A Single Cell of a Bee's Honey Comb Has the Shape

question 59

Short Answer

A single cell of a bee's honey comb has the shape shown.The surface area of this cell is given by $A=6 h s+\frac{3}{2} s^{2}\left(\frac{-\cos \theta}{\sin \theta}+\frac{\sqrt{3}}{\sin \theta}\right)$ where h, s, $\theta$ are as shown in the picture.Keeping h and s fixed, for what angle, $\theta$ , is the surface area minimal? Round to the nearest one tenth of a degree.

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Definitions:

Operator

A segment of DNA to which a repressor protein binds, regulating the expression of genes by blocking the attachment of RNA polymerase to the promoter region.

RNA Polymerase

An enzyme that synthesizes RNA from a DNA template, essential for the transcription phase of protein synthesis.

Translational Controls

Regulatory mechanisms in gene expression that control the rate and timing of protein synthesis from mRNA.

Ribosomes

Cellular structures where proteins are synthesized, reading mRNA sequences and assembling amino acids into proteins based on genetic instructions.