1) Come up with your own story to illustrate Russel’s paradox informally.

Consider the following data:

Use a 1st Order LaGrange Polynomial to interpolate the value of y corresponding to x = 2.9

Enter your answer to two decimal places:

a. 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l sin(x)sin(y) = -cos(x-y)--cos(x+ y) 1 l sin(x)cos(y) =—sin(x-y) +-sin(x + y) A DSB-FC (double sideband-full carrier) signal s(t) is given by, s(t) = n cos(2rr/cf)+ cos(2«-/mt)cos(2«-fct) What is the numeric value for the AM index of modulation, m, fors(f) ?

Differential Equations (FREE, UNDAMPED MOTION)

A 12-lb weight is placed upon the lower end of a coil spring suspended from the ceiling. The weight comes to rest in its equilibrium position, thereby stretching the spring 1.5 in. The weight is then pulled down 2 in. Below its equilibrium position and released from rest at t = 0. Find the displacement of the weight as a function of time; determine the amplitude, period, and the frequency of the resulting motion. Assume there is no resistance of the medium and no external forces.

. Recall from the previous page that for each pair a, b with a ∈ R − {0} and b ∈ R, we have a bijection fa,b : R → R where fa,b(x) = ax + b for each x ∈ R. (b) Let F = {fa,b | a ∈ R − {0}, b ∈ R}. Prove that the set F with the operation of composition of functions is a non-abelian group. You may assume that function composition is associative

The function described by f(x) = ln(x2 + 1) − e0.4x cos πx has an infinite number of zeros.

(a) Determine, within 10−6, the only negative zero.

please don't use any program while solving it, thanks.

Q(x,y) is a propositional function and the domain for the variables x & y is: {1,2,3}.

Assume Q(1,3), Q(2,1), Q(2,2), Q(2,3), Q(3,1), Q(3,2) are true, and Q(x,y) is false otherwise.

Find which statements are true.

1. ∀yƎx(Q(x,y)->Q(y,x))

2. ¬(ƎxƎy(Q(x,y)/\¬Q(y,x)))

3. ∀yƎx(Q(x,y) /\ y>=x)

A 10 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 9.8 centimeters. At time ?=0 t = 0 , the resulting mass-spring system is disturbed from its rest state by the force ?(?)=70cos(8?) F ( t ) = 70 cos ( 8 t ) . The force ?(?) F ( t ) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds.

a) Determine the spring constant ?.

b) Formulate the initial value problem for ?(?)y(t), where ?(?)y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of ?,?′,?′′,?y,y′,y′′,t.)

c) Solve the initial value problem for ?(?)y(t).

1)(a) Patty Stacey deposits $2800 at the end of each of 5 years in an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end of the 30-year period? Assume an interest rate of 10%, compounded annually. (Round your answer to the nearest cent.)
$

(b) Suppose that Patty's husband delays starting an IRA for the first 10 years he works but then makes $2800 deposits at the end of each of the next 15 years. If the interest rate is 10%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? (Round your answer to the nearest cent.)
$

(c) Does Patty or her husband have more IRA money?

PattyPatty's husband

2)

A sinking fund is established to discharge a debt of $60,000 in 20 years. If deposits are made at the end of each 6-month period and interest is paid at the rate of 8%, compounded semiannually, what is the amount of each deposit? (Round your answer to the nearest cent.)

V=[(a b), a,b E R+] with (a1 b1)+(a2 b2)=(a1a2 b1b2)and for c E R, c(a b)=(a^c b^c) is a vector space over R. Define T:R^2 to V by T[a b]= (e^a e^b). prove T is a linear transformation from R2 to V.

The Enormous State University Choral Society is planning its annual Song Festival, when it will serve three kinds of delicacies: granola treats, nutty granola treats, and nuttiest granola treats. The following table shows some of the ingredients required for a single serving of each delicacy, as well as the total amount of each ingredient available.

The society makes a profit of $6 on each serving of granola, $8 on each serving of nutty granola, and $3 on each serving of nuttiest granola. Assuming that the Choral Society can sell all that it makes, how many servings of each will maximize profits?

granola serving (s)

nutty granola serving (s)

nuttiest granola serving (s)

How much of each ingredient will be leftover?

toasted oats ounce (s)

almonds ounce (s)

raisins ounce (s)

In how many ways can the numbers 0 through (2n − 1) be arranged in 2 rows of length n in such a way such that each row and each column is increasing?

Examples (with n = 5):

and

Hint: Catalan Numbers

Explanations are much appreciated.

Let G be a group of order 105. Prove that G has a proper normal subgroup.

1. An employee is working 6 days a week from Monday to Saturday. Assume the   

     overtime for the employee is double after 40 hours. The following

     table shows his working hours.

1. Complete the table below (Show your work)

2. Find the gross earning of the employee.

A thin tube stretched across a street counts the number of pairs of wheels that pass over it. A vehicle classified as type A with eight axles register eight

counts. A vehicle classified as type B with five axles registers five counts. During a 33​-hour ​period, a traffic counter registered 213 counts. How many type A vehicles and type B

vehicles passed over the traffic​ counter? List all possible solutions.

Which of the choices below are possible solutions to the​ problem? Select all that apply.

A. 26 type A and 11 type B vehicles

B. 21 type A and 99 type B vehicles

C. 11 type A and 41 type B vehicles

D.66 type A and 3333 type B vehicles

E. 23 type A an 66 type B vehicles

F. 0 type A and 43type B vehicles

G.11 type A and 25 type B vehicles

H.33 type A and 38 type B vehicles

I.16 type A and 17 type B vehicles

J. 14 type A and 20 type B vehicles