Write the Word or Phrase That Best Completes Each Statement $\mathrm { S } = \mathrm { kd } ^ { 3 } \sin ^ { 2 } \theta \cos \theta$

question 228

Essay

Write the word or phrase that best completes each statement or answers the question.
-The strength S of a wooden beam with rectangular cross section is given by the formula $\mathrm { S } = \mathrm { kd } ^ { 3 } \sin ^ { 2 } \theta \cos \theta$ where d is the diagonal length, θ the angle illustrated, and k is a constant that varies with the type of wood used. Let d = 1 and express the strength S in terms of the constant k for θ = 45°, 50°, 55°, 60°, and 65°. Does the strength
always increase as θ gets larger?

---

Definitions:

Professional Contract

A legal agreement between a professional and an entity that outlines terms of employment or service provision.

Injury

Physical harm or damage to the body caused by external force, which may result from accidents, falls, hits, weapons, and other causes.

Marginal Utility

The change in total utility generated by consuming one additional unit of a good or service.

Uncertain Income

Income that is not guaranteed or predictable, often varying significantly over time or depending on specific conditions.