Category Archives: Mathematics

Derive expressions for the largest mass that can be lifted through a height h in the surroundings in these processes.

CHEM 301 Physical Chemistry I Homework 1- Chapters 1-2 1. Calculate the value of CP at 298 K and 1 atm pressure predicted for CH4(g) and C2H4(g) by the classical equipartition theorem. Compare the predicted results with the experimental results and calculate the percent of the measured value that arises from vibrational motions. Repeat the calculations at 800 K and 1 atm using the relation below: Cp, m ( J mol.K) =A(1)+A(2) T K +A(3) T 2 K 2 +A(4) T 3 K 3 You may get the values of A’s from Table 5 in Chapter 2. 2. An ideal gas undergoes an expansion from the initial state described by Pi, Vi, T to a final state described by Pf, Vf, T in (a) a process at the….

Find a function f(x) substantially different from fr22 that has no antiderivative (in terms of elementary fimctions).

4. Find a function f(x) substantially different from fr22 that has no antiderivative (in terms of elementary fimctions). In this problem you will approximate J (x) dx in two different ways. (a) Find the Maclaurin series of f (x) and then integrate it to find the Maclaurin series of f f (x) dx. (b) Use the above to find the 5th order Taylor polynomial for f f(x) dx. (c) Use this Taylor polynomial to find a munexical approximation for the definite inte-gral f (x) dx for t = 1 and another value of t that you choose. (d) Use Simpson’s Rule to find an approximation for g f (x) dx for the same two values of t. (e) For your approximations in (c) and (d), use the relevant….

How many five-character passcodes are there that contain at least one digit?

1) A course code at Canisius consists of three upper-case letters followed by a non-zero digitfollowed by two more digits. How many possible course codes are there? 2) A variable name in the language C++ starts with a letter and can be followed by zero or moreletters, digits, and underscore characters. How many possible five-character variable names arethere? 3) Passcodes are defined to be any combination of lower-case letters and numbers. How many five-character passcodes are there that contain at least one digit? Be sure to use the complementmethod in determining your answer.

Use Heron’s formula to find the area of the triangle.

Use Heron’s formula to find the area of the triangle. Round to the nearest square unit. 17) a = 10 meters, b 14 meters, c = 6 meters A) 48 square meters B) 12 square meters C) 23 square meters D) 46 square meters Polar coordinates of a point are given. Find the rectangular coordinates of the point. 18) (-3, -13V) Ai* 4) .4* -*) Di* Convert the rectangular equation to a polar equation that expresses r in terms of 0. A) r(cos 0 + sin 0) . 2 B) r 4 Find the specified vector or scalar. A) 151+ 8j B) 91+ 5j C)13i+ 5j D) -15i+ 5j Use the given vectors to find the specified scalar. 21) = -14i + 5j and = 10i – 8j;….

fill in the following table as you create each piece.

A train travels from St. George, Utah to Las Vegas, Nevada carrying passengers on a leisure ride. In the dessert, the winds can get pretty strong, making the train able to get from St. Geroge to Las Vegas faster than it can get from Las Vegas to St. George. In total, the 240 mile round trip takes about 17 hours. The train can go 34 miles per hour when there is no wind. Find the speed of the wind.

Distance Rate Time St. George to Las Vegas T1″ role=”presentation” data-asciimath=”T_1″ style=”display: inline-table; line-height: 0; font-size: 16.992px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;”>T1T1 Las Vegas to St. George T2″ role=”presentation” data-asciimath=”T_2″ style=”display: inline-table;….

What is the maximum burst size ?

1.       For the following flows and a GCRA(100, 500), give the conformant and non-conformant cells. Times are in cell slots at the link rate.

(a)    0, 100, 110, 12, 130, 140, 150, 160, 170, 180, 1000, 1010

(b)   0, 100, 130, 160, 190, 220, 250, 280, 310, 1000, 1030

(c)    0, 10, 20, 300, 310, 320, 600, 610, 620, 800, 810, 820, 1000, 1010, 1020, 1200, 1210, 1220, 1400, 1410, 1420, 1600, 1610, 1620

2. Assume that a cell flow has a minimum spacing of γ time units between cell emission times (γ is the minimum time between the beginnings of two cell transmissions). What is the maximum burst size for GCRA(T,τ ) ? What is the minimum time between bursts of maximum size ?

3. Assume that….

What are the (P, B) parameters in b/s and bits for each case ?

For a CBR connection, here are some values from an ATM operator:

peak cell rate (cells/s)                           100 1000 10000 100000

CDVT (microseconds)                             2900 1200 400 135

 

1. What are the (P, B) parameters in b/s and bits for each case ? How does T compare to τ ?

2. If a connection requires a peak cell rate of 1000 cells per second and a cell delay variation of 1400 microseconds, what can be done ?

3. Assume the operator allocates the peak rate to every connection at one buffer. What is the amount of buffer required to assure absence of loss ? Numerical Application for each of the following cases, where a number N of identical connections with peak cell rate P is multiplexed.

case                                                                             1         2       ….

How many cells were sent by the source in time interval [0, 401] ?

In this problem, time is counted in slots. One slot is the duration to transmit one ATM cell on the link.

1.       An ATM source S1 is constrained by GCRA(T = 50 slots, τ = 500 slots), The source sends cells according to the following algorithm.

• In a first phase, cells are sent at times t(1) = 0, t(2) = 10, t(3) = 20,…,t(n) = 10(n − 1) as long as all cells are conformant. In other words, the number n is the largest integer such that all cells sent at times t(i) = 10(i − 1), i ≤ n are conformant. The sending of cell n at time t(n) ends the first phase.

• Then the source enters the second phase. The subsequent cell n +….

What buffer size is required for the flow at the shaper ?

A flow with T-SPEC (p, M, r, b) traverses nodes 1 and 2. Node i offers a service curve ci (t) = Ri (t − Ti)+. A shaper is placed between nodes 1 and 2. The shaper forces the flow to the arrival curve z(t) = min(R2t, bt + m).

 

1. What buffer size is required for the flow at the shaper ?

2. What buffer size is required at node 2 ? What value do you find if T1 = T2 ?

3. Compare the sum of the preceding buffer sizes to the size that would be required if no re-shaping is performed.

4. Give an arrival curve for the output of node 2.

What is the maximum virtual delay if (P, B, R)=(P0, B0, R0) ?

A flow S(t) is constrained by an arrival curve α. The flow is fed into a shaper, with shaping curve σ. We assume that

α(s) = min(m + ps, b + rs)

and

σ(s) = min(P s, B + Rs)

We assume that p>r, m ≤ b and P ≥ R.

The shaper has a fixed buffer size equal to X ≥ m. We require that the buffer never overflows.

 

1. Assume that B = +∞. Find the smallest of P which guarantees that there is no buffer overflow. Let P0 be this value.

 

2. We do not assume that B = +∞ anymore, but we assume that P is set to the value P0 computed in the previous question. Find the value (B0, R0) of….