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Let's start by solving for p and q using the given equations:

Given:

x = va(sinu + cosv)

y = va(cosu - sinv)

z = 1 + sin(u - v)

To find p and q, we need to eliminate u and v from the equations. Here's how we can do it:

1. Square both sides of the first equation:

x^2 = v^2a^2(sinu + cosv)^2

2. Square both sides of the second equation:

y^2 = v^2a^2(cosu - sinv)^2

3. Add the squared equations together:

x^2 + y^2 = v^2a^2(sinu + cosv)^2 + v^2a^2(cosu - sinv)^2

4. Expand and simplify the equation:

x^2 + y^2 = v^2a^2(sin^2u + 2sinucosv + cos^2v) + v^2a^2(cos^2u - 2sinvcosu + sin^2v)

5. Combine like terms:

x^2 + y^2 = v^2a^2(sin^2u + cos^2u + sin^2v + cos^2v) + 2v^2a^2(sinucosv - sinvcosu)

6. Simplify further using trigonometric identities:

x^2 + y^2 = v^2a^2 + 2v^2a^2(sin(u + v))

7. Now, let's look at the equation for z:

z = 1 + sin(u - v)

8. Square both sides of the equation:

z^2 = (1 + sin(u - v))^2

9. Expand and simplify the equation:

z^2 = 1 + 2sin(u - v) + sin^2(u - v)

10. Substitute the value of z from the original equation:

z^2 = 1 + 2sin(u - v) + sin^2(u - v)

11. Simplify further:

z^2 = 1 + 2sin(u - v) + (1 - cos^2(u - v))

12. Simplify even more:

z^2 = 2 - cos^2(u - v) + 2sin(u - v)

13. Rearrange the equation:

cos^2(u - v) = 2 - z^2 - 2sin(u - v)

14. Substitute the value of sin(u - v) from the equation derived in step 6:

cos^2(u - v) = 2 - z^2 - 2v^2a^2

15. Take the square root of both sides:

cos(u - v) = ±√(2 - z^2 - 2v^2a^2)

16. Now, let's find sin(u - v) using the equation derived in step 6:

sin(u - v) = (x^2 + y^2 - v^2a^2) / (2va^2)

17. Substitute the values of cos(u - v) and sin(u - v) into the equation for x:

x = va(sinu + cosv)

18. Substitute the values of sin(u - v) and cos(u - v) into the equation for y:

y = va(cosu - sinv)

19. Simplify the equations further and solve for p and q:

p = arcsin((x - y) / (2va))

q = arccos((x + y) / (2va))

These are the values of p and q based on the given equations. Please note that there may be other solutions or constraints depending on the specific values of x, y, z, v, and a.

What do we know so far about why the spider family’s offspring have different traits for silk flexibility?

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1. The circular flow diagram is a model used to demonstrate how a given economic system functions through the interactions of 1st agent of economics and 2nd agent of economics. Identify the roles of each of these actors through a set of example.

Using a suitable diagram, draw and elaborate  the Circular Flow Diagram (Physical and non-Physical flow) in economies.        

What is Social Psychology?

Corteo nuziale o wa linto

Prima che inizi la processione del consenso, i due futuri sposi eseguono una processione sungkeman o semah-ureung-chik per entrambi i genitori. La sposa, affiancata dai suoi due attendenti (peunganjo), si avvicina ai suoi genitori. Solo allora la futura sposa viene scortata dal peunganjo per sedersi nella navata e attendere l'arrivo dello sposo e del suo entourage. Sungkeman viene anche portato dai suoi genitori dallo sposo per chiedere benedizioni prima di andare a casa della sposa. Lungo la strada, lo sposo e tutto il seguito hanno cantato benedizioni.

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Dopo che la famiglia della sposa ha visto l'arrivo dello sposo e del suo entourage, la famiglia lo ha preso in braccio e ha restituito le rime. Nella reciproca processione pantun, la famiglia dello sposo non può perdere, perché se perde, la processione non può continuare. Ma se la famiglia dello sposo vince in rima, il corteo successivo è lo scambio di foglie di betel da parte dei genitori degli sposi.

On 01 July 2022, Persian Ltd acquired 551,250 ordinary shares of Sumo Ltd, that is, Persian Ltd holds 70% shares in Sumo Ltd. The purchase consideration was as follows:

• Cash paid $ 950,000
• A deferred cash settlement to be paid in three years’ time of $ 475,000
• By an exchange of one share in Persian Ltd for every four shares in Sumo Ltd. The market price of Persian Ltd share at the date of acquisition was $ 2.95 and the market price of each Sumo Ltd share at the date of acquisition was $ 3.15

Legal fees associated with the acquisition were $ 10,500.

The discount rate of Persian Ltd is 10 %.

(a) Calculate the fair value consideration (Costs of investment) transferred to acquire control of Sumo Ltd at the date of acquisition. Your answer should include a brief explanation if any of the above issue(s) is/are not required to be accounted in your working(s).                    

Pittman Company is a small but growing manufacturer of telecommunications equipment. The company has no sales force of its own; rather, it relies completely on independent sales agents to market its products. These agents are paid a sales commission of 15% for all items sold.

Barbara Cheney, Pittman’s controller, has just prepared the company’s budgeted income statement for next year as follows:
 

*Primarily depreciation on storage facilities.

As Barbara handed the statement to Karl Vecci, Pittman’s president, she commented, “I went ahead and used the agents’ 15% commission rate in completing these statements, but we’ve just learned that they refuse to handle our products next year unless we increase the commission rate to 20%.”

“That’s the last straw,” Karl replied angrily. “Those agents have been demanding more and more, and this time they’ve gone too far. How can they possibly defend a 20% commission rate?”

“They claim that after paying for advertising, travel, and the other costs of promotion, there’s nothing left over for profit,” replied Barbara.

“I say it’s just plain robbery,” retorted Karl. “And I also say it’s time we dumped those guys and got our own sales force. Can you get your people to work up some cost figures for us to look at?”

“We’ve already worked them up,” said Barbara. “Several companies we know about pay a 7.5% commission to their own salespeople, along with a small salary. Of course, we would have to handle all promotion costs, too. We figure our fixed expenses would increase by $3,900,000 per year, but that would be more than offset by the $5,200,000 (20% × $26,000,000) that we would avoid on agents’ commissions.”

The breakdown of the $3,900,000 cost follows:

“Super,” replied Karl. “And I noticed that the $3,900,000 equals what we’re paying the agents under the old 15% commission rate.”

“It’s even better than that,” explained Barbara. “We can actually save $119,600 a year because that’s what we’re paying our auditors to check out the agents’ reports. So our overall administrative expenses would be less.”

“Pull all of these numbers together and we’ll show them to the executive committee tomorrow,” said Karl. “With the approval of the committee, we can move on the matter immediately.”

Required:

1. Compute Pittman Company’s break-even point in dollar sales for next year assuming:

a. The agents’ commission rate remains unchanged at 15%.

b. The agents’ commission rate is increased to 20%.

c. The company employs its own sales force.

2. Assume that Pittman Company decides to continue selling through agents and pays the 20% commission rate. Determine the dollar sales that would be required to generate the same net income as contained in the budgeted income statement for next year.

3. Determine the dollar sales at which net income would be equal regardless of whether Pittman Company sells through agents (at a 20% commission rate) or employs its own sales force.

4. Compute the degree of operating leverage that the company would expect to have at the end of next year assuming:

a. The agents’ commission rate remains unchanged at 15%.

b. The agents’ commission rate is increased to 20%.

c. The company employs its own sales force.

Use income before income taxes in your operating leverage computation.

Give an example of when you might utilise Microsoft Excel's Fill tool and describe its function.

a) Start by writing the equation of the circle. (Recall that the general form of a circle with the center at the origin is x2 + y2 = r2. 

b) Now solve this equation for y. Remember the roller coaster is above ground, so you are only interested in the positive root.

2. Graph the model of the roller coaster using the graphing calculator. Take a screenshot of your graph and paste the image below, or sketch a graph by hand

Model 1: One plan to secure the roller coaster is to use a chain fastened to two beams equidistant from the axis of symmetry of the roller coaster. You need to determine where to place the beams so that the chains are fastened to the rollercoaster at a height of 25 feet.

3. Write the equation you would need to solve to find the horizontal distance each beam is from the origin.

4. Algebraically solve the equation you found in step 3.Round your answer to the nearest hundredth.

5. Explain where to place the two beams. 

Model 2: Another plan to secure the roller coaster involves using a cable and strut. Using the center of the half-circle as the origin, the concrete strut can be modeled by the equation and the mathematical model for the cable is. The cable and the strut will intersect.

6. Graph the cable and the strut on the model of the roller coaster using the graphing calculator. Take a screenshot of your graph and paste the image below, or sketch a graph by hand. 

7. Algebraically find the point where the cable and the strut intersect. Interpret your answer. 

Model 3: Another plan to secure the roller coaster involves placing two concrete struts on either side of the center of the leg of the roller coaster to add reinforcement against southerly winds in the region. Again, using the center of the half-circle as the origin, the struts are modeled by the equations and. A vertical reinforcement beam will extend from one strut to the other when the two cables are 2 feet apart.

*Recall that a reinforcement beam will extend from one strut to the other when the two struts are 2 feet apart.

10. Explain where to place the beam.

Hi, what years are these lecture notes from please?