Consider a rocket that burns steadily. The higher pressure in the combustion chamber, the faster the propellant burns. Why is this? The relationship is such that the higher the pressure, the closer the gaseous flame is to the surface and the more effectively it can transfer heat back to the surface thereby gasifying the propellant quicker. The rate of gas generation, ?_? , can be described by the equation: ?_?=?_1 ?^?, where P is the pressure, and C1 and n are the constants for a given propellant with given exposed surface area.

The hot gas leaving the rocket must pass through the throat of the exhaust nozzle at sonic velocity.

▪The higher the pressure, the greater the density of this gas and the greater the rate of mass flow at sonic velocity. (The speed of sound in a gas is independent of pressure.) Accordingly, the rate of gas escape, ??r_e , is described by the equation: ??=?2?r_e=C_2 P where C2 is a constant, dependent on cross section area of the nozzle throat and on the velocity of sound in the combustion products.

▪What is the steady operating pressure of a solid-propellant rocket for the given values of the constants C1 , C2, and n? What values of n keep it stable?

PLEASE WRITE CLEARLY AND EXPLAIN WHY IS THE ANSWER THE WAY IT IS PLEASE THANK YOU

Explain the difference between simple and compound interest and describe a scenario when the benefits of one outweighs the other. Provide specific examples.

Find the Green's function for each of the following problem, and determine
the solution of each of the following boundary-value problem:
y" + 4y = e^x
y(0) = 0
y'(1) = 0

In the 3-month period November 1, 2014, through January 31, 2015, Hess Corp. (HES) stock decreased from $80 to $64 per share, and Exxon Mobil (XOM) stock decreased from $96 to $80 per share.† If you invested a total of $25,920 in these stocks at the beginning of November and sold them for $21,120 3 months later, how many shares of each stock did you buy?

For the Poincare plane, find two lines L1 and L2 and a point P off each such that through P there are exactly two lines parallel to both L1 and L2.

Give an example of proof by construction.

For example, prove that for every well-formed formula f in propositional logic, an equivalent WFF exists in disjunctive normal form (DNF).
HINT: Every WFF is equivalent to a truth function, and we can construct an equivalent WFF in full DNF for every truth function. Explain how.

A recent college graduate buys a new car by borrowing $22,000 at 8.4%, compounded monthly, for 4 years. She decides to pay $552 instead of the monthly payment required by the loan.

(a) What is the monthly payment required by the loan? (Round your answer to the nearest cent.)
$  

How much extra did she pay per month? (Round your answer to the nearest cent.)
$  

(b) How many $552 payments will she make to pay off the loan? (Round your answer up to the next whole number.)
payments

(c) How much will she save by paying $552 per month rather than the required payment? (Round your answer to the nearest cent.)
$

Find the eigenvalues and eigenfunctions of the Sturm-Liouville system
y"+ lamda y = 0 o<x<1
y(0) = 0
y'(1) = 0
(b) Show that the eigenfunctions Yn and Ym you obtained from the above
are orthogonal if n not= m.

factoring ax^2+bx+c with Grouping, Box Method, Star Method/Diamond Method/X-method, and Tic-Tac-Toe Method (with a>1)

1) What is the linear density in denier if 1.75 pound of yarn has a length of 110 miles?

2) How many 3.8 micronaire fibers will be in the cross-section of a 125 denier yarn?

3) If you want to make a yarn trail around a rectangular field that is 11 feet by 17 feet, what yarn mass would you need in grains if the yarn has a linear density of 55 tex?

4) How many 36 tex fibers are in the cross-section of a 65 gr/yd sliver?

5) What is the length in kilometers of 113.6 pounds of 12 ktex yarn?

6) How many 4.5 dtex fibers are in the cross-section of a 49 grain/yd sliver?

7) What is the linear density of a yarn in ktex if 0.5 miles of yarn weighs 41400 grains?

8) What is the mass in milligrams of 250 fibers in each fiber has a linear density of 3.4 denier and a length of 2.7 inches?

uniformly convergent, Analysis

how sup(fn(x)-f(x))

and fn(x)-f(x)

I don't understand how to transform from sup(fn(x)-f(x)) to fn(x)-f(x) to represent uniformly convergent

Also, please kindly draw the picture to explain sup(fn(x)-f(x))

sup=supremum

Design a spreadsheet to calculate the class’s grades. Consider the following requirements:

1. Each project will be graded from 0 to 10.
2. the contribution of each grade to the final grade are ( 7 team work assignments 10%, Project 1,2,3,4= 20%, mid term 35%, final 35%.)
3. The final test will be graded from 0 to 100, but your solution should allow different grades (i.e 80 points, 90, or 95). This flexibility is very important.
4. Program your solution to set a numeric final grade.
5. Program your solution to translate the numeric grade to the letter grade using the corresponding table

Please show steps by steps and explain the calculations.

Grading Evaluation

Let n > 5. A deck containing 4n cards has exactly n cards each of four diffrent suits numbered from the set [n].

Using the method of choice and setting up appropriate subsets in how many ways can five cards be chosen so that they contain:

(a) five consecutive cards of the same suit? (ie. the set of numbers on the cards is [i, i + 4])

(b) four of the five cards have the same number?

(c) exactly three of the cards have the same number?
(d) not more than two cards of the same suit? Hint: consider two cases.

give a justification of answers pls (set notation, bijection principal, addition or multiplication theorem, cartesian product etc...)

Use duality to answer the following application.

The Enormous State University's Business School is buying computers. The school has two models to choose from, the Pomegranate and the iZac. Each Pomegranate comes with 400 GB of memory and 80 TB of disk space, while each iZac has 300 GB of memory and 100 TB of disk space. For reasons related to its accreditation, the school would like to be able to say that it has a total of at least 49,500 GB of memory and at least 12,500 TB of disk space. If both the Pomegranate and the iZac cost $2,000 each, how many of each should the school buy to keep the cost as low as possible?

What are the shadow costs of memory and disk space?

Determine the solution of the following equation mod N.

1.7x≡2 mod 15, where N= 15

2.x≡8 mod 11, x≡3 mod 19, where N= 209

3.x≡2 mod 7, x≡2 mod 11, x≡1 mod 13, where= 1001