Math - Others Questions

11 12 Use Green s Theorem to evaluate f xe dx x dy where C is the positively oriented boundary of the region bounded by the curves y x x 2 and the x axis You must use this method to receive full credit

8 10 Evaluate fff 15xydz dx dy where E is the region bounded by 0 y 1 y x 2y 0 z 2 x y

7 10 Evaluate the iterated integral TT TU SS si 0 x sin y dy dx by reversing the order of integration

3 8 Let z x20 y10 dz where x e5t and y sin 2t Use the Chain Rule to find dt when t k TU

9 10 Evaluate the line integral f xy 3 ds where C is the curve y x 0 x 1

5 15 Use Lagrange Multipliers to find the absolute maximum of f x y z x subject to the constraint x y z z 1

6 10 Find the directional derivative of the function f x y 13exy at the point 1 0 in the direction of the vector v 3 4

7 Find the area of the triangle with sides u 0 6 0 v 4 4 4 and u v

4 10 Find an equation of the tangent plane to the surface sin xyz at the point 7 1

2 5 Give a parametric representation for the line through the point 2 5 3 that is perpendicular to both u 1 1 2 and the x axis

3 Find the range of values for x 6x 18 TE 4x 2 0 5 W 42 X 44 L 10

A company estimates that its sales will grow continuously at a rate given by the function S t 12e where S t is the rate at which sales are increasing in dollars per day on day t a Find the accumulated sales for the first 8 days b Find the sales from the 2nd day through the 5th day This is the integral from 1 to 5 a The accumulated sales for the first 8 days is Round to the nearest cent as needed

Find the area of the region bounded by the graphs of the given equations y 4x y x x 0 x 2 B C 2 S 4x x dx S dx S dx The area is

Find the area of the region bounded by the graphs of the given equations y x y x OA OB Set up the integral s that will give the area of the region Select the correct choice below and fill in any answer box e to complete the choice S S dx 0 25 dx 0 25 Q

Which answer lists the original data represented in the stem and leaf plot below 56789 5 6 2 23 3 7 83 8 52 58 58 63 63 70 80 97 52 58 58 63 63 97 52 58 63 97 52 58 58 63 63 7 8 97

A recent graduate s student loans total 18 000 If these loans are at 5 compounded quarterly for 8 years what are the quarterly payments

The data below represent the length in miles of a random sample of tornadoes in a specific represents the number of miles a particular tornado was on the ground Use the data to complete parts a throug below Click the icon to view the table of tornado lengths a Draw a histogram of the data and comment on the shape Choose the correct histogram below O C O A Relative Frequency 0 6 0 4 0 24 0 0 6 12 18 Length in miles 24 Q Q Table of cell phone bills OB Relative Frequency 0 6 0 4 0 2 0 Tornado Length in miles 1 08 2 50 0 10 0 51 4 70 5 59 0 59 8 95 2 45 0 51 7 88 2 09 1 06 20 34 5 66 5 52 0 52 23 37 0 72 0 97 3 41 2 06 8 57 0 36 5 28 0 19 0 85 0 49 0 48 7 09 1 76 0 52 1 34 14 68 0 21 0 10 2 17 13 77 0 10 4 83 0 87 1 01 0 75 2 38 1 82 3 98 0 26 1 20 1 83 6 42 0 73 5 69 6 76 4 42 1 71 0 48 3 44 6 21 3 54 1 16 7 74 1 17 8 47 0 50 0 16 9 66 0 37 1 01 0 10 1 95 0 10 0 21 0 10 9 36 0 41 1 13 8 23 0 11 3 36 0 10 0 6 18 12 Length in miles 4 99 1 82 3 47 0 10 0 12 0 24 Q Q 5 Relative Frequency 0 4 0 2 X 0 0 3 6 9 12 15 Length in miles Q Q G

A company determines that its weekly online sales S t in hundreds of dollars t weeks after online sales began can be estimated by the equation below Find the average weekly sales for the first weeks after online sales began S t 4e The average weekly sales amount is

Jessica rents a booth to sell her necklaces at a craft fair She uses the function p x c x k to determine the profit she will make if she sells different numbers of necklaces at the craft fair The expression part c x k of the function has c and k representing constants What did Jessica most likely use k to represent The cost to make each necklace The price she charges for each necklace at the fair The cost of participating in the craft fair The profit from participating in the craft fair

3 y In x 3 3 Ay 8 4 2 6 2 2 2 6

Solve the given trigonometric equation analytically Use values of x for 0 x 2 64 cos x 16 0 X radians Simplify your answer Type an exact answer using as needed Type your answer in radians Use integers or fractions for any numbers in the expression Use a comma to sepa

Solve the equation on the intervall 0 2x 12 sec x 16 0 of 10 po This question 3 points The solution set is Type an exact answer in terms of z Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression

ations Question 5 of 10 What is the analytical solution Solve the given trigonometric equation analytically and by use of a calculator Compare results Use values of x for 0 x 2 2 cos x cosx 1 This quiz 30 point s possible This question 3 point s possi X Type an exact answer using as needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression What is the solution using a calculator Round to two decimal places as needed Use comma to separate answers as needed

ations Question 10 of 10 This quiz 30 point s possible This question 1 point s possible Solve the following trignometric equation analytically and by use of a graphing calculator Compare the results Use values of x for 0 x 2 2 sin 2x cosxsin x 0 GILD Type an exact answer using zas needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression Simplify your

Solve the equation on the interval 0 0 2x 2 sin 28 7 sin 0 5 0 Question 6 of 10 This quiz 30 point s possible This question 3 point s possible Sub What is the solution in the interval 0 0 2x Select the correct choice and fill in any answer boxes in your choice below OA The solution set is Simplify your answer Type an exact answer using x as needed Type your answer in radians Use integers or fractions for any numbers in the expression Use a comma to separa as needed OB There is no solution

Find all solutions in the interval 0 2 2 sin 2x cos x sinx 0 X Type an exact answer using as needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the

Solve the given trigonometric equation analytically Use values of x for 0 x 2 16 sin x 4 0 nus possible This question 3 point s possible x radians Simplify your answer Type an exact answer using a as needed Type your answer in radians Use integers or fractions for any numbers in the expression Use a com

question 2 point s possible Solve the following trignometric equation analytically using identities if necessary for exact values if possible for values of x for 0 x 2 11 tanx 9 10 1 tan x x Type an exact answer using zas needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression Simplify your answ

3 12 pts A frozen pizza has a temperature of 30 F and is placed into a 72 F room After 15 minutes the temperature of the pizza has risen to 40 F a Use Newton s Law of Cooling to find the function that models the pizza s temperature T as a function of time t

In this question we will use a spreadsheet to approximate the root of f x x 5 3x 3 9 using Newton s method with x0 1 The picture below shows a spreadsheet being used to perform the calculation A downwards arrow indicates the contents from the cell above will be copied down 1 2 3 4 A A1 B1 C1 B C Using a spreadsheet find the following values x1 ANSWER Give your answer to at least 3 decimal places x2 ANSWER Give your answer to at least 3 decimal places

4 Describe in proper order the transformations you would apply to the grap graph of your parabola STANDARD FORM TO VERTEX FORM 5 Use your graph in demos to list the a and c values of your parabola Calculate the b value by using the formula 2ah Write your relation in standard form using the values of a b and c and then complete the square to determine the vertex form a b C K4 The standard form of my relation is

Acme Industries had sales last year of 12 000 000 They had expenses of 9 755 000 They purchase several pieces of new equipment during the year that Cost 3 000 000 to purchase Had 1 100 000 related costs to set up install etc Has a salvage value of 750 000 in 5 years Using MACRS calculate the amount of tax owed 375 500 400 780 425 000 484 500

Consider laminar boundary layer flow past the square plate arrangements in the figure below Compared to the friction drag on a single square how much larger is the drag of the four plates together as in configurations a and b

possible scenarios XYZ Low Low 200 500 0 1 500 High 600 600 400 1000 BC High Is there a dominant strategy for ABC If there is what is it and why If none why 3 pts Is there a dominant strategy for XYZ If there is what is it and why If none why 3 pts What is the likely pair of decisions What payoff will each receive 4 pts

The main cross cable between towers of a coastal suspension bridge is 60 cm in diameter and 90 m long Estimate the total drag force on this cable in crosswind of 50 miles hour Is the flow laminar or turbulent Hint Use Fig 11 31 on page 595 of our textbook to find the drag coefficient S 400 200 100 60 40 20 10 6 4 2 1 0 6 0 4 0 2 0 1 0 06 10 1 24 CD R 100 101 102 Re Smooth cylinder 103 Smooth sphere 11 8 THE DRAG COEFFICIENT 104 Drag coefficients for a sphere and long cylinder Fig 11 31 105 Rough cylinder 106

A store orders 800 units of a product every 4 months If the product is steadily depleted to 0 by the end of each 4 months the inventory on hand I at any time t during the year is shown in the figure to the right What is the average number of units on hand for a 4 month period Inventory units on hand 800 MM 4 8 12 16 t Time months Write an inventory function assume that it is continuous for the first 4 months The graph is a straight line joining 0 800 and 4 0 The inventory function for the first 4 months is 1 0

Consider an employee s whose earnings in dollars are according to the continuous strea f t 5 000e0 1 for t 0 where t is measured in years How many years will it take them to earn a combined total e 100 000 Give your answer in years to the nearest year Sorry that s incorrect Try again

A coal mining company models the income derived from the continuous production of coal as a continuous income stream using a function f t where f t 250e 0 15t where t 0 The function f t is measured in thousands of dollars per year and I is measured in years Calculate the total income derived from mining coal in the first three years Give your answer in thousands of dollars to the nearest thousand dollars Do not include commas or the dollar symbol in your answer Provide your

For the change equation dy dx find the regions where y is an increasing function of x and where y is a decreasing function of x Give your answers as intervals in the form Use the symbol oo for infinity U for combining intervals and an appropriate type of parentheses depending on whether the interval is open or closed Enter if the interval is empty Express numbers in exact form Use symbolic notation and fractions where needed y is increasing when y E y is decreasing when y E

Using the on line psychrometric chart calculate the absolute humidity in kilograms of a room containing 47kg dry air with a relative humidity of 52 and a dry bulb temperature of 21 C Round your answer to three decimal places at the answer only Answer in numbers only No units Your Answer

Assume two satellites A B are in the same orbital plane Compute the in plane satellite positions XA YA for A and XB YB for satellite B given rA is 26 705 km and re is 27 512 km and the true anomaly fA 22 8 and B fB 95 3 respectively Compute the coordinate XA O 50987 651 km 5132 254 km 24618 355 km

Assume two satellites A B are in the same orbital plane Compute the in plane satellite positions XA YA for A and XB YB for satellite B given rA is 26 705 km and rp is 27 512 km and the true anomaly fA B 22 8 and fB 95 30 respectively Compute the coordinate YB O 30687 251 km 7645 897 km 27394 378 km

Assume two satellites A B are in the same orbital plane Compute the in plane satellite positions XA YA for A and XB YB for satellite B given rA is 26 705 km and B is 27 512 km and the true anomaly fA 22 80 and f 95 30 respectively Compute the baseline distance between the two satellites O 27892 km O 12547 km 32065 km 10786 km

From the data given in the Table below compute the Z for the geodetic coordinates X Y Z for GPS receivers located at stations P on the WGS84 coordinate system Station P 40 44 29 N 7845962 32 m 4142317 304 m 1263457 78 m 074 10 40 W Geodetic Height h 17 929 m

Acme Industries had sales last year of 12 000 000 They had expenses of 9 755 000 They purchase several pieces of new equipment during the year that Cost 3 000 000 to purchase Had 1 100 000 related costs to set up install etc Has a salvage value of 750 000 in 5 years Using straight line depreciation what are the taxable earnings 1 789 000 1 850 000 1 910 000 1 987 655

The data from a simple random sample with 25 observations was used to construct the plots given probability plot that was constructed has a correlation coefficient of 0 975 Judge whether a t interval could be constructed using the data in the sample Click here to view the normal probability plot and the boxplot Click here to view the table of critical values of the correlation coefficient The normal probability plot 0 975 and the boxplot Round to three decimal places as needed the data could come from a normal population because outliers so a t interval be constructed

This is a new version of the question Make sure you start new workings Calculator not allowed Bookwork code 58 Fill in the gaps to factorise this expression 16m 8 8

President s Opponent s height cm height cm 183 172 183 176 188 168 190 190 175 170 189 169 186 192 180 179 23 24 Print President s Opponent s Di height cm height cm 188 194 170 173 181 169 182 169 Done 160 177 187 185 190 193 160 168 196 200 President s height ble for election heights Question 24 of 24 d data for the heights of a certain country s presidents and their main opponents in the election campaign Construct a scatterplot rrect graph below OB Opponents height 200 160 160 President s height 200 TT OC 200 160 160 This test 24 point s possible This question 1 point s possible Does there appear to be a correlation between the president s height and his opponent s height 200 President s height O D 200 Resume later Submit test 160 160 200 President s height Q O E

The line graph shows the goals per game average for a sporting series during the years shown During what year s shown was the average number of goals per game less than 2 6 During the year s the average number of goals per game was less than 2 6 Use a comma to separate answers as needed Ave of Goals per Game Goals per Game Average Q 3 8 3 2 2 6 2 1976 Submit test 1984 1992 2000 Year

The horizontal bar graph shows the population of the world s largest cities including their suburbs How much larger to the nearest million is City J than City H City A City B City C City D City E City F City G City H City I City J 0 5 World s Largest Cities 10 15 20 25 Population in millions City J is larger than City H by million people 30 35