Provide a mathematical definition of density. Explain the meaning of all of the symbols used in the equation. What is the unit of density? b. Two spheres are cut from a certain rock. One has a radius of 5.50 cm. The mass of the other is six times greater. Find its radius. Assume the equation x = At + Bt describes the motion of a particular ob- ject, with x having the dimension of length and t having the dimension of time. (a) Determine the dimensions of the constants A and B. (b) Find the derivative of x with respect to t. (c) Determine the dimensions of the deriv- a. с. dx ative dt
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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