Application of derivatives Questions and Answers

Northland down deep eno W WORK ONE

Henderson has 1890 00 budgeted for spending money on an upcoming trip to Country A and Country B Co ing at 1 20 per currency A and Country B s currency is trading at 1 50 per currency B She plans to spend mo he wants to have four times as much of currency A as currency B Get up and solve a system of equations to mo ain what the answer means in practical terms plete the equation that represents the total cost of purchasing currency Let x be the number of currency A and y ency B 2 y1 5 1890 00 not include the symbol in your answers Do not simplify Use integers or decimals for any numbers in the equati plete the equation that represents the relationship between the number of currency A and number of currency B Ex 1 5y 1890 0 not simplify Use integers or decimals for any numbers in the equation

Question 3 6 3 13 BE points O Points 0 of 5 1 took clothes to the cleaners three times last month First she brought 4 shirts and 1 pair of slacks and ht 6 shirts 3 pairs of slacks and 1 sports coat and paid 32 90 Finally she brought 4 shirts and 1 spo 15 How much was she charged for each shirt each pair of slacks and each sports coat 1 was charged ed for each shirt for each pair of slacks and for each sports cost

1 point Solve the initial value problem the solution is 1 co x c x 3x x x5 6x6 7x7 enter the following coefficients 0 1 2 3 5 6 0 12 4 x y 3y 0 y 0 0 y 0 1

Northland Cale I Ch 4 1 4 6 Assessment Linear Approximation Related Rates Graphing Name Go down deep enough into anything and you will find mathematics Dean Sehlieter SHOW WORK ON EACH PROBLEM FOR ANY PARTIAL CREDIT 10 pts each 5 Determine the linear approximation of f x at x a 0 and use it to approximate Leave your answer in reduced fraction form no calculator Show your steps 1CC to notimate 1 99 8 no calculator Show your steps

rthland Calc I Ch 4 1 4 deep enough into anyth ORK ON EACH PROBLEM

Let u 8 5 and v 10 3 Find v u a 18 8 b 18 2 C 2 2 d 2 8 e 8 2

A pi r sqrt r 2 n 2 a Find drldn for a cone With a lateral surface area A 1500T b Evaluate derivative When r 30 n 40

Hector pulls a rope attached to a wagon through a 3 meter tall pulley at a rate of 0 5 meters per second The handle on the wagon is 0 6 meters above the ground as shown in the figure below a Let x represent the distance from the dx wagon to the pulley Calculate dt when x equals 3 meters 7 pts 3 m 0 6 m

polynomial and use the factored P x x 3 x 2 20x

Given the region bounded by y 2x 3 1 y 8x 1 and x 0 Sketch this region using the window size of 0 3 2 17

If f x 9x 3 sin z 3 cos z then f x 9 9 3 Round your answer to the nearest hundredth 3 cos z cos z 3 sin z o and f 4

A ladder 10 ft long leans against a vertical wall If the lower end is being moved away from the wall at the rate of 6 ft sec how fast is the height of the top changing this will be a negative rate when the lower end is 6 feet from the wall The height of the top is changing at a rate of Simplify your answer ft sec 10 ft ft sec 10 ft when the lower end is 6 feet from the wall X y

The volume of a cantaloupe is approximated by V The radius is growing at the rate of 0 4 cm week when the radius is 7 1 cm How fast is the volume changing at that moment The volume is changing at a rate of about Round to one decimal place as needed weeks cm week cm cm week cm week

omework Section 7 3 omework Determine the quantity needed riangle must be the same to m

D A territory shares a 1 8 kilometer border with an area of about 6 87 square kilometers and has a maximum height of 423 meters a Determine the length of the border in mil b Determine the area of the territory in squ c Determine the height of the rock in feet

A restaurant has a main location and a traveling food truck The first matrix A shows the number of managers and associates employed The second matrix B shows the average annual cost of salary and benefits in thousands of dollars Complete parts a through c below Restaurant Food Truck a Find the matrix product AB AB Managers Associates 4 24 2 7 720 128 254 44 Simplify your answer A Salary Benefits Managers 42 Associates 23 8 4 B

K A basketball team sells tickets that cost 10 20 or for VIP seats 30 The team has sold 3210 tickets overall It has sold 163 more 20 tickets than 10 tickets The total sales are 61 940 How many tickets of each kind have been sold How many 10 tickets were sold COCOS

Abigall Henderson has 1890 00 budgeted for spending money on an upcoming trip to Country A and Country B Country A s currency is trading at 1 20 per currency A and Country B s currency is trading at 1 50 per currency B She plans to spend more time in Country A so she wants to have four times as much of currency A as currency B Set up and solve a system of equations to model this problem and explain what the answer means in practical terms Complete the equation that represents the total cost of purchasing currency Let x be the number of currency A and y the number of currency B x1 2 y1 5 1890 00 Do not include the symbol in your answers Do not simplify Use integers or decimals for any numbers in the equation Complete the equation that represents the relationship between the number of currency A and number of currency B 0 Do not simplify Use integers or decimals for any numbers in the equation

County A County B County C The population y in the year x of the counties listed is approximated by the given equations where x 10 corresponds to 2010 and y is in thousands Solve this system of equations and interpret the answer x 20y 66 x 10y 26 y 4 Points 2 of 4 Save What does the answer represent Select the correct choice below and if necessary fill in the answer boxes to complete your choice in the year OA Two counties had the same population of B All three counties had the same population of in the year C There will be infinitely many times when the three counties will have the same population D There will never be a time when all three counties have the same population D

Evaluate the indefinite integral 17 cos 25

Question 3 6 2 13 Write an augmented matrix for the following system of equations 5x 5y z 1 7x 9y 6z 8 y z 2 he entries in the matrix are www

Use an appropriate Half Angle Formula to find the exact value of the expression sin 22 5

Evaluate the expression under the given conditions cos 20 sin 0 0 in Quadrant III 5 13

Question 1 Multiple Choice Worth 4 points Federal Income Taxes and Piecewise Functions LC The graph of a piecewise function is shown 7 6 5 4 3 2 Q 9 5 N a 7 2 7 5 4 What is the end behavior of the function 1 OAs x 00 f x and as x O O As x f x and as xx 00 2 OAs x 00 f x and as x f x 00 As x f x and as x 00 0 f x 00 00 f x 00 32 4 5 6

Suppose the supply for a certain textbook is given by 2 demand is given by p 20 where p is the price and q is the quantity The graph of these equations is shown to the right Find the equilibrium quantity and the equilibrium price D and and the equilibrium price is number as needed 20 16 12 8 4 c Set the two expressions for p equal to each other and solve for q OD Find where the supply equation is equal to 20 The equilibrium quantity is 0 0 6 8 10 Quantity 27 Q 2

Find the real solutions of the following ed 4 3 2 x 6x 4x 3x 10 0

Use the Intermediate Value Theorem to show that th the zero correct to two decimal places 3 2 f x 9x 9x 3x 9 2 1

A small airplane starts flying at a constant speed of 287 km h on a heading of S65E A 82 km h wind is blowing from S81W Determine the ground velocity of the airplane Give direction as a quadrant bearing Include diagram showing the vector addition with your solution

The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on 0 Find the general solution of the given nonhomogeneous equation x 1 y x y x x y xy Y x 1 2 1 2 cos x y x sin x

Solve the differential equation by variation of parameters y 2y y et arctan t y t

5 points Let f x 1 f x 2 f 1 2x tan x sec x Find the following

1 Let I f x dx where f is the function whose graph is shown a Use the graph to find L2 R2 and M2 b Are these underestimates or overestimates of I c Use the graph to find 72 How does it compare with d For any value of n list the numbers Ln Rn Mn Tn and I in increasing order y 3 2 1 0 f 2 3 4 X

Andre invested 7000 in an investment paying 4 5 per annum compounded over eight years Would the interest earned on the investment after four years be one half of the nterest earned on the investment in eight years

Exercises Complete the exercises Show all work In 1990 the cost of a train ticket to go from Jonesville to Morsvilfe was 5 In 2000 the fare to travel the same distance increased to 12 Determine the average rate of increase of the train fare

32 What is an intermediate step a 2 cos x 1 cos x 1 0 b 2 cos x 1 cos x 1 0 c 2 cos x 1 cos x 1 0 d

To answer questions 31 33 use this equation sin x cos x 2 31 What is one identity used in the solution 1 cOS X 2 a sin 11 N XIN XIN 2 b sin c sin 2 sin 2 N X d sin sin 2 1 cosx 2 1 cos x 2 1 1 CSX 2

To answer questions 28 30 use the equation 1 cosx sinx sinx 28 What is one identity used in the solution a sin x 1 cos x b cos x sin x 1 c sin x 1 cos x d cos x 1 sin x

5 The region under the curve y sin x from 0 to 7 is rotated about the x axis Find the volume of the resulting solid

25 Another set of answers is a EIN 50 TT 3TT 2 2 b 0 TT C 0 TT

34 Use the Table of Integrals on the Reference Pages to valuate the integral 7 8 1 Jo arctan 2x dx 8 x 4x dx sin 20 23 cos 0 4 25 fx e x dx d

What are the answers 5TT 6 a b C FIG FI FI la and TT 5TT 7TT 11TT 6 6 6 6 2T 4T 5TT 3 3 3 3 G

se the equation tan x tan x 0 to answer questions 24 25 24 One set of answers is a b C d EEN ENE 5TT 4 4 77 4 4 TT 3TT

To answer questions 20 21 find the solution set of 3 secx 1 5 secx in the interva 0 x 2TT or when a table or calculator is used in the interval 0 x 360 20 What is the second from the last step a sec x 1 b sec x 4 c sec x 2 d sec x 2

11 What are the extremes of y 3sin x 3 a b 2 3 and and 2 3 3 3 c 3 and 3 d 6 and 6 3

1 6 What are the extreme values of y sin 3x 2 a 3 and 3 3 b and 2 c 1 and 1 d 5 and 5 3 2

19 What is the period of y 1 co 2 a FIFIC b 4TT C 8TT d I cos 4x

16 What is the period of y sin x a 6TT b 2TT C d sin x F FIM F

14 What is the period of y cos 2x a FIN b 2T C 4TT d TT

13 What are the extremes of y cos 2x a 1 and 1 b 2 and 2 c 4 and 4 d 1 an and 2 1 2