What are they I dont understand ( I have the formulas a

What are they? I don\’t understand πŸ™ I have the formulas and the basic knowledge of summation, but I don\’t know how to apply them or use them.

Thank you!


here, this is what you need… http://www2.seβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

(2) Alternating Harmonic Series Revisited What is wrong

(2) Alternating Harmonic Series Revisited What is wrong here: Multiply both sides of the alternating harmonic series S = 1- Β½ +1/3 ? ΒΌ +1/5 -1/6 +1/7 -1/8 +1/9 -1/10 +1/11 -1/12 +? By 2 to get 2S = 2 -1+2/3 -1/2+2/5-1/3+2/7-1/4+2/9-1/5+2/11-1/6+? Collect terms with the same denominator (match the colors, etc …) to get 2S =1-1/2 +1/3 -1/4 +1/5 -1/6 +?= S. Dividing by S gives 2 = 1.


Here \”S\” is equals to zero, so we cannot divide out \”S\” from both sides from the equation \”2S=S\”. So if we simplify it we get,




Which means sum oβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ: β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

(a) When a 4.50-V battery is connected to the plates of

(a) When a 4.50-V battery is connected to the plates of a capacitor, it stores a charge of 19.0 C. What is the value of the capacitance?

(b) If the same capacitor is connected to a 10.0-V battery, what charge is stored?


a) Q = C V

19 uC = C x 4.50 V

C = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆ) β–ˆ = β–ˆβ–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

Refer to Case Study Minimizing Biases in Performance E

Refer to Case Study :

Minimizing Biases in Performance Evaluation at Expert Engineering, Inc. it states that under various engineer titles, veteran engineer demetri worked for expert engineering inc. for almost 15 years. The firm\’s performance evaluation history is both unique and long. He has recently been promoted to the postion of principle at the engineering firm. All principles are involved in evaluating engineers because the founders of the firm believed in multiple source evaluation and feedback to prevent favoritism and promote a merit based culture . At the same time, the firm has a long history of using quality performance appraisal forms and review meeting to better ensure accurate performance evaluation. Several months ago, however the firm initiated a big hiring initiative of a dozen new engineers, nine of whom turned out to be graduates from Purdue university, which is the same university from which demetri graduated. Indeed , demetri was active in moving forward the hiring initiatives. There is tension and discontent among the other principles, who fear that a time of unchecked favoritism, baised performance rating and unfair promotion decisions is on the rise.


– Situation analysis (SWOT analysis)

– Assumptions and missing information: A case will not contain all the information that you would like it to have to decide. You may need to document what information is not included in the case, why it is important, and how you will get it

– Statement of the problem: You need to include a clear statement of the problem(s) or issue(s) facing the organization

– Develop alternatives: Once we have determined the nature of the problem, we can start thinking about ways to solve it

– Evaluation of alternatives: You need to examine the set of solutions generated in step four to determine which one to recommend

– Implementation plan: You should consider what tasks must happen to make the recommended solution work

– Evaluation and control: Who will monitor the implementation of the recommended solution and determine whether it is working?


SWOT Analysis:

Assumptions and Missing Information: The performance analysis of the employees hired from Purdue university has not been mentioned and it is being assumed that they are not as talented as the other employees in the company.

Statement of Problem: Does inclining towards favoritβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ, β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ: β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ:

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ:

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ:

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ:

I need to write a Procedure in Maple to convert Scalar

I need to write a Procedure in Maple to convert Scalar Functions from Cartesian to Polar coordinates.


1 Plug the values for r and ? into the equation x = r*cos? to find x. For example, given the polar point (1, p/4), x = 1*cos(p/4) which is x = 1/sqrt(2). 2 Plug the values for r and ? into the equation y = β–ˆβ–ˆβ–ˆ*β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ, β–ˆ = β–ˆβ–ˆ*β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ(β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ) β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ(β–ˆβ–ˆ)β–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ (β–ˆ, β–ˆ)β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ, β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ (β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ(β–ˆβ–ˆ), β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ(β–ˆβ–ˆ))β–ˆβ–ˆβ–ˆ

Ros Corporations flexible budget cost formula for indir

Ros Corporation\’s flexible budget cost formula for indirect materials, a variable cost, is $0.90 per unit of output. If the company\’s performance report for last month shows a $500 unfavorable spending variance for indirect materials and if 8,000 units of output were produced last month, then the actual costs incurred for indirect materials for the month must have been:



Here spending variance is $500 unfavourable which means actual amount spent exceeds the budgeted amount by $500.

Budgeted cost = 8000 x 0.9 = $β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ + β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ = $β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

Consider a 100 gallon tank containing 4 lbs of salt dis

Consider a 100 gallon tank containing 4 lbs of salt dissolved in water. Suppose a brine of .25 lbs of salt per gallon of water is entering the tank at 3gal/min, and the well mixed solution exits the tank at the same rate. Find an expression for the amount of salt A(t) in the tank at time t.



A(t)=4+.75x-(β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ(β–ˆ+β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ)) β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ =)β–ˆβ–ˆ

An Oil Rig is located a 10 miles from a straight coast

An Oil Rig is located a = 10 miles from a straight coastline. An Oil Refinery is located 16 miles down the coastline. The cost of putting in a pipeline from the Oil Rig to the Oil Refinery depends on whether it is on land or in the water. Rather than coming directly to the shoreline and then turning at a Right Angle, suppose that the Oil Pipeline met the shore at a point b = 6 miles from the \”Right Angle\”. If the cost is $10000 per mile for land and $17000 per mile for water, what is the cost of the Pipeline?


Distance covered in land = 16 x

Distance covered in water = sqrt(100 + x^2)

So the equation becomes

cost, C = 10000(16 x) + 17000(sqrt(100 + x^2))

Differentiate wrt x & equate to zero

dC/dx = -10000 + 17000 * x (100 + x^2)^-1/2 = 0

17000* x (100 + x^2)^-1/2 = 10000

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ* β–ˆ = β–ˆβ–ˆβ–ˆβ–ˆ(β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ + β–ˆβ–ˆβ–ˆ^β–ˆβ–ˆβ–ˆ)^β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ^β–ˆ = β–ˆβ–ˆβ–ˆβ–ˆ(β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ + β–ˆ^β–ˆβ–ˆβ–ˆ)

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ^β–ˆβ–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆ

β–ˆβ–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ(β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ &#β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ; β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ) + β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ(β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ(β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ + (β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ)^β–ˆ))

β–ˆβ–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ + β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆ = $ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

According to this chapter, family ownership structure d

According to this chapter, family ownership structure doesn\’t transfer well across generations. What is the suggested approach to mitigate this challenge?


Answer to the question:

Many families face challenges transferring the business ownership across future generations. The problems such as distribution of assets equally among the children or giving fair distribution of assets to the knowledgeable and eligible child may be faced by the families. In future, the uneven distribution may lead to clashes among the children. To avoid this, the suggested approach, in my view, would be the strategic asset allocation among the children. The active β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ, β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ, β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

A rigid cylinder contains 7.0 g of nitrogen at 20 degre

A rigid cylinder contains 7.0 g of nitrogen at 20 degrees Celsius. What is the minimum amount of heat energy that must be removed to liquefy the nitrogen.


Heat Energy H = Cp * m * T

H = Heat Energy Cp = Heat Capacity m = mass (in Kg)

T = change in temperature (in Celsius)

Heat of Condensation (Equal to Vaporisation)

H = Hc * m

Hc= Heat of condensation m= mass (in moles)

Heat Capacity of nitrogen = 0.743 kJ/kg*K.

Nitrogen is a liquid at -196 C,

so T = -196 – 20 = -216

H = Heat Capacity * β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ * β–ˆ

β–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ*β–ˆ * β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆ * β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ

β–ˆ= β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ * β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ (β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ)

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆ =β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆ β–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆ= β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ*β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ * β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ + β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ = β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ

β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ