Math - Others Questions

As a tornado moves its speed increases The function S d 90 log d 70 relates the speed of the wind S in miles per hour near the center of a tornado to the distance that the tornado has travelled d in miles Determine the distance that a tornado has travelled if the speed of the wind at the center of the tornado reaches 150 miles per hour

4 Sketch the graph of the polynomial function f x that has a zero at 2 of order 3 a zero at 4 order 2 two zeros of order 1 at 1 and 5 and a positive leading coefficient This function also passes through the point 3 16 a Determine the specific equation for f x in factored form

3 Evaluate each of the following Answers and solutions must be expressed as exact values no decimals a 2log2 2log5 2log3 log 25 b

2 Solve each of the following a 2x 1 x 2x

8 Let f x x 3 and g x x 9 Develop and algebraic and graphical model for the following f x g x y

9 Evaluate the limit if it exists 9x lim x 0 2x 5x

2 This amortization table shows the first 3 payments of William s mortga Payment Monthly Interest Principal Outstanding number payment paid paid balance 0 1 2 3 789 25 789 25 789 25 534 12 533 32 532 51 a How much money did William borrow b How much is their monthly payment 255 13 255 93 256 74 170 000 00 169 744 87 169 488 93 169 232 20

1 Tristan plans to pay back a loan of 230 000 in 5 years He makes quarterly payments at the end of each quarter The bank charges 7 8 per year compounded quarterly K4 Determine Tristan s quarterly payment using a TVM solver N 1 PV PMT FV P Y C Y DMT END EGIN

3 This amortization table shows the first 3 payments and the last 3 payments on mortgage Payment Monthly number payment 0 1 2 3 238 239 240 1343 20 1343 20 1343 20 1343 20 1343 20 1343 20 Interest Principal paid paid 976 66 974 67 972 67 21 63 14 46 7 25 366 55 368 53 370 53 b How much interest is paid 1321 57 1328 74 1335 95 a What is the total amount paid on the mortgage Outstanding balance 180 000 00 179 633 45 179 264 92 178 894 39 2664 70 1335 95 0 00

Reminder of the Equations you need to know FOR SIMPLE INTEREST I I pxrxt FUTURE VALUE OF AN ANNUITY F R 1 1 i 1 For COMPOUND INTEREST A P 1 i PRESENT VALUE OF AN ANNUITY R1 1 1 1 1 i PVR PRESENT and FUTURE VALUE CALCULATOR 1 Sue decided to invest the 1500 in savings from her part time job into a 6 month short term investment account at the bank The account earns 4 5 simple interest per year Show your work by hand a What is the accumulated amount of the investment at the end of the 6 months Interest Principal K 13 b How much simple interest was earned A 2 2 After working all summer Ryan plans on investing a portion of his savings to purchase a car in 3 years Determine the amount of summer savings he should invest now at an interest rate of 5 4 compounded semi annually if he wants to K 4 hand

Given A student of weight Fw who runs at a known speed of vo grabs a cord and swings out over a lake He releases the rope when his velocity is zero 0 R A p Find a Draw a COMPLETE free body diagram FBD of the student as he swings on the rope using the normal and tangential coordinate system b The equations of motion from the FBD in part a c The angle when he releases the rope as an expression of the given values Fw vo p etc d The tension Fe in the cord just before he releases it e Draw a COMPLETE free body diagram FBD of the student as he swings on the rope using the radial and transverse coordinate system Please assume that point C is the origin of the radial and transverse coordinate system Solution

When Albertina opened her law office she bought 19 000 worth of law books and 6800 worth of furniture She pai 1500 down and agreed to amortize the balance with semiannual payments for 5 years at 11 compounded semiannually Find the amount of each payment Then use the formula for the remaining balance to find the number of remaining payments when the loan has been reduced below 9000 What is the amount of each payment 0 Round to the nearest cent as needed How many payments remained when the loan had been reduced below 9000

Write any fractions like this 5 2pi Here is the graph of a sin wave function y 4sin x 1 4pi 2 1 Origin horizontal vertical e g pi 2 2 High value 3 Low value 4 Value of interval A 5 Value of interval B 6 Value of interval C 7 Value of interval D 8 Value of interval E High T A Low Given the

Application Simple Interest Rate Interest Principal x Time 4 INTEREST RATE An investment of 6000 paid 540 00 in SIMPLE INTEREST over a 2 year period Calculate the interest rate State your answer as a PERCENTAGE rounded to 1 decimal place 0 045 Knowledge Compound Interest 0 45 4 5 5 Penny Saver purchased a Canada Savings Bond in the amount of 1400 The interest on 84 7 12 For COMPOUND INTEREST A P 1 i 6 Penny Saver purchased a Canada Savings Bond in the amount of 1400 The interest on the bond was 5 7 compounded monthly She has the bond for 7 years What is i 0 457 0 0457 0 00457 7 Penny Saver purchased a Canada Savings Bond in the amount of 1400 The interest on the bond was 5 7 compounded monthly She has the bond for 7 years What is A or the total that the bond is worth after 7 years 3302 45 2053 36 59748 23 8 A car loan payment of 5000 is due in 4 years The bank will accept payment today at a discounted interest rate of 7 interest compounded quarterly If the payment was made today how much it be 3466 81 2981 12

1 340 is invested at the end of every 6 months for 7 years into an account that earns 4 9 interest per annum compounded semi annually What is i 0 0245 2 340 is invested at the end of every 6 months for 7 years into an account that earns 4 9 interest per annum compounded semi annually What is n 2 45 0 245 14 7 42 3 340 is invested at the end of every 6 months for 7 years into an account that earns 4 9 interest per annum compounded semi annually Calculate the Future Value 5367 23 5998 45 5597 58 4 Payments of 231 are made monthly for 3 years at 12 interest compounded monthly What is i 0 001 0 01 0 1 36 5 Payments of 231 are made monthly for 3 years at 12 interest compounded monthly What is n 24 12 6 Payments of 231 are made monthly for 3 years at 12 interest compounded monthly Calculate the Present Value 6954 83

You have charged 1 950 on a credit card that charges 14 interest If you want to make 25 monthly payments how many payments will you have to make to pay off this charge That is how many months will it take you to pay off the charge Round up to the month 7

8 A new car is purchased at a cost of 25000 The value of the car deprecia rate of 30 per year C 13 T a Write an equation to represent the value of the car after n years b What is the value of the car after 3 years c What is the value of the car after 6 years 3

6 24 30 36 4 6 Table 2 8 10 48 W M Part 0 2 192 Part 1 of 2 240 288 7500 5000 3750 3000 a Identify the table that displays direct variation and find the direct variation equation matching

Match the following Down Payment Fixed Rate Appreciation Amortization Mortgage Annuity Principal Future Value Application 1 5 6 7 8 2 An RRSP is an example of a 3 A mortgage with a constant interest rate one that doesn t change over time 4 A loan used for real estate property The amount still owed on a mortgage A series of equal payments or deposits made at regular intervals over a fixed period of time The rate at which the value of an item increases in value over time A lump sum of money paid towards the cost of a home to decrease the mortgage amount The time it takes to fully pay back a mortgage

1 Consider the 2 dimensional vector field F given by F x y e cos y e sin y Show that F is not globally invertible but that F is locally C invertible about every x y R

Draw a valid conclusion from the given premises He was told that he had to shape up or ship out He didn t shape up Therefore Click the icon to view tables of standard valid and invalid forms of arguments Which conclusion is valid O He didn t have to ship out O He had to ship out O He shaped up None of the above

Construct a truth table for the statement p q Complete the truth table below P q P q p q p q

Katie wants to create a rectangular frame for a picture She has 60 inches of material If she wants the length to be 3 more than 2 times the width what is the largest possible length Write an equation and solve O6w 6 60 21 2w 3 4 60 15 A 6w 6 60 9 4 2w 3 60 6

A laboratory designed a radio telescope that had a diameter of 280 ft and maximum depth of 46 ft a Write an equation of a parabola that models the cross section of the dish if the vertex is placed at the origin and the parabola opens up b The receiver must be placed at the focus of the parabola How far from the vertex should the receiver be located a The equation of the parabola is Simplify your answer Use integers or fractions for any numbers in the equation b The receiver should be located at approximately ft above the vertex Type an integer or decimal rounded to the nearest tenth as needed 53

Determine whether the equation is homogeneous if it is solve it If there is an initial value find the particular solution satisifying the initial value 1 y y x x 2 y xy y 2 x 2 y 1 2

Solve the following differential equations 1 y y 6y 0 2 y 2y 0

Find the explicit general solution of the differential equation If an explicit solution cannot be found an implicit solution is acceptable If there is an initial value find the solution to the initial value problem 1 y xye x 2 yy 4x y 1 3

The accompanying data shows the fossil fuels production fossil fuels consumption and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015 Complete parts a and b Click the icon to view the energy consumption a Develop line charts for each vanable and identify the characteristics of the time series that is random stationary trend seasonal or cyclical What is the line chart for the variable Fossil Fuels Production OA Fuss Fuels Prod 100 1945 Your 2015 Fess Fusts Prod B 100 1945 Year 2015 O C Fossil Fues Pr 100 1945 Your 2015 Fossil Fuel Pres D FOOD 1945 Year 2015 Year 1949 9 1950 1951 1952 1953 1954 1955 1956 10 1957 11 2958 12 1959 13 1980 14 1961 15 1967 15 1963 1964 1965 1966 1967 1968 22 1969 23 1920 24 1971 25 1972 16 1975 27 1974 28 1975 1975 1977 1978 1979 1980 1981 1982 29 30 31 32 7 a 4 15 6 J W 17 NE 39 20 12 33 34 35 Fossil Fueh Production Fossil Fuel Consumption Total Energy Consumption 28 748176 32562667 3579151 34 976732 35 349936 35 76433 37 36368 39 771452 40133484 37216337 39045218 39869117 40 307136 41781845 44 IRIZED 45 788951 47234902 50 035557 52597132 54306187 56 285569 59186071 504758 58937904 18241491 56 330758 54 733273 54 722896 55100782 55074118 58005609 59007873 58 529320 57457822 29 002099 31 631956 34008105 33 799903 34 826156 393275 37 410105 38 888151 38 925593 38716707 40 550068 42 136751 42 758245 44 08077 46500283 48 54305 50 576504 53 513987 15126873 55 50247 61 361751 63522289 54595645 67 69588 70 31386 0 62 905124 65356532 9 107176 70 991129 71893522 72 890521 69 827758 675 1093 65888374 11 981503 34615768 3697403 36 747825 37 564468 35 639382 40 307971 41 754252 41 787186 41 545028 43 465722 45 086455 45 737817 47 825437 49 644195 51 814788 54 015001 57014352 58904521 62 414507 651402 67618325 69 282843 72687967 7568569 75 962365 71 964553 75 974826 7796133 79 950406 80 858584 78 066668 76105776 25 099185 T F 1980 56 5753 060333 76647 1987 57 1667 6852067901545 1988 5 875 715571 2 7092 1989 57 4827 72 9112 84786 1990 585506 22 3322 84 485 1991 5 8717 71 8803 24 414 1903 57 6551 73 3052 1783 1993 55 0221 74 8357 87 4236 1994 58 0416 76 2564 85 0013 1995 575401 77 259591 0291 1996 58 3872 79 7847 140222 1997 58 8567 808755 56 6022 1998 593141 RE369950120 1999 576145 82 4272 652 2000 57366 4 790688145 2001 58 5413 82 9018 96 1882 2002 568557 8699 97 6451 2009 560320 04 0335 97342 2004 55 9423 85 8188 10010 2005 55 044 57943 100282 2006 55 9379 34 702 99 6295 2007 56 4556 86 2114 101 314 2008 57 587 H35521 292929 2009 56 5703 78 4966 04101 2010 54 2066 81 4121 400104 2011 60 5490 79 4469 968417 2013 07 3028 77 4868 54 416 2013 64 2015 754396 97157 2014 89 6526 8024 383174 2015 702208 79 3297 973436

The table shows the distribution of the number of motor vehicles per household Find the cumulative distribution for the table Use a value of 5 to stand for 5 or more vehicles No of Motor Vehicles 0 1 2 3 4 5 or more Proportion 0 17 0 26 0 31 0 16 0 09 0 01 Cumulative Percent Find the mean median and mode for the table If an answer does not exist enter DNE Round your mean to two decimal places mean motor vehicles median mode motor vehicles motor vehicles

Suppose that for a certain exam a teacher grades on a curve 24 2 2 0 1 13 6 13 6 30 20 lo fl lo 20 3 It is known that the mean is 65 and the standard deviation is 10 There are 45 students in the clas Frequency 34 1 34 1 What score would be necessary to obtain an A hovo 2 2 0 1

Suppose that people s heights in centimeters are normally distributed with a mean of 170 and a standard deviation of 5 We find the heights of 90 people You may need to use the standard normal distribution table Round your answers to the nearest whole number a How many would you expect to be between 170 and 180 cm tall people b How many would you expect to be taller than 177 cm people

A normal distribution has a mean of 85 1 and a standard deviation of 4 84 Find the data value corresponding to the value of z given Enter your answer to four decimal places z 0 85

The diameter of a pipe is normally distributed with a mean of 0 8 inch and a variance of 0 0004 What is the probability that the diameter of a randomly selected pipe will exceed 0 84 inch You may need to use the standard normal distribution table Round your answer to three decimal places

Suppose that the breaking strength of a rope in pounds is normally distributed with a mean of 100 pounds and a standard deviation of 17 What is the probability that a certain rope will break before being subjected to 150 pounds You may need to use the standard normal distribution table Round your answer to four decimal places

A nurse is preparing to administer amoxicillin 100 mg PO every 8 hr to a toddler who weighs 20 kg The recommended dosage range is 20 to 25 mg kg day Which of the following actions by the nurse is appropriate The nurse administers the prescribed dosage The nurse determines the prescription is above the recommended dosage range The nurse contacts the pharmacist to adjust the prescribed dosage The nurse determines the prescription is insufficient to achieve the desired effect O

a cos 3 b sin a c tan 3x and cos 2 3x 13 2 3 tan a 2 CCXX a cos a 8 Type an exact answer using radicals as needed Simplify your answer Rationalize all denominators Use integers or fractions for any numbers in the expre sin Type an exact answer using radicals as needed Simplify your answer Rationalize all denominators Use integers or fractions for any numbers in the expr tan a all denominatore Lise inteners or fractions for any numbers in the expr

Since cos t is an even function rewrite cos t as cos t cos t

What is the oxidation state of N in HNO3 If the number is positive just put in number If it is negative put in number So if the answer is 2 put in 2 If the answer is 2 put in 2

The Spice of Life Restaurant Supplies has experienced growing sales and management is looking to expand They currently own a lot near Ponce City Market Management plans to do a marketing survey in the future to investigate whether it is a good location The survey cost will be 10 000 The lot was purchased two years ago at a cost of 1 500 000 Today the property could be sold for 2 000 000 because of the increase in real estate prices The land will have to be cleared at a cost of 40 000 The company can then construct a new building at an estimated cost of 3 200 000 including landscaping and parking Finally management will hire a new manager for the location with a salary of 100 000 What is the cost of this expansion project 5 350 000 4 850 000 4 750 000 5 340 000

A project provides cash inflows of 50 000 each year for four years What is the payback period if the cost is 220 000 3 4 years 4 50 years 4 38 years 5 50 years None of the above

Able Development is currently considering a project that will produce cash inflows of 40 000 a year for 10 years The cost of the project is 200 000 What is the profitability index if the discount rate is 12 percent 1 13 1 4126 4 0

A project has cash flows of 5 200 5 000 and 4 800 in years 1 2 and 3 If the cost is 15 000 and the required return is 12 what is the NPV 45 37 465 82 2 954 63 851 49

The cash flows for a project are as follows 1 000 000 500 000 400 000 200 000 and 50 000 fa years 0 1 2 3 and 4 What is the payback period 2 75 years 2 50 years 3 75 years 2 67 years None of the above

Your firm is considering two projects that are independent Both have standard cash flows and required return is 13 You have computed the IRRs and find the following IRR Project A IRR Project B 12 5 10 8 What is your recommendation Accept B Accept A Reject both A and B I cannot make a recommendation using the IRR criteria and B ent

A three year project has an initial requirement of 900 000 for fixed assets and 300 000 for net working capital The fixed assets will be depreciated to a zero book value over the 3 year life of the project The estimated salvage value is 120 000 All of the net working capital will be recouped at the end of the 3 years The annual operating cash flow is 700 000 and the discount rate is 10 percent The tax rate is 28 percent What is the cash flow in year 0 700 000 820 000 1 200 000 900 000

A firm is considering a project that requires 150 000 of fixed assets that are classified as 7 year property for MACRS What is the book value at the end of year 3 Year 1 2 3 4 5 6 7 8 14 29 24 49 17 49 12 49 8 93 8 93 893 4 45 84 405 18 732 91 830 65 595

dering two projects that are mutually exclusive You have computed the NPVs at the firm required return and find the following NPV Project A NPV Project B 190 896 240 622 What is your recommendation Reject both projects Accept B Accept A

A four year project is expected to generate revenues of 800 000 annual variable costs of 300 000 and fixed costs each year of 100 000 The annual depreciation is 100 000 and the tax rate is 20 percent What is the annual operating cash flow 129 000 260 000 325 000 340 000 Sm

A project requires an initial investment of 100 000 and has cash inflows of 15 000 each year for 30 years What is the NPV if the required return is 10 12 041 65 69 437 40 305 56 41 403 72

Exercise 2 van der Pol with parameter Consider the van der Pol oscillator with parameter 0 x y x X 1 7 2 3 Y f Solve the system numerically Show phase plane plots for 0 5 0 5 1 3 and 5 In each case evolve to time 15 starting at xo yo 2 2 to obtain the solution curve In each case the limit cycle should be apparent as the solution curve appears to nearly connect to itself in reality it just gets really close On each plot overlay the graph of the cubic y x on the interval 2 x 2 in another color