Tutor profile: Debashree B.
Subject: Linear Algebra
Find the remainder when the polynomial x4 - 3x^2 + 7x - 10 is divided by x - 2 A. -20 B. 10 C. 8 D. 0 E. 1
According to Reminder theorem, if a polynomial in variable X is divided by (x-y) and 'y' is a real number, then the reminder is the value of the polynomial at x = y Putting 2 into the polynomial given above, we get the value (2)^4 - 3*2^2 + 7*2 -10 = 8 Hence , option C is the right anser
A man wants to buy some pens and pencils. The number of pens, p, and the number of pencils, c, are related by the equation 4p+3c=111. If the man spent $168 to buy p pens, where each pen costs an integer value between $6 and $8, inclusive, what could be the number of pencils that he bought? A. 1 or 9 B. 3 or 9 C. 4 or 6 D. 4 or 8 E. 5 or 9
The student can approach getting solution to this through elimination of wrong choices. Since the value of the pen is an integer, it can be either $6, $7 or $8 (as $6 and $8 and both inclusive here). Consider value of pen = $6 in this case, the total number of pens bought = $168/6 = 28 We can solve the value of 'c' by putting in p = 28 in the equation above. Upon putting p = 28 in the equation, we see that 4*28>111 thus the above equation doesn't hold true for value of pen = $6 We then consider value of pen = $7.. This gives us value of one pen = $168/7 =$24 Upon putting p =24 in the equation, we get $4*24+3*c = 111 or c = 5 This is one of the options we should get in the answer. Since option E above is the only option in which 5 is an answer, we can go ahead with selecting option E as the answer
Subject: Corporate Finance
Imagine that a company follows discounted Pay-back period method to analyse whether to invest in a project. The cut off period is 2 years or less. Required rate of return is 10%. Given below are the two projects with cash flows and time of cash flow as follows. Analyse if the company should go ahead with investing in the following projects.(C0, C1, C2 etc mention the cash flow in periods 0,1,2(years) etc respectively with 0 signifying the present year):
Answer: we know that, for considering investment in any project, the present value of its future cash flows are calculated. Since the company's pay-back period is two years or less,it will consider present value of its future cash flows only for the first two periods(2 years in this case), The present value of any amount is calculated as : Value of cash flow/(1+rate of return)^nth time period Hence, For project 1, present value of its cash flows for the next two years are as follows: Present value of Cash outflow in period 0 = C0 = 2000 Present value of Cash inflow in Period 1 = C1 = 500/(1+10/100)^1 = 455 Present value of Cash inflow in Period 2 = C2 = 500/(1+10/100)^2 = 413 As the present value of the project is the sum of the present values of its total cash flows in the 2-year period,project 1's present value = -2000+495+413 = -1131 (negative). Negative present value above(-1131) signifies that the company gets a negative investment if it goes ahead with the project and hence, should not proceed with the project. Going with the logic above,for project 2, the present value of cash flows are as follows: Present value of Cash outflow in period 0 = C0 = 2000 Present value of Cash inflow in Period 1 = C1 = 500/(1+10/100)^1 = 455 Present value of Cash inflow in Period 2 = C2 = 1800/(1+10/100)^2 = 1488 Project 2's total present value = -2000+455+1488 = -57 (negative) The negative value shows that the company should not invest in project 2 either. Hence , the company should not invest in any of the projects.
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