If the mathematics we use today stems from the contributions of the past, what would be the contributions of the Egyptians, Mesopotamians, and early Greeks?

Solve the system X' = (2 3 2 1)X + (t 1)

solve xy''-xy'+y=0 (using center series solution)

solve: y''+8y'+7'=f(t), y(0)=y'(0)=0, expressing your answer in terms of a convolution, using partial fractions for:

i)f(t)=e^t

ii)f(t)=t^1/2

iii) f(t)=2sin(2t)

*Please show work and explain*

Prove that a vector space V over a field F is isomorphic to the vector space L(F,V) of all linear maps from F to V.

In a study of the domestic market share of the three major automobile manufacturers A, B, and C in a certain country, it was found that their current market shares were 50%, 35%, and 15%, respectively. Furthermore, it was found that of the customers who bought a car manufactured by A, 75% would again buy a car manufactured by A, 15% would buy a car manufactured by B, and 10% would buy a car manufactured by C. Of the customers who bought a car manufactured by B, 90% would again buy a car manufactured by B, whereas 5% each would buy cars manufactured by A and C. Finally, of the customers who bought a car manufactured by C, 85% would again buy a car manufactured by C, 5% would buy a car manufactured by A, and 10% would buy a car manufactured by B. Assuming that these sentiments reflect the buying habits of customers in the future, determine the market share that will be held by each manufacturer after the next two model years. (Round your answers to the nearest percent.)

A _____%

B _______%

C _________%

Scanrio 2:Present material choices for a given building using performance properties, experimental data, sustainability and environmental consideration

P3 Discuss the benefits of product declaration and environmental certification.

P4 Present the results of relevant testing procedures to identify the performance characteristics of selected construction materials.

P5 Discuss the results in terms of the material properties and regulatory requirements, highlighting any unexpected results and why these may occur.

P6 Select construction materials for a given building based upon their performance properties in use.

I presently have $10,000 in the bank. At the beginning of each of the next 20 years, I will invest $4,000, and I expect to earn 6% interest per year. After 20 years I pay $15,000 in closeout fees on on the investment. At the end of the investment and fees how much money will I have? (answer $108,900).

I was given the answer from the professor I just need to know how to calculate this answer on Excel with formulas.

Using a boosting neural network, can you reduce the error rate? If so, to what? What might be a drawback to using this type of method, compared to logistic regression?

Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40 students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college $23,000. Assuming the college wishes to offer a total of seven sections, accommodate 220 students, and bring in $286,000 in revenues, how many sections of each course should it offer? HINT [See Example 2.] Finite Math. section(s) Applied Calculus section(s) Computer Methods

Rankine cycle experiment:

5000ml water consumed in experiment used

Time (sec): 1055

Boiler, Temp (c): 167.199

Turbine In, Temp (c):109.3

Turbine ex, Temp (c): 97.79

Boiler Pres, (KPa) : 721.315

Turbine In Pres, (KPa): 85.639

Turbine Ex Pres, (KPa): 32.826

Fuel flow, (L/Min):5.842

Generator, (RPM): 1949.185

Voltage (volts): 7.443

Current (Amps): 0.135

Power (Watts): 1.002

Calculate:

1.Mass flow rate of water/ steam in the closed cycle.

2. Specific work generated by the turbine.

3. Power generated by the turbine.

4. Heat rejected to cooling system by the condenser.

5. Specific work into the pump.

6. Heat flux introduced by the boiler

Please Help me, Ive posted this question a few times,and I don't understand why they use turbine inlet pressure instead of the boiler pressure.

Whats also confusing me is how they get h1 ,h2,h3 and h4 from the tables if the figures do not correspond.

Id really appreciate it if someone can properly explain this to me.

(12%) For the following 4 functions, check if you can calculate a constant c so that the function is a PDF over the whole plane or state that such c does not exist and the corresponding function is not a PDF (state the reason for that). Note the signs of the coefficients of x2 and y2 are all different). You do not have to calculate the constant c; just provide reasoning for if that exists or not.

f(x, y) = c e^(-x^2+xy-y^2 )

g(x, y) = c e^(-x^2+xy+y^2 )

h(x, y) = c e^(x^2+xy-y^2 )

k(x, y) = c e^(x^2+xy+y^2 )

f(x, y) = c e^(-x^2+xy-2y^2 )

g(x, y) = c e^(-x^2+xy+〖2y〗^2 )

h(x, y) = c e^(x^2+xy-2y^2 )

k(x, y) = c e^(x^2+xy+〖2y〗^2 )

Solve y"+y=u(t-pi/2)+3 delta(t-3 pi/2)-u(t-2 pi), by laplace transform methods with y(0)=y'(0)=0.

1) Find an estimate for the area under the graph of f(x)=x^2 from x=0 to x=8 using four rectangles and:

a) left end points

b) right end points

c) mid points

2) Find the volume of a solid obtained by rotating about the x-axis the region bounded by y=x^3 and y=2x.

Sketch the region, the solid, and a typical disk or washer.

Because I'm trying to learn how to solve this kind of problem in the future please show all intermediate steps so I can follow Suppose F= <xy+y, x-y^2> Let R be the triangular regiorn bounded by the curves y=x, y=4-x, and y=0, Let C be the boundary of this region, oriented counterclock wise.

a) Can you use Fundamental theorem for Line integrals to find ∮ F•dr? explain why or why not? What are the other two possible methods of finding this line integral ?

b) Find the easiest method to calculate ∮ F•dr and then evaluate the line integral using this method