Other Math Answers

1. An inductance of 1 Henry and a resistance of 2 Ohms are connected in series with an emf of E 𝑒 −𝑡 . No current is flowing initially. Find a) When the current I=10 A at t=1 sec, how much E must be? b) If E=50 volts, when will the current 5 Amp?

2. A beam L m long is simply supported at its ends and carries a uniform load of w N/m along its entire length. Determine the equation of the elastic curve and the maximum deflection of the beam.

Find the smallest positive integer N that satisfies all of the following conditions:

• N is a square.

• N is a cube.

• N is an odd number.

• N is divisible by twelve prime numbers.

How many digits does this number N have?

Let f(x), g(x) and h(x) be the functions from Problem A.1. Find the derivative λ

(x) of the

following function with respect to x:

λ(x) = f(x) · g(x) + f(x) · h(x) − g(x) · h(x)

Answer with solution:

3. A weighted voting system for voters A, B, C, D, and E is given by {35 : 29, 11, 8, 4, 2}. The weight of

voter A is 29, the weight of voter B is 11, the weight of voter C is 8, the weight of voter D is 4, and the weight of voter E is 2.

a. What is the quota?

b. What is the weight of the coalition {A, D, E}?

c. Is {A, D, E} a winning coalition?

d. Which voters are critical voters in the coalition {A, C, D, E}?

e. How many coalitions can be formed?

f. How many coalitions consist of exactly two voters?

Find the smallest positive integer N that satisfies all of the following conditions: • N is a square. • N is a cube. • N is an odd number. • N is divisible by twelve prime numbers. How many digits does this number N have? 

Prove that a ring is unitary if and only if it is a moniod under multiplication

What is use of bias in binary floating point representation.

Explain the concept of bias with the help of an example for

binary floating point numbers

Represent 0.000001235432 and 257890000012 as floating

point numbers in normalised form using chopping for first

number and rounding for second number.