Assignment on Mathematical Methods and Statistical Techniques

Mathematical
Methods and
Statistical
Techniques
M/615/1476
1/1/2020
[Type the company name]

Contents
Part 1:......................................................................................................................... 3
Problem (a).............................................................................................................. 3
Problem (b).............................................................................................................. 4
Problem (c).............................................................................................................. 5
Problem (d).............................................................................................................. 6
Problem (e).............................................................................................................. 7
Problem (f).............................................................................................................. 8
Problem (g)............................................................................................................ 10
Problem (h)............................................................................................................ 11
Problem (i)............................................................................................................. 13
Part 2:....................................................................................................................... 15
Problem (a)............................................................................................................ 15
Problem (b)............................................................................................................ 16
Problem (c)............................................................................................................ 18
Problem (d)............................................................................................................ 20
Conclusion................................................................................................................ 21
References............................................................................................................... 22
2 | P a g e

Part 1:
Problem (a)
Solution:
The Dimensions of Power, P = ML^2T^-3
And the Dimension of Voltage, V = L^0.5 M^0.5 T^-1
Since the equation of power dissipation across the Resistor is given by
3 | P a g e

So, Resistance, R is given by
So, the Dimensions of R is
(L^0.5 M^0.5 T^-1)^2/ ML^2T^-3
= L^-1T^2
Problem (b)
Solution:
The LHS of the equation is time period of Vibration of string
t with Dimension [T]
the right hand side of the equation will have the dimension
2π = no dimension
m^3 = [M^3]
l= [L^1]
F = [MLT^−2]
4 | P a g e

So, as per equation RHS has dimensioned,
([M^3] [L^1]/ [MLT^−2])^0.5
=([M^2T^2])^0.5
So, RHS dimension = [MT]
So, LHS dimension is not equal to the dimension of RHS, so the equation is not
correct.
Problem (c)
Solution:
The samples are given in the question are 2, 4, 6, 8, 10...40, in mV unit
So these are in Arithmetic progression with
First value, a= 2
Difference between consecutive numbers, d= 2 and
Number of values, n = 20
So, sum of these 20 voltage samples will be
S= n/2[2a+ (n-1) d]
S= 20/2[2*2+ (20-1)*2] =420 mV
So, the sum of these 20 voltage samples is 420 mV.
5 | P a g e

Problem (d)
6 | P a g e