An LED has a forward voltage drop of 2.25 V. As seen in the figure, it is in series with: an AC source of V(t)=V0sin(2πft) with V0= 4.00 V, f=1 Hz, and a resistor R= 200 Ω

d. The whole flash:
1) If you were watching the LED, you would see it turn on and off with a period of 1s. During the 1s period, compute how long the LED is on (the time Δt of each pulse).
2) How much light energy is emitted during the entire LED light pulse? Hint: you first need to find the total photons emitted during the whole light pulse.

A container with mass m kg is dropped by a helicopter from height h km at time t=0, with zero velocity. from the outset, its fall is controlled by gravity and the force of air resitance, f(v)= -kv, where v is the current velocity of the container. in t seconds after the drop, a parachute opens, resulting in an increase of air resistance up to f(v) = -kv. determine the time t at which the container touches the ground. and its velocity at this moment. if m = 200 kg, h = 2000 m, t = 20 s, k = 10 kg/s, and k = 400 kg/s

Billiard ball A of mass mA = 0.122 kg moving with speed vA = 2.80 m/s strikes ball B, initially at rest, of mass mB = 0.145 kg . As a result of the collision, ball A is deflected off at an angle of θ′A = 30.0∘ with a speed v′A = 2.10 m/s, and ball B moves with a speed v′B at an angle of θ′B to original direction of motion of ball A.

1) Solve these equations for the angle, θ′B, of ball B after the collision. Do not assume the collision is elastic.

2)Solve these equations for the speed, v′B, of ball B after the collision. Do not assume the collision is elastic.

Consider three gas connected gas containers as shown in the figure below.

Consider three gas connected gas containers as shown in the figure below.

CO2 (g) P = 2.13, V = 1.50L

H2(g) P = 0.861 atm, V = 1.00 L

Ar (g) p = 1.15atm, V = 2.00L

   T = 298K

Assume, that you open the two stopcock so that the gases can flow freely.

Calculate the change of the chemical potential of the entire system due to mixing the gases.

Using the change of the chemical potential of gases show that the mixing of three gases is spontaneous

Determine the value of D_mixH .

_mix = ______________________

_mixH = _____________________

1. Consider the following expression:

Everyone who is nice to all dogs is loved by somebody.

∀x (∀y dog(y) ⇒ Kind(x,y)) ⇒ (∃y Loves(y,x))

Demonstrate how to convert it to CNF. You should get:
( dog(F(x)) v (Loves(G(x),x)) ^ (~nice(x,F(x)) v Loves(G(x),x))

Step 1: Remove the biconditionals and implications.

Step 2: Move the negations inward.

Step 3: Standardize variables

Step 4: Skolemize

Step 5: Drop universal quantifiers

Step 6: Distribute v over ^

Expand 1.00 mol of a monatomic gas, initially at 3.60 kPa and 313 K, from initial volume V_i = 0.723 m³ to final volume V_f = 2.70 m³. At any instant during the expansion, the pressure p and volume V of the gas are related by p = 3.60 exp[(V_i - V)/a], with p in kilopascals, V_i and V are in cubic meters, and a = 2.10 m³. What are the final (a) pressure and (b)temperature of the gas? (c) How much work is done by the gas during the expansion? (d) What is the change in entropy of the gas for the expansion? (Hint: Use two simple reversible processes to find the entropy change.)

Requirements: Code in C++. With given information, write the solution to this problem so that it is understandable to someone with basic knowledge of C++ (ex: only keep basic libraries, keep coding shortcuts to a minimum). Also leave comments in the code (plz), the logic behind solving this problem if possible, and explanation of what the keys to solving this problem is and how to run test cases to ensure correctness of code.

Problem:

For this problem you will compute various running sums of values for positive integers.

Input

The first line of input contains a single integer P, (1 <=P <=10000), which is the number of data sets that follow. Each data set should be processed identically and independently. Each data set consists of a single line of input. It contains the data set number, K, followed by an integer N, (1 <= N <= 10000).

Output

For each data set there is one line of output. The single output line consists of the data set number, K, followed by a single space followed by three space separated integers S1, S2 and S3 such that: S1 = The sum of the first N positive integers. S2 = The sum of the first N odd integers. S3 = The sum of the first N even integers.

Sample Input

3

1 1

2 10

3 1001

Sample Output

1 1 1 2

2 55 100 110

3 501501 1002001 1003002  

A Solution that needs to be rewritten so it can be understood more easily

/*
 * Sum Kind Of Problem
 * Compute running sums of odds, evens and all integers
 * Does it 2 ways... using formulas and loops.
 * Define EASY_WAY for formulas
 * Define HARD_WAY for loops
 * Define both of them to show both results
 */
#include <stdio.h>
#include <stdlib.h>

#define EASY_WAY
#undef LONG_WAY

int main()
{
        int n, i, v, k;
#ifdef LONG_WAY
        int oddsum, evensum, sum, j;
#endif

        scanf("%d", &n);
        for(i = 1; i <= n; i++){
                scanf("%d %d", &(k), &(v));
#ifdef EASY_WAY
                printf("%d %d %d %d\n", i, v*(v+1)/2, v*v, v*(v+1));
#endif
#ifdef LONG_WAY
                oddsum = evensum = sum = 0;
                for(j = 1; j <= v; j++){
                        evensum += j*2;
                        oddsum += j*2 - 1;
                        sum += j;
                }
                printf("%d %d %d %d\n", i, sum, oddsum, evensum);
#endif
        }
        return(0);
}

Design an experiment to determine the amount of charge on a balloon. List the equipments, procedures, and equations that would be used.

Why is cyclohexane used as a solvent in this experiment instead of water? Water is much safer and much cheaper.