Logarithms

Please see the attached file for full problem description.

Find the common logarithm of

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Vectors

Please see attachment. Require problems solving, also explanations etc for better understanding of vectors. VECTOR PROBLEMS (1) Let l be the line with equation v = a + t u. Show that the shortest distance from the origin to l can be written | a × u | ...continues

Laplace transforms

Please see attachment. Require problems solving, also explanations etc for better understanding of laplace transforms.

LAPLACE TRANSFORMS

Please see attachment. Require problems solving, also explanations etc for better understanding.

Prime numbers

Prove that if p is a prime number, then p divides , for all n≥p. Here [r] denotes the greatest integer ≤ r , for any real number r. Does this result generalize to a result about instead of p ?

Induction

Prove by induction where n is a positive integer. (The questions are attached).

Binomial Expansions

Find the following. (Questions held on attachment) Find the following: a) The coefficient of x in the expansion of b) The coeffiecient of x^3yz^4 in the expansion of c) The coefficient of x^3 in the expansion of d) The coefficient of x^5 in the expansion of is equal to the coefficient of x^4 in the ...continues

Arithmetic / Geometric Progressions

Three numbers are in arithmetic progression. The sum of the three numbers is 30 and the sum of their squares is 398. What are the three numbers? b) An arithmetic series is such that its first term is a and its third term is b. The sum of the first n terms is Sn . Find S4 in terms of a and b. Given that S4, S5 , S7 are con ...continues

Solve for x

How would you go about solving for x, when x to the tenth power = 2.533836? Thanks! x^10= 2.533836