Prove the following test: Let {xn} be a sequence and lim |Xn| ^1/n = L
1. If L< 1 then {xn} is convergent to zero
2. If L> 1 then {xn} is divergent
In: Advanced Math
Solve the differential equation. x''(t)+2x'(t)+5x(t) = 2
In: Advanced Math
Find the power series solution for the equation y'' + (sinx)y = x; y(0) = 0; y'(0) = 1
Provide the recurrence relation for the coefficients and derive at least 3 non-zero terms of the solution.
In: Advanced Math
Let
f(x, y) = x2y(2 − x + y2)5 − 4x2(1 + x + y)7 + x3y2(1 − 3x − y)8.
Find the coefficient of x5y3 in the expansion of f(x, y)
In: Advanced Math
A mass of 50 g stretches a spring 3.828125 cm. If the mass is set in motion from its equilibrium position with a downward velocity of 10 cm/s, and if there is no damping, determine the position u of the mass at any time t.
Enclose arguments of functions in parentheses. For example, sin(2x).
Assume g=9.8 ms2. Enter an exact answer.
In: Advanced Math
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Quad Enterprises is considering a new 3-year expansion project that requires an initial fixed asset investment of $3.0 million. The fixed asset falls into the 3-year MACRS class (MACRS Table) and will have a market value of $231,000 after 3 years. The project requires an initial investment in net working capital of $330,000. The project is estimated to generate $2,640,000 in annual sales, with costs of $1,056,000. The tax rate is 23 percent and the required return on the project is 14 percent. |
| What is the project's year 0 net cash flow? |
| What is the project's year 1 net cash flow? |
| What is the project's year 2 net cash flow? |
| What is the project's year 3 net cash flow? |
| What is the NPV? |
In: Advanced Math
Notes 2.7 Using CRT notation, show what is going on for all the combinations you considered in Notes 2.6. Explain why gcd(s + t, 35) sometimes gave you a factor, and it sometimes did not
Notes 2.6 is:
Notes 2.6 Consider all the possible sets of two square roots s, t of 1 (mod 35) where s ≢ t (mod 35) (there are six of them, since addition is commutative (mod 35).
For all possible combinations, compute gcd(s + t, 35). Which combinations give you a single prime factor of 35?
In: Advanced Math
1.) Prove that Z+, the set of positive integers, can be expressed as a countably infinite union of disjoint countably infinite sets.
2.) Let A and B be two sets. Suppose that A and B are both countably infinite sets. Prove that there is a one-to-one correspondence between A and B.
Please show all steps. Thank you!
(I rate all answered questions)
In: Advanced Math
A person buying a personal computer system is offered a choice of three models of the basic unit, four models of keyboard, and three models of printer. How many distinct systems can be purchased?
systems
In: Advanced Math
1) Show that if A is an open set in R and k ∈ R \ {0}, then the set kA = {ka | a ∈ A} is open.
In: Advanced Math
1. Find the 100th and the nth term for each of the following sequences.
a. 50,90,130,...
b. 1,4,16,...
c. 7, 74,77,710,...
d. 197+7x327, 197+8x327, 197+9x327,...
2. Find the first five terms in sequences with the following nth terms.
a. 10n-5
b.2n-1
3. How many terms are there in each of the following sequences?
a. 11,15,19,23,...331
b. 59,60,61,62,...459
In: Advanced Math
find all primes p such that 6 is a square mod p?
please with clear hand writing
In: Advanced Math
Can you explain how kernels related with uniqueness, while images related with consistent?
In: Advanced Math
Problem 4-23 (Algorithmic)
EZ-Windows, Inc., manufactures replacement windows for the home remodeling business. In January, the company produced 15,000 windows and ended the month with 9,500 windows in inventory. EZ-Windows’ management team would like to develop a production schedule for the next three months. A smooth production schedule is obviously desirable because it maintains the current workforce and provides a similar month-to-month operation. However, given the sales forecasts, the production capacities, and the storage capabilities as shown, the management team does not think a smooth production schedule with the same production quantity each month is possible.
| February | March | April | |
| Sales forecast | 15,000 | 17,000 | 20,000 |
| Production capacity | 14,000 | 15,500 | 17,000 |
| Storage capacity | 6,000 | 6,000 | 6,000 |
The company’s cost accounting department estimates that increasing production by one window from one month to the next will increase total costs by $1.00 for each unit increase in the production level. In addition, decreasing production by one unit from one month to the next will increase total costs by $0.65 for each unit decrease in the production level. Ignoring production and inventory carrying costs, formulate and solve a linear programming model that will minimize the cost of changing production levels while still satisfying the monthly sales forecasts. If required, round your answers to two decimal places. If an amount is zero, enter "0".
Let:
F = number of windows manufactured in February
M = number of windows manufactured in March
A = number of windows manufactured in April
Im = increase in production level necessary during month m
Dm = decrease in production level necessary during month m
sm = ending inventory in month m
| Min | I1 + I2 + I3 + D1 + D2 + D3 | |
| s.t. | ||
| (1) | F - s1 = | February Demand |
| (2) | s1 + M - s2 = | March Demand |
| (3) | s2 + A - s3 = | April Demand |
| (4) | F - I1 + D1 = | Change in February Production |
| (5) | M - F - I2 + D2 = | Change in March Production |
| (6) | A - M - I3 + D3 = | Change in April Production |
| (7) | F ≤ | February Production Capacity |
| (8) | M ≤ | March Production Capacity |
| (9) | A ≤ | April Production Capacity |
| (10) | s1 ≤ | February Storage Capacity |
| (11) | s2 ≤ | March Storage Capacity |
| (12) | s3 ≤ | April Storage Capacity |
If required, round your answers to the nearest dollar.
Cost: $
In: Advanced Math