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# Algebra

### Parabola Application Word Problem : Suspension Bridge

A suspension bridge is built with its cable hanging between two vertical towers in the form of a parabola. The towers are 400 feet apart and rise 100 feet above the horizontal roadway, while the center points of the cable is 10 feet above the roadway. (a) Find the equations of the parabola (b) Find the height above the roadway

### Irreducible representation of dihedral group : D_n over C

Let D_n be the dihedral group. Classify the irreducible representations of D_n over C (complex).

### Finding the Equation of a Line Given a Slope and a Point

The line with the slope -6 that goes through (-1,-7) The line with the slope -8 that goes through (-1,-5) A developer prices condominiums in Florida at 20,000 plus \$40 per square foot of living area. Express the cost C as a function of the number of square feet of living area s. The threshold weight for an individual is

### A stationary car A is passed by a car B moving

A stationary car A is passed by a car B moving with a constant velocity of 15m/s. Two seconds later, car A starts moving with a constant acceleration of 1m/s^2 in the same direction.(If car has constant velocity acceleration must be zero) a) Using the formula s=ut + 1/2at^2,where s is the distance from the starting point in m

### Velocity, Time and Distance of a Rock After it has been Thrown

If a rock is thrown into the air on small planet with a velocity of 25 meters/second, its height in meters after t seconds is given by V = 25t ? 4.9t2. Find the velocity of the rock when t=3 A particle moves along a straight line and its position at time t is given by s(t) = 2t3 ? 27t2 + 108t where s is measured in meters and t

### Algebra Concepts Check

Week two DQ 1 1) How can you differentiate between a formula and an equation? For example. Week two DQ 2 2) What are some "Pitfalls" to watch out for in? A. Using the addition property in solving for X? B. Using the multiplication property in solving for? For example. Week two DQ 3 3) how do you remember

### Let T be a Mobius transformation, T doesn't equal to identity. Show that a Mobius transformation S commutes with T if S and T have the same fixed points.

Let T be a Mobius transformation, T doesn't equal to identity. Show that a Mobius transformation S commutes with T if S and T have the same fixed points.

### Whole number and polygon

Task1 some whole numbers can be written as the sum of consecutive whole numbers. for example: 5=2+3 12=3+4+5 some whole numbers can be written as the sum of consecutive whole numbers in more than one way. for example: 9=4+5=2+3+5 which whole numbers can be written as the sum of consecutive whole numbers? can they

### Equality

In a basketball game scrimmage, the Toros scored a total of 103 points and made three times as many field goals (2 points each) as free throws (1 point each). They also made eleven 3 point baskets. How many field goals and free throws were made?

### Simple Statistics word problem - 100 soldiers are required...

As a test 100 soldiers are required to complete 9 weeks of training 18 percent of them fail due to the short period of 9 weeks. If 2 more weeks are added, what would be the percentage of failures? Feel free to answer in an attachment if needed. I need to see how to solve this type problem in a statistical manner. You may a

### Application Problems: Velocity, Distance and Cost of Production

A 40,000 lb. rocket is launched from sea level straight up, then falls back to earth. The total flight time was 160 seconds. The rocket reached it's apex in 1 minute and 20 seconds. What altitude did the rocket reach before falling back to earth....in miles? The assembly operation takes two minutes for an operator to perform

### Arithmetic sequence

How do I find the 40th term of the arithmetic sequence knowing the general term An=(Asubscript n -1)n-3? The first term in A1=9

### Exponential form

How would I write (log subscript b) 219 = 3 in exponetial form?

### Solving a quartic equation

I can not factor or group this to set it equal to zero to determine the solution. Can you help me? 4x^4-65x^2+16=0

### Fixing a Budget

This is a sample budget prepared by Dick and Jane who are both employed. Dick is paid weekly and brings home a check for \$350.00 each week. Jane is paid every two weeks and brings home a check for \$500.00 each pay day. Jane sometimes receives an additional amount for paid overtime and Dick receives a bonus from time to time.

### Solve by the elimination method

Solve by the elimination method. -------------------------------------------------------------------------------- Solution 2x+3y=4 10x-6y=3 than I multiplying the first equation by 10 and the second equation by -2. 20x+30y=4 <= should be 40 -20x+12y=-6 =>42y=34 => y=17/21, x=11/14 how do I solve for (x

### Elimination method and substitution methods

Elimination method 1) 5r-6s=-10 6r+5s=49 2) 1/3x + 1/1y=2/3 2/3x + 3/5y=1/5 3) 5x+3y=-12 6x-3y=-54 4) p=47+q 8p=6q+404 Substitution method 1) x+y=5 y=x-3 2) r-45=0 6r-5s=133 3) 6x+3y=-36 -7x+y=60 System of equation by graphing: 1) y-2x=0 y=4x-1

### Word problem

I've attached the file. I need to know if I'm going in the right direction (in the red font), if not could you explain? (See attached file for full problem description) --- A person has 14 close friends. (a) How many ways can she invite 8 of her 14 close friends to a holiday get-together. Explain. (b) Suppose tha

### 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

### 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.

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

### 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

### 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).

### 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?