The Length $l$ , Width $w$ And Height $h$ Of a Box Change with Time

question 20

Short Answer

The length $l$ , width $w$ and height $h$ of a box change with time. At a certain instant the dimensions are $l = 3$ and $w = h = 4$ , and $l$ and $w$ are increasing at a rate of $10 \mathrm {~m} / \mathrm { s }$ while $h$ is decreasing at a rate of 1 $\mathrm { m } / \mathrm { s }$ . At that instant find the rates at which the surface area is changing.

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Definitions:

Arthropods

Arthropods are a phylum of invertebrate animals with exoskeletons, segmented bodies, and jointed limbs, including insects, arachnids, and crustaceans.

Synapomorphies

Shared derived characters or traits that are used to determine evolutionary relationships among organisms.

Exoskeletons

External skeletons that support and protect an organism's body, found in arthropods like insects, crabs, and lobsters.

Marsupial Colonization

The process by which marsupials, a group of mammals typically characterized by premature birth and continued development in the mother's pouch, spread and establish populations in new areas.