Math Answers

Show that the relation R on Z × Z defined by (a, b) R (c, d) if and only if a + d = b + c

is an equivalence relation.

Note: A relation on a set A is called an equivalence relation if it is reflexive, symmetric,

and transitive.

Show that the relation R on Z × Z defined by (a, b) R (c, d) if and only if a + d = b + c is an equivalence relation. Note: A relation on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive.

I.In each of Problems 23 through 30, use the method of reduction of order to find a second solution of the given differential equation.

1.  t^2y″ − 4ty′ + 6y = 0, y1(t) = t^2

2.  xy″ − y′ + 4x^3y = 0, x > 0; y_1(x) = sin x^2

IV. Find the general solution of the given differential equation.

11/234) y‴ − y″ − y′ + y = 0

14/234) y^(4) − 4y‴ + 4y″ = 0

I.In each of Problems 23 through 30, use the method of reduction of order to find a second solution of the given differential equation.

1.  t2y″ − 4ty′ + 6y = 0, y1(t) = t2

2.  xy″ − y′ + 4x3y = 0, x > 0; y1(x) = sin x2

A. Solve the following problems:

1. On the assumption that variables are continuous, compute for the median of the following data:

a. 1, 4, 5, 9, 11

b. 4, 8, 16, 27, 52

c. 7, 26, 31, 36, 46, 65

2. Calculate the range for the following sets of measurements:

a. 3, 6, 7, 10, 2

b. 11, 27, 32, 45, 54

3. Calculate the variance and standard deviation of the following: 13, 18, 21, 19, 16, 15.

Calculate the quartiles, (i,e., Q1 and Q3,), deciles D3 and D7, Percentiles P10, P23 and P92 for the

following data. Also find the Quartile Range and Quartile Deviation.

Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of Students 8 7 5 12 28 22 8 10

A spring is such that a 16 lb weight stretches it by 1.5 in. The weight is pulled down to a point

4 in below the equilibrium point and given an initial downward velocity of 4 ft/sec. An impressed

force of F(t) = 2 cos 74t is acting on the spring. Describe the motion.

a)     Suppose P (x, y) denotes the equation8, what will the truth values of the Propositions P (2,2), P (0,4).

Let X1,X2,...,Xn be independent and identifically distributed random variables each having pdf

f(x)=q^xP .x=0,1,2....

P+q=1

Let Sn=X1+X2+...+Xn.

Obtain the pgf of Sn and find the mean and variance of Sn