A figure with length and width, but no depth, is called _ _ _-dimensional.

Mathematics

1 answer:

k0ka [10]3 years ago

5 0

Answer: The term is called Two dimensional.

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Use lagrange multipliers to find the maximum volume of a rectangular box that is inscribed in a sphere of radius r

vesna_86 [32]

For the derivative tests method, assume that the sphere is centered at the origin, and consider the circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined

by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner by

x2+y2+z2=r2 =⇒z= r2−(x2+y2). Then the volume of a box with this coordinate for the corner is given by

V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),

and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the boundary of this domain, so we need only consider critical points contained inside the domain in order to carry this optimization out.

For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint x2 + y2 + z2 = r2<span>. </span>

7 0

3 years ago

Please answer <33 I would lava it :)

allsm [11]

Answer:

5 gallons

Step-by-step explanation:

3/4 + 6/8 + 20/8 + 1

6/8 + 6/8 + 20/8 + 8/8

40/8 = 5 gallons

3 0