Methanol liquid burns readily in air.


One way to represent this equilibrium is:
CH₃OH(l) + 3/2 O₂(g) <-------->CO₂(g) + 2 H₂O(g

We could also write this reaction three other ways, listed below. The equilibrium constants for all of the reactions are related. Write the equilibrium constant for each new reaction in terms of K, the equilibrium constant for the reaction above.

Which of the following are linear transformations?

Choose Linear Not Linear  The function f:ℝ3→ℝ2 defined byf([x y z]^T)=[x−y 3y+z]^T.

Choose Linear Not Linear  The function a:ℝ→ℝ such that a(x)=(x−1)+(x−2)^2.

Choose Linear Not Linear  The function g:M2,2(ℝ)→M2,2(ℝ) defined by g(A)=2A+[1 2

3 4] Here, M2,2(ℝ)) is the vector space of 2×2matrices with real entries.

Choose Linear Not Linear  The function h:ℝ2→ℝ defined by h([xy])=x^2−y^2.

Capital Rationing Decision for a Service Company Involving Four Proposals

Renaissance Capital Group is considering allocating a limited amount of capital investment funds among four proposals. The amount of proposed investment, estimated operating income, and net cash flow for each proposal are as follows:

The company's capital rationing policy requires a maximum cash payback period of three years. In addition, a minimum average rate of return of 12% is required on all projects. If the preceding standards are met, the net present value method and present value indexes are used to rank the remaining proposals.

Required:

1. Compute the cash payback period for each of the four proposals.

2. Giving effect to straight-line depreciation on the investments and assuming no estimated residual value, compute the average rate of return for each of the four proposals. If required, round your answers to one decimal place.

3. Using the following format, summarize the results of your computations in parts (1) and (2) by placing the calculated amounts in the first two columns on the left and indicate which proposals should be accepted for further analysis and which should be rejected. If required, round your answers to one decimal place.

4. For the proposals accepted for further analysis in part (3), compute the net present value. Use a rate of 15% and the present value of $1 table above. Round to the nearest dollar.

5. Compute the present value index for each of the proposals in part (4). If required, round your answers to two decimal places.

6. Rank the proposals from most attractive to least attractive, based on the present values of net cash flows computed in part (4).

7. Rank the proposals from most attractive to least attractive, based on the present value indexes computed in part (5).

8. The analysis indicates that although Proposal D  has the larger net present value, it is not as attractive as Proposal C  in terms of the amount of present value per dollar invested. Proposal D  requires the larger investment. Thus, management should use investment resources for Proposal C  before investing in Proposal D , absent any other qualitative considerations that may impact the decision.

Capital Rationing Decision for a Service Company Involving Four Proposals

Renaissance Capital Group is considering allocating a limited amount of capital investment funds among four proposals. The amount of proposed investment, estimated operating income, and net cash flow for each proposal are as follows:

The company's capital rationing policy requires a maximum cash payback period of three years. In addition, a minimum average rate of return of 12% is required on all projects. If the preceding standards are met, the net present value method and present value indexes are used to rank the remaining proposals.

Required:

1. Compute the cash payback period for each of the four proposals.

2. Giving effect to straight-line depreciation on the investments and assuming no estimated residual value, compute the average rate of return for each of the four proposals. If required, round your answers to one decimal place.

3. Using the following format, summarize the results of your computations in parts (1) and (2) by placing the calculated amounts in the first two columns on the left and indicate which proposals should be accepted for further analysis and which should be rejected. If required, round your answers to one decimal place.

4. For the proposals accepted for further analysis in part (3), compute the net present value. Use a rate of 15% and the present value of $1 table above. Round to the nearest dollar.

5. Compute the present value index for each of the proposals in part (4). If required, round your answers to two decimal places.

6. Rank the proposals from most attractive to least attractive, based on the present values of net cash flows computed in part (4).

7. Rank the proposals from most attractive to least attractive, based on the present value indexes computed in part (5).

8. The analysis indicates that although Proposal D  has the larger net present value, it is not as attractive as Proposal C  in terms of the amount of present value per dollar invested. Proposal D  requires the larger investment. Thus, management should use investment resources for Proposal C  before investing in Proposal D , absent any other qualitative considerations that may impact the decision.

Capital Rationing Decision for a Service Company Involving Four Proposals

Renaissance Capital Group is considering allocating a limited amount of capital investment funds among four proposals. The amount of proposed investment, estimated income from operations, and net cash flow for each proposal are as follows:

The company's capital rationing policy requires a maximum cash payback period of three years. In addition, a minimum average rate of return of 12% is required on all projects. If the preceding standards are met, the net present value method and present value indexes are used to rank the remaining proposals.

Required:

1. Compute the cash payback period for each of the four proposals.

2. Giving effect to straight-line depreciation on the investments and assuming no estimated residual value, compute the average rate of return for each of the four proposals. If required, round your answers to one decimal place.

3. Using the following format, summarize the results of your computations in parts (1) and (2) by placing the calculated amounts in the first two columns on the left and indicate which proposals should be accepted for further analysis and which should be rejected. If required, round your answers to one decimal place.

4. For the proposals accepted for further analysis in part (3), compute the net present value. Use a rate of 15% and the present value of $1 table above. Round to the nearest dollar.

5. Compute the present value index for each of the proposals in part (4). If required, round your answers to two decimal places.

6. Rank the proposals from most attractive to least attractive, based on the present values of net cash flows computed in part (4).

7. Rank the proposals from most attractive to least attractive, based on the present value indexes computed in part (5).

8. The present value indexes indicate that although Proposal D  has the larger net present value, it is not as attractive as Proposal C  in terms of the amount of present value per dollar invested. Proposal D  requires the larger investment. Thus, management should use investment resources for Proposal C  before investing in Proposal D , absent any other qualitative considerations that may impact the decision.

During the first month of operations ended July 31, Western Creations Company produced 80,000 designer cowboy hats, of which 72,000 were sold. Operating data for the month are summarized as follows:

During August, Western Creations produced 64,000 designer cowboy hats and sold 72,000 cowboy hats. Operating data for August are summarized as follows:

2 Cost of goods sold?

3-Cost of goods manufactured?

4-Inventory, July 31??

5-Total cost of goods sold?

6-Gross profit?

7-Selling and administrative expenses?

8-Income from operations??

(a) The n × n matrices A, B, C, and X satisfy the equation AX(B + CX) ?1 = C Write an expression for the matrix X in terms of A, B, and C. You may assume invertibility of any matrix when necessary.

(b) Suppose D is a 3 × 5 matrix, E is a 5 × c matrix, and F is a 4 × d matrix. Find the values of c and d for which the statement “det(DEF) = 1” can be valid. Explain your answer.

(c) Find all (real or complex) values of x such that the matrix GH is invertible, where G =

x^2, ?1

x , x ? 2

H = x ? 1 , ?2

1 , x + 1

Use the Method of Undetermined Coefficients to find the general solution

1) y''-3y'+2=cos(x)

2) y''-3y'+2=xe^x

The code below takes in values from LDR but only one LED is lit. The other 3 LEDs are always off. What can I do to correct this ?

#include "mbed.h"

AnalogIn ADC(A5);

BusOut myLEDs(D10, D11, D12, D13); //Using Bus out instead of DigitalOut for Group of signals in order to control multiple outputs  

PwmOut Led1(D10);

PwmOut Led2(D11);

PwmOut Led3(D12);

PwmOut Led4(D13);

int main(void)

{

    while(1)

    {

        float brightness;

      //LEDs.period(1);

        brightness= 1-ADC.read();

        float I_val;

        I_val =brightness*100;//Intensity value= I_val

        printf("light Level =%3.1f%%\n", I_val);//maximum of 5 significant figures and maximum of 2 decimal places.

        wait(1);

    Led1.period(1.0f);//period to be 1 second  

    Led2.period(1.0f);

    Led3.period(1.0f);

    Led4.period(1.0f);

    if(I_val<25)

    {

        Led1.write(0.0f); //duty cycle as 20% of 1 period (1 second)

        Led2.write(0.0f);

        Led3.write(0.0f);

        Led4.write(0.0f);

        break;

    }  

    else if(I_val >=25 && I_val <50)

    {

        Led1.write(0.25f);

        Led2.write(0.25f);

        Led3.write(0.25f);

        Led4.write(0.25f);        

        break;

    }

    else if(I_val >=50 && I_val <75)

    {

        Led1.write(0.50f);

        Led2.write(0.50f);

        Led3.write(0.50f);

        Led4.write(0.50f);

        break;

    }

    else if (I_val >=75 && I_val<100)

    {

        Led1.write(0.75f);

        Led2.write(0.75f);

        Led3.write(0.75f);

        Led4.write(0.75f);

        break;

    }

    else if (I_val == 100)    

    {       

        Led1.write(1);

        Led2.write(1);

        Led3.write(1);

        Led4.write(1);

        break;

    }

    else if (I_val<0 && I_val >100)

    {

        printf("ERROR!");

    }

    }

}

The task is to use mbed library with  Nucleo 64 bits STM32f303RE ARM board and the four red leds as lighting devices. There are five required levels of lighting, 1, 2, 3, 4 and off. The lighting level is controlled by the lightness/darkness detected by the LDR sensor, for example when it is very light, all the leds will be off, and when it is very dark all the four leds will be on. All the 5 levels of lighting will be corresponded to the evenly distributed ‘ReadIn’ value from the LDR. PWM control is not required for this task.

That is,  

[1.] when the darkness corresponding to 25% then one of the 4 led will be lit with 25% of duty cycle and  

[2.] when darkness is equivalent to 50% then the 2 of 4 LEDs will be lit with 50% duty cycle and   

[3.] when when darkness corresponds 75% then 3 of 4 LEDs will be lit with 75% duty cycle and    

[4.] with complete darkness all the 4 LEDs with be lit with 100% duty cycle of brightness

Depreciation by Three Methods; Partial Years

Perdue Company purchased equipment on April 1 for $65,070. The equipment was expected to have a useful life of three years, or 7,020 operating hours, and a residual valueof $1,890. The equipment was used for 1,300 hours during Year 1, 2,500 hours in Year 2, 2,100 hours in Year 3, and 1,120 hours in Year 4.

Required:

Determine the amount of depreciation expense for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, by (a) the straight-line method, (b) units-of-output method, and (c) the double-declining-balance method.

Note: FOR DECLINING BALANCE ONLY, round the multiplier to four decimal places. Then round the answer for each year to the nearest whole dollar.