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# Algebra

### Word problem proof

Six friends discover they have a total of \$21.61 with them. Show that one or more of them must have \$3.61. (Hint, use the Pigeonhole Principle.)

### Finding Products and Simplifying Exponents

Please help with the following problems. I need more detail on each problem how the solution was achieved using these steps. Thanks for your help. 2. Find the product: (x - 2)(x + 3)(x - 4) (x - 2)(x + 3)(x - 4) = 3. Simplify without having negative exponents: (- 3s-3t2)-2 (- 3s-3t2)-2 4. Conve

### Education IRA : Recursive Formula

On January 1, 1999, John's parents decide to place \$45 at the end of each month into an Education IRA. a) Find a recursive formula that represents the balance at the end of the month if the rate of return is assumed to be 6% per annum compounded monthly. b) How long will it be before the value of the account exceeds \$4000?

### Radioactive Material Decay

The attached file will tell you exactly what I need. Radioactive Decay Iodine 131 is a radioactive material that decays according to the function A(t) = A where A0 is the initial amount present and A is the amount present at time t (in days). Assume that a scientist has a sample of 100 grams of iodine 131. a. What is the

### Model with Constraints : Independence Model and Loglinear Model

Refer to the independence model, . For the corresponding loglinear model: log , where i=1, ..., I, j=1,..., J. Show that one can constrain by setting Show that one can constrain by defining Then, what does equal? --- Please see the attached file for the fully formatted problems.

X/18=21/4

### Solving Trigonomic Identities (4 Problems)

2 cot(x)=csc^2(x)*sin2(x) csc(x)+cot(x) ---------------- = cot(x)csc(x) tan(x)+sin(x) tan^2(x)sin^2(x)=tan^2(x)+cos^2(x)-1 sin^6(x)+cos^6(x)=1-3sin^2(x)cos^2(x)

### Sequences and Subsets

1) Find a sequence {E } (n =1 to infinity) of measurable sets with E E .......... Such that ( E ) E ) 2) If E is measurable subset of R Prove that given > 0, there exists an open set U E and a closed set F E such that U E) < and E F) < . 3) If E ,E are measurable subsets of [0

### Word problem with percents

An employee's new salary is \$23,100 after getting a 5% raise. What was the salary before the increase in pay?

### Word problem

Value Rent-A Car rents a luxury car at a daily rate of \$43.81 plus 5 cents per mile. A business person is allotted \$100 a day. How many miles can the business person travel for \$100.

### Quadratic Problem

R2^2 -RAR2 + RBRA = 0 NOW THE QUADRATIC EQ IS - b +/- SQRT B^2 - 4AC / 2A ------------------------------------------------------------------------------------ THE PROBLEM STARTED OFF R1 + R2 = RA AND R1 = RA -R2, THEN RB = R1R2/R1+R2. EVERYTHING WAS SOLVED FOR RB UNTIL THE ABOVE ANSWER OF R2^2 -RAR2 + RBRA = 0. THE P

### Quadratic problem with variables - missing steps

The problem is bascially done to a point. (STEP 5) Then steps are missing. I give you steps 1 to 5, then I need you to solve for R1 and R2 in terms of RA and RB. PLEASE Show all work including what I give you and show each step, each canceled term, or multiplication, or whatever. STEP 1: R1 + R2 = RA STEP2: R1 = RA -

### The Exact Homology Sequence (Exact Sequence of Triples)

Problem: Let X = X_1 / X_2, and A = X_1 / X_2. Using the exact sequence of triples, show that if the inclusion (X_1, A) --> (X, X_2) induces an isomorphism on homology, then the same holds for the inclusion (X_2, A) --> (X, X_1). Notation: X_1 is X subscript 1 / is union / is intersection --> is an inclusion map

### Isomorphic groups

I am trying to learn this material on my own to prepare for a future graduate course. I would like to see the solutions to this problem to have something to imitate when working other problems. Decide which (if any) of the following are isomorphic to which: (a) D3xS4 (b) D6xA4 (c) D4xD9 Dn=dihedral group of order 2n, A

### Heat Equation : Temperature Distribution on a Brass Rod

9. The temperature distribution u(x, t) in a 2-m long brass rod is governed by the problem ...... (a) Determine the solution for u(x, t). (b) Compute the temperature at the midpoint of the rod at the end of 1 hour. (c) Compute the time it will take for the temperature at that point to diminish to 5° C. (d) Compute the ti

### Secant ( or Chord ) Method : Algebraically Equivalent Equation

Please see the attached file for the fully formatted problems.

### Numerical Methods, 400 Undergraduate level.

The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. If there is anything unclear in the question, let me know. Thank you. (Complete problem found in attachment)

### Polynomial word problem

The width of a badminton court is 24 feet less than its length. Find polynomials that represent its perimeter and area. The actual length of a badminton court is 44 feet. Evaluate these polynomials to find the perimeter and area of the court.

### Classify the PDE's as Elliptic, Parabolic or Hyperbolic

Classify the following PDE's as elliptic, parabolic or hyperbolic. If mixed, identify the regions and classify within each region. (b) xuxx - uxy + yuxy +3uy = 1 Please see the attached file for the fully formatted problem.

### Recursively Defined Sequence : Find the 2001st Term

A sequence is define recursively by A0 = A, and An+1 = An /1 + nAn. Determine A2001.

### Sum Identity for Tangent

Find the exact value of the expression using the provided information. Find tan (B + C) given that sin C = 1/4, with C in quadrant II, and sin B = -1/2, with B in quadrant IV.

### Jordan canonical form

See attached problems

### Existence and uniqueness of solution

What is the best statement that you can make about the existence and uniqueness of the solutions of the following initial value problems? (Please see attached).

### Apply Newton's Laws of Motion - Traction Force and Wheel Reactions

See the attached file. A car has a mass of 1.4 tonne. The distance between the front and rear wheel axles is 3.6 metres and the centre of mass is positioned 1.5 metres behind the front wheel centre and 0.8 metres above the road level. These details are shown in Figure Q1 below. Figure Q 1. Car on horizontal road The car,

### Solve the Recurrence and Find the Asymptotic Bound

1. Solve the recurrence exactly and prove your solution is correct by induction. T(1) = 1 , T(n) = 2T(n-1)+2n-1 T(1) = 1, T(n) = T(n-1)+3n-3 2. Give asymptotic bound for the following: T(n) = 9T(n/3)+n2 T(n) = T(Sqrt(n))+1.

### Finding the equation of a linear transformation explicitly

Please see attached

### dimension of the solution space of the homogeneous linear system

Find a basis and the dimension of the solution space of the homogeneous linear system Ax = 0 where .... Please see the attached file for the fully formatted problem.

### Lagrange's theorem

Suppose that... Use Lagrange's Theorem Suppose that a N and a z (mod pq) where p q 3(mod 4 ) are primes. Prove that there are only four possible square roots of a modulo pq, and they are given as follows. For x,y Z given by the extended Euclidean Algorithm, such that xp +yq =1 We have Z= (xpa + yqa ),

### IV Rate Working Examples

1. Your patient is admitted from the Emergency Department with a dopamine infusion running at 16 ml/hour. The dopamine bag is labeled as 400 mg dopamine in 500 D2W. Your patient weighs 50 kg. Calculate the dose the patient is receiving. Your answer should be in mcg/kg/minute. 2. Patient is an 18-month-old experiencing profo

### Graphing Solutions to an Inequlity on a Number Line

How would I graph this equation? (X-3) (X-6)>0.