangle have (x,y,z) as vertex in positive octant.  The rectangular box has to be necessarily symmetrical about all the three axes.

Then the sides of the box would be

Volume =

Maximize volume subject to

i.e.

Use Lagrangian multipliers , we have

at the maximum

Dividing we get

Similarly

Thus we get

Hence dimensions are

(2x,2y,2z)

So dimensions are

answer: a

step-by-step explanation:

the slope of the line is 60

one point on the line is (40,10)

step-by-step explanation:

in the equation outside the parenthesis the equation always tells you the slope. in this case it is 60.

in the parenthesis is also says 40 which is x because it is near the x and 10 is y because it is near y.