Given the series of numbers:

{1.,0.612547,0.466856,0.375214,0.311459,0.264691,0.229088,0.201197,0.17884,0.160573,0.145406,0.132639,0.121764,0.112404,0.104273,0.0971538,0.0908741,0.0852989,0.08032,0.0758497,0.0718166,0.0681615,0.0648355,0.0617975,0.0590128,0.056452,0.05409,0.0519052,0.0498791,0.0479955,0.0462403,0.0446012,0.0430675,0.0416295,0.0402789,0.0390081,0.0378105,0.0366801,0.0356115,0.0346001,0.0336414,0.0327315}

What is the 100th term to 12-decimal places? How is this sequence made?

In: Advanced Math

A B C D E

Fixed Startup Cost $3400
$2200 $2750 $1800 $1200

Cost per
MW-hr
$6
$5
$7
$7 $8

Maximum Capacity 2200
1900 2600
1600 3200

**Part A:** Formulate a Binary-Integer Problem that
minimizes the total cost. Write the complete algebraic form, and
clearly state the decision variables, objective function, and the
constraints.

*Hint: Some binary variables and big number constraints are
needed in this problem*

**Part B:** Set up and solve a linear spreadsheet
model to determine the operating plan that will minimize their
overall costs. For full credit, the model must be linear (no
multiplication of changing cells, no IF statements, no MAX
statements, etc.)

In: Advanced Math

The Ponchatrain Bridge is a 16-mile toll bridge that crosses Lake Ponchatrain in New Orleans. Currently, there are 7 toll booths, each staffed by an employee. Since Hurricane Katrina, the Port Authority has been considering replacing the employees with machines. Many factors must be considered because the employees are unionized. However, one of the Port Authority's concerns is the effect that replacing the employees with machines will have on the times that drivers spend in the system. Customers arrive to any one toll booth at a rate of 12 per minute. In the exact change lanes with employees, the service time is essentially constant at 4 seconds for each driver. With machines, the average service time would still be 4 seconds, but it would be negative exponential rather than constant, because it takes time for the coins to rattle around in the machine.

For the "Exact Change Lane" with employee

The average time driver spends waiting to pay the toll = __ seconds (round your response to two decimal places).

The average time spent by a driver in the toll system (waiting and paying) = __ seconds (round your response to two decimal places)

The average number of drivers waiting in the line to pay the toll at a toll

booth=__ drivers (round your response to two decimal places).

The average number of drivers at any toll booth, namely, in the system = __ drivers (round your response to two decimal places).

For the lane with the proposed machine

The average time driver spends waiting to pay the toll = __ seconds (round your response to two decimal places).

The average time spent by a driver in the toll system (waiting and paying) = __ seconds (round your response to two decimal places).

The average number of drivers waiting in the line to pay the toll at a toll booth= __ drivers (round your response to two decimal places).

The average number of drivers at any toll booth, namely, in the system drivers __ (round your response to two decimal places).

As a result of proposed change, the average time spent per driver waiting in the line to pay the toll increases by __ (round your response to the nearest whole number).

As a result of proposed change, the average time spent per driver in the toll system increases by __ (round your response to the nearest whole number).

As a result of proposed change, the average number of drivers waiting in the line to pay the toll increases by (round your response to the nearest whole number).

As a result of proposed change, the average number of drivers at any toll booth increases by (round your response to the nearest whole number).

In: Advanced Math

t^2 y'' − 4ty' + 6y = t^4*e^t , t > 0. Use variation of parameters to find a particular solution given that y1 = t^2 and y2 = t^3 are a fundamental set of solutions to the corresponding homogeneous equation

In: Advanced Math

On a separate sheet of paper, practice the clustering technique to develop a topic for the writing assignment. Follow the instructions: 1. Choose one of the suggested topics. Write the topic in a large circle in the center. 2. Think about the topic for one or two minutes. Then write each new idea that comes into your mind in smaller circles around the large circle. 3. Think about the idea in each smaller circle for one or two minutes. Write any new ideas in even smaller circles. 4. Look over your groups of circles. Which groups have the largest number of ideas? These are probably the most productive ideas for your paragraph. TOPICS • a word that describes your home culture • an important term from your major field of study • a definition of what a good teacher is • a definition of culture shock • what the word success means to you • a definition of a what a leader is

**STEP 3:** Write the first draft. • Write FIRST
DRAFT at the top of your paper. • Begin your paragraph with a topic
sentence. Use the definition from your cluster diagram. As needed,
modify the definition so that it is like the ones you wrote in
Practice 4 on page 126. . For unity, present your supporting
information in a logical order. • Use transition signals to make
your paragraph coherent. . Try to include a word origin and/or
idiom that goes well with your topic. Pay attention to sentence
structure. Include a variety of sentence patterns: simple,
compound, and complex sentences. Use adjective clauses and
appositives. Punctuate them correctly. • Write a conclusion that
tells why the topic is important, interesting, or unique. • Write a
title. It should clearly identify your topic. For examples, look at
the titles of the models in this chapter

**write a definition paragraph on one of the
topics:**

In: Advanced Math

Real Analysis: Prove a subset of the Reals is compact if and only
if it is closed and bounded. In other words, the set of reals
satisfies the Heine-Borel property.

In: Advanced Math

Soundex produces x Model A radios and y Model B radios. Model A requires 15 min of work on Assembly Line I and 10 min of work on Assembly Line II. Model B requires 10 min of work on Assembly Line I and 12 min of work on Assembly Line II. At most, 25 labor-hours of assembly time on Line I and 22 labor-hours of assembly time on Line II are available each day. It is anticipated that Soundex will realize a profit of $15 on model A and $12 on model B. How many clock radios of each model should be produced each day in order to maximize Soundex's profit?

In: Advanced Math

Prove by induction:

1 + 1/4 + 1/9 +⋯+ 1/?^2 < 2 − 1/?,

for all integers ?>1

In: Advanced Math

The table shows the estimated percentage *P* of the
population of a certain country that are mobile-phone subscribers.
(End of year estimates are given.)

Year | 1997 | 1999 | 2001 | 2003 | 2005 | 2007 |

P |
2.1 | 8.2 | 15.7 | 25 | 45.7 | 62.5 |

(c) Estimate the instantaneous rate of growth in 2003 by sketching
a graph of *P* and measuring the slope of a tangent. (Sketch
your graph so that it is a smooth curve through the points, and so
that the tangent line has an *x*-intercept of 1999.3 and
passing through the point

(2006, 46.6). Round your answer to two decimal places.)

For part, c use the two points that are on the tangent line to
determine the slope, which is the instantaneous rate of
change.

......................................... percentage
points per year

In: Advanced Math

y"+y'-6y=1

1. general solution of corresponding homogenous equation

2. particular solution

3.solution of initial value problem with initial conditions y(0)=y'(0)=0

In: Advanced Math

Suppose x,y ∈ R and assume that x < y. Show that for all z
∈ (x,y), there exists α ∈ (0,1) so that αx+(1−α)y = z. Now, also
prove that a set X ⊆ R is convex if and only if the set X satisfies
the property that for all x,y ∈ X, with x < y, for all z ∈
(x,y), z ∈ X.

In: Advanced Math

Express the equation of the plane in explicit form

a. d = [1, -3, -5]; e = [-2, 1, -1] and f = [5, -1, -3] Express the
equation of the plane through d, e, and f explicitly

b. d = [-1, 7, -6]; e = [2, -1, 3] and f = [4, -2, 9] Express the
equation of the plane through d, e, and f explicitly

In: Advanced Math

Let A =

2 | 0 | 1 |

0 | 2 | 0 |

1 | 0 | 2 |

and eigenvalue λ1 = 3 and associated eigenvector v(1) = (1, 0, 1)t . Find the second dominant eigenvalue λ2 (or the approximation to λ2) by the Wielandt Dflation method

In: Advanced Math

1.

Use Euler's method with step size 0.50.5 to compute the approximate yy-values y1≈y(0.5), y2≈y(1),y3≈y(1.5), and y4≈y(2) of the solution of the initial-value problem

y′=1+3x−2y, y(0)=2.

y1=

y2=

y3=

y4=

2.

Consider the differential equation dy/dx=6x, with initial condition y(0)=3

**A.** Use Euler's method with two steps to
estimate y when x=1:

y(1)≈ *(Be sure not to round your
calculations at each step!)*

Now use four steps:

y(1)≈

**B.** What is the solution to this differential
equation (with the given initial condition)?

y=

**C.** What is the magnitude of the error in the
two Euler approximations you found?

Magnitude of error in Euler with 2 steps =

Magnitude of error in Euler with 4 steps =

**D.** By what factor should the error in these
approximations change (that is, the error with two steps should be
what number times the error with four)?

factor =

*(How close to this is the result you obtained
above?)*

In: Advanced Math