1.The graph of ​(x-1)^2+(y-1)^2=4 is shown on the right. Use implicit differentiation to find the slopes of the tangent lines at the points on the graph where x=2.2 .   Check your answers by visually estimating the slopes on the graph in the figure.

2.Use implicit differentiation to find y′. Then evaluate y′ at (2,1)

x^4-16y^3=ln y

What is the partial fraction decomposition of 5x^2/((x+1)(x^2+3x+2)(x^2+4))

A. Long Run vs. Short Run (40 pts) X=(1/2)L^1/4K^3/4, wL=$2, wK=$96 (dX/dL=(1/8)L^-3/4K^3/4,

dX/dK= (3/8)L^1/4K^-1/4              

1.(2 pts)________________________________ For the point L=16 and K=81, what isoquant are we on?

2.(3 pts)___________________________________ From this point (L=16, K=81), to produce the same amount of X at a cheaper cost, should we use more L and less K OR less L and more K? Explain.

3. (3 pts)_________________________________Find the equation for the output expansion path.

4. (3 pts)_________________________________ Find the long run total cost function (total cost as a function of X alone)

5.(3 pts)_________________________________ Suppose K is stuck at K=16 in the short run. Find the short run total cost function. (total cost as a function of X alone) (Hint: Problem is easier if you keep answers in fractions)

6. (12 pts) Complete the following table for Point A, Point B, and Point C. (Fraction answers are possible)

Point A: The cheapest way to produce X=64

Point B: The cheapest way to produce X=64 when K is stuck in the short run at K=16

Point C. When we're producing X that gives us the lowest average cost when K is stuck in the short run at K=16

A. Long Run vs. Short Run (40 pts) X=(1/2)L^1/4K^3/4, wL=$2, wK=$96 (dX/dL=(1/8)L^-3/4K^3/4,

dX/dK= (3/8)L^1/4K^-1/4              

1.(2 pts)________________________________ For the point L=16 and K=81, what isoquant are we on?

2.(3 pts)___________________________________ From this point (L=16, K=81), to produce the same amount of X at a cheaper cost, should we use more L and less K OR less L and more K? Explain.

3. (3 pts)_________________________________Find the equation for the output expansion path.

4. (3 pts)_________________________________ Find the long run total cost function (total cost as a function of X alone)

5.(3 pts)_________________________________ Suppose K is stuck at K=16 in the short run. Find the short run total cost function. (total cost as a function of X alone) (Hint: Problem is easier if you keep answers in fractions)

6. (12 pts) Complete the following table for Point A, Point B, and Point C. (Fraction answers are possible)

Point A: The cheapest way to produce X=64

Point B: The cheapest way to produce X=64 when K is stuck in the short run at K=16

Point C. When we're producing X that gives us the lowest average cost when K is stuck in the short run at K=16

Plastech Inc. is operating its business in Oman for many years. They are manufacturers and suppliers of different plastic articles. They are now planning to open up a web store through which, people will be able to order online and receive their goods. This online business will however require initial investment for developing the system and hiring new staff for receiving orders and delivery. This initial investment is estimated to be OMR 160,000. Information on the expected additional revenues and costs (salaries of staff, website administration etc) for next 6 years is given below:

Assuming that annual interest rate is 8% per annum and compounded annually.

a) Draw a cash flow diagram, based on the scenario given.

b) Calculate the NPW of all the future cash flows, as given above.

c) Calculate the FW at the end of year 2026 of the given cash flows.

sigmaX=11 sigmaX^2=39 sigmaY=24    sigmaY^2=164 sigmaXY=79

part a:

1.what is the predictor variable?

2. what is the criterion variable?

compute the Pearson correlation.

3. what is the covariance.

4 what is the standard deviation of the predictor variable.

5 what is the standard deviation of the criterion variable.

6 what is the Pearson's r value

7. what is the best interpretation of your Pearson correlation in Q6? A. as hours studied goes up there is a corresponding increase in score on quiz. B. As hours studied goes up there is a corresponding decrease in score on quiz.

8. The strength of the above relationship is considered.    A, weak b. moderate    c. strong.

Part B. compute the regression equation.

9. what is the numeric value for the slope?

10. what is the y-intercept?

11. what is the regression equation?

12. predict the total number of points on the quiz for a person studying 4 hours.

You find the following Treasury bond quotes. To calculate the number of years until maturity, assume that it is currently May 2016. The bonds have a par value of $1,000.

In the above table, find the Treasury bond that matures in May 2026. What is the coupon rate for this bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Coupon rate      

You find the following Treasury bond quotes. To calculate the number of years until maturity, assume that it is currently May 2016. The bonds have a par value of $1,000. Rate Maturity Mo/Yr Bid Asked Chg Ask Yld ?? May 26 103.5488 103.6370 +.3041 2.369 5.324 May 31 104.4978 104.6435 +.4317 ?? 6.173 May 41 ?? ?? +.5431 4.071 In the above table, find the Treasury bond that matures in May 2026. What is the coupon rate for this bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Coupon rate %

Use counting sort, sort the following numbers: 4, 2, 5, 4, 2, 3, 0, 2, 4, 3

On October 15, 2020, the board of directors of Ensor Materials Corporation approved a stock option plan for key executives. On January 1, 2021, 20 million stock options were granted, exercisable for 20 million shares of Ensor's $1 par common stock. The options are exercisable between January 1, 2024, and December 31, 2026, at 80% of the quoted market price on January 1, 2021, which was $15. The fair value of the 20 million options, estimated by an appropriate option pricing model, is $3 per option. Ensor chooses the option to recognize forfeitures only when they occur.

Ten percent (2 million) of the options were forfeited when an executive resigned in 2022. All other options were exercised on July 12, 2025, when the stock’s price jumped unexpectedly to $39 per share.

Required:
1. When is Ensor’s stock option measurement date?
2. Determine the compensation expense for the stock option plan in 2021. (Ignore taxes.)
3. Prepare the journal entries to reflect the effect of forfeiture of the stock options on Ensor’s financial statements for 2022 and 2023.
5. Prepare the journal entry to account for the exercise of the options in 2025.

Please provide explanation for each part