Use the Parallelogram Rule to Find the Magnitude of the Resultant

question 164

Essay

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to
one decimal place.
-Explain what is wrong with the following solution for the equation $\cos 2 \theta = \sqrt { 3 }$ in the interval $[ 0,2 \pi )$ .
$$\cos 2 \theta = \sqrt { 3 }$$
$$\cos \theta = \frac { \sqrt { 3 } } { 2 }$$
$$\theta = \frac { \pi } { 6 } \text { or } \theta = \frac { 11 \pi } { 6 }$$

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Definitions:

Triassic

The first period of the Mesozoic Era, occurring approximately 252 to 201 million years ago, marked by the recovery of life forms from the Permian extinction.

Carboniferous

A geological period around 358.9 to 298.9 million years ago, characterized by the formation of extensive coal beds.

Carbon-14 Dating

A method for determining the age of an object containing organic material by using the properties of radiocarbon.

Zircon Crystals

Mineral crystals that are valuable in dating Earth's geological events due to their uranium and thorium content.