Solve the differential equation both by undetermined coefficients and the Laplace transform: d2y/dt2– 3 dy/dt + 2y = 6 exp(3t), y(0) = 6, y’(0) = 14.
In: Advanced Math
For the Fibonacci sequence, prove the formula u2n+1 = un un+2 + (-1)n
In: Advanced Math
Consider the following differential equation: x2y"-2xy'+(x2+2)y=0
Given that y1=x cos x is a solution, find a second
linearly independent solution to the differential equation.
Write the general solution.
In: Advanced Math
In: Advanced Math
Scenario 1
Mr. Abbas sees a book displayed in a shelf of a book shop with a price tag of Rs. 85. Mr. Abbas tenders Rs. 85 on the counter and asked for the book. The book seller refuses to sale the book saying that the book is already sold and I do not have another copy of the book.
Question: Is the book seller bound to sell the book to Mr. Abbas. Why and Why not?
Scenario 2
Mr. Hameed offers to sale his car to Mr. Arshad for Rs. 95,000. Mr. Arshad offers Rs. 94,000 for the car for which Mr. Hameed refuse to sale. Subsequently, Mr. Hameed agrees to sell his car for Rs. 92,000 to Mr. Hafeez. Mr. Arshad sues Mr. Hameed for performance.
Question: As a judge, what is going to be your decision? Justify with the help of reasons.
In: Advanced Math
use the method of variation of parameters to solve y''(x)-2y'(x)=exp(x)*sin(x)
In: Advanced Math
NEW NUMBERS
Andre Greipel is the owner of a small company that produces heart rate monitors. The annual demand is for 2,250 heart rate monitors, and Andre produces these devices in batches. On average, Andre can produce 140 monitors per day during the production process. Demand for monitors has been about 35 monitors per day. The cost to set up the production process is $350, and it costs Andre $0.80 to carry 1 monitor in inventory for one year. How many monitors should Andre produce in each batch?
a) What is the optimal economic production quantity?
b) On average, how many setups are required per year (one decimal place)?
c) What is the total cost per year (holding plus setup)?
In: Advanced Math
NEW NUMBERS
Chris Froome is a purchasing agent for a firm that sell components for high performance bicycles. One of the most popular components is the TDF bicycle frame which has an annual demand of 1,750 units. The cost of each frame is $675 and the inventory carrying cost is estimated to be 18% of the cost of each frame. Chris has made a study of the costs involved in placing an order for any of the frames the firm stocks, and he has concluded that the average ordering cost of $73 per order. Furthermore, it takes about one week for an order to arrive from the supplier, and the TDF operates 50 weeks per year.
a) What is the annual ordering cost?
b) What is the annual holding cost?
c) How many orders (on average) would be placed per year?
d) What is the average inventory?
e) What is the reorder point?
f) What is the EOQ?
In: Advanced Math
Does every hyperbolic triangle have an inscribed circle? Circumscribed circle?
In: Advanced Math
In: Advanced Math
Let α be a root of x^2 +1 ∈ Z3[x]. Show that Z3(α) = {a+bα : a, b ∈ Z3} is isomorphic to Z3[x]/(x^2 + 1).
In: Advanced Math
Let X be a non-empty set and R⊆X × X be an equivalence relation. Prove that X / R is a partition of X.
In: Advanced Math
Find all of the real and imaginary zeros for the polynomial function. f(x)= 69 x^4-2x^3+62x^2-2x-7
In: Advanced Math
Solve the following differential equation using the power series method.
(1+x^2)y''-y'+y=0
In: Advanced Math
In: Advanced Math