The portion of the line \( 4x + 5y = 20 \) in the first quadrant is trisected by the lines \( L_1 \) and \( L_2 \) passing through the origin. The tangent of an angle between the lines \( L_1 \) and \( L_2 \) is:
The d-block and f-block elements of the periodic table have a wide range of applications in various fields due to their unique chemical and physical properties.
One of the most important applications of d-block elements is in the field of metallurgy. Many d-block elements, such as iron, copper, and nickel, are widely used in the production of steel, alloys, and other metals. These elements are also used in the construction of electrical wires, electronic devices, and machinery due to their high thermal and electrical conductivity.
F-block elements have unique optical and magnetic properties that make them useful in a variety of applications. For example, neodymium and samarium are used in the production of high-strength magnets for use in computer hard drives, speakers, and medical equipment. Lanthanum and gadolinium are used in the production of camera lenses, optical fibers, and x-ray screens.
D-block elements are also used in catalysis, a process that accelerates chemical reactions without being consumed in the process. These elements are used as catalysts in many industrial processes, such as the production of fertilizers, plastics, and fuels.
F-block elements also find applications in nuclear power generation, as some isotopes of actinides are used in nuclear reactors for electricity generation.
Overall, the d-block and f-block elements have a wide range of applications in various fields, including metallurgy, electronics, optics, catalysis, and energy production. The unique properties of these elements make them crucial components of many modern technologies.