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# Algebra

### 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

### 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.

### Jordan canonical form

See attached problems

### 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.

### 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

### Finding a Break-Even Point : At which month will you break even?

You are opening up a restaurant, initial cost of opening the restaurant is \$80,000, plus \$4,000 monthly expenses. Estimate f(x)=xsquared - x + 5 to be the anticipated monthly profit of the restaurant in hundreds of dollars during the xth month of business. To break even your total profit from the opening of the restaurant must

### Solve show the equations and simplify

The waste hauling company profits are stated as the difference between revenue and costs. That is P(x) = R(x) - C(x), where x is the number of tons processed. Find the maximum profit and the number of tonnage which must be processed in order to yield the maximum profit for each of the following: a) R(x) = 5x; C(x) = 0.0001x2

### Home Mortgages Fixed and Variable Rates

#4. Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). a. What are the 16 outcomes in the sample space? b. Which outcomes are in the event that exactly three of the selected mortgages are fixed rate? c. Which outcomes are in the event that all four mortgages are of the same type?

### 1. Let N1(p) denote the number of pairs of integers in [1, p - 1] in which the first is a quadratic residue and the second is a quadratic nonresidue modulo p. Prove that N1(p) = (1/4) (p - ( - 1)^((p - 1)/2)) 2. Let N2(p) denote the number of pairs of integers in [1, p - 1] in which the first is a quadratic nonresidue and the second is a quadratic residue modulo p. Prove that N2(p) = (1/4) (p - 2 + ( - 1)^((p - 1)/2)) 3. Let N3(p) denote the number of pairs of integers in [1, p - 1] in which the first is a quadratic nonresidue and the second is a quadratic nonresidue modulo p. Prove that N3(p) = (1/4) (p - 2 + ( - 1)^((p - 1)/2)) 4. Use the results of theorem 10-4 and corollary 10-1 to construct solutions of x^2 + y^2 =29. 5. Prove ( without assuming corollary 10-1) that, if p is a prime &#8801; 1 (mod 4), then there exists positive integers m, x, and y such that x^2 + y^2 =mp, with p &#9532; x, p &#9532; y, 0 < m < p [ Hint: use the proof of Theorem 11-2]. Theorem 10-4: If p is an odd prime, then &#957;(p) = (1/8)p + Ep where | Ep| < (1/4)(p)^(1/2) +2. Corollary 10-1: Every prime p &#8801; 1(mod 4) is representable as a sum of two squares. Theorem 11-2: For each prime p there exist integers A,B and C, not all zero, such that A^2 + B^2 + C^2 &#8801; 0 (mod p).

Theory of Numbers The Distribution of Quadratic Residues Sums of Squares Sums of Four S

### Solving an Equation by Substitution

Please solve: v=ab/(c+d) where v = velocity where a = 6.67*10^-11 N m^2 kg^-2 where b = 5.97*10^24kg where c = 6.37*10^3km where d = 385km could you show all workings and all terms in the equation should be in SI units

### Solving an Equation by Substituting Values

If air resistance is neglected, the number of feet "s" that an object falls during "t" seconds is given by the equation s = 16t^2. How long would it take for an engine of an airplane to reach the earth if it fell off the airplane at 32,000 feet?

### Shapley-Shubik Distribution, Weighted Voting Systems and Combina

1) Find the Shapley- Shubik distribution (in percent) for the system (7: 5,3,2,1,). 2) In a cafeteria every meal has a 5 choice main course, a 3 choice salad, and a 2 choice soup, and a 4 choice dessert. If some one ate a different complete meal every day, how many days could he eat before he would start to repeat a meal?

### Solve an Equation Word Problem

The formula 1211.1L = CA squared S is used to determine the approach speed for landing an aircraft, where L is the gross weight of the aircraft in pounds, C is the coefficient of lift, S is the surface area of the wings in square feet (ft squared), and A is the approach speed in feet per second. I need help finding A for the Pi

### Solve the Equation and Writing a Word Problem as an Equation

1. solve 2(3y+4)-5(y-2)=3y-6(y-3) 2. Four more than twice the difference of three times a number and 8 is less than twice the number.

### Solve the equation

Z/z-2 - 1/z+5 = 7/z squared + 3z - 10

### Ratio

The student-teacher ratio for Stratford High was reported to be 27.5 to 1. If there are 42 teachers, how many students are in the school?

### Complex Variable Class - Undergraduate 500 Level

Compute c&#8747; (e^cosz)(logz)dz where c is the positive oriented circle with center z0=1 and radius 1/2. Please see attached.

### How do you solve an equation?

In math class we have been assigned to answer the following question: How do you solve an equation? Please provide an example. I know how to solve an equation if it is given to me, but I do not know how to describe how to solve any equation. I hope you can help.

Prove, using the quadratic reciprocity law that (3/p) = 1 if p== 1 or 11 (mod 12) (3/p) = -1 if p==5 or 7 (mod12) for each odd prime p.

### Writing an Equation from a Word Problem : 'Separately and Both Together' Problem

With only the small valve open, all of the liquid can be drained from a large vat in 4 hours. With only the large valve open, all of the liquid can be drained in 2 hours. How long would it take to drain the vat with both valves open?

### Minimum Cost Problems for Company C

Minimum cost problem: It cost a company C dollars per hour to operate its base base division. an analyst had determined that C is related to the number of base balls produced per hour, x, by the eqauation C = 0.009x^2 - 1.8^2 + 100. What number of balls per hour should be produced to minimize the cost per hour of manufacturing

### Capacitor, Source Voltage and Maximum Charge

If a capacitor with a capacitance of 0.000005 farads is wired in a circuit with a total resistance of 5000 ohms (the standard unit of electrical resistance), how long must the capacitor be wired to a source voltage to reach 50% of its maximum charge? (Hint: Begin by expressing q as 0.5Q)

### Word Problem : Application of Sums of Odd and Even Numbers

As Jack finished a section of the novel he was reading, his wife posed a curious question: "Dear, suppose you took the page numbers of the section you just read and added them together. What would you get? Jack summed them rather hastily and said, "Well, I may have to double-check my arithmetic. It's either 412 or 512, I'm not

### Word Problem : Medical Insurance Co-Payments

On the medical insurance policy (such as BCBS), the policy holder may need to make co-payments for percriptions drugs, office visits, and proceduares until total of all co-payments reaches a specific amount. Suppose on the Gattelaro's medical policy that the co-payment for the percription drug is 50% of the cost; the co-payment

### Word Problem : Speed and Distance

Ryan starts jogging home at the rate of 6km/hr. After reaching Harbor Front, he begins jogging back home. Because of fatigue, his speed for the return trip decreases to 4.5km/h and takes 1 hour longer. Determine the total distance that Ryan jogged.

### Formula to determine variable of gross profit %

Attached is a spreadsheet with two accounts. Each account has the same retail and invoice. One school has a small enrollment and the other has a larger enrollments. There is a handling fee of \$2 per enrollment. There are only two variables that can be changed: brochure cost & incentives. Also, the larger the enrollment, the larg

### Line Equations :Find Equation Given Point and Perpendicular Line and Find Point

1: Write the standard form of the equation of the line passing through the point (1,-2) and perpendicular to the line y=-3/2x-2 2: The line through A(-3,-4) and B(-2,Y) is perpendicular to a line with a slope -1/7. Find y

### Bounded Real Sequences and Metrics

Let X be the set of all bounded real sequences ... (SEE ATTACHMENT FOR COMPLETE QUESTION) ... For points x = {x1,,x2,x3...} and y = {y1,y2,y3...} in X define: d(x,y) := SUP |xk-yk|. (k less than or equal to 1) Prove that d is a metric (remember to explain why d(x,y) is finite!) (Please explain in your own words

### Word Problem : Writing a Defining Equation and Solving the Equation

To stay competitive with the fast food restaurant across the street, the Pico de Gallo Restaurante offers a lunch special. Each lunch plate has an .80 charge for beans, rice and guacamole, and each taco oredered costs .75. Senora Taquita, across the street, only charges .35 for the beans, rice and guacamole, but charges .90 fo

### Linear Programming / Sensitivity Analysis / Optimization: Please solve in Excel using Solver add-in and also do Sensitivity Report to solve and support answers. The EnergyBoat Company

The Background The EnergyBoat, Inc. produces and distributes high quality motor boat with highly seasonal demand. To handle this seasonality, the company has several options for its supply chain aggregated planning purposes: hiring an additional workers during peak seasons, outsourcing part of the demand to a third party manu