Tutor profile: Leonardo T.
How can graphite and diamond be so different if they are both composed of pure carbon?
In a diamond, the carbon atoms are arranged tetrahedrally. Each carbon atom is attached to four other carbon atoms. It is a strong, rigid three-dimensional structure that results in an infinite network of atoms. This accounts for diamond's hardness, extraordinary strength, and durability. The carbon atoms in graphite are also arranged in an infinite array, but they are layered. Each carbon atom is bonded to three other carbon atoms and arranged at the corners of regular hexagons. Unlike diamond, graphite can be used as a lubricant or in pencils because the layers cleave readily.
In the definition of the logarithmic function, the base a is not allowed to equal 1. Why?
Because if it did, then to find the logarithm of any number would not exist since 1 raised to the power of any number always gives 1
A large man and a small boy stand facing each other on fric- tionless ice. They put their hands together and push against each other so that they move apart. (a) Who moves away with the higher speed?
According to Newton’s third law, the force exerted by the man on the boy and the force exerted by the boy on the man are an action–reaction pair, and so they must be equal in magnitude. Therefore, the boy, having the lesser mass, experiences the greater acceleration. Both individuals accelerate for the same amount of time, but the greater acceleration of the boy over this time interval results in his moving away from the interaction with the higher speed.
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