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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

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.

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.

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

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, initially travelling at


Suppose that... Use Lagrange's Theorem Please see attached.

Drug Calculations

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

Word Problem : Solving an Equation using a Substitution

The formula D^2 = 4050 / i indicates the amount of illumination (i) , in foot-candles, produced by a light source relative to the distance (d) from the source. How far from the source is the illumination equal to 50 foot-candles?

How to create a linear picture

I need some pointers on how to get started... Problem: Create your own linear picture Draw picture with straight lines only, then create a key with equations and restrictions for each of the lines in the picture. Must include the following: - picture drawn on graph paper - 10 lines minimum - 2 quadrants minimum - 1

Q* = (ad+bc) / (b+d)

If Q = a - bp Q = c + dp then I can derive that: p = (a-c) / (b+d) How do I derive that: Q = (ad+bc) / (b+d)

Variation on Fermat

The attached question is a variation on Fermat's Last Theorem. I would be grateful to anyone able to solve the problem. I would be grateful to anyone able to answer and prove the answer to the following question: If a, b, c and n are rational numbers, but they are not integers, do there always exist a, b, c and n such

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

Squared and cubed word problem

I'm thinking of a 6-digit number. The sum of the digits is 43. And only two of the following three statements about the number are true: (1) it's a square number. (2) it's a cube number, and (3) the number is under 500000

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?

Solving for the Equation of a line

Please address the following problem and include all of the required steps. Solve: Find the slope intercept form of the equation for the line parallel to y=4/3-1 that goes through points (6,-5).

Shapley-Shubik Distribution, Weighted Voting Systems and Combinations

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?