Solve the Problem $$\mathrm { S } = \mathrm { kd } ^ { 3 } \sin ^ { 2 } \theta \cos \theta$$

question 96

Short Answer

Solve the problem.
-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, $$\theta$$ the angle illustrated, and k is a constant that varies with the type of wood used. Let $\mathrm { d } = 1$ and express the strength $\mathrm { S }$ in terms of the constant $\mathrm { k }$ for $\theta = 45 ^ { \circ } , 50 ^ { \circ } , 55 ^ { \circ } , 60 ^ { \circ }$ , and $65 ^ { \circ }$ . Does the strength always increase as $\theta$ gets larger?

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Definitions:

Diffusion

Movement of molecules from an area of high concentration to one of lower concentration.

Ventilation

Respiratory process by which gases are moved into and out of the lungs.

Electrocardiogram (ECG)

Graphic record of the electrical activity of the myocardium.

Conduction System

The network of nodes and special pathways in the heart that control and coordinate the timing and sequence of the cardiac cycle (heartbeat).