Questions

Evaluate the indefinite integral 4 4 cos x In secx C 4 sin x 14 tan

Consider the functions a x x 1 x b x 2 x 3 x Which statement is always true a x b x for all values of x a x b x for all values of x a x b x when x 0 a x b x when x 0

1 5 5 t atan 5 t 1 2 log 25 t 2 1 The answer above is NOT correct Use integration by parts to evaluate the integral Jarctan arctan 5t d

First make a substitution and then use integration by parts to evaluate the integral x cos x5 dx

Evaluate the indefinite integral

If g 1 3 g 5 9 and L 9 2 g x dx 9 evaluate the integral xg x d Apowe

Suppose a particle moves along a straight line with velocity v t t2e 3 meters per second after t seconds It travels meters during the first t seconds

Use integration by parts to evaluate the integral

Use integration by parts to evaluate the integral

Approximate 1 x3dx by using Simpson s Rule with N 6

If f is continuous and F f x dx 8 evaluate f 2x dx

A book publisher has fixed costs of 360 000 and variable costs per book of 9 00 The book sells 23 00 per copy How many books must be sold to break even If the fixed cost increased would the new break even point he higher or lower If the variable cost per unit decreased would the new break even point he higher or lower

Construct the vector 0 7 c 1 2 d having initial point P Use the tools provided to move and scale the given vectors then don t forget to draw your final answer 1 0 d X P G

George is 7 and his mother is 37 In how many years will his mother be 3 times as old as he is in 8 years old when George is is is mother wil be 45 Pete is 14 and his grandfather is 54 How many years ago was his grandfather 6 times as old as Pete 7 Years ago pete s grandfather

Suppose your data values are 10 12 15 18 10 and your center is 13 Complete the table Data value 10 12 Absolute deviation 30 1 The sum of the absolute deviations is 11 Par 15 18 10 20 50 3 Par X

1 2 y a Step 1 f x 22x 3 b Step 2 c Step 3 18

Courtesy of National Portrait Gallery Winslow Homer Breezing Up A Fair Wind 1873 1876

Assume a tax rate of 6 2 on 142 800 for Social Security and 1 45 for Medicare No one will reach the maximum for FICA Complete the following payroll register Use the percentage method to calculate FIT for this weekly period Use Table 9 1 Note Do not round intermediate calculations and round your final answers to the nearest cent FICA Employee Marital status Gross pay FIT Social Security Medicare Net pay Pat Brown S 2 800 2 349 15 173 60 40 60 237 65

Suppose the population of a city can be modeled by P t 12300e0 13t where t is the number of years since 2070 persons Meanwhile the number of doctors in the city can be modeled by D t 197 205t where t is the number of years since 2070 When will the ratio of doctors to persons be the greatest Between and the ratio of

162 over the interval 0 x co Find the local Consider the function f x 2x extreme values of the function on this interval This function has a loc Select an answer value equal to at x maximum minimum

Pat Maninen earns a gross salary of 3 000 each week Assume a rate of 6 2 on 142 800 for Social Security and 1 45 for Medicar a What are Pat s first week s deductions for Social Security and Medicare Note Round your answers to the nearest cent Social Security Medicare Deductions b Will any of Pat s wages be exempt from Social Security and Medicare for the calendar year Note Leave no cells blank be certain to enter O wherever required

Find an angle between 0 and 2 that is coterminal to 2 The angle is coterminal to JT 25 2 25

An object moves along a path defined by the curve y 2x Find the point on th path closest to the point 5 0

Suppose we want to minimize the sum of the squared deviations Let our data values be a b and let our point estimate be x The sum of the squared deviations can be expressed as f x a x b x 2 The squared deviations are minimized when the point estimate is a b 2 8 Suppose we have four data values a b c d The sum of the squared deviations can be expressed as g x The squared deviations are minimized when the point estimate is x

Part OT 4 A box with a square base and open top must have a volume of 442368 cm We wish to find the dimensions of the box that minimize the amount of material used First find a formula for the surface area of the box in terms of only x the length of one side of the square base

A coffeeshop in New York City determines that it can sell 4000 cups of coffee at a price of 1 50 but for every 1 increase in the price their sales will decrease by 4400 cups and for every 1 decrease their sales will increase by 4400 cups A function giving the revenue earned when the price of coffee is dollars per cup is R x

You wants to enclose a rectangular field with five internal partitions as shown If the area of the field must be 13400 square feet what dimensions will require the least fencing Note that the internal partitions also require fencing length width a The width should be feet and the length should be

The data represent the time in minutes spent reading a political blog in a day Construct a frequency distribution using 5 classes In the table include the midpoints relative frequencies and cumulative frequencies Which class has the greatest frequency and which has the least frequency 25 5 19 24 29 6 7 19 20 26 9 19 19 3 1 4 10 10 0 23 Complete the table starting with the lowest class limit Simplify your answers Class 0 5 Frequency Midpoint Relative Frequency Cumulative Frequency 4 2 5 0 2 4

4 Consider the following sequence of numbers tn 0 1 2 3 4 5 6 7 23 37 60 14 5 9 14 Find a recursion equation of the type tn formula for t in terms of n btn 1 ctn 2 for this sequence and fin

Use integration by parts to evaluate the integral

Use integration by parts to evaluate the integral arctan

Use integration by parts to evaluate the integral In In

3 84771 At least one of the answers above is NOT correct Evaluate the following indefinite integrals A 2e 5 1 20 ex dx 2x 5e x C ex B 2 5 da 2e dx 17

Use integration by parts to evaluate the integral 6x sin

Evaluate the indefinite integral e3x si

Use integration by parts to evaluate the integral In In 8x 8

Use integration by parts to evaluate the integral 22 co 2x cos 5

Entered 1 7 t 8 2 9 Answer Preview 1 7t 8 2 9 The answer above is NOT correct Evaluate the indefinite integral 1 dt 7t 8 2 9

Evaluate the indefinite integral

Use integration by parts to evaluate the integral

Find the average value of the function f t 2te for the interval 0 7 Answer

If f is continuous and f x dx 8 evaluate f 2x dx

If 4000 is invested at an interest rate of 5 25 per year compounded continuously find the value of the investment after the given number of years Round you answers to the nearest cent a 4 years b 8 years c 12 years

Graph by hand y 5 x 7 14 x 2 x 3 1 x 1 3

Sarah Jones earns 560 per week selling life insurance for Farmer s Insurance plus 4 of sales over 5 750 Sarah s sales this month four weeks are 24 500 How much does Sarah earn this month Note Round your answer to the nearest cent Amount earned

Pat Maninen earns a gross salary of 3 000 each week Assume a rate of 6 2 on 142 800 for Social Security and 1 45 for Medicare a What are Pat s first week s deductions for Social Security and Medicare Note Round your answers to the nearest cent Deductions Social Security Medicare b Will any of Pat s wages be exempt from Social Security and Medicare for the calendar year Note Leave no cells blank be certain to enter O wherever required

Calculate the gross earning Note Round your answer to the nearest cent Number of units Rate per Gross Worker produced unit earning Cruz 975 0 48

Complete the following table Commission Employee McCarthy Total sales rate Draw 288 000 8 8 200 End of month commission received

Robin Hartman earns 565 per week plus 2 of sales over 6 500 Robin s week sales are 10 700 How much does Robin earn Amount named

6 We can describe the sequence of the formation of a sedimentary rock as being weathering erosion transportation deposition lithification Where along this sequence would you place the pro glacial clays and the outwash deposits Why