Let Q1, Q2, Q3, Q4 be constants so that R (2x + 3) sin 4x dx = (Q1x + Q2) sin 4x + (Q3x+Q4) cos 4x+C, where C is a constant of integration. Let Q = ln(3 +|Q1|+ 2|Q2|+ 3|Q3| + 4|Q4|). Then T = 5 sin2 (100Q)

satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T < 3. — (D) 3 ≤ T < 4. — (E) 4 ≤ T ≤ 5.

Find the Taylor series or polynomial generated by the following functions

a. )f(x) √ x centred at x=4 , of order 3

b.) f(x) cosh x= e^x+e^-x/(2), centred at x=0

c.) f(x) = x tan^-1x^2 , centred at x=0

d.) f(x) = 1/(√1+x^3) , centred at x=0 , of order 4

e.) f(x) = cos(2x+pie/2) centred at x= pie/4

Richard is trying to decide what combination of gum and mints to buy. Gum costs half as much as mints. If no mints are purchased, he can buy 6 pieces of gum. If no gum is purchased, he can buy 3 mints. What is the total utility if Richard buys 2 mints and 4 pieces of gum?

Mints Utility Gum Utility

1 29 1 15

2   56 2 29

3   81 3 42

4 --- 4 54

5 --- 5 65

6 --- 6 75

solve the following

1. solve the following inequality for X
2x^2 +5x <3

2. without solving the equation 2x^2 +5x =3, how would I know that it has two rational solutions.

3. 3^2(x+1) - 8.3^x+1 = 1

4. log (x+1) + log x =1

4.1. show that the above equation will have a irrational root if the base is changed to 2, and a rational root if the base is changed to 4

5. the sum of squares of two consecutive even intigers is 1 252. find the intigers

6. suppose x, 2x+1 and 3x+2 are consecutive terms in a geometric sequence. calculate x and hence find the other two terms. how can you be sure the answer is correct?

7. The sizes of angles of a triangle is in proportion 1:2:3. find the size of each angle.

1. Insomnia, a coffee bean broker, has 4 warehouses from which it can ship to 3 main buyers. The demand for coffee beans at buyer 1 is 800 pounds, at buyer 2 it is 1000, and at buyer 3 it is 500. Each warehouse holds an inventory of 2000 pounds of coffee beans. The warehouses can only ship coffee beans in full pounds. Given the transportation costs below, they need to determine how product should be shipped between the warehouses and the retailers in order to minimize total cost.

Transportation Costs ($)

a. Write a formulation for this problem, following the 4 Step approach. (Include this in your submission too)

b. Carry work over to Excel and solve via Excel Solver and report on findings:

• What is the total cost?

• How many units should be shipped between each warehouse and buyer pair?

Red-green color blindness is due to an X-linked recessive allele in humans. A widow’s peak (a hairline that comes to a peak in the middle of the forehead) is due to an autosomal dominant allele.

Consider the following family history:

• A man with a widow’s peak and normal color vision marries a color-blind woman with a straight hairline.

• The man’s father had a straight hairline, as did both of the woman’s parents.

Use the family history to make predictions about the couple’s children.

Drag the correct label to the appropriate location in the table. Not all labels will be used.

1. If the couple has a child, what is the chance that it will be a son with a widow's peak?

2. What is the chance that any son the couple has will be color blind with a straight hairline?

3. What is the chance that any daughter the couple has will be colorblind with a widow's peak?

4. Suppose the couple had a daughter with normal color vision and a widow's peak. What is the chance that she is heterozygous for both genes?

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CAPITAL BUDGETING

In December 2019, Bob Prescott, the controller for the Blue Ridge Mill, was considering the addition of new on-site long-wood woodyard. The addition would have two primary benefits: to eliminate the need to purchase short-wood from an outside supplier and create the opportunity to sell short-wood on the open market as a new market for Worldwide Paper Company (WPC). The new woodyard would allow the Blue Ridge Mill not only to reduce its operating costs but also to increase its revenues. The proposed woodyard will utilise new technology that allows tree-length logs, called long-wood, to be processed directly, whereas the current process required short-wood, which had to be purchased from the Shenandoah Mill.

This nearby mill, owned by a competitor, has excess capacity that allows it to produce more short-wood than it needs for its own pulp production. The excess is sold to several different mills, including the Blue Ridge Mill. Thus, adding the new long-wood equipment would mean that Prescott would no longer need to use the Shenandoah Mill as a short-wood supplier and that the Blue Ridge Mill would instead compete with the Shenandoah Mill by selling on the short-wood market. The question for Prescott was whether these expected benefits were enough to justify the $18m capital outlay plus the incremental investment in working capital over the six-year life of the investment.

Construction would start within a few months, and the investment outlay would be spent over two calendar years: $16m in 2020 and the remaining $2m in 2021. When the woodyard begins operating in 2021, it would significantly reduce the operating costs of the mill. These operating savings would come mostly from the difference in the cost of producing short-wood on-site versus buying it on the open market and were estimated to be $2m for 2021 and $3.5m per year thereafter.

Prescott also planned on taking advantage of the excess production capacity afforded by the new facility by selling short-wood on the open market as soon as possible. For 2021, he expected to show revenues of approximately $14m, as the facility came on-line and began to break into the new market. He expected shortwood sales to reach $20m in 2022 and continue at the $20m level through 2026. Prescott estimated that the cost of goods sold (before including depreciation expense) would be 75%.

In addition to the capital outlay of $18m, the increased revenues would necessitate higher levels of inventories and accounts receivable. Therefore the amount of working capital investment each year would equal 15% of incremental sales for the year. At the end of the life of the equipment, in 2026, all the networking capital on the books would be recoverable at cost fully.

Taxes would be paid at a 30% rate, and the equipment depreciation is to be calculated on a straight-line basis over the six-year life to zero balance. However, the new equipment is estimated to have a salvage value (scrap value) of $3m at the end of its life. WPC’s accountants have told Prescott that depreciation charges could not begin until 2021, when all the $18m had been spent and the equipment is in service.

WPC has a company policy to use 15% as the hurdle rate for such investment opportunities. The hurdle rate is based on the study of the company’s cost of capital conducted 5 years ago.

Required:

1. Prepare cash flow statement/s and compute the NPV and IRR of the proposed project. Comment on the feasibility of the project.

2. Outline reasons why Prescott may be uneasy using the 15% hurdle rate for a discount rate.

On January 1, 2018, Corp X issued 3%, 3 ½ year Bonds to the public, and also signed a 3 and 1/2 -year lease with PH Corp. Payments of $10,000 on the lease are made at the end of the year for years 1,2 and 3 and ($5,000 in the last period; year 4.) There are no provisions for a bargain purchase or an extension of the lease term. The asset has a fair value of $35,000 and has a useful economic life of 4 years. Corp. X is rated as a BBB rated company by Moody’s Investors-a rating company. Additional Facts 1-BBB Market Interest rates: Date of issue on 12/31/2019

Date of issue                         on 12/31/2019

Year 1     2%                               1.5%

Year 2    2.5%                            2.0%

Year 3    2.75%                          2.5%

Year 4    3,5%                             3.0%

Year 5     4.0%.                           4.0%

1- What is the implicit rate (IRR)on the lease?

2- What type of lease is this?

3- What are the balance sheet effects of this lease on 1/1/18 and 12/31/18?

4-what is the lease expense in 2018?

5-Present the cash flow effects of this lease for 2018.